LMFDB - Elliptic curves over $\Q$ of conductor 2856

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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 (21 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	$Ш_{\textrm{an}}$	Ш primes	Integral points	Modular degree	Faltings height	j-invariant	$abc$ quality	Szpiro ratio	Weierstrass coefficients	Weierstrass equation	mod-$m$ images	MW-generators
2856.a1	2856e1	2856.a	2856e	$1$	$1$	$ 2^{3} \cdot 3 \cdot 7 \cdot 17 $	$ - 2^{8} \cdot 3^{7} \cdot 7^{4} \cdot 17 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$102$	$2$	$0$	$0.357872302$	$1$		$6$	$5376$	$1.365669$	$-371806976516936704/89266779$	$1.01123$	$5.78124$	$[0, -1, 0, -95121, 11323557]$	$y^2=x^3-x^2-95121x+11323557$	102.2.0.?	$[(179, 14)]$
2856.b1	2856f3	2856.b	2856f	$4$	$4$	$ 2^{3} \cdot 3 \cdot 7 \cdot 17 $	$ 2^{11} \cdot 3 \cdot 7^{4} \cdot 17 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.6.0.1	2B	$2856$	$48$	$0$	$4.602150666$	$1$		$3$	$1536$	$0.606421$	$569001644066/122451$	$0.92381$	$4.35981$	$[0, -1, 0, -2192, -38772]$	$y^2=x^3-x^2-2192x-38772$	2.3.0.a.1, 4.6.0.c.1, 24.12.0-4.c.1.2, 56.12.0-4.c.1.5, 68.12.0-4.c.1.1, $\ldots$	$[(73, 430)]$
2856.b2	2856f4	2856.b	2856f	$4$	$4$	$ 2^{3} \cdot 3 \cdot 7 \cdot 17 $	$ 2^{11} \cdot 3 \cdot 7 \cdot 17^{4} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.6.0.1	2B	$2856$	$48$	$0$	$4.602150666$	$1$		$1$	$1536$	$0.606421$	$52767497666/1753941$	$0.90421$	$4.06096$	$[0, -1, 0, -992, 12012]$	$y^2=x^3-x^2-992x+12012$	2.3.0.a.1, 4.6.0.c.1, 24.12.0-4.c.1.1, 28.12.0-4.c.1.1, 136.12.0.?, $\ldots$	$[(109/2, 535/2)]$
2856.b3	2856f2	2856.b	2856f	$4$	$4$	$ 2^{3} \cdot 3 \cdot 7 \cdot 17 $	$ 2^{10} \cdot 3^{2} \cdot 7^{2} \cdot 17^{2} $	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.6.0.1	2Cs	$2856$	$48$	$0$	$2.301075333$	$1$		$7$	$768$	$0.259848$	$381775972/127449$	$0.85650$	$3.35443$	$[0, -1, 0, -152, -420]$	$y^2=x^3-x^2-152x-420$	2.6.0.a.1, 24.12.0-2.a.1.1, 28.12.0-2.a.1.1, 68.12.0-2.a.1.1, 168.24.0.?, $\ldots$	$[(22, 80)]$
2856.b4	2856f1	2856.b	2856f	$4$	$4$	$ 2^{3} \cdot 3 \cdot 7 \cdot 17 $	$ - 2^{8} \cdot 3^{4} \cdot 7 \cdot 17 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.6.0.1	2B	$2856$	$48$	$0$	$1.150537666$	$1$		$5$	$384$	$-0.086725$	$9148592/9639$	$0.79089$	$2.71130$	$[0, -1, 0, 28, -60]$	$y^2=x^3-x^2+28x-60$	2.3.0.a.1, 4.6.0.c.1, 24.12.0-4.c.1.6, 28.12.0-4.c.1.2, 68.12.0-4.c.1.2, $\ldots$	$[(4, 10)]$
2856.c1	2856h4	2856.c	2856h	$4$	$4$	$ 2^{3} \cdot 3 \cdot 7 \cdot 17 $	$ 2^{11} \cdot 3^{6} \cdot 7^{3} \cdot 17 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.24.0.103	2B	$952$	$48$	$0$	$1$	$4$	$2$	$1$	$138240$	$2.891006$	$322159999717985454060440834/4250799$	$1.10805$	$8.62890$	$[0, 1, 0, -181367424, 940067661600]$	$y^2=x^3+x^2-181367424x+940067661600$	2.3.0.a.1, 4.6.0.c.1, 8.24.0-8.p.1.7, 476.12.0.?, 952.48.0.?	$[]$
