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 (22 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	$Ш_{\textrm{an}}$	Integral points	Modular degree	Faltings height	j-invariant	$abc$ quality	Szpiro ratio	Weierstrass coefficients	Weierstrass equation	mod-$m$ images	MW-generators
6440.k2	6440j1	6440.k	6440j	$2$	$2$	$ 2^{3} \cdot 5 \cdot 7 \cdot 23 $	$ 2^{10} \cdot 5^{4} \cdot 7 \cdot 23 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.6.0.1	2B	$1288$	$12$	$0$	$1$	$1$	$1$	$2304$	$0.228820$	$188183524/100625$	$0.93120$	$2.96278$	$[0, -1, 0, -120, -100]$	$y^2=x^3-x^2-120x-100$	2.3.0.a.1, 8.6.0.c.1, 322.6.0.?, 1288.12.0.?	$[]$
12880.b2	12880i1	12880.b	12880i	$2$	$2$	$ 2^{4} \cdot 5 \cdot 7 \cdot 23 $	$ 2^{10} \cdot 5^{4} \cdot 7 \cdot 23 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.6.0.1	2B	$1288$	$12$	$0$	$0.517149198$	$1$	$9$	$4608$	$0.228820$	$188183524/100625$	$0.93120$	$2.74577$	$[0, 1, 0, -120, 100]$	$y^2=x^3+x^2-120x+100$	2.3.0.a.1, 8.6.0.c.1, 322.6.0.?, 1288.12.0.?	$[(0, 10)]$
32200.d2	32200f1	32200.d	32200f	$2$	$2$	$ 2^{3} \cdot 5^{2} \cdot 7 \cdot 23 $	$ 2^{10} \cdot 5^{10} \cdot 7 \cdot 23 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.6.0.1	2B	$1288$	$12$	$0$	$1$	$1$	$1$	$55296$	$1.033539$	$188183524/100625$	$0.93120$	$3.43372$	$[0, 1, 0, -3008, -18512]$	$y^2=x^3+x^2-3008x-18512$	2.3.0.a.1, 8.6.0.c.1, 322.6.0.?, 1288.12.0.?	$[]$
45080.d2	45080z1	45080.d	45080z	$2$	$2$	$ 2^{3} \cdot 5 \cdot 7^{2} \cdot 23 $	$ 2^{10} \cdot 5^{4} \cdot 7^{7} \cdot 23 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.6.0.1	2B	$1288$	$12$	$0$	$1$	$1$	$1$	$110592$	$1.201775$	$188183524/100625$	$0.93120$	$3.51429$	$[0, 1, 0, -5896, 46080]$	$y^2=x^3+x^2-5896x+46080$	2.3.0.a.1, 8.6.0.c.1, 322.6.0.?, 1288.12.0.?	$[]$
51520.g2	51520j1	51520.g	51520j	$2$	$2$	$ 2^{6} \cdot 5 \cdot 7 \cdot 23 $	$ 2^{16} \cdot 5^{4} \cdot 7 \cdot 23 $	$2$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.6.0.1	2B	$1288$	$12$	$0$	$3.155290500$	$1$	$11$	$36864$	$0.575394$	$188183524/100625$	$0.93120$	$2.77825$	$[0, 1, 0, -481, -1281]$	$y^2=x^3+x^2-481x-1281$	2.3.0.a.1, 8.6.0.c.1, 322.6.0.?, 1288.12.0.?	$[(-5, 32), (-3, 12)]$
51520.cd2	51520bt1	51520.cd	51520bt	$2$	$2$	$ 2^{6} \cdot 5 \cdot 7 \cdot 23 $	$ 2^{16} \cdot 5^{4} \cdot 7 \cdot 23 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.6.0.1	2B	$1288$	$12$	$0$	$3.870265100$	$1$	$3$	$36864$	$0.575394$	$188183524/100625$	$0.93120$	$2.77825$	$[0, -1, 0, -481, 1281]$	$y^2=x^3-x^2-481x+1281$	2.3.0.a.1, 8.6.0.c.1, 322.6.0.?, 1288.12.0.?	$[(471, 10200)]$
57960.k2	57960j1	57960.k	57960j	$2$	$2$	$ 2^{3} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 23 $	$ 2^{10} \cdot 3^{6} \cdot 5^{4} \cdot 7 \cdot 23 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.6.0.1	2B	$1288$	$12$	$0$	$1$	$1$	$1$	$55296$	$0.778126$	$188183524/100625$	$0.93120$	$2.97023$	$[0, 0, 0, -1083, 3782]$	$y^2=x^3-1083x+3782$	2.3.0.a.1, 8.6.0.c.1, 322.6.0.?, 1288.12.0.?	$[]$
64400.ce2	64400k1	64400.ce	64400k	$2$	$2$	$ 2^{4} \cdot 5^{2} \cdot 7 \cdot 23 $	$ 2^{10} \cdot 5^{10} \cdot 7 \cdot 23 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.6.0.1	2B	$1288$	$12$	$0$	$1$	$1$	$1$	$110592$	$1.033539$	$188183524/100625$	$0.93120$	$3.21877$	$[0, -1, 0, -3008, 18512]$	$y^2=x^3-x^2-3008x+18512$	2.3.0.a.1, 8.6.0.c.1, 322.6.0.?, 1288.12.0.?	$[]$
