LMFDB - Elliptic curves over $\Q$ of conductor 1056

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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	$Ш_{\textrm{an}}$	Integral points	Modular degree	Faltings height	j-invariant	$abc$ quality	Szpiro ratio	Weierstrass coefficients	Weierstrass equation	mod-$m$ images	MW-generators
1056.a1	1056h1	1056.a	1056h	$2$	$2$	$ 2^{5} \cdot 3 \cdot 11 $	$ 2^{6} \cdot 3 \cdot 11 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.6.0.4	2B	$264$	$12$	$0$	$0.830916017$	$1$	$5$	$96$	$-0.565074$	$1906624/33$	$0.85378$	$2.67439$	$[0, -1, 0, -10, 16]$	$y^2=x^3-x^2-10x+16$	2.3.0.a.1, 8.6.0.d.1, 66.6.0.a.1, 264.12.0.?	$[(0, 4)]$
1056.a2	1056h2	1056.a	1056h	$2$	$2$	$ 2^{5} \cdot 3 \cdot 11 $	$ - 2^{9} \cdot 3^{2} \cdot 11^{2} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.6.0.5	2B	$264$	$12$	$0$	$0.415458008$	$1$	$9$	$192$	$-0.218501$	$-8/1089$	$1.19226$	$2.97118$	$[0, -1, 0, 0, 36]$	$y^2=x^3-x^2+36$	2.3.0.a.1, 8.6.0.a.1, 132.6.0.?, 264.12.0.?	$[(0, 6)]$
1056.b1	1056c2	1056.b	1056c	$4$	$4$	$ 2^{5} \cdot 3 \cdot 11 $	$ 2^{12} \cdot 3^{2} \cdot 11 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.24.0.63	2B	$88$	$48$	$0$	$1$	$1$	$1$	$256$	$0.185220$	$4004529472/99$	$0.97266$	$4.37050$	$[0, -1, 0, -529, -4511]$	$y^2=x^3-x^2-529x-4511$	2.3.0.a.1, 4.12.0-4.c.1.2, 8.24.0-8.m.1.3, 44.24.0-44.h.1.1, 88.48.0.?	$[]$
1056.b2	1056c3	1056.b	1056c	$4$	$4$	$ 2^{5} \cdot 3 \cdot 11 $	$ 2^{9} \cdot 3^{8} \cdot 11 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.24.0.104	2B	$88$	$48$	$0$	$1$	$1$	$1$	$256$	$0.185220$	$649461896/72171$	$0.94560$	$3.81055$	$[0, -1, 0, -144, 648]$	$y^2=x^3-x^2-144x+648$	2.3.0.a.1, 4.6.0.c.1, 8.24.0-8.m.1.7, 44.12.0-4.c.1.1, 88.48.0.?	$[]$
1056.b3	1056c1	1056.b	1056c	$4$	$4$	$ 2^{5} \cdot 3 \cdot 11 $	$ 2^{6} \cdot 3^{4} \cdot 11^{2} $	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.24.0.3	2Cs	$88$	$48$	$0$	$1$	$1$	$3$	$128$	$-0.161353$	$69934528/9801$	$0.93038$	$3.19178$	$[0, -1, 0, -34, -56]$	$y^2=x^3-x^2-34x-56$	2.6.0.a.1, 4.12.0-2.a.1.1, 8.24.0-8.b.1.1, 44.24.0-44.a.1.2, 88.48.0.?	$[]$
1056.b4	1056c4	1056.b	1056c	$4$	$4$	$ 2^{5} \cdot 3 \cdot 11 $	$ - 2^{9} \cdot 3^{2} \cdot 11^{4} $	$0$	$\Z/4\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.24.0.48	2B	$88$	$48$	$0$	$1$	$1$	$3$	$256$	$0.185220$	$37259704/131769$	$0.96426$	$3.63434$	$[0, -1, 0, 56, -380]$	$y^2=x^3-x^2+56x-380$	2.3.0.a.1, 4.12.0-4.c.1.1, 8.24.0-8.d.1.2, 88.48.0.?	$[]$
1056.c1	1056b2	1056.c	1056b	$2$	$2$	$ 2^{5} \cdot 3 \cdot 11 $	$ 2^{12} \cdot 3^{3} \cdot 11^{2} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$132$	$12$	$0$	$0.730576963$	$1$	$7$	$192$	$0.122437$	$58411072/3267$	$0.96722$	$3.76327$	$[0, -1, 0, -129, -495]$	$y^2=x^3-x^2-129x-495$	2.3.0.a.1, 12.6.0.a.1, 44.6.0.c.1, 132.12.0.?	$[(-7, 4)]$
