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 (20 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
31200.z1	31200l2	31200.z	31200l	$2$	$2$	$ 2^{5} \cdot 3 \cdot 5^{2} \cdot 13 $	$ 2^{9} \cdot 3^{4} \cdot 5^{3} \cdot 13^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$520$	$12$	$0$	$1$	$1$	$1$	$14336$	$0.407947$	$26463592/13689$	$1.00478$	$2.72105$	$[0, -1, 0, -248, -408]$	$y^2=x^3-x^2-248x-408$	2.3.0.a.1, 40.6.0.b.1, 104.6.0.?, 260.6.0.?, 520.12.0.?	$[]$
31200.bd1	31200bt2	31200.bd	31200bt	$2$	$2$	$ 2^{5} \cdot 3 \cdot 5^{2} \cdot 13 $	$ 2^{9} \cdot 3^{4} \cdot 5^{9} \cdot 13^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$520$	$12$	$0$	$1$	$1$	$1$	$71680$	$1.212666$	$26463592/13689$	$1.00478$	$3.65422$	$[0, -1, 0, -6208, 63412]$	$y^2=x^3-x^2-6208x+63412$	2.3.0.a.1, 40.6.0.b.1, 104.6.0.?, 260.6.0.?, 520.12.0.?	$[]$
31200.bg1	31200cj2	31200.bg	31200cj	$2$	$2$	$ 2^{5} \cdot 3 \cdot 5^{2} \cdot 13 $	$ 2^{9} \cdot 3^{4} \cdot 5^{9} \cdot 13^{2} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$520$	$12$	$0$	$2.491879162$	$1$	$3$	$71680$	$1.212666$	$26463592/13689$	$1.00478$	$3.65422$	$[0, 1, 0, -6208, -63412]$	$y^2=x^3+x^2-6208x-63412$	2.3.0.a.1, 40.6.0.b.1, 104.6.0.?, 260.6.0.?, 520.12.0.?	$[(-73, 78)]$
31200.bk1	31200ba2	31200.bk	31200ba	$2$	$2$	$ 2^{5} \cdot 3 \cdot 5^{2} \cdot 13 $	$ 2^{9} \cdot 3^{4} \cdot 5^{3} \cdot 13^{2} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$520$	$12$	$0$	$0.527816190$	$1$	$9$	$14336$	$0.407947$	$26463592/13689$	$1.00478$	$2.72105$	$[0, 1, 0, -248, 408]$	$y^2=x^3+x^2-248x+408$	2.3.0.a.1, 40.6.0.b.1, 104.6.0.?, 260.6.0.?, 520.12.0.?	$[(-2, 30)]$
62400.i1	62400fy2	62400.i	62400fy	$2$	$2$	$ 2^{6} \cdot 3 \cdot 5^{2} \cdot 13 $	$ 2^{15} \cdot 3^{4} \cdot 5^{3} \cdot 13^{2} $	$2$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$520$	$12$	$0$	$1.006680321$	$1$	$23$	$57344$	$0.754520$	$26463592/13689$	$1.00478$	$2.92690$	$[0, -1, 0, -993, 4257]$	$y^2=x^3-x^2-993x+4257$	2.3.0.a.1, 40.6.0.b.1, 104.6.0.?, 260.6.0.?, 520.12.0.?	$[(-7, 104), (-23, 120)]$
62400.p1	62400fr2	62400.p	62400fr	$2$	$2$	$ 2^{6} \cdot 3 \cdot 5^{2} \cdot 13 $	$ 2^{15} \cdot 3^{4} \cdot 5^{9} \cdot 13^{2} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$520$	$12$	$0$	$1.202978730$	$1$	$9$	$286720$	$1.559238$	$26463592/13689$	$1.00478$	$3.80149$	$[0, -1, 0, -24833, -482463]$	$y^2=x^3-x^2-24833x-482463$	2.3.0.a.1, 40.6.0.b.1, 104.6.0.?, 260.6.0.?, 520.12.0.?	$[(-67, 936)]$
62400.hr1	62400hv2	62400.hr	62400hv	$2$	$2$	$ 2^{6} \cdot 3 \cdot 5^{2} \cdot 13 $	$ 2^{15} \cdot 3^{4} \cdot 5^{9} \cdot 13^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$520$	$12$	$0$	$1$	$1$	$1$	$286720$	$1.559238$	$26463592/13689$	$1.00478$	$3.80149$	$[0, 1, 0, -24833, 482463]$	$y^2=x^3+x^2-24833x+482463$	2.3.0.a.1, 40.6.0.b.1, 104.6.0.?, 260.6.0.?, 520.12.0.?	$[]$
