LMFDB - Elliptic curve search results

Refine search

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	Manin constant

		Sort order	Select

Results (22 matches)

Download displayed columns for results to

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	$Ш_{\textrm{an}}$	Ш primes	Integral points	Modular degree	Faltings height	j-invariant	$abc$ quality	Szpiro ratio	Weierstrass coefficients	Weierstrass equation	mod-$m$ images	MW-generators
11424.g3	11424a1	11424.g	11424a	$4$	$4$	$ 2^{5} \cdot 3 \cdot 7 \cdot 17 $	$ 2^{6} \cdot 3^{6} \cdot 7^{2} \cdot 17^{2} $	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.6.0.1	2Cs	$2856$	$48$	$0$	$3.028627034$	$1$		$7$	$5376$	$0.411701$	$57870788032/10323369$	$0.90138$	$3.09739$	$[0, -1, 0, -322, 1960]$	$y^2=x^3-x^2-322x+1960$	2.6.0.a.1, 12.12.0-2.a.1.1, 28.12.0-2.a.1.1, 84.24.0.?, 136.12.0.?, $\ldots$	$[(-18, 40)]$
11424.v3	11424v1	11424.v	11424v	$4$	$4$	$ 2^{5} \cdot 3 \cdot 7 \cdot 17 $	$ 2^{6} \cdot 3^{6} \cdot 7^{2} \cdot 17^{2} $	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.6.0.1	2Cs	$2856$	$48$	$0$	$1$	$1$		$3$	$5376$	$0.411701$	$57870788032/10323369$	$0.90138$	$3.09739$	$[0, 1, 0, -322, -1960]$	$y^2=x^3+x^2-322x-1960$	2.6.0.a.1, 12.12.0-2.a.1.1, 28.12.0-2.a.1.1, 84.24.0.?, 136.12.0.?, $\ldots$	$[ ]$
22848.m3	22848m2	22848.m	22848m	$4$	$4$	$ 2^{6} \cdot 3 \cdot 7 \cdot 17 $	$ 2^{12} \cdot 3^{6} \cdot 7^{2} \cdot 17^{2} $	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.6.0.1	2Cs	$2856$	$48$	$0$	$1$	$1$		$3$	$21504$	$0.758275$	$57870788032/10323369$	$0.90138$	$3.29785$	$[0, -1, 0, -1289, -14391]$	$y^2=x^3-x^2-1289x-14391$	2.6.0.a.1, 24.12.0-2.a.1.1, 56.12.0-2.a.1.1, 68.12.0-2.a.1.1, 84.12.0.?, $\ldots$	$[ ]$
22848.bq3	22848w2	22848.bq	22848w	$4$	$4$	$ 2^{6} \cdot 3 \cdot 7 \cdot 17 $	$ 2^{12} \cdot 3^{6} \cdot 7^{2} \cdot 17^{2} $	$2$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.6.0.1	2Cs	$2856$	$48$	$0$	$1.201766517$	$1$		$35$	$21504$	$0.758275$	$57870788032/10323369$	$0.90138$	$3.29785$	$[0, 1, 0, -1289, 14391]$	$y^2=x^3+x^2-1289x+14391$	2.6.0.a.1, 24.12.0-2.a.1.1, 56.12.0-2.a.1.1, 68.12.0-2.a.1.1, 84.12.0.?, $\ldots$	$[(31, 72), (61, 408)]$
34272.f3	34272bh1	34272.f	34272bh	$4$	$4$	$ 2^{5} \cdot 3^{2} \cdot 7 \cdot 17 $	$ 2^{6} \cdot 3^{12} \cdot 7^{2} \cdot 17^{2} $	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.12.0.1	2Cs	$2856$	$48$	$0$	$1$	$1$		$3$	$43008$	$0.961007$	$57870788032/10323369$	$0.90138$	$3.40277$	$[0, 0, 0, -2901, -50020]$	$y^2=x^3-2901x-50020$	2.6.0.a.1, 4.12.0-2.a.1.1, 84.24.0.?, 408.24.0.?, 952.24.0.?, $\ldots$	$[ ]$
