LMFDB - Elliptic curves over $\Q$ of conductor 26656

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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 (20 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
26656.a1	26656l2	26656.a	26656l	$2$	$2$	$ 2^{5} \cdot 7^{2} \cdot 17 $	$ 2^{9} \cdot 7^{6} \cdot 17^{2} $	$2$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.6.0.6	2B	$136$	$12$	$0$	$1.010390268$	$1$		$17$	$27648$	$0.669742$	$941192/289$	$0.97049$	$3.10759$	$[0, 1, 0, -800, 5704]$	$y^2=x^3+x^2-800x+5704$	2.3.0.a.1, 8.6.0.b.1, 68.6.0.c.1, 136.12.0.?	$[(30, 98), (6, 34)]$
26656.a2	26656l1	26656.a	26656l	$2$	$2$	$ 2^{5} \cdot 7^{2} \cdot 17 $	$ 2^{6} \cdot 7^{6} \cdot 17 $	$2$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.6.0.1	2B	$136$	$12$	$0$	$4.041561073$	$1$		$13$	$13824$	$0.323168$	$438976/17$	$0.96236$	$2.82869$	$[0, 1, 0, -310, -2136]$	$y^2=x^3+x^2-310x-2136$	2.3.0.a.1, 8.6.0.c.1, 34.6.0.a.1, 136.12.0.?	$[(-10, 8), (-11, 8)]$
26656.b1	26656c1	26656.b	26656c	$2$	$2$	$ 2^{5} \cdot 7^{2} \cdot 17 $	$ 2^{6} \cdot 7^{6} \cdot 17 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.6.0.3	2B	$952$	$48$	$0$	$1$	$1$		$1$	$11520$	$0.480935$	$19248832/17$	$0.91741$	$3.19969$	$[0, 1, 0, -1094, -14288]$	$y^2=x^3+x^2-1094x-14288$	2.3.0.a.1, 4.6.0.b.1, 34.6.0.a.1, 56.12.0-4.b.1.2, 68.12.0.e.1, $\ldots$	$[]$
26656.b2	26656c2	26656.b	26656c	$2$	$2$	$ 2^{5} \cdot 7^{2} \cdot 17 $	$ - 2^{12} \cdot 7^{6} \cdot 17^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.6.0.5	2B	$952$	$48$	$0$	$1$	$1$		$1$	$23040$	$0.827509$	$-140608/289$	$1.04671$	$3.27379$	$[0, 1, 0, -849, -20609]$	$y^2=x^3+x^2-849x-20609$	2.3.0.a.1, 4.6.0.a.1, 56.12.0-4.a.1.1, 68.12.0.d.1, 136.24.0.?, $\ldots$	$[]$
26656.c1	26656f1	26656.c	26656f	$1$	$1$	$ 2^{5} \cdot 7^{2} \cdot 17 $	$ - 2^{9} \cdot 7^{4} \cdot 17 $	$2$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$136$	$2$	$0$	$0.514597923$	$1$		$14$	$4032$	$0.084673$	$-392/17$	$0.76970$	$2.38678$	$[0, 1, 0, -16, 216]$	$y^2=x^3+x^2-16x+216$	136.2.0.?	$[(2, 14), (10, 34)]$
26656.d1	26656k2	26656.d	26656k	$2$	$2$	$ 2^{5} \cdot 7^{2} \cdot 17 $	$ 2^{9} \cdot 7^{10} \cdot 17^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.6.0.6	2B	$136$	$12$	$0$	$1$	$1$		$1$	$86016$	$1.341187$	$5177717000/693889$	$0.86902$	$3.95274$	$[0, 1, 0, -14128, -571320]$	$y^2=x^3+x^2-14128x-571320$	2.3.0.a.1, 8.6.0.b.1, 68.6.0.c.1, 136.12.0.?	$[]$
