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 (32 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
1710.a1	1710a2	1710.a	1710a	$2$	$2$	\( 2 \cdot 3^{2} \cdot 5 \cdot 19 \)	\( 2^{5} \cdot 3^{9} \cdot 5^{4} \cdot 19^{2} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1.707986895$	$1$		$6$	$3840$	$0.954312$	$651038076963/7220000$	$[1, -1, 0, -4875, -128539]$	\(y^2+xy=x^3-x^2-4875x-128539\)
1710.p1	1710m2	1710.p	1710m	$2$	$2$	\( 2 \cdot 3^{2} \cdot 5 \cdot 19 \)	\( 2^{5} \cdot 3^{3} \cdot 5^{4} \cdot 19^{2} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$0.108207119$	$1$		$14$	$1280$	$0.405006$	$651038076963/7220000$	$[1, -1, 1, -542, 4941]$	\(y^2+xy+y=x^3-x^2-542x+4941\)
8550.q1	8550b2	8550.q	8550b	$2$	$2$	\( 2 \cdot 3^{2} \cdot 5^{2} \cdot 19 \)	\( 2^{5} \cdot 3^{3} \cdot 5^{10} \cdot 19^{2} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1.043042238$	$1$		$6$	$30720$	$1.209726$	$651038076963/7220000$	$[1, -1, 0, -13542, 604116]$	\(y^2+xy=x^3-x^2-13542x+604116\)
8550.bl1	8550t2	8550.bl	8550t	$2$	$2$	\( 2 \cdot 3^{2} \cdot 5^{2} \cdot 19 \)	\( 2^{5} \cdot 3^{9} \cdot 5^{10} \cdot 19^{2} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1$	$1$		$0$	$92160$	$1.759031$	$651038076963/7220000$	$[1, -1, 1, -121880, -16189253]$	\(y^2+xy+y=x^3-x^2-121880x-16189253\)
13680.z1	13680w2	13680.z	13680w	$2$	$2$	\( 2^{4} \cdot 3^{2} \cdot 5 \cdot 19 \)	\( 2^{17} \cdot 3^{9} \cdot 5^{4} \cdot 19^{2} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1.126168880$	$1$		$7$	$92160$	$1.647459$	$651038076963/7220000$	$[0, 0, 0, -78003, 8304498]$	\(y^2=x^3-78003x+8304498\)
13680.bw1	13680y2	13680.bw	13680y	$2$	$2$	\( 2^{4} \cdot 3^{2} \cdot 5 \cdot 19 \)	\( 2^{17} \cdot 3^{3} \cdot 5^{4} \cdot 19^{2} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1$	$1$		$1$	$30720$	$1.098154$	$651038076963/7220000$	$[0, 0, 0, -8667, -307574]$	\(y^2=x^3-8667x-307574\)
32490.l1	32490g2	32490.l	32490g	$2$	$2$	\( 2 \cdot 3^{2} \cdot 5 \cdot 19^{2} \)	\( 2^{5} \cdot 3^{3} \cdot 5^{4} \cdot 19^{8} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1.686169680$	$1$		$6$	$460800$	$1.877226$	$651038076963/7220000$	$[1, -1, 0, -195549, -32914395]$	\(y^2+xy=x^3-x^2-195549x-32914395\)
32490.bd1	32490bd2	32490.bd	32490bd	$2$	$2$	\( 2 \cdot 3^{2} \cdot 5 \cdot 19^{2} \)	\( 2^{5} \cdot 3^{9} \cdot 5^{4} \cdot 19^{8} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1.539304426$	$1$		$6$	$1382400$	$2.426533$	$651038076963/7220000$	$[1, -1, 1, -1759943, 890448607]$	\(y^2+xy+y=x^3-x^2-1759943x+890448607\)
