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 (23 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
4488.h2	4488d2	4488.h	4488d	$2$	$2$	$ 2^{3} \cdot 3 \cdot 11 \cdot 17 $	$ - 2^{10} \cdot 3^{2} \cdot 11^{6} \cdot 17 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$2244$	$12$	$0$	$1$	$1$	$1$	$3840$	$0.883048$	$-98061470500/271048833$	$0.92244$	$4.04251$	$[0, 1, 0, -968, 27552]$	$y^2=x^3+x^2-968x+27552$	2.3.0.a.1, 68.6.0.a.1, 132.6.0.?, 2244.12.0.?	$[]$
8976.n2	8976d2	8976.n	8976d	$2$	$2$	$ 2^{4} \cdot 3 \cdot 11 \cdot 17 $	$ - 2^{10} \cdot 3^{2} \cdot 11^{6} \cdot 17 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$2244$	$12$	$0$	$1$	$1$	$1$	$7680$	$0.883048$	$-98061470500/271048833$	$0.92244$	$3.73467$	$[0, -1, 0, -968, -27552]$	$y^2=x^3-x^2-968x-27552$	2.3.0.a.1, 68.6.0.a.1, 132.6.0.?, 2244.12.0.?	$[]$
13464.i2	13464t2	13464.i	13464t	$2$	$2$	$ 2^{3} \cdot 3^{2} \cdot 11 \cdot 17 $	$ - 2^{10} \cdot 3^{8} \cdot 11^{6} \cdot 17 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$2244$	$12$	$0$	$1.497340549$	$1$	$5$	$30720$	$1.432354$	$-98061470500/271048833$	$0.92244$	$4.26869$	$[0, 0, 0, -8715, -752618]$	$y^2=x^3-8715x-752618$	2.3.0.a.1, 68.6.0.a.1, 132.6.0.?, 2244.12.0.?	$[(243, 3388)]$
26928.bh2	26928m2	26928.bh	26928m	$2$	$2$	$ 2^{4} \cdot 3^{2} \cdot 11 \cdot 17 $	$ - 2^{10} \cdot 3^{8} \cdot 11^{6} \cdot 17 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$2244$	$12$	$0$	$3.264339562$	$1$	$3$	$61440$	$1.432354$	$-98061470500/271048833$	$0.92244$	$3.97864$	$[0, 0, 0, -8715, 752618]$	$y^2=x^3-8715x+752618$	2.3.0.a.1, 68.6.0.a.1, 132.6.0.?, 2244.12.0.?	$[(22, 756)]$
35904.r2	35904m2	35904.r	35904m	$2$	$2$	$ 2^{6} \cdot 3 \cdot 11 \cdot 17 $	$ - 2^{16} \cdot 3^{2} \cdot 11^{6} \cdot 17 $	$2$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$2244$	$12$	$0$	$0.955894202$	$1$	$23$	$61440$	$1.229622$	$-98061470500/271048833$	$0.92244$	$3.63757$	$[0, -1, 0, -3873, 224289]$	$y^2=x^3-x^2-3873x+224289$	2.3.0.a.1, 68.6.0.a.1, 132.6.0.?, 2244.12.0.?	$[(-15, 528), (216, 3069)]$
35904.co2	35904ci2	35904.co	35904ci	$2$	$2$	$ 2^{6} \cdot 3 \cdot 11 \cdot 17 $	$ - 2^{16} \cdot 3^{2} \cdot 11^{6} \cdot 17 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$2244$	$12$	$0$	$14.16806690$	$1$	$1$	$61440$	$1.229622$	$-98061470500/271048833$	$0.92244$	$3.63757$	$[0, 1, 0, -3873, -224289]$	$y^2=x^3+x^2-3873x-224289$	2.3.0.a.1, 68.6.0.a.1, 132.6.0.?, 2244.12.0.?	$[(2732425/51, 4510494856/51)]$