1056.c2	1056b1	1056.c	1056b	$2$	$2$	$ 2^{5} \cdot 3 \cdot 11 $	$ - 2^{6} \cdot 3^{6} \cdot 11 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$132$	$12$	$0$	$1.461153926$	$1$	$5$	$96$	$-0.224137$	$314432/8019$	$1.04398$	$2.95598$	$[0, -1, 0, 6, -36]$	$y^2=x^3-x^2+6x-36$	2.3.0.a.1, 12.6.0.b.1, 22.6.0.a.1, 132.12.0.?	$[(4, 6)]$
1056.d1	1056a1	1056.d	1056a	$2$	$2$	$ 2^{5} \cdot 3 \cdot 11 $	$ 2^{6} \cdot 3^{3} \cdot 11 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.6.0.4	2B	$264$	$12$	$0$	$1.139644885$	$1$	$5$	$96$	$-0.175314$	$1643032000/297$	$0.96314$	$3.64519$	$[0, -1, 0, -98, 408]$	$y^2=x^3-x^2-98x+408$	2.3.0.a.1, 8.6.0.d.1, 66.6.0.a.1, 264.12.0.?	$[(4, 8)]$
1056.d2	1056a2	1056.d	1056a	$2$	$2$	$ 2^{5} \cdot 3 \cdot 11 $	$ - 2^{9} \cdot 3^{6} \cdot 11^{2} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.6.0.5	2B	$264$	$12$	$0$	$0.569822442$	$1$	$7$	$192$	$0.171259$	$-148877000/88209$	$1.12203$	$3.70024$	$[0, -1, 0, -88, 484]$	$y^2=x^3-x^2-88x+484$	2.3.0.a.1, 8.6.0.a.1, 132.6.0.?, 264.12.0.?	$[(0, 22)]$
1056.e1	1056g2	1056.e	1056g	$4$	$4$	$ 2^{5} \cdot 3 \cdot 11 $	$ 2^{9} \cdot 3^{5} \cdot 11^{2} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.24.0.102	2B	$24$	$48$	$0$	$11.10651773$	$1$	$1$	$3840$	$1.463779$	$6663712298552914184/29403$	$1.06967$	$7.12149$	$[0, -1, 0, -313632, -67500540]$	$y^2=x^3-x^2-313632x-67500540$	2.3.0.a.1, 4.6.0.c.1, 8.24.0-8.m.1.5, 12.12.0-4.c.1.2, 24.48.0-24.bi.1.3	$[(217993/3, 101750770/3)]$
1056.e2	1056g3	1056.e	1056g	$4$	$4$	$ 2^{5} \cdot 3 \cdot 11 $	$ 2^{12} \cdot 3^{5} \cdot 11^{8} $	$1$	$\Z/4\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.24.0.53	2B	$24$	$48$	$0$	$2.776629433$	$1$	$7$	$3840$	$1.463779$	$243578556889408/52089208083$	$1.05700$	$5.95271$	$[0, -1, 0, -20817, -911007]$	$y^2=x^3-x^2-20817x-911007$	2.3.0.a.1, 4.12.0-4.c.1.1, 8.24.0-8.m.1.1, 12.24.0-12.h.1.2, 24.48.0-24.bk.1.4	$[(-112, 55)]$
1056.e3	1056g1	1056.e	1056g	$4$	$4$	$ 2^{5} \cdot 3 \cdot 11 $	$ 2^{6} \cdot 3^{10} \cdot 11^{4} $	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.24.0.4	2Cs	$24$	$48$	$0$	$5.553258866$	$1$	$5$	$1920$	$1.117205$	$13015685560572352/864536409$	$1.06444$	$5.92680$	$[0, -1, 0, -19602, -1049760]$	$y^2=x^3-x^2-19602x-1049760$	2.6.0.a.1, 4.12.0-2.a.1.1, 8.24.0-8.b.1.2, 12.24.0-12.a.1.1, 24.48.0-24.f.1.3	$[(24219, 3768930)]$
1056.e4	1056g4	1056.e	1056g	$4$	$4$	$ 2^{5} \cdot 3 \cdot 11 $	$ - 2^{9} \cdot 3^{20} \cdot 11^{2} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.24.0.59	2B	$24$	$48$	$0$	$11.10651773$	$1$	$1$	$3840$	$1.463779$	$-1343891598641864/421900912521$	$1.04688$	$5.96159$	$[0, -1, 0, -18392, -1186248]$	$y^2=x^3-x^2-18392x-1186248$	2.3.0.a.1, 4.12.0-4.c.1.2, 8.24.0-8.d.1.1, 24.48.0-24.n.1.7	$[(147109/30, 10381877/30)]$