54720.f1	54720g2	54720.f	54720g	$2$	$2$	\( 2^{6} \cdot 3^{2} \cdot 5 \cdot 19 \)	\( 2^{23} \cdot 3^{3} \cdot 5^{4} \cdot 19^{2} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1$	$1$		$1$	$245760$	$1.444727$	$651038076963/7220000$	$[0, 0, 0, -34668, 2460592]$	\(y^2=x^3-34668x+2460592\)
54720.cg1	54720cu2	54720.cg	54720cu	$2$	$2$	\( 2^{6} \cdot 3^{2} \cdot 5 \cdot 19 \)	\( 2^{23} \cdot 3^{3} \cdot 5^{4} \cdot 19^{2} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1$	$1$		$1$	$245760$	$1.444727$	$651038076963/7220000$	$[0, 0, 0, -34668, -2460592]$	\(y^2=x^3-34668x-2460592\)
54720.cm1	54720n2	54720.cm	54720n	$2$	$2$	\( 2^{6} \cdot 3^{2} \cdot 5 \cdot 19 \)	\( 2^{23} \cdot 3^{9} \cdot 5^{4} \cdot 19^{2} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1.264677255$	$1$		$7$	$737280$	$1.994034$	$651038076963/7220000$	$[0, 0, 0, -312012, -66435984]$	\(y^2=x^3-312012x-66435984\)
54720.fd1	54720dd2	54720.fd	54720dd	$2$	$2$	\( 2^{6} \cdot 3^{2} \cdot 5 \cdot 19 \)	\( 2^{23} \cdot 3^{9} \cdot 5^{4} \cdot 19^{2} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$2.911004847$	$1$		$5$	$737280$	$1.994034$	$651038076963/7220000$	$[0, 0, 0, -312012, 66435984]$	\(y^2=x^3-312012x+66435984\)
68400.g1	68400do2	68400.g	68400do	$2$	$2$	\( 2^{4} \cdot 3^{2} \cdot 5^{2} \cdot 19 \)	\( 2^{17} \cdot 3^{9} \cdot 5^{10} \cdot 19^{2} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$2.376368574$	$1$		$7$	$2211840$	$2.452179$	$651038076963/7220000$	$[0, 0, 0, -1950075, 1038062250]$	\(y^2=x^3-1950075x+1038062250\)
68400.q1	68400dn2	68400.q	68400dn	$2$	$2$	\( 2^{4} \cdot 3^{2} \cdot 5^{2} \cdot 19 \)	\( 2^{17} \cdot 3^{3} \cdot 5^{10} \cdot 19^{2} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1.503787192$	$1$		$7$	$737280$	$1.902872$	$651038076963/7220000$	$[0, 0, 0, -216675, -38446750]$	\(y^2=x^3-216675x-38446750\)
83790.cp1	83790t2	83790.cp	83790t	$2$	$2$	\( 2 \cdot 3^{2} \cdot 5 \cdot 7^{2} \cdot 19 \)	\( 2^{5} \cdot 3^{9} \cdot 5^{4} \cdot 7^{6} \cdot 19^{2} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1$	$1$		$0$	$1105920$	$1.927267$	$651038076963/7220000$	$[1, -1, 0, -238884, 44566640]$	\(y^2+xy=x^3-x^2-238884x+44566640\)
83790.cr1	83790cz2	83790.cr	83790cz	$2$	$2$	\( 2 \cdot 3^{2} \cdot 5 \cdot 7^{2} \cdot 19 \)	\( 2^{5} \cdot 3^{3} \cdot 5^{4} \cdot 7^{6} \cdot 19^{2} \)	$2$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1.978336121$	$1$		$18$	$368640$	$1.377962$	$651038076963/7220000$	$[1, -1, 1, -26543, -1641769]$	\(y^2+xy+y=x^3-x^2-26543x-1641769\)
