Elliptic curve search results

Conductor	j-invariant	Rank	Torsion	Complex multiplication
Bad$\ p$	Discriminant	Regulator	Analytic order of Ш	Galois image
Isogeny class size	Isogeny class degree	Cyclic isogeny degree	$p\ $div$\ $|Ш|	Nonmax$\ \ell$
Curves per isogeny class	Reduction	Integral points	Faltings height

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Results (29 matches)

 

Label	Cremona label	Class	Cremona class	Class size	Class degree	Conductor	Discriminant	Rank	Torsion	$\textrm{End}^0(E_{\overline\Q})$	CM	Sato-Tate	Semistable	Potentially good	Nonmax $\ell$	$\ell$-adic images	mod-$\ell$ images	Regulator	$Ш_{\textrm{an}}$	Ш primes	Integral points	Modular degree	Faltings height	j-invariant	Weierstrass coefficients	Weierstrass equation
663.a6	663b6	663.a	663b	$6$	$8$	\( 3 \cdot 13 \cdot 17 \)	\( - 3^{4} \cdot 13 \cdot 17^{8} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	8.48.0.178	2B	$0.743953017$	$1$		$4$	$1024$	$1.155155$	$6439735268725823/7345472585373$	$[1, 1, 1, 3876, -89910]$	\(y^2+xy+y=x^3+x^2+3876x-89910\)
1989.e6	1989e6	1989.e	1989e	$6$	$8$	\( 3^{2} \cdot 13 \cdot 17 \)	\( - 3^{10} \cdot 13 \cdot 17^{8} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.91	2B	$13.53586267$	$1$		$0$	$8192$	$1.704462$	$6439735268725823/7345472585373$	$[1, -1, 0, 34884, 2462449]$	\(y^2+xy=x^3-x^2+34884x+2462449\)
8619.i6	8619b6	8619.i	8619b	$6$	$8$	\( 3 \cdot 13^{2} \cdot 17 \)	\( - 3^{4} \cdot 13^{7} \cdot 17^{8} \)	$0$	$\Z/4\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.48.0.166	2B	$1$	$4$	$2$	$2$	$172032$	$2.437630$	$6439735268725823/7345472585373$	$[1, 1, 0, 655041, -200807082]$	\(y^2+xy=x^3+x^2+655041x-200807082\)
10608.p6	10608ba6	10608.p	10608ba	$6$	$8$	\( 2^{4} \cdot 3 \cdot 13 \cdot 17 \)	\( - 2^{12} \cdot 3^{4} \cdot 13 \cdot 17^{8} \)	$1$	$\Z/4\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.48.0.160	2B	$4.653815995$	$1$		$5$	$65536$	$1.848303$	$6439735268725823/7345472585373$	$[0, 1, 0, 62016, 5878260]$	\(y^2=x^3+x^2+62016x+5878260\)
11271.e6	11271h6	11271.e	11271h	$6$	$8$	\( 3 \cdot 13 \cdot 17^{2} \)	\( - 3^{4} \cdot 13 \cdot 17^{14} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	16.48.0.138	2B	$9.808094233$	$1$		$0$	$294912$	$2.571762$	$6439735268725823/7345472585373$	$[1, 0, 0, 1120158, -449568063]$	\(y^2+xy=x^3+1120158x-449568063\)
16575.i6	16575f6	16575.i	16575f	$6$	$8$	\( 3 \cdot 5^{2} \cdot 13 \cdot 17 \)	\( - 3^{4} \cdot 5^{6} \cdot 13 \cdot 17^{8} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.91	2B	$1$	$4$	$2$	$0$	$131072$	$1.959875$	$6439735268725823/7345472585373$	$[1, 0, 1, 96899, -11432527]$	\(y^2+xy+y=x^3+96899x-11432527\)
25857.f6	25857h5	25857.f	25857h	$6$	$8$	\( 3^{2} \cdot 13^{2} \cdot 17 \)	\( - 3^{10} \cdot 13^{7} \cdot 17^{8} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.91	2B	$1$	$4$	$2$	$0$	$1376256$	$2.986938$	$6439735268725823/7345472585373$	$[1, -1, 1, 5895364, 5427686580]$	\(y^2+xy+y=x^3-x^2+5895364x+5427686580\)
31824.bg6	31824bk5	31824.bg	31824bk	$6$	$8$	\( 2^{4} \cdot 3^{2} \cdot 13 \cdot 17 \)	\( - 2^{12} \cdot 3^{10} \cdot 13 \cdot 17^{8} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.91	2B	$1$	$16$	$2$	$1$	$524288$	$2.397610$	$6439735268725823/7345472585373$	$[0, 0, 0, 558141, -158154878]$	\(y^2=x^3+558141x-158154878\)
32487.f6	32487l5	32487.f	32487l	$6$	$8$	\( 3 \cdot 7^{2} \cdot 13 \cdot 17 \)	\( - 3^{4} \cdot 7^{6} \cdot 13 \cdot 17^{8} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.91	2B	$3.642679484$	$1$		$2$	$393216$	$2.128113$	$6439735268725823/7345472585373$	$[1, 0, 0, 189923, 31408838]$	\(y^2+xy=x^3+189923x+31408838\)
