LMFDB - Elliptic curves over $\Q$ of conductor 1760

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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	Manin constant

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Results (26 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	$Ш_{\textrm{an}}$	Integral points	Modular degree	Faltings height	j-invariant	$abc$ quality	Szpiro ratio	Weierstrass coefficients	Weierstrass equation	mod-$m$ images	MW-generators	Manin constant
1760.a1	1760i1	1760.a	1760i	$2$	$2$	$ 2^{5} \cdot 5 \cdot 11 $	$ 2^{6} \cdot 5^{3} \cdot 11^{4} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.6.0.3	2B	$440$	$48$	$0$	$0.641719151$	$1$	$7$	$384$	$0.239909$	$3484156096/1830125$	$0.94957$	$3.49661$	$[0, 1, 0, -126, 124]$	$y^2=x^3+x^2-126x+124$	2.3.0.a.1, 4.6.0.b.1, 10.6.0.a.1, 20.12.0.e.1, 40.24.0.br.1, $\ldots$	$[(12, 22)]$	$1$
1760.a2	1760i2	1760.a	1760i	$2$	$2$	$ 2^{5} \cdot 5 \cdot 11 $	$ - 2^{12} \cdot 5^{6} \cdot 11^{2} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.6.0.5	2B	$440$	$48$	$0$	$1.283438302$	$1$	$5$	$768$	$0.586482$	$2961169856/1890625$	$0.95017$	$4.03136$	$[0, 1, 0, 479, 1455]$	$y^2=x^3+x^2+479x+1455$	2.3.0.a.1, 4.6.0.a.1, 20.12.0.d.1, 40.24.0.t.1, 88.12.0.?, $\ldots$	$[(1, 44)]$	$1$
1760.b1	1760h2	1760.b	1760h	$2$	$2$	$ 2^{5} \cdot 5 \cdot 11 $	$ 2^{12} \cdot 5^{2} \cdot 11 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$220$	$12$	$0$	$0.381631899$	$1$	$11$	$384$	$-0.069197$	$7529536/275$	$0.95985$	$3.23189$	$[0, 1, 0, -65, 175]$	$y^2=x^3+x^2-65x+175$	2.3.0.a.1, 20.6.0.c.1, 44.6.0.a.1, 220.12.0.?	$[(3, 4)]$	$1$
1760.b2	1760h1	1760.b	1760h	$2$	$2$	$ 2^{5} \cdot 5 \cdot 11 $	$ 2^{6} \cdot 5 \cdot 11^{2} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$220$	$12$	$0$	$0.763263799$	$1$	$5$	$192$	$-0.415771$	$1906624/605$	$0.81759$	$2.49158$	$[0, 1, 0, -10, -12]$	$y^2=x^3+x^2-10x-12$	2.3.0.a.1, 10.6.0.a.1, 44.6.0.b.1, 220.12.0.?	$[(-2, 2)]$	$1$
1760.c1	1760l2	1760.c	1760l	$2$	$2$	$ 2^{5} \cdot 5 \cdot 11 $	$ 2^{12} \cdot 5^{10} \cdot 11 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$220$	$12$	$0$	$0.485665542$	$1$	$9$	$1920$	$0.991124$	$2036792051776/107421875$	$1.01506$	$4.90564$	$[0, 1, 0, -4225, 99375]$	$y^2=x^3+x^2-4225x+99375$	2.3.0.a.1, 20.6.0.c.1, 44.6.0.a.1, 220.12.0.?	$[(25, 100)]$	$1$
