用户: Cybcat/神秘具体问题/Mordell

这里是 Mordell 方程的一些穷举结果的表格, 原作者 Helmut Richter, 在这里我们重新编排了其格式, 以便在香蕉空间的环境下检索. 下文中解仅表示 $\mathbf{x}\le 10^{10}$ 范围内暴力搜索得到的穷举解.

1最小解

下面两个表格记录了 $y^2=x^3+k$ 对 $|k|<1000$ 的最小解 $x$. 第一个表格统计了 $k\ge 0$ 的情况, 第二个表格统计了 $k\le 0$ 的情况.

k	+0	+1	+2	+3	+4	+5	+6	+7	+8	+9
0	0	-1	-1	1	0	-1	.	.	-2	-2
10	-1	.	-2	.	.	1	0	-2	7	5
20	.	.	3	.	-2	0	-1	-3	-3	.
30	19	-3	.	-2	.	1	-3	-1	11	.
40	6	2	.	-3	-2	.	.	.	1	0
50	-1	.	-3	.	3	9	2	-2	.	.
60	.	.	.	-3	-4	-4	.	.	-4	.
70	.	5	-2	-4	.	.	-3	.	.	45
80	-4	0	-1	.	.	.	.	.	.	-4
90	.	-3	2	.	3	.	.	18	7	1
k	+0	+1	+2	+3	+4	+5	+6	+7	+8	+9
100	-4	-1	.	.	.	4	15	13	-3	.
110	.	.	9	-4	.	.	.	3	.	53
120	1	0	-1	.	.	-5	-5	-3	-4	-5
130	.	5	4	.	-5	.	2	.	31	.
140	.	-5	3	1	0	-4	.	.	-3	.
150	-5	105	-2	.	23	.	10	.	.	.
160	.	-5	.	33	-4	.	.	.	1	0
170	-1	-3	14	.	-5	.	.	-2	.	.
180	.	.	.	.	6	-4	7	.	2	-5
190	11	.	4	.	.	1	-3	-1	3	5
k	+0	+1	+2	+3	+4	+5	+6	+7	+8	+9
200	.	.	.	.	-2	.	-5	.	-4	.
210	.	.	.	.	.	.	-6	-6	.	.
220	-6	.	.	-3	1	-6	-1	.	.	3
230	.	.	-6	-4	.	.	5	.	.	.
240	.	-6	.	.	.	.	-5	.	2	28
250	.	25	-6	.	.	1	0	-1	.	.
260	-4	.	3	.	-2	-6	.	.	6	-5
270	.	17	8	.	.	5	.	.	.	.
280	-6	2	7	-3	.	.	.	.	1	-4
290	-1	.	.	.	-5	9	10	-6	.	.
k	+0	+1	+2	+3	+4	+5	+6	+7	+8	+9
300	.	.	.	13	.	.	.	.	.	.
310	.	.	.	6	.	.	-6	.	.	.
320	-4	-5	.	1	0	-1	.	.	.	8
330	.	.	-2	7	3	.	4	-6	.	.
340	.	.	.	-7	-7	.	15	-7	.	.
350	-5	-3	-7	-4	.	.	32	.	.	-7
360	-6	0	-1	.	.	.	19	.	-7	-2
370	.	.	.	3	.	.	.	4	.	-7
380	26	-5	.	.	.	-6	7	.	-4	35
390	.	.	-7	16	.	.	70	.	.	1
k	+0	+1	+2	+3	+4	+5	+6	+7	+8	+9
400	0	-1	.	.	5	.	107	-7	-2	6
410	.	.	-6	.	-5	.	17	.	.	.
420	4	.	.	37	-7	-4	.	-3	.	.
430	.	.	.	2	.	.	.	.	.	.
440	1	-6	-1	-7	10	.	.	.	.	-5
450	.	5	.	.	.	.	.	3	.	.
460	6	.	.	.	-7	4	.	.	-3	15
470	.	.	-6	.	.	.	2	.	.	.
480	.	12	.	1	0	-1	-5	-7	.	.