34272.n3	34272u1	34272.n	34272u	$4$	$4$	$ 2^{5} \cdot 3^{2} \cdot 7 \cdot 17 $	$ 2^{6} \cdot 3^{12} \cdot 7^{2} \cdot 17^{2} $	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.12.0.1	2Cs	$2856$	$48$	$0$	$1$	$1$		$3$	$43008$	$0.961007$	$57870788032/10323369$	$0.90138$	$3.40277$	$[0, 0, 0, -2901, 50020]$	$y^2=x^3-2901x+50020$	2.6.0.a.1, 4.12.0-2.a.1.1, 84.24.0.?, 408.24.0.?, 952.24.0.?, $\ldots$	$[ ]$
68544.dv3	68544bn2	68544.dv	68544bn	$4$	$4$	$ 2^{6} \cdot 3^{2} \cdot 7 \cdot 17 $	$ 2^{12} \cdot 3^{12} \cdot 7^{2} \cdot 17^{2} $	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.12.0.1	2Cs	$2856$	$48$	$0$	$4.229573193$	$1$		$5$	$172032$	$1.307581$	$57870788032/10323369$	$0.90138$	$3.56444$	$[0, 0, 0, -11604, -400160]$	$y^2=x^3-11604x-400160$	2.6.0.a.1, 8.12.0-2.a.1.1, 84.12.0.?, 168.24.0.?, 204.12.0.?, $\ldots$	$[(485, 10395)]$
68544.dz3	68544cn2	68544.dz	68544cn	$4$	$4$	$ 2^{6} \cdot 3^{2} \cdot 7 \cdot 17 $	$ 2^{12} \cdot 3^{12} \cdot 7^{2} \cdot 17^{2} $	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.12.0.1	2Cs	$2856$	$48$	$0$	$1$	$1$		$3$	$172032$	$1.307581$	$57870788032/10323369$	$0.90138$	$3.56444$	$[0, 0, 0, -11604, 400160]$	$y^2=x^3-11604x+400160$	2.6.0.a.1, 8.12.0-2.a.1.1, 84.12.0.?, 168.24.0.?, 204.12.0.?, $\ldots$	$[ ]$
79968.f3	79968bx1	79968.f	79968bx	$4$	$4$	$ 2^{5} \cdot 3 \cdot 7^{2} \cdot 17 $	$ 2^{6} \cdot 3^{6} \cdot 7^{8} \cdot 17^{2} $	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.12.0.1	2Cs	$2856$	$48$	$0$	$1$	$1$		$3$	$258048$	$1.384657$	$57870788032/10323369$	$0.90138$	$3.59770$	$[0, -1, 0, -15794, 640704]$	$y^2=x^3-x^2-15794x+640704$	2.6.0.a.1, 4.12.0-2.a.1.1, 84.24.0.?, 408.24.0.?, 952.24.0.?, $\ldots$	$[ ]$
79968.bv3	79968be1	79968.bv	79968be	$4$	$4$	$ 2^{5} \cdot 3 \cdot 7^{2} \cdot 17 $	$ 2^{6} \cdot 3^{6} \cdot 7^{8} \cdot 17^{2} $	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.12.0.1	2Cs	$2856$	$48$	$0$	$1$	$1$		$3$	$258048$	$1.384657$	$57870788032/10323369$	$0.90138$	$3.59770$	$[0, 1, 0, -15794, -640704]$	$y^2=x^3+x^2-15794x-640704$	2.6.0.a.1, 4.12.0-2.a.1.1, 84.24.0.?, 408.24.0.?, 952.24.0.?, $\ldots$	$[ ]$
159936.dw3	159936jy2	159936.dw	159936jy	$4$	$4$	$ 2^{6} \cdot 3 \cdot 7^{2} \cdot 17 $	$ 2^{12} \cdot 3^{6} \cdot 7^{8} \cdot 17^{2} $	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.12.0.1	2Cs	$2856$	$48$	$0$	$5.397439685$	$1$		$5$	$1032192$	$1.731230$	$57870788032/10323369$	$0.90138$	$3.73667$	$[0, -1, 0, -63177, -5062455]$	$y^2=x^3-x^2-63177x-5062455$	2.6.0.a.1, 8.12.0-2.a.1.1, 84.12.0.?, 168.24.0.?, 204.12.0.?, $\ldots$	$[(485, 8840)]$
