LMFDB - Elliptic curves over $\Q$ of conductor 1248

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 (24 matches)

Download to Pari/GP SageMath Magma Oscar

Label	Cremona label	Class	Cremona class	Class size	Class degree	Conductor	Discriminant	Rank	Torsion	$\textrm{End}^0(E_{\overline\Q})$	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	Weierstrass coefficients	Weierstrass equation	mod-$m$ images
1248.a1	1248a1	1248.a	1248a	$2$	$2$	$ 2^{5} \cdot 3 \cdot 13 $	$ 2^{6} \cdot 3^{4} \cdot 13 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.6.0.3	2B	$312$	$48$	$0$	$0.833215920$	$1$	$5$	$128$	$-0.358298$	$5088448/1053$	$[0, -1, 0, -14, -12]$	$y^2=x^3-x^2-14x-12$	2.3.0.a.1, 4.6.0.b.1, 24.12.0-4.b.1.4, 26.6.0.b.1, 52.12.0.e.1, $\ldots$
1248.a2	1248a2	1248.a	1248a	$2$	$2$	$ 2^{5} \cdot 3 \cdot 13 $	$ - 2^{12} \cdot 3^{2} \cdot 13^{2} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.6.0.5	2B	$312$	$48$	$0$	$0.416607960$	$1$	$11$	$256$	$-0.011725$	$778688/1521$	$[0, -1, 0, 31, -111]$	$y^2=x^3-x^2+31x-111$	2.3.0.a.1, 4.6.0.a.1, 24.12.0-4.a.1.1, 52.12.0.d.1, 104.24.0.?, $\ldots$
1248.b1	1248h2	1248.b	1248h	$4$	$4$	$ 2^{5} \cdot 3 \cdot 13 $	$ 2^{9} \cdot 3^{3} \cdot 13 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.12.0.6	2B	$312$	$48$	$0$	$6.992997795$	$1$	$1$	$768$	$0.512716$	$11339065490696/351$	$[0, -1, 0, -3744, -86940]$	$y^2=x^3-x^2-3744x-86940$	2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.5, 12.12.0-4.c.1.2, 24.24.0-24.ba.1.4, $\ldots$
1248.b2	1248h3	1248.b	1248h	$4$	$4$	$ 2^{5} \cdot 3 \cdot 13 $	$ 2^{12} \cdot 3^{3} \cdot 13^{4} $	$1$	$\Z/4\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.12.0.7	2B	$312$	$48$	$0$	$1.748249448$	$1$	$9$	$768$	$0.512716$	$1360251712/771147$	$[0, -1, 0, -369, 513]$	$y^2=x^3-x^2-369x+513$	2.3.0.a.1, 4.12.0-4.c.1.1, 12.24.0-12.h.1.2, 104.24.0.?, 312.48.0.?
1248.b3	1248h1	1248.b	1248h	$4$	$4$	$ 2^{5} \cdot 3 \cdot 13 $	$ 2^{6} \cdot 3^{6} \cdot 13^{2} $	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.12.0.1	2Cs	$312$	$48$	$0$	$3.496498897$	$1$	$5$	$384$	$0.166143$	$22235451328/123201$	$[0, -1, 0, -234, -1296]$	$y^2=x^3-x^2-234x-1296$	2.6.0.a.1, 4.12.0-2.a.1.1, 12.24.0-12.a.1.1, 104.24.0.?, 312.48.0.?
1248.b4	1248h4	1248.b	1248h	$4$	$4$	$ 2^{5} \cdot 3 \cdot 13 $	$ - 2^{9} \cdot 3^{12} \cdot 13 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.12.0.8	2B	$312$	$48$	$0$	$6.992997795$	$1$	$1$	$768$	$0.512716$	$-245314376/6908733$	$[0, -1, 0, -104, -2856]$	$y^2=x^3-x^2-104x-2856$	2.3.0.a.1, 4.12.0-4.c.1.2, 24.24.0-24.ba.1.16, 104.24.0.?, 312.48.0.?
1248.c1	1248g2	1248.c	1248g	$2$	$2$	$ 2^{5} \cdot 3 \cdot 13 $	$ 2^{12} \cdot 3 \cdot 13^{2} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$156$	$12$	$0$	$1.065924653$	$1$	$5$	$128$	$-0.095314$	$1000000/507$	$[0, -1, 0, -33, -15]$	$y^2=x^3-x^2-33x-15$	2.3.0.a.1, 12.6.0.a.1, 52.6.0.c.1, 156.12.0.?
