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.i2	6440g2	6440.i	6440g	$2$	$2$	$ 2^{3} \cdot 5 \cdot 7 \cdot 23 $	$ - 2^{10} \cdot 5 \cdot 7^{2} \cdot 23^{2} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$3220$	$12$	$0$	$1.497872035$	$1$	$5$	$1280$	$0.240068$	$16078716/129605$	$0.85853$	$2.97413$	$[0, 0, 0, 53, 534]$	$y^2=x^3+53x+534$	2.3.0.a.1, 20.6.0.a.1, 644.6.0.?, 3220.12.0.?	$[(-5, 12)]$
12880.l2	12880j2	12880.l	12880j	$2$	$2$	$ 2^{4} \cdot 5 \cdot 7 \cdot 23 $	$ - 2^{10} \cdot 5 \cdot 7^{2} \cdot 23^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$3220$	$12$	$0$	$1$	$1$	$1$	$2560$	$0.240068$	$16078716/129605$	$0.85853$	$2.75629$	$[0, 0, 0, 53, -534]$	$y^2=x^3+53x-534$	2.3.0.a.1, 20.6.0.a.1, 644.6.0.?, 3220.12.0.?	$[]$
32200.n2	32200h2	32200.n	32200h	$2$	$2$	$ 2^{3} \cdot 5^{2} \cdot 7 \cdot 23 $	$ - 2^{10} \cdot 5^{7} \cdot 7^{2} \cdot 23^{2} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$3220$	$12$	$0$	$1.183492931$	$1$	$3$	$30720$	$1.044788$	$16078716/129605$	$0.85853$	$3.44331$	$[0, 0, 0, 1325, 66750]$	$y^2=x^3+1325x+66750$	2.3.0.a.1, 20.6.0.a.1, 644.6.0.?, 3220.12.0.?	$[(15, 300)]$
45080.p2	45080r2	45080.p	45080r	$2$	$2$	$ 2^{3} \cdot 5 \cdot 7^{2} \cdot 23 $	$ - 2^{10} \cdot 5 \cdot 7^{8} \cdot 23^{2} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$3220$	$12$	$0$	$3.668483326$	$1$	$3$	$61440$	$1.213024$	$16078716/129605$	$0.85853$	$3.52358$	$[0, 0, 0, 2597, -183162]$	$y^2=x^3+2597x-183162$	2.3.0.a.1, 20.6.0.a.1, 644.6.0.?, 3220.12.0.?	$[(67, 540)]$
51520.x2	51520b2	51520.x	51520b	$2$	$2$	$ 2^{6} \cdot 5 \cdot 7 \cdot 23 $	$ - 2^{16} \cdot 5 \cdot 7^{2} \cdot 23^{2} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$3220$	$12$	$0$	$2.600237146$	$1$	$3$	$20480$	$0.586642$	$16078716/129605$	$0.85853$	$2.78743$	$[0, 0, 0, 212, 4272]$	$y^2=x^3+212x+4272$	2.3.0.a.1, 20.6.0.a.1, 644.6.0.?, 3220.12.0.?	$[(4, 72)]$
51520.bc2	51520bu2	51520.bc	51520bu	$2$	$2$	$ 2^{6} \cdot 5 \cdot 7 \cdot 23 $	$ - 2^{16} \cdot 5 \cdot 7^{2} \cdot 23^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$3220$	$12$	$0$	$1$	$1$	$1$	$20480$	$0.586642$	$16078716/129605$	$0.85853$	$2.78743$	$[0, 0, 0, 212, -4272]$	$y^2=x^3+212x-4272$	2.3.0.a.1, 20.6.0.a.1, 644.6.0.?, 3220.12.0.?	$[]$
57960.e2	57960n2	57960.e	57960n	$2$	$2$	$ 2^{3} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 23 $	$ - 2^{10} \cdot 3^{6} \cdot 5 \cdot 7^{2} \cdot 23^{2} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$3220$	$12$	$0$	$0.931558303$	$1$	$7$	$40960$	$0.789374$	$16078716/129605$	$0.85853$	$2.97931$	$[0, 0, 0, 477, -14418]$	$y^2=x^3+477x-14418$	2.3.0.a.1, 20.6.0.a.1, 644.6.0.?, 3220.12.0.?	$[(87, 828)]$
64400.bc2	64400b2	64400.bc	64400b	$2$	$2$	$ 2^{4} \cdot 5^{2} \cdot 7 \cdot 23 $	$ - 2^{10} \cdot 5^{7} \cdot 7^{2} \cdot 23^{2} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$3220$	$12$	$0$	$1.510866728$	$1$	$5$	$61440$	$1.044788$	$16078716/129605$	$0.85853$	$3.22776$	$[0, 0, 0, 1325, -66750]$	$y^2=x^3+1325x-66750$	2.3.0.a.1, 20.6.0.a.1, 644.6.0.?, 3220.12.0.?	$[(35, 150)]$