159936.ju3	159936hk2	159936.ju	159936hk	$4$	$4$	$ 2^{6} \cdot 3 \cdot 7^{2} \cdot 17 $	$ 2^{12} \cdot 3^{6} \cdot 7^{8} \cdot 17^{2} $	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.12.0.1	2Cs	$2856$	$48$	$0$	$1$	$1$		$3$	$1032192$	$1.731230$	$57870788032/10323369$	$0.90138$	$3.73667$	$[0, 1, 0, -63177, 5062455]$	$y^2=x^3+x^2-63177x+5062455$	2.6.0.a.1, 8.12.0-2.a.1.1, 84.12.0.?, 168.24.0.?, 204.12.0.?, $\ldots$	$[ ]$
194208.f3	194208w1	194208.f	194208w	$4$	$4$	$ 2^{5} \cdot 3 \cdot 7 \cdot 17^{2} $	$ 2^{6} \cdot 3^{6} \cdot 7^{2} \cdot 17^{8} $	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.12.0.1	2Cs	$2856$	$48$	$0$	$1$	$1$		$3$	$1548288$	$1.828308$	$57870788032/10323369$	$0.90138$	$3.77275$	$[0, -1, 0, -93154, -9070736]$	$y^2=x^3-x^2-93154x-9070736$	2.6.0.a.1, 8.12.0-2.a.1.1, 84.12.0.?, 168.24.0.?, 204.12.0.?, $\ldots$	$[ ]$
194208.bq3	194208bk1	194208.bq	194208bk	$4$	$4$	$ 2^{5} \cdot 3 \cdot 7 \cdot 17^{2} $	$ 2^{6} \cdot 3^{6} \cdot 7^{2} \cdot 17^{8} $	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.12.0.1	2Cs	$2856$	$48$	$0$	$3.672486001$	$1$		$7$	$1548288$	$1.828308$	$57870788032/10323369$	$0.90138$	$3.77275$	$[0, 1, 0, -93154, 9070736]$	$y^2=x^3+x^2-93154x+9070736$	2.6.0.a.1, 8.12.0-2.a.1.1, 84.12.0.?, 168.24.0.?, 204.12.0.?, $\ldots$	$[(104, 720)]$
239904.cw3	239904cw1	239904.cw	239904cw	$4$	$4$	$ 2^{5} \cdot 3^{2} \cdot 7^{2} \cdot 17 $	$ 2^{6} \cdot 3^{12} \cdot 7^{8} \cdot 17^{2} $	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.6.0.1	2Cs	$2856$	$48$	$0$	$1$	$1$		$3$	$2064384$	$1.933962$	$57870788032/10323369$	$0.90138$	$3.81075$	$[0, 0, 0, -142149, 17156860]$	$y^2=x^3-142149x+17156860$	2.6.0.a.1, 12.12.0-2.a.1.1, 28.12.0-2.a.1.1, 84.24.0.?, 136.12.0.?, $\ldots$	$[ ]$
239904.di3	239904di1	239904.di	239904di	$4$	$4$	$ 2^{5} \cdot 3^{2} \cdot 7^{2} \cdot 17 $	$ 2^{6} \cdot 3^{12} \cdot 7^{8} \cdot 17^{2} $	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.6.0.1	2Cs	$2856$	$48$	$0$	$9.490716758$	$1$		$3$	$2064384$	$1.933962$	$57870788032/10323369$	$0.90138$	$3.81075$	$[0, 0, 0, -142149, -17156860]$	$y^2=x^3-142149x-17156860$	2.6.0.a.1, 12.12.0-2.a.1.1, 28.12.0-2.a.1.1, 84.24.0.?, 136.12.0.?, $\ldots$	$[(-136640/31, 12643470/31)]$
285600.g3	285600g1	285600.g	285600g	$4$	$4$	$ 2^{5} \cdot 3 \cdot 5^{2} \cdot 7 \cdot 17 $	$ 2^{6} \cdot 3^{6} \cdot 5^{6} \cdot 7^{2} \cdot 17^{2} $	$2$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.6.0.1	2Cs	$14280$	$48$	$0$	$5.393885793$	$1$		$17$	$688128$	$1.216421$	$57870788032/10323369$	$0.90138$	$3.07243$	$[0, -1, 0, -8058, -228888]$	$y^2=x^3-x^2-8058x-228888$	2.6.0.a.1, 60.12.0-2.a.1.1, 84.12.0.?, 140.12.0.?, 408.12.0.?, $\ldots$	$[(-58, 200), (-34, 68)]$