26656.d2	26656k1	26656.d	26656k	$2$	$2$	$ 2^{5} \cdot 7^{2} \cdot 17 $	$ 2^{6} \cdot 7^{8} \cdot 17 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.6.0.1	2B	$136$	$12$	$0$	$1$	$4$	$2$	$1$	$43008$	$0.994613$	$37259704000/833$	$1.04949$	$3.94234$	$[0, 1, 0, -13638, -617576]$	$y^2=x^3+x^2-13638x-617576$	2.3.0.a.1, 8.6.0.c.1, 34.6.0.a.1, 136.12.0.?	$[]$
26656.e1	26656e1	26656.e	26656e	$1$	$1$	$ 2^{5} \cdot 7^{2} \cdot 17 $	$ - 2^{9} \cdot 7^{10} \cdot 17 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$136$	$2$	$0$	$5.820290768$	$1$		$0$	$28224$	$1.057627$	$-392/17$	$0.76970$	$3.53247$	$[0, 1, 0, -800, 75676]$	$y^2=x^3+x^2-800x+75676$	136.2.0.?	$[(205/2, 3317/2)]$
26656.f1	26656d1	26656.f	26656d	$2$	$2$	$ 2^{5} \cdot 7^{2} \cdot 17 $	$ 2^{6} \cdot 7^{6} \cdot 17 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.6.0.4	2B	$136$	$12$	$0$	$3.602954951$	$1$		$3$	$5760$	$0.299479$	$216000/17$	$0.77446$	$2.75910$	$[0, 0, 0, -245, -1372]$	$y^2=x^3-245x-1372$	2.3.0.a.1, 8.6.0.d.1, 34.6.0.a.1, 136.12.0.?	$[(43, 260)]$
26656.f2	26656d2	26656.f	26656d	$2$	$2$	$ 2^{5} \cdot 7^{2} \cdot 17 $	$ - 2^{9} \cdot 7^{6} \cdot 17^{2} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.6.0.5	2B	$136$	$12$	$0$	$7.205909903$	$1$		$1$	$11520$	$0.646052$	$27000/289$	$1.24244$	$3.03994$	$[0, 0, 0, 245, -6174]$	$y^2=x^3+245x-6174$	2.3.0.a.1, 8.6.0.a.1, 68.6.0.c.1, 136.12.0.?	$[(1026/5, 33774/5)]$
26656.g1	26656g1	26656.g	26656g	$2$	$2$	$ 2^{5} \cdot 7^{2} \cdot 17 $	$ 2^{6} \cdot 7^{6} \cdot 17 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.6.0.4	2B	$136$	$12$	$0$	$1$	$1$		$1$	$5760$	$0.299479$	$216000/17$	$0.77446$	$2.75910$	$[0, 0, 0, -245, 1372]$	$y^2=x^3-245x+1372$	2.3.0.a.1, 8.6.0.d.1, 34.6.0.a.1, 136.12.0.?	$[]$
26656.g2	26656g2	26656.g	26656g	$2$	$2$	$ 2^{5} \cdot 7^{2} \cdot 17 $	$ - 2^{9} \cdot 7^{6} \cdot 17^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.6.0.5	2B	$136$	$12$	$0$	$1$	$1$		$1$	$11520$	$0.646052$	$27000/289$	$1.24244$	$3.03994$	$[0, 0, 0, 245, 6174]$	$y^2=x^3+245x+6174$	2.3.0.a.1, 8.6.0.a.1, 68.6.0.c.1, 136.12.0.?	$[]$
26656.h1	26656j2	26656.h	26656j	$2$	$2$	$ 2^{5} \cdot 7^{2} \cdot 17 $	$ 2^{9} \cdot 7^{6} \cdot 17^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.6.0.6	2B	$136$	$12$	$0$	$1$	$1$		$1$	$27648$	$0.669742$	$941192/289$	$0.97049$	$3.10759$	$[0, -1, 0, -800, -5704]$	$y^2=x^3-x^2-800x-5704$	2.3.0.a.1, 8.6.0.b.1, 68.6.0.c.1, 136.12.0.?	$[]$
26656.h2	26656j1	26656.h	26656j	$2$	$2$	$ 2^{5} \cdot 7^{2} \cdot 17 $	$ 2^{6} \cdot 7^{6} \cdot 17 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.6.0.1	2B	$136$	$12$	$0$	$1$	$1$		$1$	$13824$	$0.323168$	$438976/17$	$0.96236$	$2.82869$	$[0, -1, 0, -310, 2136]$	$y^2=x^3-x^2-310x+2136$	2.3.0.a.1, 8.6.0.c.1, 34.6.0.a.1, 136.12.0.?	$[]$