49368.be2	49368bi2	49368.be	49368bi	$2$	$2$	$ 2^{3} \cdot 3 \cdot 11^{2} \cdot 17 $	$ - 2^{10} \cdot 3^{2} \cdot 11^{12} \cdot 17 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$2244$	$12$	$0$	$18.23028763$	$1$	$1$	$460800$	$2.081997$	$-98061470500/271048833$	$0.92244$	$4.47684$	$[0, 1, 0, -117168, -37140336]$	$y^2=x^3+x^2-117168x-37140336$	2.3.0.a.1, 68.6.0.a.1, 132.6.0.?, 2244.12.0.?	$[(155976208/561, 913452987916/561)]$
76296.i2	76296a2	76296.i	76296a	$2$	$2$	$ 2^{3} \cdot 3 \cdot 11 \cdot 17^{2} $	$ - 2^{10} \cdot 3^{2} \cdot 11^{6} \cdot 17^{7} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$2244$	$12$	$0$	$1$	$1$	$1$	$1105920$	$2.299656$	$-98061470500/271048833$	$0.92244$	$4.53582$	$[0, -1, 0, -279848, 137041884]$	$y^2=x^3-x^2-279848x+137041884$	2.3.0.a.1, 68.6.0.a.1, 132.6.0.?, 2244.12.0.?	$[]$
98736.v2	98736o2	98736.v	98736o	$2$	$2$	$ 2^{4} \cdot 3 \cdot 11^{2} \cdot 17 $	$ - 2^{10} \cdot 3^{2} \cdot 11^{12} \cdot 17 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$2244$	$12$	$0$	$3.517296531$	$1$	$3$	$921600$	$2.081997$	$-98061470500/271048833$	$0.92244$	$4.20701$	$[0, -1, 0, -117168, 37140336]$	$y^2=x^3-x^2-117168x+37140336$	2.3.0.a.1, 68.6.0.a.1, 132.6.0.?, 2244.12.0.?	$[(-315, 6534)]$
107712.bx2	107712bi2	107712.bx	107712bi	$2$	$2$	$ 2^{6} \cdot 3^{2} \cdot 11 \cdot 17 $	$ - 2^{16} \cdot 3^{8} \cdot 11^{6} \cdot 17 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$2244$	$12$	$0$	$3.686174585$	$1$	$5$	$491520$	$1.778929$	$-98061470500/271048833$	$0.92244$	$3.86155$	$[0, 0, 0, -34860, -6020944]$	$y^2=x^3-34860x-6020944$	2.3.0.a.1, 68.6.0.a.1, 132.6.0.?, 2244.12.0.?	$[(280, 2484)]$
107712.dd2	107712ey2	107712.dd	107712ey	$2$	$2$	$ 2^{6} \cdot 3^{2} \cdot 11 \cdot 17 $	$ - 2^{16} \cdot 3^{8} \cdot 11^{6} \cdot 17 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$2244$	$12$	$0$	$1.952589831$	$1$	$5$	$491520$	$1.778929$	$-98061470500/271048833$	$0.92244$	$3.86155$	$[0, 0, 0, -34860, 6020944]$	$y^2=x^3-34860x+6020944$	2.3.0.a.1, 68.6.0.a.1, 132.6.0.?, 2244.12.0.?	$[(53, 2079)]$
112200.be2	112200bn2	112200.be	112200bn	$2$	$2$	$ 2^{3} \cdot 3 \cdot 5^{2} \cdot 11 \cdot 17 $	$ - 2^{10} \cdot 3^{2} \cdot 5^{6} \cdot 11^{6} \cdot 17 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$2244$	$12$	$0$	$4.367173712$	$1$	$3$	$552960$	$1.687767$	$-98061470500/271048833$	$0.92244$	$3.75392$	$[0, -1, 0, -24208, 3492412]$	$y^2=x^3-x^2-24208x+3492412$	2.3.0.a.1, 68.6.0.a.1, 132.6.0.?, 2244.12.0.?	$[(86, 1428)]$
