LMFDB - Elliptic curves over $\Q$ of conductor 5056

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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 (30 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
5056.a1	5056o1	5056.a	5056o	$1$	$1$	$ 2^{6} \cdot 79 $	$ 2^{14} \cdot 79 $	$2$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$316$	$2$	$0$	$0.319876973$	$1$	$16$	$1152$	$-0.135873$	$148176/79$	$0.72007$	$2.53393$	$[0, 0, 0, -28, 16]$	$y^2=x^3-28x+16$	316.2.0.?	$[(-2, 8), (6, 8)]$
5056.b1	5056p1	5056.b	5056p	$1$	$1$	$ 2^{6} \cdot 79 $	$ 2^{26} \cdot 79 $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$316$	$2$	$0$	$1$	$1$	$0$	$6144$	$0.573143$	$72511713/20224$	$0.89606$	$3.58522$	$[0, 0, 0, -556, -3632]$	$y^2=x^3-556x-3632$	316.2.0.?	$[]$
5056.c1	5056f2	5056.c	5056f	$2$	$2$	$ 2^{6} \cdot 79 $	$ 2^{19} \cdot 79^{2} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.6.0.6	2B	$632$	$12$	$0$	$1.155825409$	$1$	$3$	$2304$	$0.549255$	$81182737/12482$	$0.85973$	$3.59846$	$[0, 1, 0, -577, 4383]$	$y^2=x^3+x^2-577x+4383$	2.3.0.a.1, 8.6.0.b.1, 316.6.0.?, 632.12.0.?	$[(27, 96)]$
5056.c2	5056f1	5056.c	5056f	$2$	$2$	$ 2^{6} \cdot 79 $	$ - 2^{20} \cdot 79 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.6.0.1	2B	$632$	$12$	$0$	$2.311650818$	$1$	$3$	$1152$	$0.202681$	$103823/316$	$0.80009$	$2.98725$	$[0, 1, 0, 63, 415]$	$y^2=x^3+x^2+63x+415$	2.3.0.a.1, 8.6.0.c.1, 158.6.0.?, 632.12.0.?	$[(13, 60)]$
5056.d1	5056i3	5056.d	5056i	$3$	$9$	$ 2^{6} \cdot 79 $	$ 2^{36} \cdot 79 $	$2$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	9.12.0.1	3B	$5688$	$144$	$3$	$4.559108961$	$1$	$6$	$23040$	$1.719580$	$15698803397448457/20709376$	$1.00146$	$5.83573$	$[0, -1, 0, -333857, -74137439]$	$y^2=x^3-x^2-333857x-74137439$	3.4.0.a.1, 9.12.0.a.1, 24.8.0-3.a.1.1, 72.24.0.?, 316.2.0.?, $\ldots$	$[(857, 16384), (-333, 4)]$
5056.d2	5056i2	5056.d	5056i	$3$	$9$	$ 2^{6} \cdot 79 $	$ 2^{24} \cdot 79^{3} $	$2$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.12.0.1	3Cs	$5688$	$144$	$3$	$0.506567662$	$1$	$12$	$7680$	$1.170273$	$59914169497/31554496$	$0.96798$	$4.37282$	$[0, -1, 0, -5217, -41759]$	$y^2=x^3-x^2-5217x-41759$	3.12.0.a.1, 24.24.0-3.a.1.1, 316.2.0.?, 711.36.0.?, 948.24.1.?, $\ldots$	$[(745, 20224), (-45, 316)]$
5056.d3	5056i1	5056.d	5056i	$3$	$9$	$ 2^{6} \cdot 79 $	$ 2^{20} \cdot 79 $	$2$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	9.12.0.1	3B	$5688$	$144$	$3$	$0.506567662$	$1$	$14$	$2560$	$0.620967$	$11134383337/316$	$0.90937$	$4.17549$	$[0, -1, 0, -2977, 63521]$	$y^2=x^3-x^2-2977x+63521$	3.4.0.a.1, 9.12.0.a.1, 24.8.0-3.a.1.2, 72.24.0.?, 316.2.0.?, $\ldots$	$[(25, 64), (31, 8)]$
