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.i1	6440g1	6440.i	6440g	$2$	$2$	$ 2^{3} \cdot 5 \cdot 7 \cdot 23 $	$ 2^{8} \cdot 5^{2} \cdot 7 \cdot 23 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$3220$	$12$	$0$	$0.748936017$	$1$	$7$	$640$	$-0.106505$	$44851536/4025$	$0.75606$	$2.64120$	$[0, 0, 0, -47, 114]$	$y^2=x^3-47x+114$	2.3.0.a.1, 20.6.0.b.1, 322.6.0.?, 3220.12.0.?	$[(5, 2)]$
12880.l1	12880j1	12880.l	12880j	$2$	$2$	$ 2^{4} \cdot 5 \cdot 7 \cdot 23 $	$ 2^{8} \cdot 5^{2} \cdot 7 \cdot 23 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$3220$	$12$	$0$	$1$	$1$	$1$	$1280$	$-0.106505$	$44851536/4025$	$0.75606$	$2.44774$	$[0, 0, 0, -47, -114]$	$y^2=x^3-47x-114$	2.3.0.a.1, 20.6.0.b.1, 322.6.0.?, 3220.12.0.?	$[]$
32200.n1	32200h1	32200.n	32200h	$2$	$2$	$ 2^{3} \cdot 5^{2} \cdot 7 \cdot 23 $	$ 2^{8} \cdot 5^{8} \cdot 7 \cdot 23 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$3220$	$12$	$0$	$2.366985862$	$1$	$3$	$15360$	$0.698214$	$44851536/4025$	$0.75606$	$3.16200$	$[0, 0, 0, -1175, 14250]$	$y^2=x^3-1175x+14250$	2.3.0.a.1, 20.6.0.b.1, 322.6.0.?, 3220.12.0.?	$[(-30, 150)]$
45080.p1	45080r1	45080.p	45080r	$2$	$2$	$ 2^{3} \cdot 5 \cdot 7^{2} \cdot 23 $	$ 2^{8} \cdot 5^{2} \cdot 7^{7} \cdot 23 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$3220$	$12$	$0$	$1.834241663$	$1$	$5$	$30720$	$0.866450$	$44851536/4025$	$0.75606$	$3.25111$	$[0, 0, 0, -2303, -39102]$	$y^2=x^3-2303x-39102$	2.3.0.a.1, 20.6.0.b.1, 322.6.0.?, 3220.12.0.?	$[(-31, 50)]$
51520.x1	51520b1	51520.x	51520b	$2$	$2$	$ 2^{6} \cdot 5 \cdot 7 \cdot 23 $	$ 2^{14} \cdot 5^{2} \cdot 7 \cdot 23 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$3220$	$12$	$0$	$1.300118573$	$1$	$5$	$10240$	$0.240068$	$44851536/4025$	$0.75606$	$2.51831$	$[0, 0, 0, -188, 912]$	$y^2=x^3-188x+912$	2.3.0.a.1, 20.6.0.b.1, 322.6.0.?, 3220.12.0.?	$[(-4, 40)]$
51520.bc1	51520bu1	51520.bc	51520bu	$2$	$2$	$ 2^{6} \cdot 5 \cdot 7 \cdot 23 $	$ 2^{14} \cdot 5^{2} \cdot 7 \cdot 23 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$3220$	$12$	$0$	$1$	$1$	$1$	$10240$	$0.240068$	$44851536/4025$	$0.75606$	$2.51831$	$[0, 0, 0, -188, -912]$	$y^2=x^3-188x-912$	2.3.0.a.1, 20.6.0.b.1, 322.6.0.?, 3220.12.0.?	$[]$
57960.e1	57960n1	57960.e	57960n	$2$	$2$	$ 2^{3} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 23 $	$ 2^{8} \cdot 3^{6} \cdot 5^{2} \cdot 7 \cdot 23 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$3220$	$12$	$0$	$1.863116607$	$1$	$5$	$20480$	$0.442801$	$44851536/4025$	$0.75606$	$2.71308$	$[0, 0, 0, -423, -3078]$	$y^2=x^3-423x-3078$	2.3.0.a.1, 20.6.0.b.1, 322.6.0.?, 3220.12.0.?	$[(27, 72)]$
64400.bc1	64400b1	64400.bc	64400b	$2$	$2$	$ 2^{4} \cdot 5^{2} \cdot 7 \cdot 23 $	$ 2^{8} \cdot 5^{8} \cdot 7 \cdot 23 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$3220$	$12$	$0$	$3.021733457$	$1$	$3$	$30720$	$0.698214$	$44851536/4025$	$0.75606$	$2.96406$	$[0, 0, 0, -1175, -14250]$	$y^2=x^3-1175x-14250$	2.3.0.a.1, 20.6.0.b.1, 322.6.0.?, 3220.12.0.?	$[(210, 3000)]$