162450.ck1	162450ez2	162450.ck	162450ez	$2$	$2$	\( 2 \cdot 3^{2} \cdot 5^{2} \cdot 19^{2} \)	\( 2^{5} \cdot 3^{9} \cdot 5^{10} \cdot 19^{8} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1$	$4$	$2$	$0$	$33177600$	$3.231251$	$651038076963/7220000$	$[1, -1, 0, -43998567, 111262077341]$	\(y^2+xy=x^3-x^2-43998567x+111262077341\)
162450.eu1	162450ck2	162450.eu	162450ck	$2$	$2$	\( 2 \cdot 3^{2} \cdot 5^{2} \cdot 19^{2} \)	\( 2^{5} \cdot 3^{3} \cdot 5^{10} \cdot 19^{8} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$3.122260932$	$1$		$2$	$11059200$	$2.681946$	$651038076963/7220000$	$[1, -1, 1, -4888730, -4119188103]$	\(y^2+xy+y=x^3-x^2-4888730x-4119188103\)
206910.cr1	206910fa2	206910.cr	206910fa	$2$	$2$	\( 2 \cdot 3^{2} \cdot 5 \cdot 11^{2} \cdot 19 \)	\( 2^{5} \cdot 3^{3} \cdot 5^{4} \cdot 11^{6} \cdot 19^{2} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1$	$1$		$0$	$1382400$	$1.603954$	$651038076963/7220000$	$[1, -1, 0, -65544, -6380192]$	\(y^2+xy=x^3-x^2-65544x-6380192\)
206910.dv1	206910cm2	206910.dv	206910cm	$2$	$2$	\( 2 \cdot 3^{2} \cdot 5 \cdot 11^{2} \cdot 19 \)	\( 2^{5} \cdot 3^{9} \cdot 5^{4} \cdot 11^{6} \cdot 19^{2} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1$	$1$		$0$	$4147200$	$2.153259$	$651038076963/7220000$	$[1, -1, 1, -589898, 172855081]$	\(y^2+xy+y=x^3-x^2-589898x+172855081\)
259920.dj1	259920dj2	259920.dj	259920dj	$2$	$2$	\( 2^{4} \cdot 3^{2} \cdot 5 \cdot 19^{2} \)	\( 2^{17} \cdot 3^{9} \cdot 5^{4} \cdot 19^{8} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$12.13295241$	$1$		$1$	$33177600$	$3.119678$	$651038076963/7220000$	$[0, 0, 0, -28159083, -56960551782]$	\(y^2=x^3-28159083x-56960551782\)
259920.gx1	259920gx2	259920.gx	259920gx	$2$	$2$	\( 2^{4} \cdot 3^{2} \cdot 5 \cdot 19^{2} \)	\( 2^{17} \cdot 3^{3} \cdot 5^{4} \cdot 19^{8} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1$	$1$		$1$	$11059200$	$2.570374$	$651038076963/7220000$	$[0, 0, 0, -3128787, 2109650066]$	\(y^2=x^3-3128787x+2109650066\)
273600.n1	273600n2	273600.n	273600n	$2$	$2$	\( 2^{6} \cdot 3^{2} \cdot 5^{2} \cdot 19 \)	\( 2^{23} \cdot 3^{3} \cdot 5^{10} \cdot 19^{2} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1$	$1$		$1$	$5898240$	$2.249447$	$651038076963/7220000$	$[0, 0, 0, -866700, -307574000]$	\(y^2=x^3-866700x-307574000\)
273600.cg1	273600cg2	273600.cg	273600cg	$2$	$2$	\( 2^{6} \cdot 3^{2} \cdot 5^{2} \cdot 19 \)	\( 2^{23} \cdot 3^{9} \cdot 5^{10} \cdot 19^{2} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1$	$1$		$1$	$17694720$	$2.798752$	$651038076963/7220000$	$[0, 0, 0, -7800300, 8304498000]$	\(y^2=x^3-7800300x+8304498000\)