1248.c2	1248g1	1248.c	1248g	$2$	$2$	$ 2^{5} \cdot 3 \cdot 13 $	$ 2^{6} \cdot 3^{2} \cdot 13 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$156$	$12$	$0$	$0.532962326$	$1$	$7$	$64$	$-0.441888$	$10648000/117$	$[0, -1, 0, -18, 36]$	$y^2=x^3-x^2-18x+36$	2.3.0.a.1, 12.6.0.b.1, 26.6.0.b.1, 156.12.0.?
1248.d1	1248b2	1248.d	1248b	$2$	$2$	$ 2^{5} \cdot 3 \cdot 13 $	$ 2^{12} \cdot 3^{5} \cdot 13^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$156$	$12$	$0$	$1$	$1$	$1$	$640$	$0.516811$	$61162984000/41067$	$[0, -1, 0, -1313, -17871]$	$y^2=x^3-x^2-1313x-17871$	2.3.0.a.1, 12.6.0.a.1, 52.6.0.c.1, 156.12.0.?
1248.d2	1248b1	1248.d	1248b	$2$	$2$	$ 2^{5} \cdot 3 \cdot 13 $	$ 2^{6} \cdot 3^{10} \cdot 13 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$156$	$12$	$0$	$1$	$1$	$1$	$320$	$0.170238$	$1643032000/767637$	$[0, -1, 0, -98, -132]$	$y^2=x^3-x^2-98x-132$	2.3.0.a.1, 12.6.0.b.1, 26.6.0.b.1, 156.12.0.?
1248.e1	1248f1	1248.e	1248f	$2$	$2$	$ 2^{5} \cdot 3 \cdot 13 $	$ 2^{6} \cdot 3^{8} \cdot 13^{3} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.12.0.22	2B	$104$	$48$	$0$	$1$	$1$	$1$	$768$	$0.691796$	$42246001231552/14414517$	$[0, -1, 0, -2902, 61132]$	$y^2=x^3-x^2-2902x+61132$	2.3.0.a.1, 4.6.0.b.1, 8.12.0-4.b.1.2, 26.6.0.b.1, 52.12.0.e.1, $\ldots$
1248.e2	1248f2	1248.e	1248f	$2$	$2$	$ 2^{5} \cdot 3 \cdot 13 $	$ - 2^{12} \cdot 3^{4} \cdot 13^{6} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.12.0.37	2B	$104$	$48$	$0$	$1$	$1$	$1$	$1536$	$1.038370$	$-420526439488/390971529$	$[0, -1, 0, -2497, 78385]$	$y^2=x^3-x^2-2497x+78385$	2.3.0.a.1, 4.6.0.a.1, 8.12.0-4.a.1.1, 52.12.0.d.1, 104.48.0.?
1248.f1	1248e3	1248.f	1248e	$4$	$4$	$ 2^{5} \cdot 3 \cdot 13 $	$ 2^{9} \cdot 3^{3} \cdot 13 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.12.0.6	2B	$312$	$48$	$0$	$1.560471980$	$1$	$3$	$768$	$0.512716$	$11339065490696/351$	$[0, 1, 0, -3744, 86940]$	$y^2=x^3+x^2-3744x+86940$	2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.5, 12.12.0-4.c.1.1, 24.24.0-24.ba.1.12, $\ldots$
1248.f2	1248e2	1248.f	1248e	$4$	$4$	$ 2^{5} \cdot 3 \cdot 13 $	$ 2^{12} \cdot 3^{3} \cdot 13^{4} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.12.0.8	2B	$312$	$48$	$0$	$0.390117995$	$1$	$9$	$768$	$0.512716$	$1360251712/771147$	$[0, 1, 0, -369, -513]$	$y^2=x^3+x^2-369x-513$	2.3.0.a.1, 4.12.0-4.c.1.2, 12.24.0-12.h.1.1, 104.24.0.?, 312.48.0.?
1248.f3	1248e1	1248.f	1248e	$4$	$4$	$ 2^{5} \cdot 3 \cdot 13 $	$ 2^{6} \cdot 3^{6} \cdot 13^{2} $	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.12.0.1	2Cs	$312$	$48$	$0$	$0.780235990$	$1$	$11$	$384$	$0.166143$	$22235451328/123201$	$[0, 1, 0, -234, 1296]$	$y^2=x^3+x^2-234x+1296$	2.6.0.a.1, 4.12.0-2.a.1.1, 12.24.0-12.a.1.2, 104.24.0.?, 312.48.0.?
1248.f4	1248e4	1248.f	1248e	$4$	$4$	$ 2^{5} \cdot 3 \cdot 13 $	$ - 2^{9} \cdot 3^{12} \cdot 13 $	$1$	$\Z/4\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.12.0.7	2B	$312$	$48$	$0$	$1.560471980$	$1$	$9$	$768$	$0.512716$	$-245314376/6908733$	$[0, 1, 0, -104, 2856]$	$y^2=x^3+x^2-104x+2856$	2.3.0.a.1, 4.12.0-4.c.1.1, 24.24.0-24.ba.1.8, 104.24.0.?, 312.48.0.?
