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
9240.j2	9240t2	9240.j	9240t	$2$	$2$	$ 2^{3} \cdot 3 \cdot 5 \cdot 7 \cdot 11 $	$ - 2^{11} \cdot 3 \cdot 5^{2} \cdot 7^{6} \cdot 11^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$9240$	$12$	$0$	$1$	$1$	$1$	$19968$	$1.112801$	$-12624273557282/1067664675$	$0.91461$	$4.15359$	$[0, -1, 0, -6160, 201292]$	$y^2=x^3-x^2-6160x+201292$	2.3.0.a.1, 24.6.0.b.1, 1540.6.0.?, 9240.12.0.?	$[]$
18480.cy2	18480be2	18480.cy	18480be	$2$	$2$	$ 2^{4} \cdot 3 \cdot 5 \cdot 7 \cdot 11 $	$ - 2^{11} \cdot 3 \cdot 5^{2} \cdot 7^{6} \cdot 11^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$9240$	$12$	$0$	$1$	$1$	$1$	$39936$	$1.112801$	$-12624273557282/1067664675$	$0.91461$	$3.86054$	$[0, 1, 0, -6160, -201292]$	$y^2=x^3+x^2-6160x-201292$	2.3.0.a.1, 24.6.0.b.1, 1540.6.0.?, 9240.12.0.?	$[]$
27720.a2	27720e2	27720.a	27720e	$2$	$2$	$ 2^{3} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 11 $	$ - 2^{11} \cdot 3^{7} \cdot 5^{2} \cdot 7^{6} \cdot 11^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$9240$	$12$	$0$	$1$	$1$	$1$	$159744$	$1.662107$	$-12624273557282/1067664675$	$0.91461$	$4.35188$	$[0, 0, 0, -55443, -5379442]$	$y^2=x^3-55443x-5379442$	2.3.0.a.1, 24.6.0.b.1, 1540.6.0.?, 9240.12.0.?	$[]$
46200.dg2	46200bm2	46200.dg	46200bm	$2$	$2$	$ 2^{3} \cdot 3 \cdot 5^{2} \cdot 7 \cdot 11 $	$ - 2^{11} \cdot 3 \cdot 5^{8} \cdot 7^{6} \cdot 11^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$9240$	$12$	$0$	$1$	$1$	$1$	$479232$	$1.917519$	$-12624273557282/1067664675$	$0.91461$	$4.43026$	$[0, 1, 0, -154008, 24853488]$	$y^2=x^3+x^2-154008x+24853488$	2.3.0.a.1, 24.6.0.b.1, 1540.6.0.?, 9240.12.0.?	$[]$
55440.cc2	55440x2	55440.cc	55440x	$2$	$2$	$ 2^{4} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 11 $	$ - 2^{11} \cdot 3^{7} \cdot 5^{2} \cdot 7^{6} \cdot 11^{2} $	$2$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$9240$	$12$	$0$	$0.215921563$	$1$	$45$	$319488$	$1.662107$	$-12624273557282/1067664675$	$0.91461$	$4.07572$	$[0, 0, 0, -55443, 5379442]$	$y^2=x^3-55443x+5379442$	2.3.0.a.1, 24.6.0.b.1, 1540.6.0.?, 9240.12.0.?	$[(-43, 2772), (69, 1372)]$
64680.ct2	64680cy2	64680.ct	64680cy	$2$	$2$	$ 2^{3} \cdot 3 \cdot 5 \cdot 7^{2} \cdot 11 $	$ - 2^{11} \cdot 3 \cdot 5^{2} \cdot 7^{12} \cdot 11^{2} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$9240$	$12$	$0$	$17.92627884$	$1$	$1$	$958464$	$2.085754$	$-12624273557282/1067664675$	$0.91461$	$4.47794$	$[0, 1, 0, -301856, -68439456]$	$y^2=x^3+x^2-301856x-68439456$	2.3.0.a.1, 24.6.0.b.1, 1540.6.0.?, 9240.12.0.?	$[(2364200941/1578, 88015967924885/1578)]$
73920.bz2	73920ez2	73920.bz	73920ez	$2$	$2$	$ 2^{6} \cdot 3 \cdot 5 \cdot 7 \cdot 11 $	$ - 2^{17} \cdot 3 \cdot 5^{2} \cdot 7^{6} \cdot 11^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$9240$	$12$	$0$	$1$	$1$	$1$	$319488$	$1.459373$	$-12624273557282/1067664675$	$0.91461$	$3.75413$	$[0, -1, 0, -24641, -1585695]$	$y^2=x^3-x^2-24641x-1585695$	2.3.0.a.1, 24.6.0.b.1, 1540.6.0.?, 9240.12.0.?	$[]$
73920.et2	73920cd2	73920.et	73920cd	$2$	$2$	$ 2^{6} \cdot 3 \cdot 5 \cdot 7 \cdot 11 $	$ - 2^{17} \cdot 3 \cdot 5^{2} \cdot 7^{6} \cdot 11^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$9240$	$12$	$0$	$1$	$1$	$1$	$319488$	$1.459373$	$-12624273557282/1067664675$	$0.91461$	$3.75413$	$[0, 1, 0, -24641, 1585695]$	$y^2=x^3+x^2-24641x+1585695$	2.3.0.a.1, 24.6.0.b.1, 1540.6.0.?, 9240.12.0.?	$[]$