490	.	.	-2	.	.	.	9	.	7	.
k	+0	+1	+2	+3	+4	+5	+6	+7	+8	+9
500	5	.	3	.	25	-6	47	13	.	.
510	.	-3	-8	-8	.	.	-8	.	11	133
520	.	-8	.	.	.	-5	.	.	-8	0
530	-1	85	.	.	.	.	.	-8	.	-7
540	-6	.	.	.	33	74	.	.	-8	3
550	.	5	.	.	.	.	-3	7	.	.
560	.	-8	.	17	.	.	-5	9	-7	.
570	.	.	.	.	51	1	-8	-6	.	.
580	.	.	43	.	-2	.	.	.	22	.
590	.	.	.	-8	15	.	.	.	3	-7
k	+0	+1	+2	+3	+4	+5	+6	+7	+8	+9
600	10	.	23	-3	5	11	.	.	.	-5
610	.	.	-8	.	.	.	-6	2	7	.
620	14	.	219	.	1	0	-1	.	.	.
630	.	89	-7	-8	.	269	.	.	67	.
640	-4	.	.	.	8	.	.	.	.	3
650	.	.	-3	.	-5	.	-8	-6	.	5
660	.	.	.	.	.	4	.	-7	2	.
670	.	.	.	12	.	1	0	-1	.	.
680	.	-8	.	.	-2	.	179	49	.	-4
690	.	.	.	.	11	.	34	.	.	.
k	+0	+1	+2	+3	+4	+5	+6	+7	+8	+9
700	-6	-5	3	-3	-7	.	39	.	-8	.
710	19	.	17	8	.	9	5	.	.	13
720	4	2	.	.	.	.	.	.	1	-9
730	-9	.	.	-9	.	.	.	-8	-9	21
740	-4	.	.	-7	.	-9	7	.	86	.
750	-5	.	.	.	-9	.	-3	3	.	25
760	.	.	.	.	10	-9	27	.	-8	.
770	.	.	12	.	.	5	2	4	-9	.
780	.	.	.	1	-7	-1	.	.	.	.
790	.	.	-6	-9	.	.	.	.	.	.
k	+0	+1	+2	+3	+4	+5	+6	+7	+8	+9
800	.	-8	.	.	16	.	35	.	6	.
810	-9	-3	149	7	3	.	.	24	.	.
820	.	.	.	.	38	.	.	-7	13	-9
830	.	.	.	2	31	.	-8	.	.	.
840	1	-6	-1	.	.	.	.	.	-4	-2
850	-9	.	.	.	-5	.	14	8	.	.
860	.	.	.	17	.	.	.	.	-3	.
870	.	9	-7	-9	.	.	37	.	11	.
880	.	.	7	.	.	19	.	.	.	30
890	71	.	-6	.	.	.	.	4	-9	1
k	+0	+1	+2	+3	+4	+5	+6	+7	+8	+9
900	0	-1	.	.	.	-4	55	.	-2	-5
910	.	.	-8	.	.	.	.	.	.	-7
920	26	.	.	.	.	-9	.	-3	.	.
930	.	.	8	.	3	.	10	.	.	13
940	6	.	.	.	.	-6	.	.	.	.
950	.	.	9	-8	-9	.	.	.	.	.
960	1	0	-1	.	-4	.	-5	69	-7	-2
970	.	265	.	11	.	.	12	14	.	.
980	.	15	.	.	.	-9	.	.	-3	.
990	.	.	.	.	.	.	-8	3	.	.

-k	+0	+1	+2	+3	+4	+5	+6	+7	+8	+9
0	0	1	3	.	2	.	.	2	2	.
10	.	3	.	17	.	4	.	.	3	7
20	6	.	.	3	.	5	3	3	4	.
30	.	.	.	.	.	11	.	.	.	4
40	14	.	.	.	5	21	.	6	4	65
50	.	.	.	9	7	4	18	.	.	.
60	4	5	.	4	4	.	.	23	.	.
