LMFDB - Elliptic curves over $\Q$ of conductor 336

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

		Sort order	Select

Results (26 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
336.a1	336e5	336.a	336e	$6$	$8$	$ 2^{4} \cdot 3 \cdot 7 $	$ 2^{12} \cdot 3 \cdot 7^{2} $	$1$	$\Z/4\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	16.48.0.32	2B	$336$	$192$	$1$	$2.985196834$	$1$		$7$	$256$	$0.767352$	$53297461115137/147$	$1.05087$	$6.86332$	$[0, -1, 0, -12544, 544960]$	$y^2=x^3-x^2-12544x+544960$	2.3.0.a.1, 4.12.0-4.c.1.1, 8.24.0-8.n.1.2, 12.24.0-12.h.1.2, 16.48.0-16.e.2.7, $\ldots$	$[(90, 370)]$
336.a2	336e4	336.a	336e	$6$	$8$	$ 2^{4} \cdot 3 \cdot 7 $	$ 2^{12} \cdot 3^{2} \cdot 7^{4} $	$1$	$\Z/2\Z\oplus\Z/4\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.48.0.25	2Cs	$168$	$192$	$1$	$1.492598417$	$1$		$19$	$128$	$0.420779$	$13027640977/21609$	$1.08149$	$5.43364$	$[0, -1, 0, -784, 8704]$	$y^2=x^3-x^2-784x+8704$	2.6.0.a.1, 4.24.0-4.b.1.3, 8.48.0-8.e.1.9, 12.48.0-12.c.1.1, 24.96.0-24.j.2.3, $\ldots$	$[(18, 10)]$
336.a3	336e3	336.a	336e	$6$	$8$	$ 2^{4} \cdot 3 \cdot 7 $	$ 2^{12} \cdot 3^{8} \cdot 7 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.48.0.176	2B	$336$	$192$	$1$	$1.492598417$	$1$		$5$	$128$	$0.420779$	$6570725617/45927$	$1.00160$	$5.31598$	$[0, -1, 0, -624, -5760]$	$y^2=x^3-x^2-624x-5760$	2.3.0.a.1, 4.12.0-4.c.1.2, 8.48.0-8.bb.1.3, 28.24.0-28.h.1.1, 48.96.0-48.bf.1.7, $\ldots$	$[(-14, 6)]$
336.a4	336e6	336.a	336e	$6$	$8$	$ 2^{4} \cdot 3 \cdot 7 $	$ - 2^{12} \cdot 3 \cdot 7^{8} $	$1$	$\Z/4\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.48.0.161	2B	$336$	$192$	$1$	$0.746299208$	$1$		$11$	$256$	$0.767352$	$-4354703137/17294403$	$1.04266$	$5.59976$	$[0, -1, 0, -544, 13888]$	$y^2=x^3-x^2-544x+13888$	2.3.0.a.1, 4.12.0-4.c.1.1, 6.6.0.a.1, 8.48.0-8.bb.2.4, 12.24.0-12.g.1.2, $\ldots$	$[(32, 168)]$
336.a5	336e2	336.a	336e	$6$	$8$	$ 2^{4} \cdot 3 \cdot 7 $	$ 2^{12} \cdot 3^{4} \cdot 7^{2} $	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.48.0.32	2Cs	$168$	$192$	$1$	$0.746299208$	$1$		$13$	$64$	$0.074205$	$7189057/3969$	$1.14862$	$4.14395$	$[0, -1, 0, -64, 64]$	$y^2=x^3-x^2-64x+64$	2.6.0.a.1, 4.24.0-4.b.1.1, 8.48.0-8.e.2.4, 24.96.0-24.w.2.2, 28.48.0-28.c.1.3, $\ldots$	$[(0, 8)]$
336.a6	336e1	336.a	336e	$6$	$8$	$ 2^{4} \cdot 3 \cdot 7 $	$ - 2^{12} \cdot 3^{2} \cdot 7 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	16.48.0.43	2B	$336$	$192$	$1$	$0.373149604$	$1$		$11$	$32$	$-0.272368$	$103823/63$	$0.97868$	$3.41548$	$[0, -1, 0, 16, 0]$	$y^2=x^3-x^2+16x$	2.3.0.a.1, 4.12.0-4.c.1.2, 8.24.0-8.n.1.6, 14.6.0.b.1, 16.48.0-16.e.1.6, $\ldots$	$[(2, 6)]$