273600.og1	273600og2	273600.og	273600og	$2$	$2$	\( 2^{6} \cdot 3^{2} \cdot 5^{2} \cdot 19 \)	\( 2^{23} \cdot 3^{9} \cdot 5^{10} \cdot 19^{2} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1$	$1$		$1$	$17694720$	$2.798752$	$651038076963/7220000$	$[0, 0, 0, -7800300, -8304498000]$	\(y^2=x^3-7800300x-8304498000\)
273600.qa1	273600qa2	273600.qa	273600qa	$2$	$2$	\( 2^{6} \cdot 3^{2} \cdot 5^{2} \cdot 19 \)	\( 2^{23} \cdot 3^{3} \cdot 5^{10} \cdot 19^{2} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1$	$1$		$1$	$5898240$	$2.249447$	$651038076963/7220000$	$[0, 0, 0, -866700, 307574000]$	\(y^2=x^3-866700x+307574000\)
288990.cb1	288990cb2	288990.cb	288990cb	$2$	$2$	\( 2 \cdot 3^{2} \cdot 5 \cdot 13^{2} \cdot 19 \)	\( 2^{5} \cdot 3^{3} \cdot 5^{4} \cdot 13^{6} \cdot 19^{2} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1$	$1$		$0$	$3010560$	$1.687481$	$651038076963/7220000$	$[1, -1, 0, -91545, 10581325]$	\(y^2+xy=x^3-x^2-91545x+10581325\)
288990.gz1	288990gz2	288990.gz	288990gz	$2$	$2$	\( 2 \cdot 3^{2} \cdot 5 \cdot 13^{2} \cdot 19 \)	\( 2^{5} \cdot 3^{9} \cdot 5^{4} \cdot 13^{6} \cdot 19^{2} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1$	$1$		$0$	$9031680$	$2.236786$	$651038076963/7220000$	$[1, -1, 1, -823907, -284871869]$	\(y^2+xy+y=x^3-x^2-823907x-284871869\)
418950.f1	418950f2	418950.f	418950f	$2$	$2$	\( 2 \cdot 3^{2} \cdot 5^{2} \cdot 7^{2} \cdot 19 \)	\( 2^{5} \cdot 3^{3} \cdot 5^{10} \cdot 7^{6} \cdot 19^{2} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$3.849832587$	$1$		$4$	$8847360$	$2.182682$	$651038076963/7220000$	$[1, -1, 0, -663567, -205884659]$	\(y^2+xy=x^3-x^2-663567x-205884659\)
418950.qx1	418950qx2	418950.qx	418950qx	$2$	$2$	\( 2 \cdot 3^{2} \cdot 5^{2} \cdot 7^{2} \cdot 19 \)	\( 2^{5} \cdot 3^{9} \cdot 5^{10} \cdot 7^{6} \cdot 19^{2} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1$	$1$		$0$	$26542080$	$2.731987$	$651038076963/7220000$	$[1, -1, 1, -5972105, 5564857897]$	\(y^2+xy+y=x^3-x^2-5972105x+5564857897\)
494190.cs1	494190cs2	494190.cs	494190cs	$2$	$2$	\( 2 \cdot 3^{2} \cdot 5 \cdot 17^{2} \cdot 19 \)	\( 2^{5} \cdot 3^{9} \cdot 5^{4} \cdot 17^{6} \cdot 19^{2} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1$	$1$		$0$	$18923520$	$2.370918$	$651038076963/7220000$	$[1, -1, 0, -1408929, -637147747]$	\(y^2+xy=x^3-x^2-1408929x-637147747\)
494190.el1	494190el2	494190.el	494190el	$2$	$2$	\( 2 \cdot 3^{2} \cdot 5 \cdot 17^{2} \cdot 19 \)	\( 2^{5} \cdot 3^{3} \cdot 5^{4} \cdot 17^{6} \cdot 19^{2} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1$	$1$		$0$	$6307840$	$1.821613$	$651038076963/7220000$	$[1, -1, 1, -156548, 23650247]$	\(y^2+xy+y=x^3-x^2-156548x+23650247\)