70	.	8	6	.	99	.	5	.	.	20
80	.	13	.	27	.	.	.	7	.	5
90	.	.	.	.	.	6	.	.	.	.
-k	+0	+1	+2	+3	+4	+5	+6	+7	+8	+9
100	5	.	.	.	9	.	11	143	.	5
110	.	.	8	.	.	.	5	.	7	.
120	.	5	.	.	5	5	15	16	12	.
130	.	.	.	.	.	6	.	.	.	47
140	.	.	.	14	.	.	195	7	197	.
150	175	8	6	9	.	51	.	.	.	10
160	.	.	.	.	.	.	.	6	.	.
170	59	.	13	.	7	11	.	.	.	.
180	6	.	.	.	62	.	163	.	8	.
190	.	6	.	257	.	.	.	.	.	7
-k	+0	+1	+2	+3	+4	+5	+6	+7	+8	+9
200	6	.	.	.	.	.	.	6	.	.
210	.	.	6	.	.	6	6	.	.	.
220	.	.	7	8	.	.	.	.	.	.
230	.	.	.	377	.	79	21	.	.	15
240	.	.	11	7	14	9	.	.	.	25
250	.	83	16	.	.	.	8	.	.	.
260	.	13	7	.	.	.	.	.	.	.
270	39	10	.	.	.	.	.	41	.	7
280	.	.	.	.	12	.	23	8	9	17
290	.	.	98	57	7	.	.	.	19	399
-k	+0	+1	+2	+3	+4	+5	+6	+7	+8	+9
300	.	401	.	.	.	.	.	7	102	.
310	.	.	.	.	.	.	8	.	7	.
320	.	.	.	.	10	.	.	7	.	9
330	.	.	.	.	7	.	.	.	.	7
340	.	.	7	7	.	.	.	.	13	.
350	15	.	.	.	.	119	18	.	.	12
360	.	.	27	.	29	.	11815	.	8	.
370	11	123	.	.	.	10	.	.	.	.
380	.	.	.	.	.	.	.	.	.	.
390	.	8	.	.	.	.	.	.	.	.
-k	+0	+1	+2	+3	+4	+5	+6	+7	+8	+9
400	.	.	.	.	.	9	.	.	.	.
410	.	.	8	.	.	26	.	.	.	.
420	.	.	.	.	10	21	.	.	.	.
430	.	8	12	13	.	.	.	.	.	35
440	9	.	.	.	.	.	.	22	8	.
450	.	.	.	.	.	114	.	.	.	15
460	.	.	.	8	129	.	.	.	.	.
470	.	10	.	9	.	.	8	37	.	.
480	.	.	.	.	.	.	.	8	.	.
490	11	.	.	.	.	34	8	.	.	167
-k	+0	+1	+2	+3	+4	+5	+6	+7	+8	+9
500	.	.	.	8	9	.	675	.	8	.
510	.	8	8	.	.	171	10	.	.	.
520	.	.	.	.	45	.	.	.	.	.
530	.	.	.	9	.	14	.	.	.	.
540	.	.	.	.	.	.	43	11	.	.
550	31	.	.	.	.	.	.	17	.	10
560	9	.	.	.	.	.	15	.	.	.
570	.	.	12	.	.	.	.	.	.	.
580	194	.	.	38	.	9	115	783	.	785
590	.	.	.	33	.	.	198	13	.	24
-k	+0	+1	+2	+3	+4	+5	+6	+7	+8	+9
600	10	.	11	.	20	.	.	.	9	.
610	.	.	21	.	.	16	.	.	19	.
620	.	.	127	.	.	.	.	.	14	9
630	.	58	.	.	.	.	28	.	.	10
640	.	.	.	.	.	.	.	42	9	.
650	.	.	53	.	.	11	.	.	.	.
660	.	.	.	94	.	9	.	223	.	.
670	.	15	.	29	75	.	10	.	.	.
680	9	.	.	227	.	49	.	.	17	.
690	.	.	.	9	.	.	.	.	.	.