5056.e1	5056r2	5056.e	5056r	$2$	$5$	$ 2^{6} \cdot 79 $	$ 2^{22} \cdot 79^{5} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$5$	5.12.0.2	5B.4.2	$3160$	$48$	$1$	$0.695821931$	$1$	$2$	$46080$	$2.181831$	$1413378216646643521/49232902384$	$1.01962$	$6.36340$	$[0, -1, 0, -1496321, 704984737]$	$y^2=x^3-x^2-1496321x+704984737$	5.12.0.a.2, 40.24.0-5.a.2.1, 316.2.0.?, 1580.24.1.?, 3160.48.1.?	$[(699, 316)]$
5056.e2	5056r1	5056.e	5056r	$2$	$5$	$ 2^{6} \cdot 79 $	$ 2^{38} \cdot 79 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$5$	5.12.0.1	5B.4.1	$3160$	$48$	$1$	$3.479109655$	$1$	$2$	$9216$	$1.377111$	$8194759433281/82837504$	$0.96131$	$4.94952$	$[0, -1, 0, -26881, -1672543]$	$y^2=x^3-x^2-26881x-1672543$	5.12.0.a.1, 40.24.0-5.a.1.1, 316.2.0.?, 1580.24.1.?, 3160.48.1.?	$[(-101, 44)]$
5056.f1	5056s1	5056.f	5056s	$1$	$1$	$ 2^{6} \cdot 79 $	$ 2^{14} \cdot 79 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$316$	$2$	$0$	$0.261029413$	$1$	$6$	$1152$	$0.269263$	$2533446736/79$	$0.86232$	$3.67679$	$[0, -1, 0, -721, 7697]$	$y^2=x^3-x^2-721x+7697$	316.2.0.?	$[(17, 8)]$
5056.g1	5056g1	5056.g	5056g	$1$	$1$	$ 2^{6} \cdot 79 $	$ 2^{16} \cdot 79 $	$2$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$316$	$2$	$0$	$0.425619931$	$1$	$14$	$1024$	$0.009334$	$470596/79$	$1.06719$	$2.83199$	$[0, -1, 0, -65, 193]$	$y^2=x^3-x^2-65x+193$	316.2.0.?	$[(9, 16), (-7, 16)]$
5056.h1	5056q1	5056.h	5056q	$1$	$1$	$ 2^{6} \cdot 79 $	$ 2^{20} \cdot 79 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$316$	$2$	$0$	$1.561822046$	$1$	$2$	$1536$	$0.269156$	$4826809/316$	$0.94063$	$3.26750$	$[0, -1, 0, -225, -1151]$	$y^2=x^3-x^2-225x-1151$	316.2.0.?	$[(-9, 8)]$
5056.i1	5056u1	5056.i	5056u	$1$	$1$	$ 2^{6} \cdot 79 $	$ 2^{6} \cdot 79 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$316$	$2$	$0$	$1.008612217$	$1$	$2$	$256$	$-0.599169$	$140608/79$	$0.88181$	$1.87758$	$[0, -1, 0, -4, 2]$	$y^2=x^3-x^2-4x+2$	316.2.0.?	$[(-1, 2)]$
5056.j1	5056t1	5056.j	5056t	$1$	$1$	$ 2^{6} \cdot 79 $	$ 2^{18} \cdot 79 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$316$	$2$	$0$	$1.311146669$	$1$	$2$	$1024$	$0.144680$	$912673/79$	$0.78348$	$3.07221$	$[0, -1, 0, -129, -479]$	$y^2=x^3-x^2-129x-479$	316.2.0.?	$[(-5, 4)]$
5056.k1	5056h1	5056.k	5056h	$1$	$1$	$ 2^{6} \cdot 79 $	$ 2^{6} \cdot 79 $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$316$	$2$	$0$	$1$	$1$	$0$	$320$	$-0.422530$	$24897088/79$	$0.79495$	$2.48456$	$[0, -1, 0, -24, -38]$	$y^2=x^3-x^2-24x-38$	316.2.0.?	$[]$
