LMFDB - Elliptic curve search results

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Conductor	Discriminant	j-invariant	Rank

Bad$\ p$	Curves per isogeny class	Complex multiplication	Torsion

Isogeny class degree	Cyclic isogeny degree	Isogeny class size	Integral points

Analytic order of Ш	$p\ $div$\ $\|Ш\|	Regulator	Reduction	Faltings height

Galois image	Adelic level	Adelic index	Adelic genus

Nonmax$\ \ell$	$abc$ quality	Szpiro ratio

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Results (24 matches)

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Label	Cremona label	Class	Cremona class	Class size	Class degree	Conductor	Discriminant	Rank	Torsion	$\textrm{End}^0(E_{\overline\Q})$	Sato-Tate	Nonmax $\ell$	$\ell$-adic images	mod-$\ell$ images	Adelic level	Adelic index	Adelic genus	Regulator	$Ш_{\textrm{an}}$	Ш primes	Integral points	Modular degree	Faltings height	j-invariant	$abc$ quality	Szpiro ratio	Weierstrass coefficients	Weierstrass equation	mod-$m$ images	MW-generators
14520.bl2	14520bp2	14520.bl	14520bp	$2$	$2$	$ 2^{3} \cdot 3 \cdot 5 \cdot 11^{2} $	$ - 2^{10} \cdot 3^{2} \cdot 5^{8} \cdot 11^{9} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$132$	$12$	$0$	$1$	$1$		$1$	$337920$	$2.362068$	$-23758298924/3515625$	$0.96866$	$5.49200$	$[0, 1, 0, -803480, 310369728]$	$y^2=x^3+x^2-803480x+310369728$	2.3.0.a.1, 12.6.0.f.1, 22.6.0.a.1, 132.12.0.?	$[]$
14520.bo2	14520t2	14520.bo	14520t	$2$	$2$	$ 2^{3} \cdot 3 \cdot 5 \cdot 11^{2} $	$ - 2^{10} \cdot 3^{2} \cdot 5^{8} \cdot 11^{3} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$132$	$12$	$0$	$1.535326317$	$1$		$7$	$30720$	$1.163122$	$-23758298924/3515625$	$0.96866$	$3.99070$	$[0, 1, 0, -6640, -235600]$	$y^2=x^3+x^2-6640x-235600$	2.3.0.a.1, 12.6.0.f.1, 22.6.0.a.1, 132.12.0.?	$[(220, 3000)]$
29040.bg2	29040m2	29040.bg	29040m	$2$	$2$	$ 2^{4} \cdot 3 \cdot 5 \cdot 11^{2} $	$ - 2^{10} \cdot 3^{2} \cdot 5^{8} \cdot 11^{3} $	$2$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$132$	$12$	$0$	$0.303306711$	$1$		$35$	$61440$	$1.163122$	$-23758298924/3515625$	$0.96866$	$3.72153$	$[0, -1, 0, -6640, 235600]$	$y^2=x^3-x^2-6640x+235600$	2.3.0.a.1, 12.6.0.f.1, 22.6.0.a.1, 132.12.0.?	$[(70, 330), (-20, 600)]$
29040.bs2	29040l2	29040.bs	29040l	$2$	$2$	$ 2^{4} \cdot 3 \cdot 5 \cdot 11^{2} $	$ - 2^{10} \cdot 3^{2} \cdot 5^{8} \cdot 11^{9} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$132$	$12$	$0$	$1$	$1$		$1$	$675840$	$2.362068$	$-23758298924/3515625$	$0.96866$	$5.12157$	$[0, -1, 0, -803480, -310369728]$	$y^2=x^3-x^2-803480x-310369728$	2.3.0.a.1, 12.6.0.f.1, 22.6.0.a.1, 132.12.0.?	$[]$