1760.c2	1760l1	1760.c	1760l	$2$	$2$	$ 2^{5} \cdot 5 \cdot 11 $	$ 2^{6} \cdot 5^{5} \cdot 11^{2} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$220$	$12$	$0$	$0.242832771$	$1$	$9$	$960$	$0.644550$	$125330290485184/378125$	$1.03653$	$4.90038$	$[0, 1, 0, -4170, 102268]$	$y^2=x^3+x^2-4170x+102268$	2.3.0.a.1, 10.6.0.a.1, 44.6.0.b.1, 220.12.0.?	$[(36, 10)]$	$1$
1760.d1	1760a1	1760.d	1760a	$1$	$1$	$ 2^{5} \cdot 5 \cdot 11 $	$ - 2^{9} \cdot 5^{7} \cdot 11 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$440$	$2$	$0$	$3.918139026$	$1$	$2$	$1120$	$0.685399$	$-7458308028872/859375$	$0.95809$	$4.80109$	$[0, -1, 0, -3256, -70444]$	$y^2=x^3-x^2-3256x-70444$	440.2.0.?	$[(68, 134)]$	$1$
1760.e1	1760d1	1760.e	1760d	$1$	$1$	$ 2^{5} \cdot 5 \cdot 11 $	$ - 2^{9} \cdot 5^{5} \cdot 11^{7} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$440$	$2$	$0$	$1$	$1$	$0$	$3360$	$1.271381$	$-5833944216008/60897409375$	$1.00755$	$5.16247$	$[0, -1, 0, -3000, -275000]$	$y^2=x^3-x^2-3000x-275000$	440.2.0.?	$[ ]$	$1$
1760.f1	1760m1	1760.f	1760m	$1$	$1$	$ 2^{5} \cdot 5 \cdot 11 $	$ - 2^{9} \cdot 5 \cdot 11 $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$440$	$2$	$0$	$1$	$1$	$0$	$96$	$-0.467276$	$-8/55$	$0.89440$	$2.36857$	$[0, -1, 0, 0, -8]$	$y^2=x^3-x^2-8$	440.2.0.?	$[ ]$	$1$
1760.g1	1760j2	1760.g	1760j	$4$	$4$	$ 2^{5} \cdot 5 \cdot 11 $	$ 2^{9} \cdot 5 \cdot 11 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.12.0.6	2B	$440$	$48$	$0$	$6.088936818$	$1$	$1$	$256$	$0.132576$	$43688592648/55$	$0.95203$	$4.11326$	$[0, 0, 0, -587, -5474]$	$y^2=x^3-587x-5474$	2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.5, 40.24.0-40.y.1.13, 44.12.0-4.c.1.2, $\ldots$	$[(385/2, 7287/2)]$	$1$
1760.g2	1760j3	1760.g	1760j	$4$	$4$	$ 2^{5} \cdot 5 \cdot 11 $	$ 2^{12} \cdot 5^{4} \cdot 11 $	$1$	$\Z/4\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.12.0.7	2B	$440$	$48$	$0$	$1.522234204$	$1$	$9$	$256$	$0.132576$	$21024576/6875$	$0.86453$	$3.36929$	$[0, 0, 0, -92, 224]$	$y^2=x^3-92x+224$	2.3.0.a.1, 4.12.0-4.c.1.1, 40.24.0-40.y.1.2, 44.24.0-44.h.1.2, 440.48.0.?	$[(13, 35)]$	$1$
1760.g3	1760j1	1760.g	1760j	$4$	$4$	$ 2^{5} \cdot 5 \cdot 11 $	$ 2^{6} \cdot 5^{2} \cdot 11^{2} $	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.12.0.1	2Cs	$440$	$48$	$0$	$3.044468409$	$1$	$5$	$128$	$-0.213998$	$87528384/3025$	$0.95393$	$3.00363$	$[0, 0, 0, -37, -84]$	$y^2=x^3-37x-84$	2.6.0.a.1, 4.12.0-2.a.1.1, 40.24.0-40.b.1.4, 44.24.0-44.a.1.1, 440.48.0.?	$[(95, 924)]$	$1$