90160.bo2	90160p2	90160.bo	90160p	$2$	$2$	$ 2^{4} \cdot 5 \cdot 7^{2} \cdot 23 $	$ - 2^{10} \cdot 5 \cdot 7^{8} \cdot 23^{2} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$3220$	$12$	$0$	$2.378181837$	$1$	$3$	$122880$	$1.213024$	$16078716/129605$	$0.85853$	$3.30952$	$[0, 0, 0, 2597, 183162]$	$y^2=x^3+2597x+183162$	2.3.0.a.1, 20.6.0.a.1, 644.6.0.?, 3220.12.0.?	$[(154, 2058)]$
115920.bz2	115920w2	115920.bz	115920w	$2$	$2$	$ 2^{4} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 23 $	$ - 2^{10} \cdot 3^{6} \cdot 5 \cdot 7^{2} \cdot 23^{2} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$3220$	$12$	$0$	$0.913288836$	$1$	$7$	$81920$	$0.789374$	$16078716/129605$	$0.85853$	$2.80221$	$[0, 0, 0, 477, 14418]$	$y^2=x^3+477x+14418$	2.3.0.a.1, 20.6.0.a.1, 644.6.0.?, 3220.12.0.?	$[(3, 126)]$
148120.x2	148120n2	148120.x	148120n	$2$	$2$	$ 2^{3} \cdot 5 \cdot 7 \cdot 23^{2} $	$ - 2^{10} \cdot 5 \cdot 7^{2} \cdot 23^{8} $	$2$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$3220$	$12$	$0$	$14.35959990$	$1$	$7$	$675840$	$1.807816$	$16078716/129605$	$0.85853$	$3.77102$	$[0, 0, 0, 28037, -6497178]$	$y^2=x^3+28037x-6497178$	2.3.0.a.1, 20.6.0.a.1, 644.6.0.?, 3220.12.0.?	$[(782, 22218), (979, 30972)]$
225400.bs2	225400cf2	225400.bs	225400cf	$2$	$2$	$ 2^{3} \cdot 5^{2} \cdot 7^{2} \cdot 23 $	$ - 2^{10} \cdot 5^{7} \cdot 7^{8} \cdot 23^{2} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$3220$	$12$	$0$	$5.986469594$	$1$	$1$	$1474560$	$2.017742$	$16078716/129605$	$0.85853$	$3.84694$	$[0, 0, 0, 64925, -22895250]$	$y^2=x^3+64925x-22895250$	2.3.0.a.1, 20.6.0.a.1, 644.6.0.?, 3220.12.0.?	$[(7826/5, 662676/5)]$
257600.cw2	257600cw2	257600.cw	257600cw	$2$	$2$	$ 2^{6} \cdot 5^{2} \cdot 7 \cdot 23 $	$ - 2^{16} \cdot 5^{7} \cdot 7^{2} \cdot 23^{2} $	$2$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$3220$	$12$	$0$	$5.558009414$	$1$	$11$	$491520$	$1.391361$	$16078716/129605$	$0.85853$	$3.20242$	$[0, 0, 0, 5300, -534000]$	$y^2=x^3+5300x-534000$	2.3.0.a.1, 20.6.0.a.1, 644.6.0.?, 3220.12.0.?	$[(410, 8400), (160, 2100)]$
257600.dk2	257600dk2	257600.dk	257600dk	$2$	$2$	$ 2^{6} \cdot 5^{2} \cdot 7 \cdot 23 $	$ - 2^{16} \cdot 5^{7} \cdot 7^{2} \cdot 23^{2} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$3220$	$12$	$0$	$2.655158249$	$1$	$5$	$491520$	$1.391361$	$16078716/129605$	$0.85853$	$3.20242$	$[0, 0, 0, 5300, 534000]$	$y^2=x^3+5300x+534000$	2.3.0.a.1, 20.6.0.a.1, 644.6.0.?, 3220.12.0.?	$[(40, 900)]$
289800.dh2	289800dh2	289800.dh	289800dh	$2$	$2$	$ 2^{3} \cdot 3^{2} \cdot 5^{2} \cdot 7 \cdot 23 $	$ - 2^{10} \cdot 3^{6} \cdot 5^{7} \cdot 7^{2} \cdot 23^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$3220$	$12$	$0$	$1$	$1$	$1$	$983040$	$1.594093$	$16078716/129605$	$0.85853$	$3.36586$	$[0, 0, 0, 11925, -1802250]$	$y^2=x^3+11925x-1802250$	2.3.0.a.1, 20.6.0.a.1, 644.6.0.?, 3220.12.0.?	$[]$