90160.bo1	90160p1	90160.bo	90160p	$2$	$2$	$ 2^{4} \cdot 5 \cdot 7^{2} \cdot 23 $	$ 2^{8} \cdot 5^{2} \cdot 7^{7} \cdot 23 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$3220$	$12$	$0$	$1.189090918$	$1$	$5$	$61440$	$0.866450$	$44851536/4025$	$0.75606$	$3.05359$	$[0, 0, 0, -2303, 39102]$	$y^2=x^3-2303x+39102$	2.3.0.a.1, 20.6.0.b.1, 322.6.0.?, 3220.12.0.?	$[(14, 98)]$
115920.bz1	115920w1	115920.bz	115920w	$2$	$2$	$ 2^{4} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 23 $	$ 2^{8} \cdot 3^{6} \cdot 5^{2} \cdot 7 \cdot 23 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$3220$	$12$	$0$	$1.826577672$	$1$	$5$	$40960$	$0.442801$	$44851536/4025$	$0.75606$	$2.55181$	$[0, 0, 0, -423, 3078]$	$y^2=x^3-423x+3078$	2.3.0.a.1, 20.6.0.b.1, 322.6.0.?, 3220.12.0.?	$[(18, 36)]$
148120.x1	148120n1	148120.x	148120n	$2$	$2$	$ 2^{3} \cdot 5 \cdot 7 \cdot 23^{2} $	$ 2^{8} \cdot 5^{2} \cdot 7 \cdot 23^{7} $	$2$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$3220$	$12$	$0$	$3.589899976$	$1$	$9$	$337920$	$1.461243$	$44851536/4025$	$0.75606$	$3.52577$	$[0, 0, 0, -24863, -1387038]$	$y^2=x^3-24863x-1387038$	2.3.0.a.1, 20.6.0.b.1, 322.6.0.?, 3220.12.0.?	$[(299, 4232), (-79, 290)]$
225400.bs1	225400cf1	225400.bs	225400cf	$2$	$2$	$ 2^{3} \cdot 5^{2} \cdot 7^{2} \cdot 23 $	$ 2^{8} \cdot 5^{8} \cdot 7^{7} \cdot 23 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$3220$	$12$	$0$	$2.993234797$	$1$	$3$	$737280$	$1.671169$	$44851536/4025$	$0.75606$	$3.61005$	$[0, 0, 0, -57575, -4887750]$	$y^2=x^3-57575x-4887750$	2.3.0.a.1, 20.6.0.b.1, 322.6.0.?, 3220.12.0.?	$[(2135, 98000)]$
257600.cw1	257600cw1	257600.cw	257600cw	$2$	$2$	$ 2^{6} \cdot 5^{2} \cdot 7 \cdot 23 $	$ 2^{14} \cdot 5^{8} \cdot 7 \cdot 23 $	$2$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$3220$	$12$	$0$	$5.558009414$	$1$	$9$	$245760$	$1.044788$	$44851536/4025$	$0.75606$	$2.96806$	$[0, 0, 0, -4700, -114000]$	$y^2=x^3-4700x-114000$	2.3.0.a.1, 20.6.0.b.1, 322.6.0.?, 3220.12.0.?	$[(-40, 100), (114, 912)]$
257600.dk1	257600dk1	257600.dk	257600dk	$2$	$2$	$ 2^{6} \cdot 5^{2} \cdot 7 \cdot 23 $	$ 2^{14} \cdot 5^{8} \cdot 7 \cdot 23 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$3220$	$12$	$0$	$1.327579124$	$1$	$5$	$245760$	$1.044788$	$44851536/4025$	$0.75606$	$2.96806$	$[0, 0, 0, -4700, 114000]$	$y^2=x^3-4700x+114000$	2.3.0.a.1, 20.6.0.b.1, 322.6.0.?, 3220.12.0.?	$[(80, 500)]$
289800.dh1	289800dh1	289800.dh	289800dh	$2$	$2$	$ 2^{3} \cdot 3^{2} \cdot 5^{2} \cdot 7 \cdot 23 $	$ 2^{8} \cdot 3^{6} \cdot 5^{8} \cdot 7 \cdot 23 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$3220$	$12$	$0$	$1$	$1$	$1$	$491520$	$1.247520$	$44851536/4025$	$0.75606$	$3.13370$	$[0, 0, 0, -10575, -384750]$	$y^2=x^3-10575x-384750$	2.3.0.a.1, 20.6.0.b.1, 322.6.0.?, 3220.12.0.?	$[]$