26656.i1	26656b1	26656.i	26656b	$2$	$2$	$ 2^{5} \cdot 7^{2} \cdot 17 $	$ 2^{6} \cdot 7^{6} \cdot 17 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.6.0.3	2B	$952$	$48$	$0$	$1$	$1$		$1$	$11520$	$0.480935$	$19248832/17$	$0.91741$	$3.19969$	$[0, -1, 0, -1094, 14288]$	$y^2=x^3-x^2-1094x+14288$	2.3.0.a.1, 4.6.0.b.1, 34.6.0.a.1, 56.12.0-4.b.1.2, 68.12.0.e.1, $\ldots$	$[]$
26656.i2	26656b2	26656.i	26656b	$2$	$2$	$ 2^{5} \cdot 7^{2} \cdot 17 $	$ - 2^{12} \cdot 7^{6} \cdot 17^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.6.0.5	2B	$952$	$48$	$0$	$1$	$1$		$1$	$23040$	$0.827509$	$-140608/289$	$1.04671$	$3.27379$	$[0, -1, 0, -849, 20609]$	$y^2=x^3-x^2-849x+20609$	2.3.0.a.1, 4.6.0.a.1, 56.12.0-4.a.1.1, 68.12.0.d.1, 136.24.0.?, $\ldots$	$[]$
26656.j1	26656a1	26656.j	26656a	$1$	$1$	$ 2^{5} \cdot 7^{2} \cdot 17 $	$ - 2^{9} \cdot 7^{4} \cdot 17 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$136$	$2$	$0$	$8.224536247$	$1$		$0$	$4032$	$0.084673$	$-392/17$	$0.76970$	$2.38678$	$[0, -1, 0, -16, -216]$	$y^2=x^3-x^2-16x-216$	136.2.0.?	$[(3717/2, 226491/2)]$
26656.k1	26656h2	26656.k	26656h	$2$	$2$	$ 2^{5} \cdot 7^{2} \cdot 17 $	$ 2^{9} \cdot 7^{10} \cdot 17^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.6.0.6	2B	$136$	$12$	$0$	$1$	$1$		$1$	$86016$	$1.341187$	$5177717000/693889$	$0.86902$	$3.95274$	$[0, -1, 0, -14128, 571320]$	$y^2=x^3-x^2-14128x+571320$	2.3.0.a.1, 8.6.0.b.1, 68.6.0.c.1, 136.12.0.?	$[]$
26656.k2	26656h1	26656.k	26656h	$2$	$2$	$ 2^{5} \cdot 7^{2} \cdot 17 $	$ 2^{6} \cdot 7^{8} \cdot 17 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.6.0.1	2B	$136$	$12$	$0$	$1$	$1$		$1$	$43008$	$0.994613$	$37259704000/833$	$1.04949$	$3.94234$	$[0, -1, 0, -13638, 617576]$	$y^2=x^3-x^2-13638x+617576$	2.3.0.a.1, 8.6.0.c.1, 34.6.0.a.1, 136.12.0.?	$[]$
26656.l1	26656i1	26656.l	26656i	$1$	$1$	$ 2^{5} \cdot 7^{2} \cdot 17 $	$ - 2^{9} \cdot 7^{10} \cdot 17 $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$136$	$2$	$0$	$1$	$4$	$2$	$0$	$28224$	$1.057627$	$-392/17$	$0.76970$	$3.53247$	$[0, -1, 0, -800, -75676]$	$y^2=x^3-x^2-800x-75676$	136.2.0.?	$[]$

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Elliptic 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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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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