296240.bi2	296240bi2	296240.bi	296240bi	$2$	$2$	$ 2^{4} \cdot 5 \cdot 7 \cdot 23^{2} $	$ - 2^{10} \cdot 5 \cdot 7^{2} \cdot 23^{8} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$3220$	$12$	$0$	$1$	$1$	$1$	$1351680$	$1.807816$	$16078716/129605$	$0.85853$	$3.56355$	$[0, 0, 0, 28037, 6497178]$	$y^2=x^3+28037x+6497178$	2.3.0.a.1, 20.6.0.a.1, 644.6.0.?, 3220.12.0.?	$[]$
360640.ey2	360640ey2	360640.ey	360640ey	$2$	$2$	$ 2^{6} \cdot 5 \cdot 7^{2} \cdot 23 $	$ - 2^{16} \cdot 5 \cdot 7^{8} \cdot 23^{2} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$3220$	$12$	$0$	$5.341160095$	$1$	$3$	$983040$	$1.559597$	$16078716/129605$	$0.85853$	$3.27598$	$[0, 0, 0, 10388, -1465296]$	$y^2=x^3+10388x-1465296$	2.3.0.a.1, 20.6.0.a.1, 644.6.0.?, 3220.12.0.?	$[(340, 6432)]$
360640.fi2	360640fi2	360640.fi	360640fi	$2$	$2$	$ 2^{6} \cdot 5 \cdot 7^{2} \cdot 23 $	$ - 2^{16} \cdot 5 \cdot 7^{8} \cdot 23^{2} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$3220$	$12$	$0$	$2.260328869$	$1$	$5$	$983040$	$1.559597$	$16078716/129605$	$0.85853$	$3.27598$	$[0, 0, 0, 10388, 1465296]$	$y^2=x^3+10388x+1465296$	2.3.0.a.1, 20.6.0.a.1, 644.6.0.?, 3220.12.0.?	$[(-35, 1029)]$
405720.er2	405720er2	405720.er	405720er	$2$	$2$	$ 2^{3} \cdot 3^{2} \cdot 5 \cdot 7^{2} \cdot 23 $	$ - 2^{10} \cdot 3^{6} \cdot 5 \cdot 7^{8} \cdot 23^{2} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$3220$	$12$	$0$	$2.208142374$	$1$	$3$	$1966080$	$1.762329$	$16078716/129605$	$0.85853$	$3.43450$	$[0, 0, 0, 23373, 4945374]$	$y^2=x^3+23373x+4945374$	2.3.0.a.1, 20.6.0.a.1, 644.6.0.?, 3220.12.0.?	$[(399, 8820)]$
450800.da2	450800da2	450800.da	450800da	$2$	$2$	$ 2^{4} \cdot 5^{2} \cdot 7^{2} \cdot 23 $	$ - 2^{10} \cdot 5^{7} \cdot 7^{8} \cdot 23^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$3220$	$12$	$0$	$1$	$1$	$1$	$2949120$	$2.017742$	$16078716/129605$	$0.85853$	$3.64213$	$[0, 0, 0, 64925, 22895250]$	$y^2=x^3+64925x+22895250$	2.3.0.a.1, 20.6.0.a.1, 644.6.0.?, 3220.12.0.?	$[]$
463680.jx2	463680jx2	463680.jx	463680jx	$2$	$2$	$ 2^{6} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 23 $	$ - 2^{16} \cdot 3^{6} \cdot 5 \cdot 7^{2} \cdot 23^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$3220$	$12$	$0$	$1$	$1$	$1$	$655360$	$1.135948$	$16078716/129605$	$0.85853$	$2.82323$	$[0, 0, 0, 1908, -115344]$	$y^2=x^3+1908x-115344$	2.3.0.a.1, 20.6.0.a.1, 644.6.0.?, 3220.12.0.?	$[]$
463680.lz2	463680lz2	463680.lz	463680lz	$2$	$2$	$ 2^{6} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 23 $	$ - 2^{16} \cdot 3^{6} \cdot 5 \cdot 7^{2} \cdot 23^{2} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$3220$	$12$	$0$	$1.083928981$	$1$	$7$	$655360$	$1.135948$	$16078716/129605$	$0.85853$	$2.82323$	$[0, 0, 0, 1908, 115344]$	$y^2=x^3+1908x+115344$	2.3.0.a.1, 20.6.0.a.1, 644.6.0.?, 3220.12.0.?	$[(10, 368)]$

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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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