336.b1	336a4	336.b	336a	$4$	$6$	$ 2^{4} \cdot 3 \cdot 7 $	$ 2^{8} \cdot 3^{2} \cdot 7^{3} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2, 3$	2.3.0.1, 3.4.0.1	2B, 3B	$84$	$96$	$1$	$1$	$1$		$1$	$144$	$0.414809$	$2640279346000/3087$	$1.02245$	$5.87011$	$[0, -1, 0, -1828, 30700]$	$y^2=x^3-x^2-1828x+30700$	2.3.0.a.1, 3.4.0.a.1, 6.12.0.a.1, 12.48.0-12.j.1.2, 28.6.0.a.1, $\ldots$	$[]$
336.b2	336a3	336.b	336a	$4$	$6$	$ 2^{4} \cdot 3 \cdot 7 $	$ - 2^{4} \cdot 3 \cdot 7^{6} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2, 3$	2.3.0.1, 3.4.0.1	2B, 3B	$84$	$96$	$1$	$1$	$1$		$1$	$72$	$0.068235$	$-10061824000/352947$	$1.07286$	$4.44610$	$[0, -1, 0, -113, 516]$	$y^2=x^3-x^2-113x+516$	2.3.0.a.1, 3.4.0.a.1, 6.24.0.b.1, 12.48.0-6.b.1.4, 28.6.0.b.1, $\ldots$	$[]$
336.b3	336a2	336.b	336a	$4$	$6$	$ 2^{4} \cdot 3 \cdot 7 $	$ 2^{8} \cdot 3^{6} \cdot 7 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2, 3$	2.3.0.1, 3.4.0.1	2B, 3B	$84$	$96$	$1$	$1$	$1$		$1$	$48$	$-0.134497$	$9826000/5103$	$0.97243$	$3.72104$	$[0, -1, 0, -28, 28]$	$y^2=x^3-x^2-28x+28$	2.3.0.a.1, 3.4.0.a.1, 6.12.0.a.1, 12.48.0-12.j.1.4, 28.6.0.a.1, $\ldots$	$[]$
336.b4	336a1	336.b	336a	$4$	$6$	$ 2^{4} \cdot 3 \cdot 7 $	$ - 2^{4} \cdot 3^{3} \cdot 7^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2, 3$	2.3.0.1, 3.4.0.1	2B, 3B	$84$	$96$	$1$	$1$	$1$		$1$	$24$	$-0.481071$	$2048000/1323$	$1.10843$	$2.97484$	$[0, -1, 0, 7, 0]$	$y^2=x^3-x^2+7x$	2.3.0.a.1, 3.4.0.a.1, 6.24.0.b.1, 12.48.0-6.b.1.1, 28.6.0.b.1, $\ldots$	$[]$
336.c1	336b3	336.c	336b	$4$	$4$	$ 2^{4} \cdot 3 \cdot 7 $	$ 2^{10} \cdot 3^{4} \cdot 7 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.12.0.8	2B	$168$	$48$	$0$	$1$	$1$		$1$	$64$	$0.006959$	$381775972/567$	$0.96461$	$4.58850$	$[0, -1, 0, -152, -672]$	$y^2=x^3-x^2-152x-672$	2.3.0.a.1, 4.12.0-4.c.1.2, 24.24.0-24.z.1.16, 28.24.0-28.h.1.1, 168.48.0.?	$[]$
336.c2	336b2	336.c	336b	$4$	$4$	$ 2^{4} \cdot 3 \cdot 7 $	$ 2^{8} \cdot 3^{2} \cdot 7^{2} $	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.12.0.1	2Cs	$84$	$48$	$0$	$1$	$1$		$3$	$32$	$-0.339614$	$810448/441$	$0.95393$	$3.29210$	$[0, -1, 0, -12, 0]$	$y^2=x^3-x^2-12x$	2.6.0.a.1, 4.12.0-2.a.1.1, 12.24.0-12.b.1.1, 28.24.0-28.a.1.2, 84.48.0.?	$[]$
336.c3	336b1	336.c	336b	$4$	$4$	$ 2^{4} \cdot 3 \cdot 7 $	$ 2^{4} \cdot 3 \cdot 7 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.12.0.6	2B	$168$	$48$	$0$	$1$	$1$		$1$	$16$	$-0.686188$	$2725888/21$	$0.93026$	$3.02399$	$[0, -1, 0, -7, 10]$	$y^2=x^3-x^2-7x+10$	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.z.1.12, $\ldots$	$[]$