148104.bo2	148104ca2	148104.bo	148104ca	$2$	$2$	$ 2^{3} \cdot 3^{2} \cdot 11^{2} \cdot 17 $	$ - 2^{10} \cdot 3^{8} \cdot 11^{12} \cdot 17 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$2244$	$12$	$0$	$7.419925862$	$1$	$3$	$3686400$	$2.631302$	$-98061470500/271048833$	$0.92244$	$4.61739$	$[0, 0, 0, -1054515, 1001734558]$	$y^2=x^3-1054515x+1001734558$	2.3.0.a.1, 68.6.0.a.1, 132.6.0.?, 2244.12.0.?	$[(94886, 29226582)]$
152592.ch2	152592cs2	152592.ch	152592cs	$2$	$2$	$ 2^{4} \cdot 3 \cdot 11 \cdot 17^{2} $	$ - 2^{10} \cdot 3^{2} \cdot 11^{6} \cdot 17^{7} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$2244$	$12$	$0$	$1$	$1$	$1$	$2211840$	$2.299656$	$-98061470500/271048833$	$0.92244$	$4.27240$	$[0, 1, 0, -279848, -137041884]$	$y^2=x^3+x^2-279848x-137041884$	2.3.0.a.1, 68.6.0.a.1, 132.6.0.?, 2244.12.0.?	$[]$
219912.o2	219912bv2	219912.o	219912bv	$2$	$2$	$ 2^{3} \cdot 3 \cdot 7^{2} \cdot 11 \cdot 17 $	$ - 2^{10} \cdot 3^{2} \cdot 7^{6} \cdot 11^{6} \cdot 17 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$2244$	$12$	$0$	$4.755227185$	$1$	$3$	$1105920$	$1.856003$	$-98061470500/271048833$	$0.92244$	$3.71268$	$[0, -1, 0, -47448, -9545220]$	$y^2=x^3-x^2-47448x-9545220$	2.3.0.a.1, 68.6.0.a.1, 132.6.0.?, 2244.12.0.?	$[(3834, 236964)]$
224400.eu2	224400gq2	224400.eu	224400gq	$2$	$2$	$ 2^{4} \cdot 3 \cdot 5^{2} \cdot 11 \cdot 17 $	$ - 2^{10} \cdot 3^{2} \cdot 5^{6} \cdot 11^{6} \cdot 17 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$2244$	$12$	$0$	$1$	$1$	$1$	$1105920$	$1.687767$	$-98061470500/271048833$	$0.92244$	$3.54274$	$[0, 1, 0, -24208, -3492412]$	$y^2=x^3+x^2-24208x-3492412$	2.3.0.a.1, 68.6.0.a.1, 132.6.0.?, 2244.12.0.?	$[]$
228888.bn2	228888o2	228888.bn	228888o	$2$	$2$	$ 2^{3} \cdot 3^{2} \cdot 11 \cdot 17^{2} $	$ - 2^{10} \cdot 3^{8} \cdot 11^{6} \cdot 17^{7} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$2244$	$12$	$0$	$10.36595267$	$1$	$1$	$8847360$	$2.848961$	$-98061470500/271048833$	$0.92244$	$4.66616$	$[0, 0, 0, -2518635, -3697612234]$	$y^2=x^3-2518635x-3697612234$	2.3.0.a.1, 68.6.0.a.1, 132.6.0.?, 2244.12.0.?	$[(61259/5, 8699348/5)]$
296208.cn2	296208cn2	296208.cn	296208cn	$2$	$2$	$ 2^{4} \cdot 3^{2} \cdot 11^{2} \cdot 17 $	$ - 2^{10} \cdot 3^{8} \cdot 11^{12} \cdot 17 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$2244$	$12$	$0$	$8.411561589$	$1$	$1$	$7372800$	$2.631302$	$-98061470500/271048833$	$0.92244$	$4.36336$	$[0, 0, 0, -1054515, -1001734558]$	$y^2=x^3-1054515x-1001734558$	2.3.0.a.1, 68.6.0.a.1, 132.6.0.?, 2244.12.0.?	$[(20497/2, 2863809/2)]$
