LMFDB - Elliptic curves over $\Q$ of conductor 1225

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	Nonmax$\ \ell$	Adelic level	Adelic index	Adelic genus

		Sort order	Select

Results (21 matches)

Download displayed columns to Pari/GP SageMath Magma Oscar

Label	Cremona label	Class	Cremona class	Class size	Class degree	Conductor	Discriminant	Rank	Torsion	$\textrm{End}^0(E_{\overline\Q})$	CM	Sato-Tate	Potentially good	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	Weierstrass coefficients	Weierstrass equation	mod-$m$ images
1225.a1	1225j2	1225.a	1225j	$2$	$5$	$ 5^{2} \cdot 7^{2} $	$ - 5^{3} \cdot 7^{11} $	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$		$5$	5.12.0.1	5B.4.1	$70$	$48$	$1$	$0.776960684$	$1$	$4$	$1920$	$1.027147$	$-2887553024/16807$	$[0, 1, 1, -7268, -242126]$	$y^2+y=x^3+x^2-7268x-242126$	5.12.0.a.1, 10.24.0-5.a.1.2, 35.24.0-5.a.1.2, 70.48.1-70.d.1.3
1225.a2	1225j1	1225.a	1225j	$2$	$5$	$ 5^{2} \cdot 7^{2} $	$ - 5^{3} \cdot 7^{7} $	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$		$5$	5.12.0.2	5B.4.2	$70$	$48$	$1$	$0.155392136$	$1$	$6$	$384$	$0.222429$	$4096/7$	$[0, 1, 1, 82, 424]$	$y^2+y=x^3+x^2+82x+424$	5.12.0.a.2, 10.24.0-5.a.2.1, 35.24.0-5.a.2.2, 70.48.1-70.d.2.2
1225.b1	1225h2	1225.b	1225h	$2$	$37$	$ 5^{2} \cdot 7^{2} $	$ - 5^{3} \cdot 7^{2} $	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓	$37$	37.114.4.2	37B.8.2	$5180$	$2736$	$97$	$6.477204378$	$1$	$2$	$1776$	$1.270485$	$-162677523113838677$	$[1, 1, 1, -208083, -36621194]$	$y^2+xy+y=x^3+x^2-208083x-36621194$	20.2.0.a.1, 37.114.4.b.2, 148.228.10.?, 185.228.10.?, 259.342.16.?, $\ldots$
1225.b2	1225h1	1225.b	1225h	$2$	$37$	$ 5^{2} \cdot 7^{2} $	$ - 5^{3} \cdot 7^{2} $	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓	$37$	37.114.4.1	37B.8.1	$5180$	$2736$	$97$	$0.175059577$	$1$	$6$	$48$	$-0.534974$	$-9317$	$[1, 1, 1, -8, 6]$	$y^2+xy+y=x^3+x^2-8x+6$	20.2.0.a.1, 37.114.4.b.1, 148.228.10.?, 185.228.10.?, 259.342.16.?, $\ldots$
1225.c1	1225b4	1225.c	1225b	$4$	$14$	$ 5^{2} \cdot 7^{2} $	$ 5^{6} \cdot 7^{9} $	$0$	$\Z/2\Z$	$\Q(\sqrt{-7})$	$-28$	$N(\mathrm{U}(1))$	✓							$1$	$1$	$0$	$2016$	$1.325109$	$16581375$	$[1, -1, 1, -45555, 3753572]$	$y^2+xy+y=x^3-x^2-45555x+3753572$
1225.c2	1225b3	1225.c	1225b	$4$	$14$	$ 5^{2} \cdot 7^{2} $	$ - 5^{6} \cdot 7^{9} $	$0$	$\Z/2\Z$	$\Q(\sqrt{-7})$	$-7$	$N(\mathrm{U}(1))$	✓							$1$	$1$	$1$	$1008$	$0.978536$	$-3375$	$[1, -1, 1, -2680, 66322]$	$y^2+xy+y=x^3-x^2-2680x+66322$
1225.c3	1225b2	1225.c	1225b	$4$	$14$	$ 5^{2} \cdot 7^{2} $	$ 5^{6} \cdot 7^{3} $	$0$	$\Z/2\Z$	$\Q(\sqrt{-7})$	$-28$	$N(\mathrm{U}(1))$	✓							$1$	$1$	$0$	$288$	$0.352154$	$16581375$	$[1, -1, 1, -930, -10678]$	$y^2+xy+y=x^3-x^2-930x-10678$