92400.s2	92400d2	92400.s	92400d	$2$	$2$	$ 2^{4} \cdot 3 \cdot 5^{2} \cdot 7 \cdot 11 $	$ - 2^{11} \cdot 3 \cdot 5^{8} \cdot 7^{6} \cdot 11^{2} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$9240$	$12$	$0$	$2.587531117$	$1$	$5$	$958464$	$1.917519$	$-12624273557282/1067664675$	$0.91461$	$4.16169$	$[0, -1, 0, -154008, -24853488]$	$y^2=x^3-x^2-154008x-24853488$	2.3.0.a.1, 24.6.0.b.1, 1540.6.0.?, 9240.12.0.?	$[(512, 5500)]$
101640.bi2	101640q2	101640.bi	101640q	$2$	$2$	$ 2^{3} \cdot 3 \cdot 5 \cdot 7 \cdot 11^{2} $	$ - 2^{11} \cdot 3 \cdot 5^{2} \cdot 7^{6} \cdot 11^{8} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$9240$	$12$	$0$	$1$	$1$	$1$	$2396160$	$2.311749$	$-12624273557282/1067664675$	$0.91461$	$4.53761$	$[0, -1, 0, -745400, -264938100]$	$y^2=x^3-x^2-745400x-264938100$	2.3.0.a.1, 24.6.0.b.1, 1540.6.0.?, 9240.12.0.?	$[]$
129360.y2	129360p2	129360.y	129360p	$2$	$2$	$ 2^{4} \cdot 3 \cdot 5 \cdot 7^{2} \cdot 11 $	$ - 2^{11} \cdot 3 \cdot 5^{2} \cdot 7^{12} \cdot 11^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$9240$	$12$	$0$	$1$	$1$	$1$	$1916928$	$2.085754$	$-12624273557282/1067664675$	$0.91461$	$4.21424$	$[0, -1, 0, -301856, 68439456]$	$y^2=x^3-x^2-301856x+68439456$	2.3.0.a.1, 24.6.0.b.1, 1540.6.0.?, 9240.12.0.?	$[]$
138600.dq2	138600bi2	138600.dq	138600bi	$2$	$2$	$ 2^{3} \cdot 3^{2} \cdot 5^{2} \cdot 7 \cdot 11 $	$ - 2^{11} \cdot 3^{7} \cdot 5^{8} \cdot 7^{6} \cdot 11^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$9240$	$12$	$0$	$1$	$1$	$1$	$3833856$	$2.466827$	$-12624273557282/1067664675$	$0.91461$	$4.57592$	$[0, 0, 0, -1386075, -672430250]$	$y^2=x^3-1386075x-672430250$	2.3.0.a.1, 24.6.0.b.1, 1540.6.0.?, 9240.12.0.?	$[]$
194040.dw2	194040cz2	194040.dw	194040cz	$2$	$2$	$ 2^{3} \cdot 3^{2} \cdot 5 \cdot 7^{2} \cdot 11 $	$ - 2^{11} \cdot 3^{7} \cdot 5^{2} \cdot 7^{12} \cdot 11^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$9240$	$12$	$0$	$1$	$1$	$1$	$7667712$	$2.635063$	$-12624273557282/1067664675$	$0.91461$	$4.61528$	$[0, 0, 0, -2716707, 1845148606]$	$y^2=x^3-2716707x+1845148606$	2.3.0.a.1, 24.6.0.b.1, 1540.6.0.?, 9240.12.0.?	$[]$
203280.ge2	203280fh2	203280.ge	203280fh	$2$	$2$	$ 2^{4} \cdot 3 \cdot 5 \cdot 7 \cdot 11^{2} $	$ - 2^{11} \cdot 3 \cdot 5^{2} \cdot 7^{6} \cdot 11^{8} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$9240$	$12$	$0$	$1$	$1$	$1$	$4792320$	$2.311749$	$-12624273557282/1067664675$	$0.91461$	$4.28028$	$[0, 1, 0, -745400, 264938100]$	$y^2=x^3+x^2-745400x+264938100$	2.3.0.a.1, 24.6.0.b.1, 1540.6.0.?, 9240.12.0.?	$[]$
221760.jy2	221760jm2	221760.jy	221760jm	$2$	$2$	$ 2^{6} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 11 $	$ - 2^{17} \cdot 3^{7} \cdot 5^{2} \cdot 7^{6} \cdot 11^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$9240$	$12$	$0$	$1$	$1$	$1$	$2555904$	$2.008678$	$-12624273557282/1067664675$	$0.91461$	$3.95457$	$[0, 0, 0, -221772, -43035536]$	$y^2=x^3-221772x-43035536$	2.3.0.a.1, 24.6.0.b.1, 1540.6.0.?, 9240.12.0.?	$[]$