33813.i6	33813n5	33813.i	33813n	$6$	$8$	\( 3^{2} \cdot 13 \cdot 17^{2} \)	\( - 3^{10} \cdot 13 \cdot 17^{14} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.91	2B	$40.39521359$	$1$		$0$	$2359296$	$3.121067$	$6439735268725823/7345472585373$	$[1, -1, 0, 10081422, 12138337701]$	\(y^2+xy=x^3-x^2+10081422x+12138337701\)
42432.bb6	42432bl5	42432.bb	42432bl	$6$	$8$	\( 2^{6} \cdot 3 \cdot 13 \cdot 17 \)	\( - 2^{18} \cdot 3^{4} \cdot 13 \cdot 17^{8} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.48.0.228	2B	$2.219556802$	$1$		$3$	$524288$	$2.194878$	$6439735268725823/7345472585373$	$[0, -1, 0, 248063, 46778017]$	\(y^2=x^3-x^2+248063x+46778017\)
42432.cf6	42432s5	42432.cf	42432s	$6$	$8$	\( 2^{6} \cdot 3 \cdot 13 \cdot 17 \)	\( - 2^{18} \cdot 3^{4} \cdot 13 \cdot 17^{8} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.48.0.212	2B	$3.593207050$	$1$		$3$	$524288$	$2.194878$	$6439735268725823/7345472585373$	$[0, 1, 0, 248063, -46778017]$	\(y^2=x^3+x^2+248063x-46778017\)
49725.f6	49725i5	49725.f	49725i	$6$	$8$	\( 3^{2} \cdot 5^{2} \cdot 13 \cdot 17 \)	\( - 3^{10} \cdot 5^{6} \cdot 13 \cdot 17^{8} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.91	2B	$2.750552988$	$1$		$4$	$1048576$	$2.509182$	$6439735268725823/7345472585373$	$[1, -1, 1, 872095, 308678222]$	\(y^2+xy+y=x^3-x^2+872095x+308678222\)
80223.j6	80223c5	80223.j	80223c	$6$	$8$	\( 3 \cdot 11^{2} \cdot 13 \cdot 17 \)	\( - 3^{4} \cdot 11^{6} \cdot 13 \cdot 17^{8} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.91	2B	$1$	$1$		$0$	$1310720$	$2.354103$	$6439735268725823/7345472585373$	$[1, 1, 0, 468994, 122014941]$	\(y^2+xy=x^3+x^2+468994x+122014941\)
97461.q6	97461m5	97461.q	97461m	$6$	$8$	\( 3^{2} \cdot 7^{2} \cdot 13 \cdot 17 \)	\( - 3^{10} \cdot 7^{6} \cdot 13 \cdot 17^{8} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.91	2B	$1$	$1$		$0$	$3145728$	$2.677418$	$6439735268725823/7345472585373$	$[1, -1, 0, 1709307, -848038626]$	\(y^2+xy=x^3-x^2+1709307x-848038626\)
127296.u6	127296cg5	127296.u	127296cg	$6$	$8$	\( 2^{6} \cdot 3^{2} \cdot 13 \cdot 17 \)	\( - 2^{18} \cdot 3^{10} \cdot 13 \cdot 17^{8} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.91	2B	$11.93074767$	$1$		$3$	$4194304$	$2.744183$	$6439735268725823/7345472585373$	$[0, 0, 0, 2232564, -1265239024]$	\(y^2=x^3+2232564x-1265239024\)
127296.bb6	127296h5	127296.bb	127296h	$6$	$8$	\( 2^{6} \cdot 3^{2} \cdot 13 \cdot 17 \)	\( - 2^{18} \cdot 3^{10} \cdot 13 \cdot 17^{8} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.91	2B	$1$	$4$	$2$	$1$	$4194304$	$2.744183$	$6439735268725823/7345472585373$	$[0, 0, 0, 2232564, 1265239024]$	\(y^2=x^3+2232564x+1265239024\)
137904.cv6	137904p6	137904.cv	137904p	$6$	$8$	\( 2^{4} \cdot 3 \cdot 13^{2} \cdot 17 \)	\( - 2^{12} \cdot 3^{4} \cdot 13^{7} \cdot 17^{8} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.48.0.184	2B	$1$	$1$		$1$	$11010048$	$3.130779$	$6439735268725823/7345472585373$	$[0, 1, 0, 10480648, 12872614548]$	\(y^2=x^3+x^2+10480648x+12872614548\)
146523.y6	146523s5	146523.y	146523s	$6$	$8$	\( 3 \cdot 13^{2} \cdot 17^{2} \)	\( - 3^{4} \cdot 13^{7} \cdot 17^{14} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	16.48.0.143	2B	$1$	$4$	$2$	$0$	$49545216$	$3.854237$	$6439735268725823/7345472585373$	$[1, 0, 1, 189306698, -987890341111]$	\(y^2+xy+y=x^3+189306698x-987890341111\)
