LMFDB - Elliptic curves over $\Q$ of conductor 1120

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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 (28 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
1120.a1	1120j1	1120.a	1120j	$1$	$1$	$ 2^{5} \cdot 5 \cdot 7 $	$ - 2^{12} \cdot 5^{11} \cdot 7^{5} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$70$	$2$	$0$	$1$	$1$		$0$	$10560$	$1.665676$	$722603599520256/820654296875$	$1.08491$	$6.05770$	$[0, 0, 0, 29912, -1953488]$	$y^2=x^3+29912x-1953488$	70.2.0.a.1	$[]$
1120.b1	1120n1	1120.b	1120n	$1$	$1$	$ 2^{5} \cdot 5 \cdot 7 $	$ - 2^{12} \cdot 5 \cdot 7 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$70$	$2$	$0$	$0.373794789$	$1$		$6$	$192$	$-0.326784$	$13824/35$	$0.66491$	$2.71587$	$[0, 0, 0, 8, 16]$	$y^2=x^3+8x+16$	70.2.0.a.1	$[(0, 4)]$
1120.c1	1120d1	1120.c	1120d	$1$	$1$	$ 2^{5} \cdot 5 \cdot 7 $	$ - 2^{12} \cdot 5^{3} \cdot 7 $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$70$	$2$	$0$	$1$	$1$		$0$	$192$	$0.169222$	$-738763264/875$	$0.89330$	$4.09343$	$[0, -1, 0, -301, -1915]$	$y^2=x^3-x^2-301x-1915$	70.2.0.a.1	$[]$
1120.d1	1120k1	1120.d	1120k	$1$	$1$	$ 2^{5} \cdot 5 \cdot 7 $	$ - 2^{12} \cdot 5 \cdot 7^{3} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$70$	$2$	$0$	$0.159593369$	$1$		$8$	$192$	$0.029607$	$-6229504/1715$	$0.82351$	$3.46837$	$[0, -1, 0, -61, 245]$	$y^2=x^3-x^2-61x+245$	70.2.0.a.1	$[(11, 28)]$
1120.e1	1120h1	1120.e	1120h	$1$	$1$	$ 2^{5} \cdot 5 \cdot 7 $	$ - 2^{12} \cdot 5^{3} \cdot 7^{7} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$70$	$2$	$0$	$0.063898324$	$1$		$10$	$1344$	$0.924726$	$-88478050816/102942875$	$0.97384$	$4.93170$	$[0, -1, 0, -1485, 38725]$	$y^2=x^3-x^2-1485x+38725$	70.2.0.a.1	$[(15, 140)]$
1120.f1	1120g1	1120.f	1120g	$1$	$1$	$ 2^{5} \cdot 5 \cdot 7 $	$ - 2^{12} \cdot 5^{5} \cdot 7 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$70$	$2$	$0$	$0.162019727$	$1$		$6$	$320$	$0.206293$	$1124864/21875$	$0.91387$	$3.66544$	$[0, -1, 0, 35, 437]$	$y^2=x^3-x^2+35x+437$	70.2.0.a.1	$[(-1, 20)]$
1120.g1	1120i2	1120.g	1120i	$4$	$4$	$ 2^{5} \cdot 5 \cdot 7 $	$ 2^{12} \cdot 5 \cdot 7 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.12.0.12	2B	$280$	$48$	$0$	$1$	$1$		$1$	$192$	$-0.010833$	$179406144/35$	$0.91443$	$3.89155$	$[0, 0, 0, -188, -992]$	$y^2=x^3-188x-992$	2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.2, 20.12.0-4.c.1.1, 28.12.0-4.c.1.2, $\ldots$	$[]$