-k	+0	+1	+2	+3	+4	+5	+6	+7	+8	+9
700	.	.	103	112	9	.	11	.	.	.
710	.	10	.	9	.	.	.	.	23	14
720	9	.	.	.	.	9	55	32	9	9
730	.	.	16	.	.	106	.	.	.	.
740	.	25	.	.	10	.	.	.	.	.
750	.	.	.	13	.	11	30	.	.	.
760	254	.	.	.	92	.	1183	12	.	1025
770	.	.	.	.	15	10	258	.	.	.
780	.	.	47	.	.	.	.	.	.	.
790	.	18	.	.	.	.	.	21	.	.
-k	+0	+1	+2	+3	+4	+5	+6	+7	+8	+9
800	41	.	11	.	10	.	.	.	14	.
810	.	.	.	.	.	.	.	17	.	.
820	.	.	.	.	.	.	.	.	12	.
830	.	10	68	.	.	.	.	.	.	.
840	.	.	.	.	.	.	.	11	.	.
850	35	.	.	.	.	.	10	.	.	287
860	36	.	.	.	.	.	1155	.	1157	.
870	.	.	.	.	.	15	.	.	.	10
880	.	.	51	.	.	.	.	12	34	.
890	11	31	56	.	.	14	.	.	.	.
-k	+0	+1	+2	+3	+4	+5	+6	+7	+8	+9
900	10	13	.	.	.	.	.	.	77	.
910	.	.	.	.	27	.	.	.	.	10
920	.	.	.	.	37	.	.	28	.	.
930	19	11	18	.	.	26	10	.	.	.
940	.	.	.	.	12	141	.	.	.	.
950	.	10	.	.	187	.	.	.	.	.
960	16	.	.	.	10	.	.	.	33	.
970	11	1295	13	1297	15	10	.	.	.	.
980	14	.	.	.	10	.	.	.	.	.
990	.	10	.	.	.	.	10	.	.	10

2更多解

下面的表格记录了 $y^2=x^3+k$ 对 $|k|<1000$ 的解数超过 $1$ 时的所有解 $(x,y)$. 注意, 这里不包含有唯一解的情形, 唯一解的信息已在前一节的表格中给出.

k=1	#sol=3
(-1,0)	(0,1)	(2,3)
k=-4	#sol=2
(2,2)	(5,11)
k=-7	#sol=2
(2,1)	(32,181)
k=8	#sol=4
(-2,0)	(1,3)	(2,4)	(46,312)
k=9	#sol=5
(-2,1)	(0,3)	(3,6)	(6,15)
(40,253)
k=-11	#sol=2
(3,4)	(15,58)
k=12	#sol=2
(-2,2)	(13,47)
k=15	#sol=2
(1,4)	(109,1138)
k=17	#sol=8
(-2,3)	(-1,4)	(2,5)	(4,9)
(8,23)	(43,282)	(52,375)	(5234,378661)
k=24	#sol=4
(-2,4)	(1,5)	(10,32)	(8158,736844)
k=-26	#sol=2
(3,1)	(35,207)
k=28	#sol=2
(-3,1)	(2,6)
k=-28	#sol=3
(4,6)	(8,22)	(37,225)
k=36	#sol=4
(-3,3)	(0,6)	(4,10)	(12,42)
k=37	#sol=3
(-1,6)	(3,8)	(243,3788)
k=-39	#sol=3
(4,5)	(10,31)	(22,103)
k=44	#sol=2
(-2,6)	(5,13)
k=-47	#sol=3
(6,13)	(12,41)	(63,500)
k=-48	#sol=2
(4,4)	(28,148)
k=-53	#sol=2
(9,26)	(29,156)
k=-55	#sol=2
(4,3)	(56,419)
k=57	#sol=3
(-2,7)	(4,11)	(7,20)
k=-60	#sol=2
(4,2)	(136,1586)
k=63	#sol=2
(-3,6)	(1,8)
k=-63	#sol=2
(4,1)	(568,13537)
k=64	#sol=3
(-4,0)	(0,8)	(8,24)
k=65	#sol=4
(-4,1)	(-1,8)	(14,53)	(584,14113)
k=68	#sol=2
(-4,2)	(152,1874)
k=73	#sol=6
(-4,3)	(2,9)	(3,10)	(6,17)
(72,611)	(356,6717)
k=-76	#sol=2
(5,7)	(101,1015)
k=80	#sol=4