221760.mg2	221760bh2	221760.mg	221760bh	$2$	$2$	$ 2^{6} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 11 $	$ - 2^{17} \cdot 3^{7} \cdot 5^{2} \cdot 7^{6} \cdot 11^{2} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$9240$	$12$	$0$	$0.618374225$	$1$	$7$	$2555904$	$2.008678$	$-12624273557282/1067664675$	$0.91461$	$3.95457$	$[0, 0, 0, -221772, 43035536]$	$y^2=x^3-221772x+43035536$	2.3.0.a.1, 24.6.0.b.1, 1540.6.0.?, 9240.12.0.?	$[(82, 5040)]$
277200.gi2	277200gi2	277200.gi	277200gi	$2$	$2$	$ 2^{4} \cdot 3^{2} \cdot 5^{2} \cdot 7 \cdot 11 $	$ - 2^{11} \cdot 3^{7} \cdot 5^{8} \cdot 7^{6} \cdot 11^{2} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$9240$	$12$	$0$	$2.448841232$	$1$	$3$	$7667712$	$2.466827$	$-12624273557282/1067664675$	$0.91461$	$4.32284$	$[0, 0, 0, -1386075, 672430250]$	$y^2=x^3-1386075x+672430250$	2.3.0.a.1, 24.6.0.b.1, 1540.6.0.?, 9240.12.0.?	$[(655, 6750)]$
304920.cl2	304920cl2	304920.cl	304920cl	$2$	$2$	$ 2^{3} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 11^{2} $	$ - 2^{11} \cdot 3^{7} \cdot 5^{2} \cdot 7^{6} \cdot 11^{8} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$9240$	$12$	$0$	$2.760415632$	$1$	$3$	$19169280$	$2.861053$	$-12624273557282/1067664675$	$0.91461$	$4.66484$	$[0, 0, 0, -6708603, 7160037302]$	$y^2=x^3-6708603x+7160037302$	2.3.0.a.1, 24.6.0.b.1, 1540.6.0.?, 9240.12.0.?	$[(1342, 23958)]$
323400.cv2	323400cv2	323400.cv	323400cv	$2$	$2$	$ 2^{3} \cdot 3 \cdot 5^{2} \cdot 7^{2} \cdot 11 $	$ - 2^{11} \cdot 3 \cdot 5^{8} \cdot 7^{12} \cdot 11^{2} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$9240$	$12$	$0$	$20.06773803$	$1$	$1$	$23003136$	$2.890476$	$-12624273557282/1067664675$	$0.91461$	$4.67103$	$[0, -1, 0, -7546408, -8539839188]$	$y^2=x^3-x^2-7546408x-8539839188$	2.3.0.a.1, 24.6.0.b.1, 1540.6.0.?, 9240.12.0.?	$[(4498904697/901, 253178100081250/901)]$
369600.gz2	369600gz2	369600.gz	369600gz	$2$	$2$	$ 2^{6} \cdot 3 \cdot 5^{2} \cdot 7 \cdot 11 $	$ - 2^{17} \cdot 3 \cdot 5^{8} \cdot 7^{6} \cdot 11^{2} $	$2$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$9240$	$12$	$0$	$1.062827975$	$1$	$21$	$7667712$	$2.264091$	$-12624273557282/1067664675$	$0.91461$	$4.03607$	$[0, -1, 0, -616033, 199443937]$	$y^2=x^3-x^2-616033x+199443937$	2.3.0.a.1, 24.6.0.b.1, 1540.6.0.?, 9240.12.0.?	$[(-423, 19600), (312, 6125)]$
369600.or2	369600or2	369600.or	369600or	$2$	$2$	$ 2^{6} \cdot 3 \cdot 5^{2} \cdot 7 \cdot 11 $	$ - 2^{17} \cdot 3 \cdot 5^{8} \cdot 7^{6} \cdot 11^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$9240$	$12$	$0$	$1$	$1$	$1$	$7667712$	$2.264091$	$-12624273557282/1067664675$	$0.91461$	$4.03607$	$[0, 1, 0, -616033, -199443937]$	$y^2=x^3+x^2-616033x-199443937$	2.3.0.a.1, 24.6.0.b.1, 1540.6.0.?, 9240.12.0.?	$[]$
388080.ok2	388080ok2	388080.ok	388080ok	$2$	$2$	$ 2^{4} \cdot 3^{2} \cdot 5 \cdot 7^{2} \cdot 11 $	$ - 2^{11} \cdot 3^{7} \cdot 5^{2} \cdot 7^{12} \cdot 11^{2} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$9240$	$12$	$0$	$5.437018578$	$1$	$3$	$15335424$	$2.635063$	$-12624273557282/1067664675$	$0.91461$	$4.36669$	$[0, 0, 0, -2716707, -1845148606]$	$y^2=x^3-2716707x-1845148606$	2.3.0.a.1, 24.6.0.b.1, 1540.6.0.?, 9240.12.0.?	$[(4445, 271852)]$

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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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