90160.cw2	90160i1	90160.cw	90160i	$2$	$2$	$ 2^{4} \cdot 5 \cdot 7^{2} \cdot 23 $	$ 2^{10} \cdot 5^{4} \cdot 7^{7} \cdot 23 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.6.0.1	2B	$1288$	$12$	$0$	$1$	$1$	$1$	$221184$	$1.201775$	$188183524/100625$	$0.93120$	$3.30079$	$[0, -1, 0, -5896, -46080]$	$y^2=x^3-x^2-5896x-46080$	2.3.0.a.1, 8.6.0.c.1, 322.6.0.?, 1288.12.0.?	$[]$
115920.bj2	115920bb1	115920.bj	115920bb	$2$	$2$	$ 2^{4} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 23 $	$ 2^{10} \cdot 3^{6} \cdot 5^{4} \cdot 7 \cdot 23 $	$2$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.6.0.1	2B	$1288$	$12$	$0$	$3.139840744$	$1$	$13$	$110592$	$0.778126$	$188183524/100625$	$0.93120$	$2.79367$	$[0, 0, 0, -1083, -3782]$	$y^2=x^3-1083x-3782$	2.3.0.a.1, 8.6.0.c.1, 322.6.0.?, 1288.12.0.?	$[(-13, 90), (-6, 50)]$
148120.bo2	148120u1	148120.bo	148120u	$2$	$2$	$ 2^{3} \cdot 5 \cdot 7 \cdot 23^{2} $	$ 2^{10} \cdot 5^{4} \cdot 7 \cdot 23^{7} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.6.0.1	2B	$1288$	$12$	$0$	$1$	$1$	$1$	$1216512$	$1.796566$	$188183524/100625$	$0.93120$	$3.76266$	$[0, -1, 0, -63656, 1725500]$	$y^2=x^3-x^2-63656x+1725500$	2.3.0.a.1, 8.6.0.c.1, 322.6.0.?, 1288.12.0.?	$[]$
225400.ch2	225400cq1	225400.ch	225400cq	$2$	$2$	$ 2^{3} \cdot 5^{2} \cdot 7^{2} \cdot 23 $	$ 2^{10} \cdot 5^{10} \cdot 7^{7} \cdot 23 $	$2$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.6.0.1	2B	$1288$	$12$	$0$	$8.508702177$	$1$	$5$	$2654208$	$2.006493$	$188183524/100625$	$0.93120$	$3.83887$	$[0, -1, 0, -147408, 6054812]$	$y^2=x^3-x^2-147408x+6054812$	2.3.0.a.1, 8.6.0.c.1, 322.6.0.?, 1288.12.0.?	$[(677, 14700), (2, 2400)]$
257600.k2	257600k1	257600.k	257600k	$2$	$2$	$ 2^{6} \cdot 5^{2} \cdot 7 \cdot 23 $	$ 2^{16} \cdot 5^{10} \cdot 7 \cdot 23 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.6.0.1	2B	$1288$	$12$	$0$	$1.606148392$	$1$	$5$	$884736$	$1.380112$	$188183524/100625$	$0.93120$	$3.19443$	$[0, 1, 0, -12033, 136063]$	$y^2=x^3+x^2-12033x+136063$	2.3.0.a.1, 8.6.0.c.1, 322.6.0.?, 1288.12.0.?	$[(-57, 800)]$
257600.fw2	257600fw1	257600.fw	257600fw	$2$	$2$	$ 2^{6} \cdot 5^{2} \cdot 7 \cdot 23 $	$ 2^{16} \cdot 5^{10} \cdot 7 \cdot 23 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.6.0.1	2B	$1288$	$12$	$0$	$1$	$1$	$1$	$884736$	$1.380112$	$188183524/100625$	$0.93120$	$3.19443$	$[0, -1, 0, -12033, -136063]$	$y^2=x^3-x^2-12033x-136063$	2.3.0.a.1, 8.6.0.c.1, 322.6.0.?, 1288.12.0.?	$[]$
289800.ei2	289800ei1	289800.ei	289800ei	$2$	$2$	$ 2^{3} \cdot 3^{2} \cdot 5^{2} \cdot 7 \cdot 23 $	$ 2^{10} \cdot 3^{6} \cdot 5^{10} \cdot 7 \cdot 23 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.6.0.1	2B	$1288$	$12$	$0$	$6.160468402$	$1$	$1$	$1327104$	$1.582846$	$188183524/100625$	$0.93120$	$3.35795$	$[0, 0, 0, -27075, 472750]$	$y^2=x^3-27075x+472750$	2.3.0.a.1, 8.6.0.c.1, 322.6.0.?, 1288.12.0.?	$[(-7530/7, 343750/7)]$