5056.l1	5056n3	5056.l	5056n	$3$	$9$	$ 2^{6} \cdot 79 $	$ 2^{36} \cdot 79 $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	9.12.0.1	3B	$5688$	$144$	$3$	$1$	$1$	$0$	$23040$	$1.719580$	$15698803397448457/20709376$	$1.00146$	$5.83573$	$[0, 1, 0, -333857, 74137439]$	$y^2=x^3+x^2-333857x+74137439$	3.4.0.a.1, 9.12.0.a.1, 24.8.0-3.a.1.3, 72.24.0.?, 316.2.0.?, $\ldots$	$[]$
5056.l2	5056n2	5056.l	5056n	$3$	$9$	$ 2^{6} \cdot 79 $	$ 2^{24} \cdot 79^{3} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.12.0.1	3Cs	$5688$	$144$	$3$	$1$	$1$	$0$	$7680$	$1.170273$	$59914169497/31554496$	$0.96798$	$4.37282$	$[0, 1, 0, -5217, 41759]$	$y^2=x^3+x^2-5217x+41759$	3.12.0.a.1, 24.24.0-3.a.1.2, 316.2.0.?, 711.36.0.?, 948.24.1.?, $\ldots$	$[]$
5056.l3	5056n1	5056.l	5056n	$3$	$9$	$ 2^{6} \cdot 79 $	$ 2^{20} \cdot 79 $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	9.12.0.1	3B	$5688$	$144$	$3$	$1$	$1$	$0$	$2560$	$0.620967$	$11134383337/316$	$0.90937$	$4.17549$	$[0, 1, 0, -2977, -63521]$	$y^2=x^3+x^2-2977x-63521$	3.4.0.a.1, 9.12.0.a.1, 24.8.0-3.a.1.4, 72.24.0.?, 316.2.0.?, $\ldots$	$[]$
5056.m1	5056b2	5056.m	5056b	$2$	$5$	$ 2^{6} \cdot 79 $	$ 2^{22} \cdot 79^{5} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$5$	5.12.0.2	5B.4.2	$3160$	$48$	$1$	$8.068866399$	$1$	$0$	$46080$	$2.181831$	$1413378216646643521/49232902384$	$1.01962$	$6.36340$	$[0, 1, 0, -1496321, -704984737]$	$y^2=x^3+x^2-1496321x-704984737$	5.12.0.a.2, 40.24.0-5.a.2.3, 316.2.0.?, 1580.24.1.?, 3160.48.1.?	$[(-312941/21, 363392/21)]$
5056.m2	5056b1	5056.m	5056b	$2$	$5$	$ 2^{6} \cdot 79 $	$ 2^{38} \cdot 79 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$5$	5.12.0.1	5B.4.1	$3160$	$48$	$1$	$1.613773279$	$1$	$0$	$9216$	$1.377111$	$8194759433281/82837504$	$0.96131$	$4.94952$	$[0, 1, 0, -26881, 1672543]$	$y^2=x^3+x^2-26881x+1672543$	5.12.0.a.1, 40.24.0-5.a.1.3, 316.2.0.?, 1580.24.1.?, 3160.48.1.?	$[(67/3, 32768/3)]$
5056.n1	5056c1	5056.n	5056c	$1$	$1$	$ 2^{6} \cdot 79 $	$ 2^{14} \cdot 79 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$316$	$2$	$0$	$2.409911286$	$1$	$0$	$1152$	$0.269263$	$2533446736/79$	$0.86232$	$3.67679$	$[0, 1, 0, -721, -7697]$	$y^2=x^3+x^2-721x-7697$	316.2.0.?	$[(-143/3, 8/3)]$
5056.o1	5056a1	5056.o	5056a	$1$	$1$	$ 2^{6} \cdot 79 $	$ 2^{20} \cdot 79 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$316$	$2$	$0$	$0.568720027$	$1$	$4$	$1536$	$0.269156$	$4826809/316$	$0.94063$	$3.26750$	$[0, 1, 0, -225, 1151]$	$y^2=x^3+x^2-225x+1151$	316.2.0.?	$[(19, 64)]$