1225.c4	1225b1	1225.c	1225b	$4$	$14$	$ 5^{2} \cdot 7^{2} $	$ - 5^{6} \cdot 7^{3} $	$0$	$\Z/2\Z$	$\Q(\sqrt{-7})$	$-7$	$N(\mathrm{U}(1))$	✓							$1$	$1$	$1$	$144$	$0.005581$	$-3375$	$[1, -1, 1, -55, -178]$	$y^2+xy+y=x^3-x^2-55x-178$
1225.d1	1225f2	1225.d	1225f	$2$	$37$	$ 5^{2} \cdot 7^{2} $	$ - 5^{3} \cdot 7^{8} $	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓	$37$	37.114.4.2	37B.8.2	$5180$	$2736$	$97$	$1$	$1$	$0$	$12432$	$2.243439$	$-162677523113838677$	$[1, 0, 0, -10196068, 12530481277]$	$y^2+xy=x^3-10196068x+12530481277$	20.2.0.a.1, 37.114.4.b.2, 148.228.10.?, 185.456.10.?, 259.342.16.?, $\ldots$
1225.d2	1225f1	1225.d	1225f	$2$	$37$	$ 5^{2} \cdot 7^{2} $	$ - 5^{3} \cdot 7^{8} $	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓	$37$	37.114.4.1	37B.8.1	$5180$	$2736$	$97$	$1$	$1$	$0$	$336$	$0.437981$	$-9317$	$[1, 0, 0, -393, -3298]$	$y^2+xy=x^3-393x-3298$	20.2.0.a.1, 37.114.4.b.1, 148.228.10.?, 185.456.10.?, 259.342.16.?, $\ldots$
1225.e1	1225a3	1225.e	1225a	$3$	$9$	$ 5^{2} \cdot 7^{2} $	$ - 5^{15} \cdot 7^{7} $	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$		$3$	9.12.0.1	3B	$630$	$144$	$3$	$1$	$1$	$0$	$6912$	$1.905136$	$-250523582464/13671875$	$[0, 1, 1, -160883, 25929019]$	$y^2+y=x^3+x^2-160883x+25929019$	3.4.0.a.1, 6.8.0-3.a.1.2, 9.12.0.a.1, 18.24.0-9.a.1.2, 63.36.0.e.2, $\ldots$
1225.e2	1225a1	1225.e	1225a	$3$	$9$	$ 5^{2} \cdot 7^{2} $	$ - 5^{7} \cdot 7^{7} $	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$		$3$	9.12.0.1	3B	$630$	$144$	$3$	$1$	$1$	$0$	$768$	$0.806524$	$-262144/35$	$[0, 1, 1, -1633, -28731]$	$y^2+y=x^3+x^2-1633x-28731$	3.4.0.a.1, 6.8.0-3.a.1.1, 9.12.0.a.1, 18.24.0-9.a.1.1, 63.36.0.e.1, $\ldots$
1225.e3	1225a2	1225.e	1225a	$3$	$9$	$ 5^{2} \cdot 7^{2} $	$ - 5^{9} \cdot 7^{9} $	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$		$3$	3.12.0.1	3Cs	$630$	$144$	$3$	$1$	$1$	$0$	$2304$	$1.355829$	$71991296/42875$	$[0, 1, 1, 10617, 75394]$	$y^2+y=x^3+x^2+10617x+75394$	3.12.0.a.1, 6.24.0-3.a.1.1, 63.36.0.b.1, 70.2.0.a.1, 105.24.0.?, $\ldots$
1225.f1	1225e2	1225.f	1225e	$2$	$37$	$ 5^{2} \cdot 7^{2} $	$ - 5^{9} \cdot 7^{8} $	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓	$37$	37.114.4.2	37B.8.2	$5180$	$2736$	$97$	$1$	$1$	$0$	$62160$	$3.048161$	$-162677523113838677$	$[1, 1, 0, -254901700, 1566310159625]$	$y^2+xy=x^3+x^2-254901700x+1566310159625$	20.2.0.a.1, 37.114.4.b.2, 148.228.10.?, 185.456.10.?, 259.342.16.?, $\ldots$