336600.ee2	336600ee2	336600.ee	336600ee	$2$	$2$	$ 2^{3} \cdot 3^{2} \cdot 5^{2} \cdot 11 \cdot 17 $	$ - 2^{10} \cdot 3^{8} \cdot 5^{6} \cdot 11^{6} \cdot 17 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$2244$	$12$	$0$	$3.644848300$	$1$	$3$	$4423680$	$2.237072$	$-98061470500/271048833$	$0.92244$	$3.94781$	$[0, 0, 0, -217875, -94077250]$	$y^2=x^3-217875x-94077250$	2.3.0.a.1, 68.6.0.a.1, 132.6.0.?, 2244.12.0.?	$[(3910, 242550)]$
394944.db2	394944db2	394944.db	394944db	$2$	$2$	$ 2^{6} \cdot 3 \cdot 11^{2} \cdot 17 $	$ - 2^{16} \cdot 3^{2} \cdot 11^{12} \cdot 17 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$2244$	$12$	$0$	$12.59174074$	$1$	$1$	$7372800$	$2.428570$	$-98061470500/271048833$	$0.92244$	$4.07716$	$[0, -1, 0, -468673, -296654015]$	$y^2=x^3-x^2-468673x-296654015$	2.3.0.a.1, 68.6.0.a.1, 132.6.0.?, 2244.12.0.?	$[(5482753/16, 12830964993/16)]$
394944.gp2	394944gp2	394944.gp	394944gp	$2$	$2$	$ 2^{6} \cdot 3 \cdot 11^{2} \cdot 17 $	$ - 2^{16} \cdot 3^{2} \cdot 11^{12} \cdot 17 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$2244$	$12$	$0$	$11.65061528$	$1$	$1$	$7372800$	$2.428570$	$-98061470500/271048833$	$0.92244$	$4.07716$	$[0, 1, 0, -468673, 296654015]$	$y^2=x^3+x^2-468673x+296654015$	2.3.0.a.1, 68.6.0.a.1, 132.6.0.?, 2244.12.0.?	$[(15781/15, 54850996/15)]$
439824.ey2	439824ey2	439824.ey	439824ey	$2$	$2$	$ 2^{4} \cdot 3 \cdot 7^{2} \cdot 11 \cdot 17 $	$ - 2^{10} \cdot 3^{2} \cdot 7^{6} \cdot 11^{6} \cdot 17 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$2244$	$12$	$0$	$1.382097732$	$1$	$5$	$2211840$	$1.856003$	$-98061470500/271048833$	$0.92244$	$3.51463$	$[0, 1, 0, -47448, 9545220]$	$y^2=x^3+x^2-47448x+9545220$	2.3.0.a.1, 68.6.0.a.1, 132.6.0.?, 2244.12.0.?	$[(-208, 3234)]$
457776.cl2	457776cl2	457776.cl	457776cl	$2$	$2$	$ 2^{4} \cdot 3^{2} \cdot 11 \cdot 17^{2} $	$ - 2^{10} \cdot 3^{8} \cdot 11^{6} \cdot 17^{7} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$2244$	$12$	$0$	$1.129264678$	$1$	$5$	$17694720$	$2.848961$	$-98061470500/271048833$	$0.92244$	$4.41802$	$[0, 0, 0, -2518635, 3697612234]$	$y^2=x^3-2518635x+3697612234$	2.3.0.a.1, 68.6.0.a.1, 132.6.0.?, 2244.12.0.?	$[(170, 57222)]$

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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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Results (23 matches)

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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