(-4,4)	(1,9)	(4,12)	(44,292)
k=89	#sol=4
(-4,5)	(-2,9)	(10,33)	(55,408)
k=100	#sol=6
(-4,6)	(0,10)	(5,15)	(20,90)
(24,118)	(2660,137190)
k=-100	#sol=3
(5,5)	(10,30)	(34,198)
k=101	#sol=2
(-1,10)	(95,926)
k=-104	#sol=3
(9,25)	(30,164)	(42,272)
k=108	#sol=4
(-3,9)	(-2,10)	(6,18)	(366,7002)
k=-109	#sol=2
(5,4)	(145,1746)
k=113	#sol=6
(-4,7)	(2,11)	(8,25)	(11,38)
(26,133)	(422,8669)
k=-116	#sol=4
(5,3)	(6,10)	(38,234)	(158,1986)
k=121	#sol=2
(0,11)	(12,43)
k=128	#sol=2
(-4,8)	(17,71)
k=129	#sol=3
(-5,2)	(-2,11)	(16,65)
k=-135	#sol=3
(6,9)	(19,82)	(24,117)
k=141	#sol=3
(-5,4)	(7,22)	(3067,169852)
k=145	#sol=4
(-4,9)	(-1,12)	(6,19)	(54,397)
k=-147	#sol=2
(7,14)	(91,868)
k=148	#sol=2
(-3,11)	(21,97)
k=-152	#sol=3
(6,8)	(17,69)	(26,132)
k=161	#sol=4
(-5,6)	(2,13)	(4,15)	(190,2619)
k=164	#sol=3
(-4,10)	(5,17)	(8,26)
k=168	#sol=2
(1,13)	(22,104)
k=169	#sol=3
(0,13)	(3,14)	(78,689)
k=171	#sol=3
(-3,12)	(9,30)	(937,28682)
k=-174	#sol=3
(7,13)	(799,22585)	(5215,376601)
k=-180	#sol=2
(6,6)	(69,573)
k=-191	#sol=3
(6,5)	(255,4072)	(810,23053)
k=196	#sol=3
(-3,13)	(0,14)	(84,770)
k=197	#sol=2
(-1,14)	(19,84)
k=198	#sol=2
(3,15)	(27,141)
k=-200	#sol=3
(6,4)	(9,23)	(66,536)
k=204	#sol=2
(-2,14)	(13,49)
k=-207	#sol=7
(6,3)	(12,39)	(18,75)	(31,172)
(312,5511)	(331,6022)	(367806,223063347)
k=208	#sol=2
(-4,12)	(12,44)
k=-212	#sol=2
(6,2)	(717,19199)
k=-215	#sol=2
(6,1)	(2904,156493)
k=-216	#sol=3
(6,0)	(10,28)	(33,189)
k=217	#sol=5
(-6,1)	(2,15)	(8,27)	(39,244)
(2928,158437)
k=220	#sol=2
(-6,2)	(741,20171)
k=225	#sol=13
(-6,3)	(-5,10)	(0,15)	(4,17)
(6,21)	(10,35)	(15,60)	(30,165)
(60,465)	(180,2415)	(336,6159)	(351,6576)
(720114,611085363)
k=232	#sol=2
(-6,4)	(9,31)
k=233	#sol=4
(-4,13)	(-2,15)	(7,24)	(202,2871)
k=-242	#sol=2
(11,33)	(323,5805)
k=-244	#sol=3
(14,50)	(22,102)	(325,5859)
k=248	#sol=2
(2,16)	(41,263)
k=252	#sol=5
(-6,6)	(-3,15)	(18,78)	(58,442)
(93,897)
k=-256	#sol=2
(8,16)	(20,88)
k=260	#sol=4
(-4,14)	(4,18)	(16,66)	(29,157)
k=269	#sol=2
(-5,12)	(11,40)
k=-277	#sol=2
(41,262)	(317,5644)
k=281	#sol=3
(2,17)	(14,55)	(20,91)
k=289	#sol=3
(-4,15)	(0,17)	(68,561)