1056.f1	1056e1	1056.f	1056e	$2$	$2$	$ 2^{5} \cdot 3 \cdot 11 $	$ 2^{6} \cdot 3 \cdot 11 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.6.0.4	2B	$264$	$12$	$0$	$1$	$1$	$1$	$96$	$-0.565074$	$1906624/33$	$0.85378$	$2.67439$	$[0, 1, 0, -10, -16]$	$y^2=x^3+x^2-10x-16$	2.3.0.a.1, 8.6.0.d.1, 66.6.0.a.1, 264.12.0.?	$[]$
1056.f2	1056e2	1056.f	1056e	$2$	$2$	$ 2^{5} \cdot 3 \cdot 11 $	$ - 2^{9} \cdot 3^{2} \cdot 11^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.6.0.5	2B	$264$	$12$	$0$	$1$	$1$	$1$	$192$	$-0.218501$	$-8/1089$	$1.19226$	$2.97118$	$[0, 1, 0, 0, -36]$	$y^2=x^3+x^2-36$	2.3.0.a.1, 8.6.0.a.1, 132.6.0.?, 264.12.0.?	$[]$
1056.g1	1056f2	1056.g	1056f	$2$	$2$	$ 2^{5} \cdot 3 \cdot 11 $	$ 2^{12} \cdot 3^{3} \cdot 11^{2} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$132$	$12$	$0$	$0.194236205$	$1$	$11$	$192$	$0.122437$	$58411072/3267$	$0.96722$	$3.76327$	$[0, 1, 0, -129, 495]$	$y^2=x^3+x^2-129x+495$	2.3.0.a.1, 12.6.0.a.1, 44.6.0.c.1, 132.12.0.?	$[(3, 12)]$
1056.g2	1056f1	1056.g	1056f	$2$	$2$	$ 2^{5} \cdot 3 \cdot 11 $	$ - 2^{6} \cdot 3^{6} \cdot 11 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$132$	$12$	$0$	$0.388472410$	$1$	$9$	$96$	$-0.224137$	$314432/8019$	$1.04398$	$2.95598$	$[0, 1, 0, 6, 36]$	$y^2=x^3+x^2+6x+36$	2.3.0.a.1, 12.6.0.b.1, 22.6.0.a.1, 132.12.0.?	$[(0, 6)]$
1056.h1	1056i3	1056.h	1056i	$4$	$4$	$ 2^{5} \cdot 3 \cdot 11 $	$ 2^{12} \cdot 3^{2} \cdot 11 $	$1$	$\Z/4\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.24.0.53	2B	$88$	$48$	$0$	$1.882158067$	$1$	$7$	$256$	$0.185220$	$4004529472/99$	$0.97266$	$4.37050$	$[0, 1, 0, -529, 4511]$	$y^2=x^3+x^2-529x+4511$	2.3.0.a.1, 4.12.0-4.c.1.1, 8.24.0-8.m.1.1, 44.24.0-44.h.1.2, 88.48.0.?	$[(-5, 84)]$
1056.h2	1056i2	1056.h	1056i	$4$	$4$	$ 2^{5} \cdot 3 \cdot 11 $	$ 2^{9} \cdot 3^{8} \cdot 11 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.24.0.102	2B	$88$	$48$	$0$	$0.470539516$	$1$	$9$	$256$	$0.185220$	$649461896/72171$	$0.94560$	$3.81055$	$[0, 1, 0, -144, -648]$	$y^2=x^3+x^2-144x-648$	2.3.0.a.1, 4.6.0.c.1, 8.24.0-8.m.1.5, 44.12.0-4.c.1.2, 88.48.0.?	$[(-6, 6)]$
1056.h3	1056i1	1056.h	1056i	$4$	$4$	$ 2^{5} \cdot 3 \cdot 11 $	$ 2^{6} \cdot 3^{4} \cdot 11^{2} $	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.24.0.4	2Cs	$88$	$48$	$0$	$0.941079033$	$1$	$9$	$128$	$-0.161353$	$69934528/9801$	$0.93038$	$3.19178$	$[0, 1, 0, -34, 56]$	$y^2=x^3+x^2-34x+56$	2.6.0.a.1, 4.12.0-2.a.1.1, 8.24.0-8.b.1.2, 44.24.0-44.a.1.1, 88.48.0.?	$[(5, 6)]$