1120.g2	1120i3	1120.g	1120i	$4$	$4$	$ 2^{5} \cdot 5 \cdot 7 $	$ 2^{9} \cdot 5^{4} \cdot 7 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.12.0.8	2B	$280$	$48$	$0$	$1$	$1$		$1$	$192$	$-0.010833$	$123505992/4375$	$0.97359$	$3.54221$	$[0, 0, 0, -83, 282]$	$y^2=x^3-83x+282$	2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.4, 28.12.0-4.c.1.1, 40.24.0-40.y.1.14, $\ldots$	$[]$
1120.g3	1120i1	1120.g	1120i	$4$	$4$	$ 2^{5} \cdot 5 \cdot 7 $	$ 2^{6} \cdot 5^{2} \cdot 7^{2} $	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.12.0.1	2Cs	$280$	$48$	$0$	$1$	$1$		$3$	$96$	$-0.357407$	$3796416/1225$	$0.97255$	$2.75007$	$[0, 0, 0, -13, -12]$	$y^2=x^3-13x-12$	2.6.0.a.1, 8.12.0-2.a.1.1, 20.12.0-2.a.1.1, 28.12.0-2.a.1.1, 40.24.0-40.b.1.2, $\ldots$	$[]$
1120.g4	1120i4	1120.g	1120i	$4$	$4$	$ 2^{5} \cdot 5 \cdot 7 $	$ - 2^{9} \cdot 5 \cdot 7^{4} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.12.0.7	2B	$280$	$48$	$0$	$1$	$1$		$1$	$192$	$-0.010833$	$10941048/12005$	$0.90537$	$3.19699$	$[0, 0, 0, 37, -82]$	$y^2=x^3+37x-82$	2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.3, 20.12.0-4.c.1.2, 40.24.0-40.s.1.2, $\ldots$	$[]$
1120.h1	1120c3	1120.h	1120c	$4$	$4$	$ 2^{5} \cdot 5 \cdot 7 $	$ 2^{12} \cdot 5 \cdot 7 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.12.0.12	2B	$280$	$48$	$0$	$1$	$1$		$1$	$192$	$-0.010833$	$179406144/35$	$0.91443$	$3.89155$	$[0, 0, 0, -188, 992]$	$y^2=x^3-188x+992$	2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.2, 20.12.0-4.c.1.2, 28.12.0-4.c.1.1, $\ldots$	$[]$
1120.h2	1120c2	1120.h	1120c	$4$	$4$	$ 2^{5} \cdot 5 \cdot 7 $	$ 2^{9} \cdot 5^{4} \cdot 7 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.12.0.7	2B	$280$	$48$	$0$	$1$	$1$		$1$	$192$	$-0.010833$	$123505992/4375$	$0.97359$	$3.54221$	$[0, 0, 0, -83, -282]$	$y^2=x^3-83x-282$	2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.3, 28.12.0-4.c.1.2, 40.24.0-40.y.1.6, $\ldots$	$[]$
1120.h3	1120c1	1120.h	1120c	$4$	$4$	$ 2^{5} \cdot 5 \cdot 7 $	$ 2^{6} \cdot 5^{2} \cdot 7^{2} $	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.12.0.1	2Cs	$280$	$48$	$0$	$1$	$1$		$3$	$96$	$-0.357407$	$3796416/1225$	$0.97255$	$2.75007$	$[0, 0, 0, -13, 12]$	$y^2=x^3-13x+12$	2.6.0.a.1, 8.12.0-2.a.1.1, 20.12.0-2.a.1.1, 28.12.0-2.a.1.1, 40.24.0-40.b.1.3, $\ldots$	$[]$
1120.h4	1120c4	1120.h	1120c	$4$	$4$	$ 2^{5} \cdot 5 \cdot 7 $	$ - 2^{9} \cdot 5 \cdot 7^{4} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.12.0.8	2B	$280$	$48$	$0$	$1$	$1$		$1$	$192$	$-0.010833$	$10941048/12005$	$0.90537$	$3.19699$	$[0, 0, 0, 37, 82]$	$y^2=x^3+37x+82$	2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.4, 20.12.0-4.c.1.1, 40.24.0-40.s.1.4, $\ldots$	$[]$