180336.bg6	180336bp6	180336.bg	180336bp	$6$	$8$	\( 2^{4} \cdot 3 \cdot 13 \cdot 17^{2} \)	\( - 2^{12} \cdot 3^{4} \cdot 13 \cdot 17^{14} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	16.48.0.137	2B	$8.575038807$	$4$	$2$	$3$	$18874368$	$3.264912$	$6439735268725823/7345472585373$	$[0, -1, 0, 17922528, 28772356032]$	\(y^2=x^3-x^2+17922528x+28772356032\)
215475.t6	215475p5	215475.t	215475p	$6$	$8$	\( 3 \cdot 5^{2} \cdot 13^{2} \cdot 17 \)	\( - 3^{4} \cdot 5^{6} \cdot 13^{7} \cdot 17^{8} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.91	2B	$1$	$4$	$2$	$0$	$22020096$	$3.242348$	$6439735268725823/7345472585373$	$[1, 0, 0, 16376012, -25133637283]$	\(y^2+xy=x^3+16376012x-25133637283\)
239343.f6	239343f6	239343.f	239343f	$6$	$8$	\( 3 \cdot 13 \cdot 17 \cdot 19^{2} \)	\( - 3^{4} \cdot 13 \cdot 17^{8} \cdot 19^{6} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.91	2B	$1$	$1$		$0$	$7077888$	$2.627377$	$6439735268725823/7345472585373$	$[1, 0, 1, 1399228, 627885299]$	\(y^2+xy+y=x^3+1399228x+627885299\)
240669.p6	240669p5	240669.p	240669p	$6$	$8$	\( 3^{2} \cdot 11^{2} \cdot 13 \cdot 17 \)	\( - 3^{10} \cdot 11^{6} \cdot 13 \cdot 17^{8} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.91	2B	$1$	$1$		$0$	$10485760$	$2.903408$	$6439735268725823/7345472585373$	$[1, -1, 1, 4220941, -3290182464]$	\(y^2+xy+y=x^3-x^2+4220941x-3290182464\)
265200.bo6	265200bo6	265200.bo	265200bo	$6$	$8$	\( 2^{4} \cdot 3 \cdot 5^{2} \cdot 13 \cdot 17 \)	\( - 2^{12} \cdot 3^{4} \cdot 5^{6} \cdot 13 \cdot 17^{8} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.91	2B	$1$	$4$	$2$	$1$	$8388608$	$2.653023$	$6439735268725823/7345472585373$	$[0, -1, 0, 1550392, 731681712]$	\(y^2=x^3-x^2+1550392x+731681712\)
281775.bm6	281775bm5	281775.bm	281775bm	$6$	$8$	\( 3 \cdot 5^{2} \cdot 13 \cdot 17^{2} \)	\( - 3^{4} \cdot 5^{6} \cdot 13 \cdot 17^{14} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.91	2B	$28.99177525$	$1$		$0$	$37748736$	$3.376480$	$6439735268725823/7345472585373$	$[1, 1, 0, 28003950, -56196007875]$	\(y^2+xy=x^3+x^2+28003950x-56196007875\)
350727.c6	350727c6	350727.c	350727c	$6$	$8$	\( 3 \cdot 13 \cdot 17 \cdot 23^{2} \)	\( - 3^{4} \cdot 13 \cdot 17^{8} \cdot 23^{6} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.91	2B	$19.95971410$	$1$		$0$	$12976128$	$2.722904$	$6439735268725823/7345472585373$	$[1, 1, 1, 2050393, 1114436738]$	\(y^2+xy+y=x^3+x^2+2050393x+1114436738\)
413712.bb6	413712bb5	413712.bb	413712bb	$6$	$8$	\( 2^{4} \cdot 3^{2} \cdot 13^{2} \cdot 17 \)	\( - 2^{12} \cdot 3^{10} \cdot 13^{7} \cdot 17^{8} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.91	2B	$16.67276991$	$1$		$1$	$88080384$	$3.680084$	$6439735268725823/7345472585373$	$[0, 0, 0, 94325829, -347466266966]$	\(y^2=x^3+94325829x-347466266966\)
422331.bq6	422331bq6	422331.bq	422331bq	$6$	$8$	\( 3 \cdot 7^{2} \cdot 13^{2} \cdot 17 \)	\( - 3^{4} \cdot 7^{6} \cdot 13^{7} \cdot 17^{8} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.91	2B	$6.243369831$	$1$		$0$	$66060288$	$3.410587$	$6439735268725823/7345472585373$	$[1, 0, 1, 32096983, 68973120101]$	\(y^2+xy+y=x^3+32096983x+68973120101\)
439569.z6	439569z6	439569.z	439569z	$6$	$8$	\( 3^{2} \cdot 13^{2} \cdot 17^{2} \)	\( - 3^{10} \cdot 13^{7} \cdot 17^{14} \)	$2$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.91	2B	$76.50167907$	$1$		$2$	$396361728$	$4.403542$	$6439735268725823/7345472585373$	$[1, -1, 1, 1703760286, 26673039209990]$	\(y^2+xy+y=x^3-x^2+1703760286x+26673039209990\)