62400.ib1	62400ig2	62400.ib	62400ig	$2$	$2$	$ 2^{6} \cdot 3 \cdot 5^{2} \cdot 13 $	$ 2^{15} \cdot 3^{4} \cdot 5^{3} \cdot 13^{2} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$520$	$12$	$0$	$1.339438221$	$1$	$5$	$57344$	$0.754520$	$26463592/13689$	$1.00478$	$2.92690$	$[0, 1, 0, -993, -4257]$	$y^2=x^3+x^2-993x-4257$	2.3.0.a.1, 40.6.0.b.1, 104.6.0.?, 260.6.0.?, 520.12.0.?	$[(-6, 39)]$
93600.i1	93600fa2	93600.i	93600fa	$2$	$2$	$ 2^{5} \cdot 3^{2} \cdot 5^{2} \cdot 13 $	$ 2^{9} \cdot 3^{10} \cdot 5^{3} \cdot 13^{2} $	$2$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$520$	$12$	$0$	$1.681686848$	$1$	$15$	$114688$	$0.957253$	$26463592/13689$	$1.00478$	$3.03575$	$[0, 0, 0, -2235, -13250]$	$y^2=x^3-2235x-13250$	2.3.0.a.1, 40.6.0.b.1, 104.6.0.?, 260.6.0.?, 520.12.0.?	$[(-31, 162), (89, 702)]$
93600.m1	93600cn2	93600.m	93600cn	$2$	$2$	$ 2^{5} \cdot 3^{2} \cdot 5^{2} \cdot 13 $	$ 2^{9} \cdot 3^{10} \cdot 5^{9} \cdot 13^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$520$	$12$	$0$	$1$	$1$	$1$	$573440$	$1.761972$	$26463592/13689$	$1.00478$	$3.87936$	$[0, 0, 0, -55875, 1656250]$	$y^2=x^3-55875x+1656250$	2.3.0.a.1, 40.6.0.b.1, 104.6.0.?, 260.6.0.?, 520.12.0.?	$[]$
93600.er1	93600cm2	93600.er	93600cm	$2$	$2$	$ 2^{5} \cdot 3^{2} \cdot 5^{2} \cdot 13 $	$ 2^{9} \cdot 3^{10} \cdot 5^{9} \cdot 13^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$520$	$12$	$0$	$1$	$1$	$1$	$573440$	$1.761972$	$26463592/13689$	$1.00478$	$3.87936$	$[0, 0, 0, -55875, -1656250]$	$y^2=x^3-55875x-1656250$	2.3.0.a.1, 40.6.0.b.1, 104.6.0.?, 260.6.0.?, 520.12.0.?	$[]$
93600.ev1	93600ey2	93600.ev	93600ey	$2$	$2$	$ 2^{5} \cdot 3^{2} \cdot 5^{2} \cdot 13 $	$ 2^{9} \cdot 3^{10} \cdot 5^{3} \cdot 13^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$520$	$12$	$0$	$1$	$1$	$1$	$114688$	$0.957253$	$26463592/13689$	$1.00478$	$3.03575$	$[0, 0, 0, -2235, 13250]$	$y^2=x^3-2235x+13250$	2.3.0.a.1, 40.6.0.b.1, 104.6.0.?, 260.6.0.?, 520.12.0.?	$[]$
187200.t1	187200f2	187200.t	187200f	$2$	$2$	$ 2^{6} \cdot 3^{2} \cdot 5^{2} \cdot 13 $	$ 2^{15} \cdot 3^{10} \cdot 5^{9} \cdot 13^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$520$	$12$	$0$	$1$	$1$	$1$	$2293760$	$2.108547$	$26463592/13689$	$1.00478$	$4.00044$	$[0, 0, 0, -223500, 13250000]$	$y^2=x^3-223500x+13250000$	2.3.0.a.1, 40.6.0.b.1, 104.6.0.?, 260.6.0.?, 520.12.0.?	$[]$
187200.bm1	187200h2	187200.bm	187200h	$2$	$2$	$ 2^{6} \cdot 3^{2} \cdot 5^{2} \cdot 13 $	$ 2^{15} \cdot 3^{10} \cdot 5^{3} \cdot 13^{2} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$520$	$12$	$0$	$1.611525054$	$1$	$5$	$458752$	$1.303827$	$26463592/13689$	$1.00478$	$3.20500$	$[0, 0, 0, -8940, -106000]$	$y^2=x^3-8940x-106000$	2.3.0.a.1, 40.6.0.b.1, 104.6.0.?, 260.6.0.?, 520.12.0.?	$[(-56, 468)]$