43560.j2	43560i2	43560.j	43560i	$2$	$2$	$ 2^{3} \cdot 3^{2} \cdot 5 \cdot 11^{2} $	$ - 2^{10} \cdot 3^{8} \cdot 5^{8} \cdot 11^{9} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$132$	$12$	$0$	$1$	$1$		$1$	$2703360$	$2.911377$	$-23758298924/3515625$	$0.96866$	$5.54425$	$[0, 0, 0, -7231323, -8387213978]$	$y^2=x^3-7231323x-8387213978$	2.3.0.a.1, 12.6.0.f.1, 22.6.0.a.1, 132.12.0.?	$[]$
43560.x2	43560bp2	43560.x	43560bp	$2$	$2$	$ 2^{3} \cdot 3^{2} \cdot 5 \cdot 11^{2} $	$ - 2^{10} \cdot 3^{8} \cdot 5^{8} \cdot 11^{3} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$132$	$12$	$0$	$1.650929930$	$1$		$5$	$245760$	$1.712427$	$-23758298924/3515625$	$0.96866$	$4.19736$	$[0, 0, 0, -59763, 6301438]$	$y^2=x^3-59763x+6301438$	2.3.0.a.1, 12.6.0.f.1, 22.6.0.a.1, 132.12.0.?	$[(11, 2376)]$
72600.t2	72600ch2	72600.t	72600ch	$2$	$2$	$ 2^{3} \cdot 3 \cdot 5^{2} \cdot 11^{2} $	$ - 2^{10} \cdot 3^{2} \cdot 5^{14} \cdot 11^{3} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$132$	$12$	$0$	$1$	$1$		$1$	$737280$	$1.967840$	$-23758298924/3515625$	$0.96866$	$4.27963$	$[0, -1, 0, -166008, -29117988]$	$y^2=x^3-x^2-166008x-29117988$	2.3.0.a.1, 12.6.0.f.1, 22.6.0.a.1, 132.12.0.?	$[]$
72600.bn2	72600c2	72600.bn	72600c	$2$	$2$	$ 2^{3} \cdot 3 \cdot 5^{2} \cdot 11^{2} $	$ - 2^{10} \cdot 3^{2} \cdot 5^{14} \cdot 11^{9} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$132$	$12$	$0$	$6.249819370$	$1$		$3$	$8110080$	$3.166786$	$-23758298924/3515625$	$0.96866$	$5.56505$	$[0, -1, 0, -20087008, 38836390012]$	$y^2=x^3-x^2-20087008x+38836390012$	2.3.0.a.1, 12.6.0.f.1, 22.6.0.a.1, 132.12.0.?	$[(6762, 460600)]$
87120.t2	87120r2	87120.t	87120r	$2$	$2$	$ 2^{4} \cdot 3^{2} \cdot 5 \cdot 11^{2} $	$ - 2^{10} \cdot 3^{8} \cdot 5^{8} \cdot 11^{3} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$132$	$12$	$0$	$1$	$1$		$1$	$491520$	$1.712427$	$-23758298924/3515625$	$0.96866$	$3.94159$	$[0, 0, 0, -59763, -6301438]$	$y^2=x^3-59763x-6301438$	2.3.0.a.1, 12.6.0.f.1, 22.6.0.a.1, 132.12.0.?	$[]$
87120.cj2	87120q2	87120.cj	87120q	$2$	$2$	$ 2^{4} \cdot 3^{2} \cdot 5 \cdot 11^{2} $	$ - 2^{10} \cdot 3^{8} \cdot 5^{8} \cdot 11^{9} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$132$	$12$	$0$	$1$	$1$		$1$	$5406720$	$2.911377$	$-23758298924/3515625$	$0.96866$	$5.20641$	$[0, 0, 0, -7231323, 8387213978]$	$y^2=x^3-7231323x+8387213978$	2.3.0.a.1, 12.6.0.f.1, 22.6.0.a.1, 132.12.0.?	$[]$
116160.m2	116160i2	116160.m	116160i	$2$	$2$	$ 2^{6} \cdot 3 \cdot 5 \cdot 11^{2} $	$ - 2^{16} \cdot 3^{2} \cdot 5^{8} \cdot 11^{9} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$132$	$12$	$0$	$7.224314447$	$1$		$1$	$5406720$	$2.708641$	$-23758298924/3515625$	$0.96866$	$4.86939$	$[0, -1, 0, -3213921, 2486171745]$	$y^2=x^3-x^2-3213921x+2486171745$	2.3.0.a.1, 12.6.0.f.1, 22.6.0.a.1, 132.12.0.?	$[(57247/7, 6180000/7)]$