296240.bi1	296240bi1	296240.bi	296240bi	$2$	$2$	$ 2^{4} \cdot 5 \cdot 7 \cdot 23^{2} $	$ 2^{8} \cdot 5^{2} \cdot 7 \cdot 23^{7} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$3220$	$12$	$0$	$1$	$1$	$1$	$675840$	$1.461243$	$44851536/4025$	$0.75606$	$3.33179$	$[0, 0, 0, -24863, 1387038]$	$y^2=x^3-24863x+1387038$	2.3.0.a.1, 20.6.0.b.1, 322.6.0.?, 3220.12.0.?	$[]$
360640.ey1	360640ey1	360640.ey	360640ey	$2$	$2$	$ 2^{6} \cdot 5 \cdot 7^{2} \cdot 23 $	$ 2^{14} \cdot 5^{2} \cdot 7^{7} \cdot 23 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$3220$	$12$	$0$	$2.670580047$	$1$	$5$	$491520$	$1.213024$	$44851536/4025$	$0.75606$	$3.04779$	$[0, 0, 0, -9212, -312816]$	$y^2=x^3-9212x-312816$	2.3.0.a.1, 20.6.0.b.1, 322.6.0.?, 3220.12.0.?	$[(-52, 160)]$
360640.fi1	360640fi1	360640.fi	360640fi	$2$	$2$	$ 2^{6} \cdot 5 \cdot 7^{2} \cdot 23 $	$ 2^{14} \cdot 5^{2} \cdot 7^{7} \cdot 23 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$3220$	$12$	$0$	$1.130164434$	$1$	$5$	$491520$	$1.213024$	$44851536/4025$	$0.75606$	$3.04779$	$[0, 0, 0, -9212, 312816]$	$y^2=x^3-9212x+312816$	2.3.0.a.1, 20.6.0.b.1, 322.6.0.?, 3220.12.0.?	$[(77, 245)]$
405720.er1	405720er1	405720.er	405720er	$2$	$2$	$ 2^{3} \cdot 3^{2} \cdot 5 \cdot 7^{2} \cdot 23 $	$ 2^{8} \cdot 3^{6} \cdot 5^{2} \cdot 7^{7} \cdot 23 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$3220$	$12$	$0$	$4.416284749$	$1$	$3$	$983040$	$1.415756$	$44851536/4025$	$0.75606$	$3.20838$	$[0, 0, 0, -20727, 1055754]$	$y^2=x^3-20727x+1055754$	2.3.0.a.1, 20.6.0.b.1, 322.6.0.?, 3220.12.0.?	$[(-62, 1450)]$
450800.da1	450800da1	450800.da	450800da	$2$	$2$	$ 2^{4} \cdot 5^{2} \cdot 7^{2} \cdot 23 $	$ 2^{8} \cdot 5^{8} \cdot 7^{7} \cdot 23 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$3220$	$12$	$0$	$1$	$1$	$1$	$1474560$	$1.671169$	$44851536/4025$	$0.75606$	$3.41784$	$[0, 0, 0, -57575, 4887750]$	$y^2=x^3-57575x+4887750$	2.3.0.a.1, 20.6.0.b.1, 322.6.0.?, 3220.12.0.?	$[]$
463680.jx1	463680jx1	463680.jx	463680jx	$2$	$2$	$ 2^{6} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 23 $	$ 2^{14} \cdot 3^{6} \cdot 5^{2} \cdot 7 \cdot 23 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$3220$	$12$	$0$	$1$	$1$	$1$	$327680$	$0.789374$	$44851536/4025$	$0.75606$	$2.59943$	$[0, 0, 0, -1692, -24624]$	$y^2=x^3-1692x-24624$	2.3.0.a.1, 20.6.0.b.1, 322.6.0.?, 3220.12.0.?	$[]$
463680.lz1	463680lz1	463680.lz	463680lz	$2$	$2$	$ 2^{6} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 23 $	$ 2^{14} \cdot 3^{6} \cdot 5^{2} \cdot 7 \cdot 23 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$3220$	$12$	$0$	$2.167857963$	$1$	$5$	$327680$	$0.789374$	$44851536/4025$	$0.75606$	$2.59943$	$[0, 0, 0, -1692, 24624]$	$y^2=x^3-1692x+24624$	2.3.0.a.1, 20.6.0.b.1, 322.6.0.?, 3220.12.0.?	$[(34, 80)]$

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Elliptic curves over $\Q$
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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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