1225.f2	1225e1	1225.f	1225e	$2$	$37$	$ 5^{2} \cdot 7^{2} $	$ - 5^{9} \cdot 7^{8} $	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓	$37$	37.114.4.1	37B.8.1	$5180$	$2736$	$97$	$1$	$1$	$0$	$1680$	$1.242701$	$-9317$	$[1, 1, 0, -9825, -412250]$	$y^2+xy=x^3+x^2-9825x-412250$	20.2.0.a.1, 37.114.4.b.1, 148.228.10.?, 185.456.10.?, 259.342.16.?, $\ldots$
1225.g1	1225g2	1225.g	1225g	$2$	$37$	$ 5^{2} \cdot 7^{2} $	$ - 5^{9} \cdot 7^{2} $	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓	$37$	37.114.4.2	37B.8.2	$5180$	$2736$	$97$	$34.79035741$	$1$	$0$	$8880$	$2.075203$	$-162677523113838677$	$[1, 0, 1, -5202076, -4567245077]$	$y^2+xy+y=x^3-5202076x-4567245077$	20.2.0.a.1, 37.114.4.b.2, 148.228.10.?, 185.228.10.?, 259.342.16.?, $\ldots$
1225.g2	1225g1	1225.g	1225g	$2$	$37$	$ 5^{2} \cdot 7^{2} $	$ - 5^{9} \cdot 7^{2} $	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓	$37$	37.114.4.1	37B.8.1	$5180$	$2736$	$97$	$0.940279930$	$1$	$2$	$240$	$0.269745$	$-9317$	$[1, 0, 1, -201, 1173]$	$y^2+xy+y=x^3-201x+1173$	20.2.0.a.1, 37.114.4.b.1, 148.228.10.?, 185.228.10.?, 259.342.16.?, $\ldots$
1225.h1	1225d1	1225.h	1225d	$1$	$1$	$ 5^{2} \cdot 7^{2} $	$ - 5^{9} \cdot 7^{9} $	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$		$3$	3.3.0.1	3Nn	$210$	$12$	$1$	$1$	$1$	$0$	$8064$	$1.360912$	$-110592/125$	$[0, 0, 1, -8575, -525219]$	$y^2+y=x^3-8575x-525219$	3.3.0.a.1, 21.6.0.a.1, 30.6.0.c.1, 70.2.0.a.1, 210.12.1.?
1225.i1	1225i2	1225.i	1225i	$2$	$5$	$ 5^{2} \cdot 7^{2} $	$ - 5^{9} \cdot 7^{11} $	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$		$5$	5.12.0.1	5B.4.1	$70$	$48$	$1$	$8.564033026$	$1$	$0$	$9600$	$1.831867$	$-2887553024/16807$	$[0, -1, 1, -181708, -29902307]$	$y^2+y=x^3-x^2-181708x-29902307$	5.12.0.a.1, 10.24.0-5.a.1.1, 35.24.0-5.a.1.1, 70.48.1-70.d.1.1
1225.i2	1225i1	1225.i	1225i	$2$	$5$	$ 5^{2} \cdot 7^{2} $	$ - 5^{9} \cdot 7^{7} $	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$		$5$	5.12.0.2	5B.4.2	$70$	$48$	$1$	$1.712806605$	$1$	$0$	$1920$	$1.027147$	$4096/7$	$[0, -1, 1, 2042, 48943]$	$y^2+y=x^3-x^2+2042x+48943$	5.12.0.a.2, 10.24.0-5.a.2.2, 35.24.0-5.a.2.1, 70.48.1-70.d.2.1
1225.j1	1225c1	1225.j	1225c	$1$	$1$	$ 5^{2} \cdot 7^{2} $	$ - 5^{9} \cdot 7^{3} $	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$		$3$	3.3.0.1	3Nn	$210$	$12$	$1$	$1$	$1$	$0$	$1152$	$0.387958$	$-110592/125$	$[0, 0, 1, -175, 1531]$	$y^2+y=x^3-175x+1531$	3.3.0.a.1, 21.6.0.a.1, 30.6.0.c.1, 70.2.0.a.1, 210.12.1.?

Download displayed columns to Pari/GP SageMath Magma Oscar

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 $\F_{q}$

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Learn more

Refine search

Results (21 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 (21 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