336.c4	336b4	336.c	336b	$4$	$4$	$ 2^{4} \cdot 3 \cdot 7 $	$ - 2^{10} \cdot 3 \cdot 7^{4} $	$0$	$\Z/4\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.12.0.7	2B	$168$	$48$	$0$	$1$	$1$		$3$	$64$	$0.006959$	$11696828/7203$	$1.01215$	$3.98932$	$[0, -1, 0, 48, -48]$	$y^2=x^3-x^2+48x-48$	2.3.0.a.1, 4.12.0-4.c.1.1, 6.6.0.a.1, 12.24.0-12.g.1.2, 56.24.0-56.ba.1.4, $\ldots$	$[]$
336.d1	336d3	336.d	336d	$6$	$8$	$ 2^{4} \cdot 3 \cdot 7 $	$ 2^{14} \cdot 3^{2} \cdot 7 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	16.96.0.147	2B	$112$	$192$	$1$	$1$	$4$	$2$	$1$	$384$	$0.882248$	$268498407453697/252$	$1.05727$	$7.14128$	$[0, 1, 0, -21504, -1220940]$	$y^2=x^3+x^2-21504x-1220940$	2.3.0.a.1, 4.12.0-4.c.1.2, 8.48.0-8.bb.2.3, 16.96.0-16.z.2.4, 28.24.0-28.h.1.1, $\ldots$	$[]$
336.d2	336d5	336.d	336d	$6$	$8$	$ 2^{4} \cdot 3 \cdot 7 $	$ 2^{13} \cdot 3^{4} \cdot 7^{8} $	$0$	$\Z/8\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.96.0.157	2B	$112$	$192$	$1$	$1$	$1$		$7$	$768$	$1.228823$	$84448510979617/933897762$	$1.05309$	$6.94244$	$[0, 1, 0, -14624, 669300]$	$y^2=x^3+x^2-14624x+669300$	2.3.0.a.1, 4.12.0-4.c.1.1, 8.96.0-8.p.1.2, 112.192.1.?	$[]$
336.d3	336d4	336.d	336d	$6$	$8$	$ 2^{4} \cdot 3 \cdot 7 $	$ 2^{14} \cdot 3^{8} \cdot 7^{4} $	$0$	$\Z/2\Z\oplus\Z/4\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.96.0.33	2Cs	$56$	$192$	$1$	$1$	$1$		$7$	$384$	$0.882248$	$124475734657/63011844$	$1.06499$	$5.82164$	$[0, 1, 0, -1664, -9804]$	$y^2=x^3+x^2-1664x-9804$	2.6.0.a.1, 4.24.0-4.b.1.3, 8.96.0-8.f.1.5, 56.192.1-56.bp.2.3	$[]$
336.d4	336d2	336.d	336d	$6$	$8$	$ 2^{4} \cdot 3 \cdot 7 $	$ 2^{16} \cdot 3^{4} \cdot 7^{2} $	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.96.0.56	2Cs	$56$	$192$	$1$	$1$	$1$		$3$	$192$	$0.535675$	$65597103937/63504$	$1.01692$	$5.71152$	$[0, 1, 0, -1344, -19404]$	$y^2=x^3+x^2-1344x-19404$	2.6.0.a.1, 4.24.0-4.b.1.1, 8.96.0-8.i.1.4, 28.48.0-28.c.1.3, 56.192.1-56.by.1.1	$[]$
336.d5	336d1	336.d	336d	$6$	$8$	$ 2^{4} \cdot 3 \cdot 7 $	$ - 2^{20} \cdot 3^{2} \cdot 7 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	16.96.0.146	2B	$112$	$192$	$1$	$1$	$1$		$1$	$96$	$0.189101$	$-7189057/16128$	$0.98224$	$4.41633$	$[0, 1, 0, -64, -460]$	$y^2=x^3+x^2-64x-460$	2.3.0.a.1, 4.12.0-4.c.1.2, 8.48.0-8.bb.1.3, 14.6.0.b.1, 16.96.0-16.z.1.1, $\ldots$	$[]$