296240.g2	296240g1	296240.g	296240g	$2$	$2$	$ 2^{4} \cdot 5 \cdot 7 \cdot 23^{2} $	$ 2^{10} \cdot 5^{4} \cdot 7 \cdot 23^{7} $	$2$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.6.0.1	2B	$1288$	$12$	$0$	$3.422247466$	$1$	$13$	$2433024$	$1.796566$	$188183524/100625$	$0.93120$	$3.55565$	$[0, 1, 0, -63656, -1725500]$	$y^2=x^3+x^2-63656x-1725500$	2.3.0.a.1, 8.6.0.c.1, 322.6.0.?, 1288.12.0.?	$[(-146, 2116), (-6096/7, 709918/7)]$
360640.bi2	360640bi1	360640.bi	360640bi	$2$	$2$	$ 2^{6} \cdot 5 \cdot 7^{2} \cdot 23 $	$ 2^{16} \cdot 5^{4} \cdot 7^{7} \cdot 23 $	$2$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.6.0.1	2B	$1288$	$12$	$0$	$1.507836564$	$1$	$21$	$1769472$	$1.548347$	$188183524/100625$	$0.93120$	$3.26820$	$[0, 1, 0, -23585, -392225]$	$y^2=x^3+x^2-23585x-392225$	2.3.0.a.1, 8.6.0.c.1, 322.6.0.?, 1288.12.0.?	$[(-75, 980), (170, 735)]$
360640.ij2	360640ij1	360640.ij	360640ij	$2$	$2$	$ 2^{6} \cdot 5 \cdot 7^{2} \cdot 23 $	$ 2^{16} \cdot 5^{4} \cdot 7^{7} \cdot 23 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.6.0.1	2B	$1288$	$12$	$0$	$1$	$1$	$1$	$1769472$	$1.548347$	$188183524/100625$	$0.93120$	$3.26820$	$[0, -1, 0, -23585, 392225]$	$y^2=x^3-x^2-23585x+392225$	2.3.0.a.1, 8.6.0.c.1, 322.6.0.?, 1288.12.0.?	$[]$
405720.ge2	405720ge1	405720.ge	405720ge	$2$	$2$	$ 2^{3} \cdot 3^{2} \cdot 5 \cdot 7^{2} \cdot 23 $	$ 2^{10} \cdot 3^{6} \cdot 5^{4} \cdot 7^{7} \cdot 23 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.6.0.1	2B	$1288$	$12$	$0$	$1$	$1$	$1$	$2654208$	$1.751081$	$188183524/100625$	$0.93120$	$3.42679$	$[0, 0, 0, -53067, -1297226]$	$y^2=x^3-53067x-1297226$	2.3.0.a.1, 8.6.0.c.1, 322.6.0.?, 1288.12.0.?	$[]$
450800.bk2	450800bk1	450800.bk	450800bk	$2$	$2$	$ 2^{4} \cdot 5^{2} \cdot 7^{2} \cdot 23 $	$ 2^{10} \cdot 5^{10} \cdot 7^{7} \cdot 23 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.6.0.1	2B	$1288$	$12$	$0$	$3.066217500$	$1$	$5$	$5308416$	$2.006493$	$188183524/100625$	$0.93120$	$3.63448$	$[0, 1, 0, -147408, -6054812]$	$y^2=x^3+x^2-147408x-6054812$	2.3.0.a.1, 8.6.0.c.1, 322.6.0.?, 1288.12.0.?	$[(-166, 3724)]$
463680.im2	463680im1	463680.im	463680im	$2$	$2$	$ 2^{6} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 23 $	$ 2^{16} \cdot 3^{6} \cdot 5^{4} \cdot 7 \cdot 23 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.6.0.1	2B	$1288$	$12$	$0$	$1.405790495$	$1$	$7$	$884736$	$1.124699$	$188183524/100625$	$0.93120$	$2.81560$	$[0, 0, 0, -4332, 30256]$	$y^2=x^3-4332x+30256$	2.3.0.a.1, 8.6.0.c.1, 322.6.0.?, 1288.12.0.?	$[(-28, 360)]$
463680.nl2	463680nl1	463680.nl	463680nl	$2$	$2$	$ 2^{6} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 23 $	$ 2^{16} \cdot 3^{6} \cdot 5^{4} \cdot 7 \cdot 23 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.6.0.1	2B	$1288$	$12$	$0$	$1$	$1$	$1$	$884736$	$1.124699$	$188183524/100625$	$0.93120$	$2.81560$	$[0, 0, 0, -4332, -30256]$	$y^2=x^3-4332x-30256$	2.3.0.a.1, 8.6.0.c.1, 322.6.0.?, 1288.12.0.?	$[]$

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Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
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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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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