k=294	#sol=2
(-5,13)	(211,3065)
k=297	#sol=9
(-6,9)	(-2,17)	(3,18)	(4,19)
(12,45)	(34,199)	(48,333)	(1362,50265)
(93844,28748141)
k=-307	#sol=4
(7,6)	(11,32)	(71,598)	(939787,911054064)
k=316	#sol=7
(-6,10)	(-3,17)	(2,18)	(5,21)
(50,354)	(90,854)	(162,2062)
k=337	#sol=2
(-6,11)	(24,119)
k=343	#sol=2
(-7,0)	(21,98)
k=-343	#sol=5
(7,0)	(8,13)	(14,49)	(28,147)
(154,1911)
k=346	#sol=2
(15,61)	(159,2005)
k=350	#sol=2
(-5,15)	(11,41)
k=353	#sol=4
(-4,17)	(2,19)	(38,235)	(117188,40116655)
k=359	#sol=3
(-7,4)	(5,22)	(73,624)
k=360	#sol=5
(-6,12)	(1,19)	(6,24)	(9,33)
(346,6436)
k=-362	#sol=2
(27,139)	(483,10615)
k=-364	#sol=2
(29,155)	(485,10681)
k=-368	#sol=7
(8,12)	(9,19)	(24,116)	(32,180)
(48,332)	(944,29004)	(1313,47577)
k=369	#sol=2
(-2,19)	(10,37)
k=-375	#sol=2
(10,25)	(16,61)
k=377	#sol=4
(4,21)	(22,105)	(23,112)	(47044,10203669)
k=388	#sol=6
(-4,18)	(-3,19)	(8,30)	(12,46)
(341,6297)	(1376,51042)
k=-391	#sol=2
(8,11)	(50,353)
k=392	#sol=3
(-7,7)	(2,20)	(14,56)
k=404	#sol=2
(5,23)	(13,51)
k=-405	#sol=2
(9,18)	(61,476)
k=409	#sol=2
(6,25)	(18,79)
k=414	#sol=3
(-5,17)	(3,21)	(3075,170517)
k=-424	#sol=3
(10,24)	(17,67)	(142,1692)
k=427	#sol=3
(-3,20)	(9,34)	(30333,5282908)
k=-431	#sol=9
(8,9)	(11,30)	(20,87)	(30,163)
(36,215)	(138,1621)	(150,1837)	(575,13788)
(3903,243836)
k=433	#sol=3
(2,21)	(11,42)	(36,217)
k=-433	#sol=2
(13,42)	(577,13860)
k=-440	#sol=3
(9,17)	(14,48)	(146,1764)
k=441	#sol=4
(-6,15)	(0,21)	(7,28)	(42,273)
k=443	#sol=2
(-7,10)	(77,676)
k=-448	#sol=2
(8,8)	(128,1448)
k=449	#sol=4
(-5,18)	(-2,21)	(8,31)	(176,2335)
k=-459	#sol=3
(15,54)	(19,80)	(67,548)
k=464	#sol=3
(-7,11)	(-4,20)	(20,92)
k=-471	#sol=2
(10,23)	(4528,304691)
k=-476	#sol=2
(8,6)	(240,3718)
k=481	#sol=2
(12,47)	(27,142)
k=485	#sol=2
(-1,22)	(31,174)
k=492	#sol=2
(-2,22)	(118,1282)
k=-496	#sol=6
(8,4)	(16,60)	(25,123)	(40,252)
(113,1201)	(560,13252)
k=-503	#sol=8
(8,3)	(12,35)	(18,73)	(23,108)
(44,291)	(134,1551)	(294,5041)	(1008,32003)
k=505	#sol=4
(-6,17)	(-4,21)	(14,57)	(371,7146)
k=-508	#sol=4
(8,2)	(284,4786)	(677,17615)	(2288,109442)
k=-511	#sol=2
(8,1)	(9200,882433)