1120.i1	1120l3	1120.i	1120l	$4$	$4$	$ 2^{5} \cdot 5 \cdot 7 $	$ 2^{9} \cdot 5^{2} \cdot 7^{2} $	$1$	$\Z/4\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.48.0.170	2B	$560$	$192$	$3$	$2.683418990$	$1$		$5$	$768$	$0.776027$	$481927184300808/1225$	$1.08132$	$5.70384$	$[0, 0, 0, -13067, 574926]$	$y^2=x^3-13067x+574926$	2.3.0.a.1, 4.12.0-4.c.1.1, 8.48.0-8.y.1.3, 80.96.0.?, 112.96.1.?, $\ldots$	$[(-103, 910)]$
1120.i2	1120l2	1120.i	1120l	$4$	$4$	$ 2^{5} \cdot 5 \cdot 7 $	$ 2^{9} \cdot 5^{2} \cdot 7^{8} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.48.0.185	2B	$560$	$192$	$3$	$2.683418990$	$1$		$3$	$768$	$0.776027$	$262389836808/144120025$	$1.06498$	$4.63339$	$[0, 0, 0, -1067, 3026]$	$y^2=x^3-1067x+3026$	2.3.0.a.1, 4.12.0-4.c.1.2, 8.48.0-8.y.1.4, 80.96.0.?, 112.96.1.?, $\ldots$	$[(2, 30)]$
1120.i3	1120l1	1120.i	1120l	$4$	$4$	$ 2^{5} \cdot 5 \cdot 7 $	$ 2^{6} \cdot 5^{4} \cdot 7^{4} $	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.48.0.37	2Cs	$560$	$192$	$3$	$1.341709495$	$1$		$9$	$384$	$0.429453$	$942344950464/1500625$	$1.16391$	$4.51932$	$[0, 0, 0, -817, 8976]$	$y^2=x^3-817x+8976$	2.6.0.a.1, 4.24.0-4.a.1.1, 8.48.0-8.a.1.1, 56.96.1-56.c.1.2, 80.96.0.?, $\ldots$	$[(7, 60)]$
1120.i4	1120l4	1120.i	1120l	$4$	$4$	$ 2^{5} \cdot 5 \cdot 7 $	$ - 2^{12} \cdot 5^{8} \cdot 7^{2} $	$1$	$\Z/4\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.48.0.62	2B	$560$	$192$	$3$	$0.670854747$	$1$		$13$	$768$	$0.776027$	$-5053029696/19140625$	$1.12450$	$4.65483$	$[0, 0, 0, -572, 14464]$	$y^2=x^3-572x+14464$	2.3.0.a.1, 4.24.0-4.d.1.1, 8.48.0-8.x.1.1, 56.96.1-56.ep.1.2, 80.96.0.?, $\ldots$	$[(58, 420)]$
1120.j1	1120o2	1120.j	1120o	$4$	$4$	$ 2^{5} \cdot 5 \cdot 7 $	$ 2^{9} \cdot 5^{2} \cdot 7^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.48.0.185	2B	$560$	$192$	$3$	$1$	$4$	$2$	$1$	$768$	$0.776027$	$481927184300808/1225$	$1.08132$	$5.70384$	$[0, 0, 0, -13067, -574926]$	$y^2=x^3-13067x-574926$	2.3.0.a.1, 4.12.0-4.c.1.2, 8.48.0-8.y.1.4, 80.96.0.?, 112.96.1.?, $\ldots$	$[]$
1120.j2	1120o3	1120.j	1120o	$4$	$4$	$ 2^{5} \cdot 5 \cdot 7 $	$ 2^{9} \cdot 5^{2} \cdot 7^{8} $	$0$	$\Z/4\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.48.0.170	2B	$560$	$192$	$3$	$1$	$1$		$3$	$768$	$0.776027$	$262389836808/144120025$	$1.06498$	$4.63339$	$[0, 0, 0, -1067, -3026]$	$y^2=x^3-1067x-3026$	2.3.0.a.1, 4.12.0-4.c.1.1, 8.48.0-8.y.1.3, 80.96.0.?, 112.96.1.?, $\ldots$	$[]$