2856.c2	2856h3	2856.c	2856h	$4$	$4$	$ 2^{3} \cdot 3 \cdot 7 \cdot 17 $	$ 2^{11} \cdot 3^{6} \cdot 7^{12} \cdot 17^{4} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.24.0.58	2B	$952$	$48$	$0$	$1$	$1$		$1$	$138240$	$2.891006$	$79260902459030376659234/842751810121431609$	$1.04228$	$7.58456$	$[0, 1, 0, -11364624, 14606337312]$	$y^2=x^3+x^2-11364624x+14606337312$	2.3.0.a.1, 4.12.0-4.c.1.2, 8.24.0-8.k.1.1, 952.48.0.?	$[]$
2856.c3	2856h2	2856.c	2856h	$4$	$4$	$ 2^{3} \cdot 3 \cdot 7 \cdot 17 $	$ 2^{10} \cdot 3^{12} \cdot 7^{6} \cdot 17^{2} $	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.24.0.1	2Cs	$952$	$48$	$0$	$1$	$1$		$3$	$69120$	$2.544434$	$157304700372188331121828/18069292138401$	$1.04207$	$7.58359$	$[0, 1, 0, -11335464, 14685722496]$	$y^2=x^3+x^2-11335464x+14685722496$	2.6.0.a.1, 4.12.0-2.a.1.1, 8.24.0-8.a.1.2, 476.24.0.?, 952.48.0.?	$[]$
2856.c4	2856h1	2856.c	2856h	$4$	$4$	$ 2^{3} \cdot 3 \cdot 7 \cdot 17 $	$ - 2^{8} \cdot 3^{24} \cdot 7^{3} \cdot 17 $	$0$	$\Z/4\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.24.0.50	2B	$952$	$48$	$0$	$1$	$1$		$3$	$34560$	$2.197861$	$-152435594466395827792/1646846627220711$	$1.01679$	$6.53962$	$[0, 1, 0, -706644, 230527296]$	$y^2=x^3+x^2-706644x+230527296$	2.3.0.a.1, 4.12.0-4.c.1.1, 8.24.0-8.p.1.1, 238.6.0.?, 476.24.0.?, $\ldots$	$[]$
2856.d1	2856c3	2856.d	2856c	$4$	$4$	$ 2^{3} \cdot 3 \cdot 7 \cdot 17 $	$ 2^{10} \cdot 3 \cdot 7 \cdot 17^{4} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.12.0.8	2B	$2856$	$48$	$0$	$1$	$1$		$1$	$1280$	$0.511873$	$17418812548/1753941$	$0.95006$	$3.83456$	$[0, 1, 0, -544, -4624]$	$y^2=x^3+x^2-544x-4624$	2.3.0.a.1, 4.12.0-4.c.1.2, 42.6.0.a.1, 84.24.0.?, 136.24.0.?, $\ldots$	$[]$
2856.d2	2856c2	2856.d	2856c	$4$	$4$	$ 2^{3} \cdot 3 \cdot 7 \cdot 17 $	$ 2^{8} \cdot 3^{2} \cdot 7^{2} \cdot 17^{2} $	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.12.0.1	2Cs	$1428$	$48$	$0$	$1$	$1$		$3$	$640$	$0.165300$	$830321872/127449$	$0.90584$	$3.27786$	$[0, 1, 0, -124, 416]$	$y^2=x^3+x^2-124x+416$	2.6.0.a.1, 4.12.0-2.a.1.1, 68.24.0-68.a.1.1, 84.24.0.?, 1428.48.0.?	$[]$
2856.d3	2856c1	2856.d	2856c	$4$	$4$	$ 2^{3} \cdot 3 \cdot 7 \cdot 17 $	$ 2^{4} \cdot 3 \cdot 7 \cdot 17 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.12.0.6	2B	$2856$	$48$	$0$	$1$	$1$		$1$	$320$	$-0.181274$	$11745974272/357$	$0.89450$	$3.26238$	$[0, 1, 0, -119, 462]$	$y^2=x^3+x^2-119x+462$	2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.5, 68.12.0-4.c.1.2, 84.12.0.?, $\ldots$	$[]$
2856.d4	2856c4	2856.d	2856c	$4$	$4$	$ 2^{3} \cdot 3 \cdot 7 \cdot 17 $	$ - 2^{10} \cdot 3^{4} \cdot 7^{4} \cdot 17 $	$0$	$\Z/4\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.12.0.7	2B	$2856$	$48$	$0$	$1$	$1$		$3$	$1280$	$0.511873$	$1083360092/3306177$	$0.89785$	$3.66804$	$[0, 1, 0, 216, 2592]$	$y^2=x^3+x^2+216x+2592$	2.3.0.a.1, 4.12.0-4.c.1.1, 68.24.0-68.h.1.2, 168.24.0.?, 2856.48.0.?	$[]$