k=512	#sol=5
(-8,0)	(-7,13)	(4,24)	(8,32)
(184,2496)
k=513	#sol=3
(-8,1)	(6,27)	(9232,887041)
k=516	#sol=3
(-8,2)	(40,254)	(2320,111746)
k=-516	#sol=4
(10,22)	(13,41)	(181,2435)	(418,8546)
k=521	#sol=4
(-8,3)	(2,23)	(10,39)	(1040,33539)
k=528	#sol=4
(-8,4)	(1,23)	(16,68)	(592,14404)
k=-535	#sol=2
(14,47)	(2156,100109)
k=537	#sol=4
(-8,5)	(-2,23)	(19,86)	(124,1381)
k=540	#sol=2
(-6,18)	(21,99)
k=548	#sol=5
(-8,6)	(-4,22)	(28,150)	(61,477)
(272,4486)
k=556	#sol=2
(-3,23)	(30,166)
k=561	#sol=2
(-8,7)	(4,25)
k=568	#sol=7
(-7,15)	(2,24)	(6,28)	(18,80)
(57,431)	(161,2043)	(1137,38339)
k=575	#sol=2
(1,24)	(29,158)
k=576	#sol=5
(-8,8)	(0,24)	(12,48)	(24,120)
(160,2024)
k=577	#sol=3
(-6,19)	(-1,24)	(8,33)
k=593	#sol=3
(-8,9)	(-4,23)	(76,663)
k=-593	#sol=2
(33,188)	(909,27406)
k=612	#sol=3
(-8,10)	(4,26)	(13,53)
k=-615	#sol=2
(16,59)	(46,311)
k=618	#sol=2
(7,31)	(421351,273505487)
k=625	#sol=3
(0,25)	(6,29)	(75,650)
k=633	#sol=3
(-8,11)	(-2,25)	(46,313)
k=-639	#sol=4
(10,19)	(12,33)	(27,138)	(654,16725)
k=640	#sol=2
(-4,24)	(9,37)
k=-648	#sol=6
(9,9)	(18,72)	(22,100)	(54,396)
(97,955)	(1809,76941)
k=649	#sol=4
(3,26)	(20,93)	(26,135)	(1398,52271)
k=656	#sol=2
(-8,12)	(80,716)
k=659	#sol=2
(5,28)	(5393,396046)
k=665	#sol=3
(4,27)	(16,69)	(44,293)
k=-674	#sol=2
(75,649)	(899,26955)
k=-676	#sol=6
(10,18)	(13,39)	(26,130)	(130,1482)
(338,6214)	(901,27045)
k=-680	#sol=2
(9,7)	(8394,769048)
k=681	#sol=4
(-8,13)	(7,32)	(10,41)	(82,743)
k=684	#sol=3
(-2,26)	(6,30)	(45,303)
k=701	#sol=2
(-5,24)	(247,3882)
k=702	#sol=2
(3,27)	(139,1639)
k=-704	#sol=3
(9,5)	(12,32)	(60,464)
k=716	#sol=2
(5,29)	(110,1154)
k=721	#sol=3
(2,27)	(15,64)	(32,183)
k=-728	#sol=2
(9,1)	(74,636)
k=729	#sol=3
(-9,0)	(0,27)	(18,81)
k=730	#sol=3
(-9,1)	(-1,27)	(231,3511)
k=-732	#sol=3
(16,58)	(52,374)	(76,662)
k=737	#sol=4
(-8,15)	(-2,27)	(14,59)	(59,454)
k=740	#sol=2
(-4,26)	(3296,189226)
k=745	#sol=4
(-9,4)	(-6,23)	(6,31)	(96,941)
k=-755	#sol=3
(11,24)	(39,242)	(891,26596)
k=757	#sol=2
(3,28)	(2063,93702)
k=-767	#sol=2
(12,31)	(1023,32720)
k=768	#sol=2
(-8,16)	(52,376)
k=775	#sol=2