1120.j3	1120o1	1120.j	1120o	$4$	$4$	$ 2^{5} \cdot 5 \cdot 7 $	$ 2^{6} \cdot 5^{4} \cdot 7^{4} $	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.48.0.37	2Cs	$560$	$192$	$3$	$1$	$1$		$3$	$384$	$0.429453$	$942344950464/1500625$	$1.16391$	$4.51932$	$[0, 0, 0, -817, -8976]$	$y^2=x^3-817x-8976$	2.6.0.a.1, 4.24.0-4.a.1.1, 8.48.0-8.a.1.1, 56.96.1-56.c.1.2, 80.96.0.?, $\ldots$	$[]$
1120.j4	1120o4	1120.j	1120o	$4$	$4$	$ 2^{5} \cdot 5 \cdot 7 $	$ - 2^{12} \cdot 5^{8} \cdot 7^{2} $	$0$	$\Z/4\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.48.0.62	2B	$560$	$192$	$3$	$1$	$1$		$3$	$768$	$0.776027$	$-5053029696/19140625$	$1.12450$	$4.65483$	$[0, 0, 0, -572, -14464]$	$y^2=x^3-572x-14464$	2.3.0.a.1, 4.24.0-4.d.1.1, 8.48.0-8.x.1.1, 56.96.1-56.ep.1.2, 80.96.0.?, $\ldots$	$[]$
1120.k1	1120a1	1120.k	1120a	$1$	$1$	$ 2^{5} \cdot 5 \cdot 7 $	$ - 2^{12} \cdot 5^{3} \cdot 7 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$70$	$2$	$0$	$0.540824968$	$1$		$4$	$192$	$0.169222$	$-738763264/875$	$0.89330$	$4.09343$	$[0, 1, 0, -301, 1915]$	$y^2=x^3+x^2-301x+1915$	70.2.0.a.1	$[(9, 4)]$
1120.l1	1120b1	1120.l	1120b	$1$	$1$	$ 2^{5} \cdot 5 \cdot 7 $	$ - 2^{12} \cdot 5 \cdot 7^{3} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$70$	$2$	$0$	$1.603779247$	$1$		$4$	$192$	$0.029607$	$-6229504/1715$	$0.82351$	$3.46837$	$[0, 1, 0, -61, -245]$	$y^2=x^3+x^2-61x-245$	70.2.0.a.1	$[(9, 4)]$
1120.m1	1120m1	1120.m	1120m	$1$	$1$	$ 2^{5} \cdot 5 \cdot 7 $	$ - 2^{12} \cdot 5^{5} \cdot 7 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$70$	$2$	$0$	$0.306406935$	$1$		$4$	$320$	$0.206293$	$1124864/21875$	$0.91387$	$3.66544$	$[0, 1, 0, 35, -437]$	$y^2=x^3+x^2+35x-437$	70.2.0.a.1	$[(21, 100)]$
1120.n1	1120f1	1120.n	1120f	$1$	$1$	$ 2^{5} \cdot 5 \cdot 7 $	$ - 2^{12} \cdot 5^{3} \cdot 7^{7} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$70$	$2$	$0$	$1$	$1$		$0$	$1344$	$0.924726$	$-88478050816/102942875$	$0.97384$	$4.93170$	$[0, 1, 0, -1485, -38725]$	$y^2=x^3+x^2-1485x-38725$	70.2.0.a.1	$[]$
1120.o1	1120e1	1120.o	1120e	$1$	$1$	$ 2^{5} \cdot 5 \cdot 7 $	$ - 2^{12} \cdot 5^{11} \cdot 7^{5} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$70$	$2$	$0$	$1$	$1$		$0$	$10560$	$1.665676$	$722603599520256/820654296875$	$1.08491$	$6.05770$	$[0, 0, 0, 29912, 1953488]$	$y^2=x^3+29912x+1953488$	70.2.0.a.1	$[]$
1120.p1	1120p1	1120.p	1120p	$1$	$1$	$ 2^{5} \cdot 5 \cdot 7 $	$ - 2^{12} \cdot 5 \cdot 7 $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$70$	$2$	$0$	$1$	$1$		$0$	$192$	$-0.326784$	$13824/35$	$0.66491$	$2.71587$	$[0, 0, 0, 8, -16]$	$y^2=x^3+8x-16$	70.2.0.a.1	$[]$

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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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