5056.p1	5056l1	5056.p	5056l	$1$	$1$	$ 2^{6} \cdot 79 $	$ 2^{16} \cdot 79 $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$316$	$2$	$0$	$1$	$1$	$0$	$1024$	$0.009334$	$470596/79$	$1.06719$	$2.83199$	$[0, 1, 0, -65, -193]$	$y^2=x^3+x^2-65x-193$	316.2.0.?	$[]$
5056.q1	5056e1	5056.q	5056e	$1$	$1$	$ 2^{6} \cdot 79 $	$ 2^{6} \cdot 79 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$316$	$2$	$0$	$1.134784762$	$1$	$2$	$320$	$-0.422530$	$24897088/79$	$0.79495$	$2.48456$	$[0, 1, 0, -24, 38]$	$y^2=x^3+x^2-24x+38$	316.2.0.?	$[(1, 4)]$
5056.r1	5056d1	5056.r	5056d	$1$	$1$	$ 2^{6} \cdot 79 $	$ 2^{18} \cdot 79 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$316$	$2$	$0$	$0.592504438$	$1$	$4$	$1024$	$0.144680$	$912673/79$	$0.78348$	$3.07221$	$[0, 1, 0, -129, 479]$	$y^2=x^3+x^2-129x+479$	316.2.0.?	$[(-5, 32)]$
5056.s1	5056m1	5056.s	5056m	$1$	$1$	$ 2^{6} \cdot 79 $	$ 2^{6} \cdot 79 $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$316$	$2$	$0$	$1$	$1$	$0$	$256$	$-0.599169$	$140608/79$	$0.88181$	$1.87758$	$[0, 1, 0, -4, -2]$	$y^2=x^3+x^2-4x-2$	316.2.0.?	$[]$
5056.t1	5056v2	5056.t	5056v	$2$	$2$	$ 2^{6} \cdot 79 $	$ 2^{19} \cdot 79^{2} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.6.0.6	2B	$632$	$12$	$0$	$2.825314101$	$1$	$3$	$2304$	$0.549255$	$81182737/12482$	$0.85973$	$3.59846$	$[0, -1, 0, -577, -4383]$	$y^2=x^3-x^2-577x-4383$	2.3.0.a.1, 8.6.0.b.1, 316.6.0.?, 632.12.0.?	$[(1413, 53088)]$
5056.t2	5056v1	5056.t	5056v	$2$	$2$	$ 2^{6} \cdot 79 $	$ - 2^{20} \cdot 79 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.6.0.1	2B	$632$	$12$	$0$	$5.650628202$	$1$	$1$	$1152$	$0.202681$	$103823/316$	$0.80009$	$2.98725$	$[0, -1, 0, 63, -415]$	$y^2=x^3-x^2+63x-415$	2.3.0.a.1, 8.6.0.c.1, 158.6.0.?, 632.12.0.?	$[(263/7, 2400/7)]$
5056.u1	5056j1	5056.u	5056j	$1$	$1$	$ 2^{6} \cdot 79 $	$ 2^{14} \cdot 79 $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$316$	$2$	$0$	$1$	$1$	$0$	$1152$	$-0.135873$	$148176/79$	$0.72007$	$2.53393$	$[0, 0, 0, -28, -16]$	$y^2=x^3-28x-16$	316.2.0.?	$[]$
5056.v1	5056k1	5056.v	5056k	$1$	$1$	$ 2^{6} \cdot 79 $	$ 2^{26} \cdot 79 $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$316$	$2$	$0$	$1$	$1$	$0$	$6144$	$0.573143$	$72511713/20224$	$0.89606$	$3.58522$	$[0, 0, 0, -556, 3632]$	$y^2=x^3-556x+3632$	316.2.0.?	$[]$

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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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