2856.e1	2856d2	2856.e	2856d	$2$	$2$	$ 2^{3} \cdot 3 \cdot 7 \cdot 17 $	$ 2^{11} \cdot 3^{2} \cdot 7^{2} \cdot 17^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.6.0.6	2B	$952$	$12$	$0$	$1$	$1$		$1$	$1280$	$0.368895$	$2204605874/127449$	$0.87230$	$3.66191$	$[0, 1, 0, -344, -2448]$	$y^2=x^3+x^2-344x-2448$	2.3.0.a.1, 8.6.0.b.1, 476.6.0.?, 952.12.0.?	$[]$
2856.e2	2856d1	2856.e	2856d	$2$	$2$	$ 2^{3} \cdot 3 \cdot 7 \cdot 17 $	$ - 2^{10} \cdot 3^{4} \cdot 7 \cdot 17 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.6.0.1	2B	$952$	$12$	$0$	$1$	$1$		$1$	$640$	$0.022321$	$415292/9639$	$0.84540$	$2.95765$	$[0, 1, 0, 16, -144]$	$y^2=x^3+x^2+16x-144$	2.3.0.a.1, 8.6.0.c.1, 238.6.0.?, 952.12.0.?	$[]$
2856.f1	2856b1	2856.f	2856b	$1$	$1$	$ 2^{3} \cdot 3 \cdot 7 \cdot 17 $	$ - 2^{8} \cdot 3^{11} \cdot 7^{2} \cdot 17^{3} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$102$	$2$	$0$	$0.024340533$	$1$		$18$	$4224$	$1.180925$	$135037162496/42645837339$	$1.04060$	$4.70949$	$[0, 1, 0, 679, 159051]$	$y^2=x^3+x^2+679x+159051$	102.2.0.?	$[(67, 714)]$
2856.g1	2856j1	2856.g	2856j	$1$	$1$	$ 2^{3} \cdot 3 \cdot 7 \cdot 17 $	$ - 2^{8} \cdot 3^{5} \cdot 7^{6} \cdot 17 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$102$	$2$	$0$	$0.077041609$	$1$		$10$	$1920$	$0.807953$	$721888256/486008019$	$1.02597$	$4.14730$	$[0, 1, 0, 119, 17003]$	$y^2=x^3+x^2+119x+17003$	102.2.0.?	$[(-7, 126)]$
2856.h1	2856g1	2856.h	2856g	$1$	$1$	$ 2^{3} \cdot 3 \cdot 7 \cdot 17 $	$ - 2^{11} \cdot 3^{3} \cdot 7^{3} \cdot 17 $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$2856$	$2$	$0$	$1$	$1$		$0$	$864$	$0.311499$	$-2/157437$	$1.17529$	$3.39896$	$[0, 1, 0, 0, -864]$	$y^2=x^3+x^2-864$	2856.2.0.?	$[]$
2856.i1	2856a2	2856.i	2856a	$2$	$2$	$ 2^{3} \cdot 3 \cdot 7 \cdot 17 $	$ 2^{11} \cdot 3^{8} \cdot 7^{2} \cdot 17^{6} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.6.0.6	2B	$952$	$12$	$0$	$1$	$1$		$1$	$33792$	$1.939281$	$1044942448578893426/7759962920241$	$1.00580$	$6.17243$	$[0, 1, 0, -268472, 53108208]$	$y^2=x^3+x^2-268472x+53108208$	2.3.0.a.1, 8.6.0.b.1, 476.6.0.?, 952.12.0.?	$[]$
2856.i2	2856a1	2856.i	2856a	$2$	$2$	$ 2^{3} \cdot 3 \cdot 7 \cdot 17 $	$ - 2^{10} \cdot 3^{16} \cdot 7 \cdot 17^{3} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.6.0.1	2B	$952$	$12$	$0$	$1$	$1$		$1$	$16896$	$1.592707$	$-23707171994692/1480419781911$	$1.02023$	$5.33088$	$[0, 1, 0, -6032, 1879920]$	$y^2=x^3+x^2-6032x+1879920$	2.3.0.a.1, 8.6.0.c.1, 238.6.0.?, 952.12.0.?	$[]$
2856.j1	2856i1	2856.j	2856i	$1$	$1$	$ 2^{3} \cdot 3 \cdot 7 \cdot 17 $	$ - 2^{8} \cdot 3 \cdot 7^{2} \cdot 17 $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$102$	$2$	$0$	$1$	$1$		$0$	$640$	$-0.058546$	$-307981312/2499$	$1.05298$	$3.15497$	$[0, 1, 0, -89, -357]$	$y^2=x^3+x^2-89x-357$	102.2.0.?	$[]$

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Elliptic curves over $\Q$
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Genus 2 curves over $\Q$
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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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