1760.g4	1760j4	1760.g	1760j	$4$	$4$	$ 2^{5} \cdot 5 \cdot 11 $	$ - 2^{9} \cdot 5 \cdot 11^{4} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.12.0.8	2B	$440$	$48$	$0$	$6.088936818$	$1$	$1$	$256$	$0.132576$	$474552/73205$	$1.28812$	$3.33067$	$[0, 0, 0, 13, -294]$	$y^2=x^3+13x-294$	2.3.0.a.1, 4.12.0-4.c.1.2, 40.24.0-40.s.1.1, 88.24.0.?, 440.48.0.?	$[(265/6, 3059/6)]$	$1$
1760.h1	1760f3	1760.h	1760f	$4$	$4$	$ 2^{5} \cdot 5 \cdot 11 $	$ 2^{9} \cdot 5 \cdot 11 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.12.0.6	2B	$440$	$48$	$0$	$3.755027704$	$1$	$3$	$256$	$0.132576$	$43688592648/55$	$0.95203$	$4.11326$	$[0, 0, 0, -587, 5474]$	$y^2=x^3-587x+5474$	2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.5, 40.24.0-40.y.1.5, 44.12.0-4.c.1.1, $\ldots$	$[(50, 318)]$	$1$
1760.h2	1760f2	1760.h	1760f	$4$	$4$	$ 2^{5} \cdot 5 \cdot 11 $	$ 2^{12} \cdot 5^{4} \cdot 11 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.12.0.8	2B	$440$	$48$	$0$	$0.938756926$	$1$	$5$	$256$	$0.132576$	$21024576/6875$	$0.86453$	$3.36929$	$[0, 0, 0, -92, -224]$	$y^2=x^3-92x-224$	2.3.0.a.1, 4.12.0-4.c.1.2, 40.24.0-40.y.1.10, 44.24.0-44.h.1.1, 440.48.0.?	$[(-3, 5)]$	$1$
1760.h3	1760f1	1760.h	1760f	$4$	$4$	$ 2^{5} \cdot 5 \cdot 11 $	$ 2^{6} \cdot 5^{2} \cdot 11^{2} $	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.12.0.1	2Cs	$440$	$48$	$0$	$1.877513852$	$1$	$7$	$128$	$-0.213998$	$87528384/3025$	$0.95393$	$3.00363$	$[0, 0, 0, -37, 84]$	$y^2=x^3-37x+84$	2.6.0.a.1, 4.12.0-2.a.1.1, 40.24.0-40.b.1.1, 44.24.0-44.a.1.2, 440.48.0.?	$[(-5, 12)]$	$1$
1760.h4	1760f4	1760.h	1760f	$4$	$4$	$ 2^{5} \cdot 5 \cdot 11 $	$ - 2^{9} \cdot 5 \cdot 11^{4} $	$1$	$\Z/4\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.12.0.7	2B	$440$	$48$	$0$	$3.755027704$	$1$	$3$	$256$	$0.132576$	$474552/73205$	$1.28812$	$3.33067$	$[0, 0, 0, 13, 294]$	$y^2=x^3+13x+294$	2.3.0.a.1, 4.12.0-4.c.1.1, 40.24.0-40.s.1.3, 88.24.0.?, 440.48.0.?	$[(-15/2, 111/2)]$	$1$
1760.i1	1760c1	1760.i	1760c	$1$	$1$	$ 2^{5} \cdot 5 \cdot 11 $	$ - 2^{9} \cdot 5^{7} \cdot 11 $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$440$	$2$	$0$	$1$	$1$	$0$	$1120$	$0.685399$	$-7458308028872/859375$	$0.95809$	$4.80109$	$[0, 1, 0, -3256, 70444]$	$y^2=x^3+x^2-3256x+70444$	440.2.0.?	$[ ]$	$1$
1760.j1	1760k1	1760.j	1760k	$1$	$1$	$ 2^{5} \cdot 5 \cdot 11 $	$ - 2^{9} \cdot 5 \cdot 11 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$440$	$2$	$0$	$0.540154219$	$1$	$4$	$96$	$-0.467276$	$-8/55$	$0.89440$	$2.36857$	$[0, 1, 0, 0, 8]$	$y^2=x^3+x^2+8$	440.2.0.?	$[(-2, 2)]$	$1$