1056.h4	1056i4	1056.h	1056i	$4$	$4$	$ 2^{5} \cdot 3 \cdot 11 $	$ - 2^{9} \cdot 3^{2} \cdot 11^{4} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.24.0.59	2B	$88$	$48$	$0$	$1.882158067$	$1$	$3$	$256$	$0.185220$	$37259704/131769$	$0.96426$	$3.63434$	$[0, 1, 0, 56, 380]$	$y^2=x^3+x^2+56x+380$	2.3.0.a.1, 4.12.0-4.c.1.2, 8.24.0-8.d.1.1, 88.48.0.?	$[(-1, 18)]$
1056.i1	1056j1	1056.i	1056j	$2$	$2$	$ 2^{5} \cdot 3 \cdot 11 $	$ 2^{6} \cdot 3^{3} \cdot 11 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.6.0.4	2B	$264$	$12$	$0$	$1$	$1$	$1$	$96$	$-0.175314$	$1643032000/297$	$0.96314$	$3.64519$	$[0, 1, 0, -98, -408]$	$y^2=x^3+x^2-98x-408$	2.3.0.a.1, 8.6.0.d.1, 66.6.0.a.1, 264.12.0.?	$[]$
1056.i2	1056j2	1056.i	1056j	$2$	$2$	$ 2^{5} \cdot 3 \cdot 11 $	$ - 2^{9} \cdot 3^{6} \cdot 11^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.6.0.5	2B	$264$	$12$	$0$	$1$	$1$	$1$	$192$	$0.171259$	$-148877000/88209$	$1.12203$	$3.70024$	$[0, 1, 0, -88, -484]$	$y^2=x^3+x^2-88x-484$	2.3.0.a.1, 8.6.0.a.1, 132.6.0.?, 264.12.0.?	$[]$
1056.j1	1056d3	1056.j	1056d	$4$	$4$	$ 2^{5} \cdot 3 \cdot 11 $	$ 2^{9} \cdot 3^{5} \cdot 11^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.24.0.104	2B	$24$	$48$	$0$	$1$	$1$	$1$	$3840$	$1.463779$	$6663712298552914184/29403$	$1.06967$	$7.12149$	$[0, 1, 0, -313632, 67500540]$	$y^2=x^3+x^2-313632x+67500540$	2.3.0.a.1, 4.6.0.c.1, 8.24.0-8.m.1.7, 12.12.0-4.c.1.1, 24.48.0-24.bi.1.4	$[]$
1056.j2	1056d2	1056.j	1056d	$4$	$4$	$ 2^{5} \cdot 3 \cdot 11 $	$ 2^{12} \cdot 3^{5} \cdot 11^{8} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.24.0.63	2B	$24$	$48$	$0$	$1$	$1$	$1$	$3840$	$1.463779$	$243578556889408/52089208083$	$1.05700$	$5.95271$	$[0, 1, 0, -20817, 911007]$	$y^2=x^3+x^2-20817x+911007$	2.3.0.a.1, 4.12.0-4.c.1.2, 8.24.0-8.m.1.3, 12.24.0-12.h.1.1, 24.48.0-24.bk.1.1	$[]$
1056.j3	1056d1	1056.j	1056d	$4$	$4$	$ 2^{5} \cdot 3 \cdot 11 $	$ 2^{6} \cdot 3^{10} \cdot 11^{4} $	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.24.0.3	2Cs	$24$	$48$	$0$	$1$	$1$	$3$	$1920$	$1.117205$	$13015685560572352/864536409$	$1.06444$	$5.92680$	$[0, 1, 0, -19602, 1049760]$	$y^2=x^3+x^2-19602x+1049760$	2.6.0.a.1, 4.12.0-2.a.1.1, 8.24.0-8.b.1.1, 12.24.0-12.a.1.2, 24.48.0-24.f.1.2	$[]$
1056.j4	1056d4	1056.j	1056d	$4$	$4$	$ 2^{5} \cdot 3 \cdot 11 $	$ - 2^{9} \cdot 3^{20} \cdot 11^{2} $	$0$	$\Z/4\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.24.0.48	2B	$24$	$48$	$0$	$1$	$1$	$3$	$3840$	$1.463779$	$-1343891598641864/421900912521$	$1.04688$	$5.96159$	$[0, 1, 0, -18392, 1186248]$	$y^2=x^3+x^2-18392x+1186248$	2.3.0.a.1, 4.12.0-4.c.1.1, 8.24.0-8.d.1.2, 24.48.0-24.n.1.5	$[]$

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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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