116160.bw2	116160d2	116160.bw	116160d	$2$	$2$	$ 2^{6} \cdot 3 \cdot 5 \cdot 11^{2} $	$ - 2^{16} \cdot 3^{2} \cdot 5^{8} \cdot 11^{3} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$132$	$12$	$0$	$8.772674476$	$1$		$1$	$491520$	$1.509695$	$-23758298924/3515625$	$0.96866$	$3.63577$	$[0, -1, 0, -26561, -1858239]$	$y^2=x^3-x^2-26561x-1858239$	2.3.0.a.1, 12.6.0.f.1, 22.6.0.a.1, 132.12.0.?	$[(36701/2, 7029495/2)]$
116160.fp2	116160hl2	116160.fp	116160hl	$2$	$2$	$ 2^{6} \cdot 3 \cdot 5 \cdot 11^{2} $	$ - 2^{16} \cdot 3^{2} \cdot 5^{8} \cdot 11^{3} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$132$	$12$	$0$	$3.099045347$	$1$		$3$	$491520$	$1.509695$	$-23758298924/3515625$	$0.96866$	$3.63577$	$[0, 1, 0, -26561, 1858239]$	$y^2=x^3+x^2-26561x+1858239$	2.3.0.a.1, 12.6.0.f.1, 22.6.0.a.1, 132.12.0.?	$[(106, 495)]$
116160.gl2	116160hi2	116160.gl	116160hi	$2$	$2$	$ 2^{6} \cdot 3 \cdot 5 \cdot 11^{2} $	$ - 2^{16} \cdot 3^{2} \cdot 5^{8} \cdot 11^{9} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$132$	$12$	$0$	$38.24107892$	$1$		$1$	$5406720$	$2.708641$	$-23758298924/3515625$	$0.96866$	$4.86939$	$[0, 1, 0, -3213921, -2486171745]$	$y^2=x^3+x^2-3213921x-2486171745$	2.3.0.a.1, 12.6.0.f.1, 22.6.0.a.1, 132.12.0.?	$[(2334655120431956274/14654441, 3515082565007296592888245821/14654441)]$
145200.gv2	145200hv2	145200.gv	145200hv	$2$	$2$	$ 2^{4} \cdot 3 \cdot 5^{2} \cdot 11^{2} $	$ - 2^{10} \cdot 3^{2} \cdot 5^{14} \cdot 11^{9} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$132$	$12$	$0$	$1$	$4$	$2$	$1$	$16220160$	$3.166786$	$-23758298924/3515625$	$0.96866$	$5.24051$	$[0, 1, 0, -20087008, -38836390012]$	$y^2=x^3+x^2-20087008x-38836390012$	2.3.0.a.1, 12.6.0.f.1, 22.6.0.a.1, 132.12.0.?	$[]$
145200.ke2	145200ir2	145200.ke	145200ir	$2$	$2$	$ 2^{4} \cdot 3 \cdot 5^{2} \cdot 11^{2} $	$ - 2^{10} \cdot 3^{2} \cdot 5^{14} \cdot 11^{3} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$132$	$12$	$0$	$1$	$1$		$1$	$1474560$	$1.967840$	$-23758298924/3515625$	$0.96866$	$4.03005$	$[0, 1, 0, -166008, 29117988]$	$y^2=x^3+x^2-166008x+29117988$	2.3.0.a.1, 12.6.0.f.1, 22.6.0.a.1, 132.12.0.?	$[]$
217800.ck2	217800fh2	217800.ck	217800fh	$2$	$2$	$ 2^{3} \cdot 3^{2} \cdot 5^{2} \cdot 11^{2} $	$ - 2^{10} \cdot 3^{8} \cdot 5^{14} \cdot 11^{3} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$132$	$12$	$0$	$1$	$1$		$1$	$5898240$	$2.517147$	$-23758298924/3515625$	$0.96866$	$4.43340$	$[0, 0, 0, -1494075, 787679750]$	$y^2=x^3-1494075x+787679750$	2.3.0.a.1, 12.6.0.f.1, 22.6.0.a.1, 132.12.0.?	$[]$
217800.ey2	217800cj2	217800.ey	217800cj	$2$	$2$	$ 2^{3} \cdot 3^{2} \cdot 5^{2} \cdot 11^{2} $	$ - 2^{10} \cdot 3^{8} \cdot 5^{14} \cdot 11^{9} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$132$	$12$	$0$	$27.81882355$	$1$		$1$	$64880640$	$3.716095$	$-23758298924/3515625$	$0.96866$	$5.60393$	$[0, 0, 0, -180783075, -1048401747250]$	$y^2=x^3-180783075x-1048401747250$	2.3.0.a.1, 12.6.0.f.1, 22.6.0.a.1, 132.12.0.?	$[(13761969465091/22351, 43067244323665305864/22351)]$