1248.g1	1248i1	1248.g	1248i	$2$	$2$	$ 2^{5} \cdot 3 \cdot 13 $	$ 2^{6} \cdot 3^{4} \cdot 13 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.6.0.3	2B	$312$	$48$	$0$	$0.426142225$	$1$	$9$	$128$	$-0.358298$	$5088448/1053$	$[0, 1, 0, -14, 12]$	$y^2=x^3+x^2-14x+12$	2.3.0.a.1, 4.6.0.b.1, 24.12.0-4.b.1.4, 26.6.0.b.1, 52.12.0.e.1, $\ldots$
1248.g2	1248i2	1248.g	1248i	$2$	$2$	$ 2^{5} \cdot 3 \cdot 13 $	$ - 2^{12} \cdot 3^{2} \cdot 13^{2} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.6.0.5	2B	$312$	$48$	$0$	$0.852284451$	$1$	$5$	$256$	$-0.011725$	$778688/1521$	$[0, 1, 0, 31, 111]$	$y^2=x^3+x^2+31x+111$	2.3.0.a.1, 4.6.0.a.1, 24.12.0-4.a.1.1, 52.12.0.d.1, 104.24.0.?, $\ldots$
1248.h1	1248d2	1248.h	1248d	$2$	$2$	$ 2^{5} \cdot 3 \cdot 13 $	$ 2^{12} \cdot 3^{5} \cdot 13^{2} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$156$	$12$	$0$	$0.160149900$	$1$	$13$	$640$	$0.516811$	$61162984000/41067$	$[0, 1, 0, -1313, 17871]$	$y^2=x^3+x^2-1313x+17871$	2.3.0.a.1, 12.6.0.a.1, 52.6.0.c.1, 156.12.0.?
1248.h2	1248d1	1248.h	1248d	$2$	$2$	$ 2^{5} \cdot 3 \cdot 13 $	$ 2^{6} \cdot 3^{10} \cdot 13 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$156$	$12$	$0$	$0.320299800$	$1$	$9$	$320$	$0.170238$	$1643032000/767637$	$[0, 1, 0, -98, 132]$	$y^2=x^3+x^2-98x+132$	2.3.0.a.1, 12.6.0.b.1, 26.6.0.b.1, 156.12.0.?
1248.i1	1248j2	1248.i	1248j	$2$	$2$	$ 2^{5} \cdot 3 \cdot 13 $	$ 2^{12} \cdot 3 \cdot 13^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$156$	$12$	$0$	$1$	$1$	$1$	$128$	$-0.095314$	$1000000/507$	$[0, 1, 0, -33, 15]$	$y^2=x^3+x^2-33x+15$	2.3.0.a.1, 12.6.0.a.1, 52.6.0.c.1, 156.12.0.?
1248.i2	1248j1	1248.i	1248j	$2$	$2$	$ 2^{5} \cdot 3 \cdot 13 $	$ 2^{6} \cdot 3^{2} \cdot 13 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$156$	$12$	$0$	$1$	$1$	$1$	$64$	$-0.441888$	$10648000/117$	$[0, 1, 0, -18, -36]$	$y^2=x^3+x^2-18x-36$	2.3.0.a.1, 12.6.0.b.1, 26.6.0.b.1, 156.12.0.?
1248.j1	1248c1	1248.j	1248c	$2$	$2$	$ 2^{5} \cdot 3 \cdot 13 $	$ 2^{6} \cdot 3^{8} \cdot 13^{3} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.12.0.22	2B	$104$	$48$	$0$	$1$	$1$	$1$	$768$	$0.691796$	$42246001231552/14414517$	$[0, 1, 0, -2902, -61132]$	$y^2=x^3+x^2-2902x-61132$	2.3.0.a.1, 4.6.0.b.1, 8.12.0-4.b.1.2, 26.6.0.b.1, 52.12.0.e.1, $\ldots$
1248.j2	1248c2	1248.j	1248c	$2$	$2$	$ 2^{5} \cdot 3 \cdot 13 $	$ - 2^{12} \cdot 3^{4} \cdot 13^{6} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.12.0.37	2B	$104$	$48$	$0$	$1$	$1$	$1$	$1536$	$1.038370$	$-420526439488/390971529$	$[0, 1, 0, -2497, -78385]$	$y^2=x^3+x^2-2497x-78385$	2.3.0.a.1, 4.6.0.a.1, 8.12.0-4.a.1.1, 52.12.0.d.1, 104.48.0.?

Download 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 (24 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 (24 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