(5,30)	(41,264)
k=-775	#sol=7
(10,15)	(19,78)	(20,85)	(70,585)
(80,715)	(16750,2167815)	(26530,4321215)
k=-782	#sol=2
(47,321)	(87,811)
k=784	#sol=4
(-7,21)	(0,28)	(8,36)	(56,420)
k=785	#sol=2
(-1,28)	(11,46)
k=792	#sol=4
(-6,24)	(-2,28)	(9,39)	(177,2355)
k=793	#sol=3
(-9,8)	(-4,27)	(62,489)
k=801	#sol=3
(-8,17)	(-5,26)	(22,107)
k=-802	#sol=2
(11,23)	(307,5379)
k=804	#sol=2
(16,70)	(88,826)
k=-804	#sol=3
(10,14)	(82,742)	(157,1967)
k=-828	#sol=5
(12,30)	(13,37)	(24,114)	(108,1122)
(4464,298254)
k=829	#sol=2
(-9,10)	(23,114)
k=-831	#sol=2
(10,13)	(220,3263)
k=836	#sol=5
(-8,18)	(4,30)	(5,31)	(20,94)
(3712,226158)
k=841	#sol=3
(-6,25)	(0,29)	(87,812)
k=-847	#sol=7
(11,22)	(16,57)	(22,99)	(86,797)
(88,825)	(638,16115)	(657547,533200074)
k=849	#sol=3
(-2,29)	(10,43)	(28,151)
k=850	#sol=2
(-9,11)	(15,65)
k=-856	#sol=2
(10,12)	(230,3488)
k=857	#sol=2
(8,37)	(104,1061)
k=868	#sol=2
(-3,29)	(36,218)
k=873	#sol=9
(-9,12)	(-8,19)	(3,30)	(6,33)
(12,51)	(66,537)	(178,2375)	(432,8979)
(978,30585)
k=-875	#sol=2
(15,50)	(291,4964)
k=885	#sol=2
(19,88)	(68239,17825798)
k=-888	#sol=3
(34,196)	(73,623)	(334,6104)
k=892	#sol=5
(-6,26)	(2,30)	(18,82)	(29,159)
(53,387)
k=-895	#sol=2
(14,43)	(116,1249)
k=899	#sol=3
(1,30)	(5,32)	(11393,1216066)
k=-900	#sol=2
(10,10)	(205,2935)
k=901	#sol=2
(-1,30)	(467,10092)
k=-914	#sol=2
(27,137)	(1779,75035)
k=927	#sol=2
(-3,30)	(33,192)
k=-931	#sol=2
(11,20)	(23,106)
k=940	#sol=3
(6,34)	(21,101)	(54,398)
k=-944	#sol=5
(12,28)	(17,63)	(20,84)	(164,2100)
(2364,114940)
k=945	#sol=2
(-6,27)	(16,71)
k=953	#sol=3
(-8,21)	(2,31)	(7,36)
k=954	#sol=2
(-9,15)	(63,501)
k=960	#sol=3
(1,31)	(4,32)	(436,9104)
k=964	#sol=3
(-4,30)	(5,33)	(48,334)
k=-964	#sol=4
(10,6)	(322,5778)	(605,14881)	(4402,292062)
k=-975	#sol=2
(10,5)	(880,26105)
k=-980	#sol=5
(14,42)	(21,91)	(29,153)	(126,1414)
(326,5886)
k=-984	#sol=3
(10,4)	(25,121)	(769,21325)
k=985	#sol=2
(-9,16)	(1011,32146)
k=988	#sol=2
(-3,31)	(42,274)
k=-991	#sol=2
(10,3)	(2480,123503)
k=-996	#sol=2
(10,2)	(5605,419627)
k=-999	#sol=6
(10,1)	(12,27)	(40,251)	(147,1782)
(174,2295)	(22480,3370501)