348480.kx2	348480kx2	348480.kx	348480kx	$2$	$2$	$ 2^{6} \cdot 3^{2} \cdot 5 \cdot 11^{2} $	$ - 2^{16} \cdot 3^{8} \cdot 5^{8} \cdot 11^{9} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$132$	$12$	$0$	$4.812432255$	$1$		$5$	$43253760$	$3.257950$	$-23758298924/3515625$	$0.96866$	$4.96672$	$[0, 0, 0, -28925292, -67097711824]$	$y^2=x^3-28925292x-67097711824$	2.3.0.a.1, 12.6.0.f.1, 22.6.0.a.1, 132.12.0.?	$[(10285, 850509)]$
348480.ll2	348480ll2	348480.ll	348480ll	$2$	$2$	$ 2^{6} \cdot 3^{2} \cdot 5 \cdot 11^{2} $	$ - 2^{16} \cdot 3^{8} \cdot 5^{8} \cdot 11^{3} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$132$	$12$	$0$	$1$	$1$		$1$	$3932160$	$2.059002$	$-23758298924/3515625$	$0.96866$	$3.83930$	$[0, 0, 0, -239052, -50411504]$	$y^2=x^3-239052x-50411504$	2.3.0.a.1, 12.6.0.f.1, 22.6.0.a.1, 132.12.0.?	$[]$
348480.oz2	348480oz2	348480.oz	348480oz	$2$	$2$	$ 2^{6} \cdot 3^{2} \cdot 5 \cdot 11^{2} $	$ - 2^{16} \cdot 3^{8} \cdot 5^{8} \cdot 11^{9} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$132$	$12$	$0$	$1$	$1$		$1$	$43253760$	$3.257950$	$-23758298924/3515625$	$0.96866$	$4.96672$	$[0, 0, 0, -28925292, 67097711824]$	$y^2=x^3-28925292x+67097711824$	2.3.0.a.1, 12.6.0.f.1, 22.6.0.a.1, 132.12.0.?	$[]$
348480.po2	348480po2	348480.po	348480po	$2$	$2$	$ 2^{6} \cdot 3^{2} \cdot 5 \cdot 11^{2} $	$ - 2^{16} \cdot 3^{8} \cdot 5^{8} \cdot 11^{3} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$132$	$12$	$0$	$1.204850963$	$1$		$7$	$3932160$	$2.059002$	$-23758298924/3515625$	$0.96866$	$3.83930$	$[0, 0, 0, -239052, 50411504]$	$y^2=x^3-239052x+50411504$	2.3.0.a.1, 12.6.0.f.1, 22.6.0.a.1, 132.12.0.?	$[(328, 2700)]$
435600.ev2	435600ev2	435600.ev	435600ev	$2$	$2$	$ 2^{4} \cdot 3^{2} \cdot 5^{2} \cdot 11^{2} $	$ - 2^{10} \cdot 3^{8} \cdot 5^{14} \cdot 11^{9} $	$2$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$132$	$12$	$0$	$7.930305108$	$1$		$15$	$129761280$	$3.716095$	$-23758298924/3515625$	$0.96866$	$5.30477$	$[0, 0, 0, -180783075, 1048401747250]$	$y^2=x^3-180783075x+1048401747250$	2.3.0.a.1, 12.6.0.f.1, 22.6.0.a.1, 132.12.0.?	$[(4235, 598950), (31145, 5062500)]$
435600.px2	435600px2	435600.px	435600px	$2$	$2$	$ 2^{4} \cdot 3^{2} \cdot 5^{2} \cdot 11^{2} $	$ - 2^{10} \cdot 3^{8} \cdot 5^{14} \cdot 11^{3} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$132$	$12$	$0$	$1$	$1$		$1$	$11796480$	$2.517147$	$-23758298924/3515625$	$0.96866$	$4.19673$	$[0, 0, 0, -1494075, -787679750]$	$y^2=x^3-1494075x-787679750$	2.3.0.a.1, 12.6.0.f.1, 22.6.0.a.1, 132.12.0.?	$[]$

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Elliptic curves over $\Q$
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Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

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