1760.k1	1760g1	1760.k	1760g	$1$	$1$	$ 2^{5} \cdot 5 \cdot 11 $	$ - 2^{9} \cdot 5^{5} \cdot 11^{7} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$440$	$2$	$0$	$0.085014604$	$1$	$8$	$3360$	$1.271381$	$-5833944216008/60897409375$	$1.00755$	$5.16247$	$[0, 1, 0, -3000, 275000]$	$y^2=x^3+x^2-3000x+275000$	440.2.0.?	$[(-50, 550)]$	$1$
1760.l1	1760b1	1760.l	1760b	$2$	$2$	$ 2^{5} \cdot 5 \cdot 11 $	$ 2^{6} \cdot 5^{3} \cdot 11^{4} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.6.0.3	2B	$440$	$48$	$0$	$2.311299198$	$1$	$3$	$384$	$0.239909$	$3484156096/1830125$	$0.94957$	$3.49661$	$[0, -1, 0, -126, -124]$	$y^2=x^3-x^2-126x-124$	2.3.0.a.1, 4.6.0.b.1, 10.6.0.a.1, 20.12.0.e.1, 40.24.0.br.1, $\ldots$	$[(-10, 6)]$	$1$
1760.l2	1760b2	1760.l	1760b	$2$	$2$	$ 2^{5} \cdot 5 \cdot 11 $	$ - 2^{12} \cdot 5^{6} \cdot 11^{2} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.6.0.5	2B	$440$	$48$	$0$	$1.155649599$	$1$	$5$	$768$	$0.586482$	$2961169856/1890625$	$0.95017$	$4.03136$	$[0, -1, 0, 479, -1455]$	$y^2=x^3-x^2+479x-1455$	2.3.0.a.1, 4.6.0.a.1, 20.12.0.d.1, 40.24.0.t.1, 88.12.0.?, $\ldots$	$[(21, 132)]$	$1$
1760.m1	1760n2	1760.m	1760n	$2$	$2$	$ 2^{5} \cdot 5 \cdot 11 $	$ 2^{12} \cdot 5^{10} \cdot 11 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$220$	$12$	$0$	$1$	$1$	$1$	$1920$	$0.991124$	$2036792051776/107421875$	$1.01506$	$4.90564$	$[0, -1, 0, -4225, -99375]$	$y^2=x^3-x^2-4225x-99375$	2.3.0.a.1, 20.6.0.c.1, 44.6.0.a.1, 220.12.0.?	$[ ]$	$1$
1760.m2	1760n1	1760.m	1760n	$2$	$2$	$ 2^{5} \cdot 5 \cdot 11 $	$ 2^{6} \cdot 5^{5} \cdot 11^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$220$	$12$	$0$	$1$	$1$	$1$	$960$	$0.644550$	$125330290485184/378125$	$1.03653$	$4.90038$	$[0, -1, 0, -4170, -102268]$	$y^2=x^3-x^2-4170x-102268$	2.3.0.a.1, 10.6.0.a.1, 44.6.0.b.1, 220.12.0.?	$[ ]$	$1$
1760.n1	1760e2	1760.n	1760e	$2$	$2$	$ 2^{5} \cdot 5 \cdot 11 $	$ 2^{12} \cdot 5^{2} \cdot 11 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$220$	$12$	$0$	$1$	$1$	$1$	$384$	$-0.069197$	$7529536/275$	$0.95985$	$3.23189$	$[0, -1, 0, -65, -175]$	$y^2=x^3-x^2-65x-175$	2.3.0.a.1, 20.6.0.c.1, 44.6.0.a.1, 220.12.0.?	$[ ]$	$1$
1760.n2	1760e1	1760.n	1760e	$2$	$2$	$ 2^{5} \cdot 5 \cdot 11 $	$ 2^{6} \cdot 5 \cdot 11^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$220$	$12$	$0$	$1$	$1$	$1$	$192$	$-0.415771$	$1906624/605$	$0.81759$	$2.49158$	$[0, -1, 0, -10, 12]$	$y^2=x^3-x^2-10x+12$	2.3.0.a.1, 10.6.0.a.1, 44.6.0.b.1, 220.12.0.?	$[ ]$	$1$

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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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