336.d6	336d6	336.d	336d	$6$	$8$	$ 2^{4} \cdot 3 \cdot 7 $	$ - 2^{13} \cdot 3^{16} \cdot 7^{2} $	$0$	$\Z/4\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	16.96.0.91	2B	$112$	$192$	$1$	$1$	$1$		$3$	$768$	$1.228823$	$6359387729183/4218578658$	$1.08314$	$6.49785$	$[0, 1, 0, 6176, -69388]$	$y^2=x^3+x^2+6176x-69388$	2.3.0.a.1, 4.12.0-4.c.1.1, 8.48.0-8.k.1.2, 16.96.0-16.e.1.2, 56.96.0-56.bc.1.8, $\ldots$	$[]$
336.e1	336c3	336.e	336c	$4$	$4$	$ 2^{4} \cdot 3 \cdot 7 $	$ 2^{10} \cdot 3^{3} \cdot 7 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.12.0.6	2B	$168$	$48$	$0$	$1$	$1$		$1$	$192$	$0.528189$	$7080974546692/189$	$1.03534$	$6.27801$	$[0, 1, 0, -4032, -99900]$	$y^2=x^3+x^2-4032x-99900$	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.z.1.4, $\ldots$	$[]$
336.e2	336c4	336.e	336c	$4$	$4$	$ 2^{4} \cdot 3 \cdot 7 $	$ 2^{10} \cdot 3^{12} \cdot 7 $	$0$	$\Z/4\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.12.0.7	2B	$168$	$48$	$0$	$1$	$1$		$3$	$192$	$0.528189$	$6522128932/3720087$	$1.09944$	$5.07639$	$[0, 1, 0, -392, 228]$	$y^2=x^3+x^2-392x+228$	2.3.0.a.1, 4.12.0-4.c.1.1, 24.24.0-24.z.1.8, 28.24.0-28.h.1.2, 168.48.0.?	$[]$
336.e3	336c2	336.e	336c	$4$	$4$	$ 2^{4} \cdot 3 \cdot 7 $	$ 2^{8} \cdot 3^{6} \cdot 7^{2} $	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.12.0.1	2Cs	$84$	$48$	$0$	$1$	$1$		$3$	$96$	$0.181615$	$6940769488/35721$	$0.97939$	$4.84877$	$[0, 1, 0, -252, -1620]$	$y^2=x^3+x^2-252x-1620$	2.6.0.a.1, 4.12.0-2.a.1.1, 12.24.0-12.b.1.2, 28.24.0-28.a.1.1, 84.48.0.?	$[]$
336.e4	336c1	336.e	336c	$4$	$4$	$ 2^{4} \cdot 3 \cdot 7 $	$ - 2^{4} \cdot 3^{3} \cdot 7^{4} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.12.0.8	2B	$168$	$48$	$0$	$1$	$1$		$1$	$48$	$-0.164958$	$-2725888/64827$	$1.07980$	$3.66691$	$[0, 1, 0, -7, -52]$	$y^2=x^3+x^2-7x-52$	2.3.0.a.1, 4.12.0-4.c.1.2, 6.6.0.a.1, 12.24.0-12.g.1.1, 56.24.0-56.ba.1.12, $\ldots$	$[]$
336.f1	336f2	336.f	336f	$2$	$2$	$ 2^{4} \cdot 3 \cdot 7 $	$ 2^{8} \cdot 3^{2} \cdot 7 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$84$	$12$	$0$	$1$	$1$		$1$	$48$	$-0.323987$	$20720464/63$	$0.91015$	$3.84930$	$[0, 1, 0, -36, 72]$	$y^2=x^3+x^2-36x+72$	2.3.0.a.1, 12.6.0.c.1, 28.6.0.a.1, 84.12.0.?	$[]$
336.f2	336f1	336.f	336f	$2$	$2$	$ 2^{4} \cdot 3 \cdot 7 $	$ - 2^{4} \cdot 3 \cdot 7^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$84$	$12$	$0$	$1$	$1$		$1$	$24$	$-0.670560$	$-16384/147$	$1.05520$	$2.62678$	$[0, 1, 0, -1, 2]$	$y^2=x^3+x^2-x+2$	2.3.0.a.1, 6.6.0.a.1, 28.6.0.b.1, 84.12.0.?	$[]$

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 $\F_{q}$

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Learn more

Refine search

Results (26 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 (26 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