187200.pe1	187200bw2	187200.pe	187200bw	$2$	$2$	$ 2^{6} \cdot 3^{2} \cdot 5^{2} \cdot 13 $	$ 2^{15} \cdot 3^{10} \cdot 5^{3} \cdot 13^{2} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$520$	$12$	$0$	$1.039478828$	$1$	$7$	$458752$	$1.303827$	$26463592/13689$	$1.00478$	$3.20500$	$[0, 0, 0, -8940, 106000]$	$y^2=x^3-8940x+106000$	2.3.0.a.1, 40.6.0.b.1, 104.6.0.?, 260.6.0.?, 520.12.0.?	$[(-46, 648)]$
187200.pt1	187200cc2	187200.pt	187200cc	$2$	$2$	$ 2^{6} \cdot 3^{2} \cdot 5^{2} \cdot 13 $	$ 2^{15} \cdot 3^{10} \cdot 5^{9} \cdot 13^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$520$	$12$	$0$	$1$	$1$	$1$	$2293760$	$2.108547$	$26463592/13689$	$1.00478$	$4.00044$	$[0, 0, 0, -223500, -13250000]$	$y^2=x^3-223500x-13250000$	2.3.0.a.1, 40.6.0.b.1, 104.6.0.?, 260.6.0.?, 520.12.0.?	$[]$
405600.c1	405600c2	405600.c	405600c	$2$	$2$	$ 2^{5} \cdot 3 \cdot 5^{2} \cdot 13^{2} $	$ 2^{9} \cdot 3^{4} \cdot 5^{9} \cdot 13^{8} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$520$	$12$	$0$	$1$	$1$	$1$	$12042240$	$2.495140$	$26463592/13689$	$1.00478$	$4.12017$	$[0, -1, 0, -1049208, 135119412]$	$y^2=x^3-x^2-1049208x+135119412$	2.3.0.a.1, 40.6.0.b.1, 104.6.0.?, 260.6.0.?, 520.12.0.?	$[]$
405600.o1	405600o2	405600.o	405600o	$2$	$2$	$ 2^{5} \cdot 3 \cdot 5^{2} \cdot 13^{2} $	$ 2^{9} \cdot 3^{4} \cdot 5^{3} \cdot 13^{8} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$520$	$12$	$0$	$3.844443361$	$1$	$3$	$2408448$	$1.690422$	$26463592/13689$	$1.00478$	$3.37235$	$[0, -1, 0, -41968, -1064168]$	$y^2=x^3-x^2-41968x-1064168$	2.3.0.a.1, 40.6.0.b.1, 104.6.0.?, 260.6.0.?, 520.12.0.?	$[(1257, 43940)]$
405600.gq1	405600gq2	405600.gq	405600gq	$2$	$2$	$ 2^{5} \cdot 3 \cdot 5^{2} \cdot 13^{2} $	$ 2^{9} \cdot 3^{4} \cdot 5^{3} \cdot 13^{8} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$520$	$12$	$0$	$1$	$1$	$1$	$2408448$	$1.690422$	$26463592/13689$	$1.00478$	$3.37235$	$[0, 1, 0, -41968, 1064168]$	$y^2=x^3+x^2-41968x+1064168$	2.3.0.a.1, 40.6.0.b.1, 104.6.0.?, 260.6.0.?, 520.12.0.?	$[]$
405600.hd1	405600hd2	405600.hd	405600hd	$2$	$2$	$ 2^{5} \cdot 3 \cdot 5^{2} \cdot 13^{2} $	$ 2^{9} \cdot 3^{4} \cdot 5^{9} \cdot 13^{8} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$520$	$12$	$0$	$11.68099727$	$1$	$1$	$12042240$	$2.495140$	$26463592/13689$	$1.00478$	$4.12017$	$[0, 1, 0, -1049208, -135119412]$	$y^2=x^3+x^2-1049208x-135119412$	2.3.0.a.1, 40.6.0.b.1, 104.6.0.?, 260.6.0.?, 520.12.0.?	$[(-528813/59, 936386412/59)]$

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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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