285600.ge3	285600ge1	285600.ge	285600ge	$4$	$4$	$ 2^{5} \cdot 3 \cdot 5^{2} \cdot 7 \cdot 17 $	$ 2^{6} \cdot 3^{6} \cdot 5^{6} \cdot 7^{2} \cdot 17^{2} $	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.6.0.1	2Cs	$14280$	$48$	$0$	$1.510576951$	$1$		$9$	$688128$	$1.216421$	$57870788032/10323369$	$0.90138$	$3.07243$	$[0, 1, 0, -8058, 228888]$	$y^2=x^3+x^2-8058x+228888$	2.6.0.a.1, 60.12.0-2.a.1.1, 84.12.0.?, 140.12.0.?, 408.12.0.?, $\ldots$	$[(18, 300)]$
388416.dp3	388416dp2	388416.dp	388416dp	$4$	$4$	$ 2^{6} \cdot 3 \cdot 7 \cdot 17^{2} $	$ 2^{12} \cdot 3^{6} \cdot 7^{2} \cdot 17^{8} $	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.12.0.1	2Cs	$2856$	$48$	$0$	$1$	$4$	$2$	$3$	$6193152$	$2.174881$	$57870788032/10323369$	$0.90138$	$3.89271$	$[0, -1, 0, -372617, 72938505]$	$y^2=x^3-x^2-372617x+72938505$	2.6.0.a.1, 4.12.0-2.a.1.1, 84.24.0.?, 408.24.0.?, 952.24.0.?, $\ldots$	$[ ]$
388416.hg3	388416hg2	388416.hg	388416hg	$4$	$4$	$ 2^{6} \cdot 3 \cdot 7 \cdot 17^{2} $	$ 2^{12} \cdot 3^{6} \cdot 7^{2} \cdot 17^{8} $	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.12.0.1	2Cs	$2856$	$48$	$0$	$1$	$1$		$3$	$6193152$	$2.174881$	$57870788032/10323369$	$0.90138$	$3.89271$	$[0, 1, 0, -372617, -72938505]$	$y^2=x^3+x^2-372617x-72938505$	2.6.0.a.1, 4.12.0-2.a.1.1, 84.24.0.?, 408.24.0.?, 952.24.0.?, $\ldots$	$[ ]$
479808.dh3	479808dh2	479808.dh	479808dh	$4$	$4$	$ 2^{6} \cdot 3^{2} \cdot 7^{2} \cdot 17 $	$ 2^{12} \cdot 3^{12} \cdot 7^{8} \cdot 17^{2} $	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.6.0.1	2Cs	$2856$	$48$	$0$	$2.292042699$	$1$		$11$	$8257536$	$2.280537$	$57870788032/10323369$	$0.90138$	$3.92675$	$[0, 0, 0, -568596, -137254880]$	$y^2=x^3-568596x-137254880$	2.6.0.a.1, 24.12.0-2.a.1.1, 56.12.0-2.a.1.1, 68.12.0-2.a.1.2, 84.12.0.?, $\ldots$	$[(-322, 3528)]$
479808.ew3	479808ew2	479808.ew	479808ew	$4$	$4$	$ 2^{6} \cdot 3^{2} \cdot 7^{2} \cdot 17 $	$ 2^{12} \cdot 3^{12} \cdot 7^{8} \cdot 17^{2} $	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.6.0.1	2Cs	$2856$	$48$	$0$	$4.611962438$	$1$		$7$	$8257536$	$2.280537$	$57870788032/10323369$	$0.90138$	$3.92675$	$[0, 0, 0, -568596, 137254880]$	$y^2=x^3-568596x+137254880$	2.6.0.a.1, 24.12.0-2.a.1.1, 56.12.0-2.a.1.1, 68.12.0-2.a.1.2, 84.12.0.?, $\ldots$	$[(-803, 8721)]$

Download displayed columns for results to

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Learn more

Refine search

Results (22 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.

Learn more

Refine search Advanced search options

Results (22 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.

Refine search