LMFDB - Elliptic curves over $\Q$ of conductor 1456

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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	$Ш_{\textrm{an}}$	Integral points	Modular degree	Faltings height	j-invariant	$abc$ quality	Szpiro ratio	Weierstrass coefficients	Weierstrass equation	mod-$m$ images	MW-generators
1456.a1	1456k1	1456.a	1456k	$1$	$1$	$ 2^{4} \cdot 7 \cdot 13 $	$ - 2^{13} \cdot 7^{3} \cdot 13 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$728$	$2$	$0$	$0.080276374$	$1$	$12$	$864$	$0.135290$	$4019679/8918$	$1.11550$	$3.37286$	$[0, 0, 0, 53, 250]$	$y^2=x^3+53x+250$	728.2.0.?	$[(13, 56)]$
1456.b1	1456f1	1456.b	1456f	$1$	$1$	$ 2^{4} \cdot 7 \cdot 13 $	$ - 2^{19} \cdot 7 \cdot 13^{5} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$728$	$2$	$0$	$1$	$1$	$0$	$3360$	$1.007584$	$-1207949625/332678528$	$1.06089$	$4.85996$	$[0, 0, 0, -355, -56222]$	$y^2=x^3-355x-56222$	728.2.0.?	$[]$
1456.c1	1456c1	1456.c	1456c	$1$	$1$	$ 2^{4} \cdot 7 \cdot 13 $	$ - 2^{8} \cdot 7 \cdot 13^{7} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$182$	$2$	$0$	$3.963292106$	$1$	$2$	$1344$	$0.808213$	$530208386048/439239619$	$0.96694$	$4.46790$	$[0, 1, 0, 1071, -8501]$	$y^2=x^3+x^2+1071x-8501$	182.2.0.?	$[(30, 227)]$
1456.d1	1456g3	1456.d	1456g	$3$	$9$	$ 2^{4} \cdot 7 \cdot 13 $	$ - 2^{13} \cdot 7 \cdot 13 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	9.12.0.1	3B	$6552$	$144$	$3$	$0.486052662$	$1$	$2$	$2592$	$1.373604$	$-424962187484640625/182$	$1.05379$	$6.71503$	$[0, -1, 0, -250608, 48371776]$	$y^2=x^3-x^2-250608x+48371776$	3.4.0.a.1, 9.12.0.a.1, 12.8.0-3.a.1.2, 36.24.0-9.a.1.1, 728.2.0.?, $\ldots$	$[(288, 40)]$
1456.d2	1456g2	1456.d	1456g	$3$	$9$	$ 2^{4} \cdot 7 \cdot 13 $	$ - 2^{15} \cdot 7^{3} \cdot 13^{3} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.12.0.1	3Cs	$6552$	$144$	$3$	$0.162017554$	$1$	$8$	$864$	$0.824298$	$-795309684625/6028568$	$0.94067$	$4.90602$	$[0, -1, 0, -3088, 67520]$	$y^2=x^3-x^2-3088x+67520$	3.12.0.a.1, 12.24.0-3.a.1.1, 728.2.0.?, 819.36.0.?, 2184.48.1.?, $\ldots$	$[(8, 208)]$
1456.d3	1456g1	1456.d	1456g	$3$	$9$	$ 2^{4} \cdot 7 \cdot 13 $	$ - 2^{21} \cdot 7 \cdot 13 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	9.12.0.1	3B	$6552$	$144$	$3$	$0.486052662$	$1$	$4$	$288$	$0.274992$	$37595375/46592$	$0.87083$	$3.55498$	$[0, -1, 0, 112, 448]$	$y^2=x^3-x^2+112x+448$	3.4.0.a.1, 9.12.0.a.1, 12.8.0-3.a.1.1, 36.24.0-9.a.1.2, 728.2.0.?, $\ldots$	$[(24, 128)]$
1456.e1	1456l1	1456.e	1456l	$1$	$1$	$ 2^{4} \cdot 7 \cdot 13 $	$ - 2^{23} \cdot 7^{7} \cdot 13 $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$728$	$2$	$0$	$1$	$1$	$0$	$7392$	$1.564314$	$-10824513276632329/21926008832$	$0.99602$	$6.21160$	$[0, -1, 0, -73736, -7695632]$	$y^2=x^3-x^2-73736x-7695632$	728.2.0.?	$[]$
1456.f1	1456e1	1456.f	1456e	$1$	$1$	$ 2^{4} \cdot 7 \cdot 13 $	$ - 2^{8} \cdot 7^{5} \cdot 13 $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$182$	$2$	$0$	$1$	$1$	$0$	$480$	$0.363437$	$-86044336128/218491$	$0.99544$	$4.21884$	$[0, 0, 0, -584, -5444]$	$y^2=x^3-584x-5444$	182.2.0.?	$[]$
1456.g1	1456j1	1456.g	1456j	$1$	$1$	$ 2^{4} \cdot 7 \cdot 13 $	$ - 2^{12} \cdot 7 \cdot 13 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$182$	$2$	$0$	$1.471942741$	$1$	$2$	$160$	$-0.243182$	$110592/91$	$0.71571$	$2.73653$	$[0, 0, 0, 16, -16]$	$y^2=x^3+16x-16$	182.2.0.?	$[(1, 1)]$
1456.h1	1456d1	1456.h	1456d	$1$	$1$	$ 2^{4} \cdot 7 \cdot 13 $	$ - 2^{8} \cdot 7 \cdot 13^{3} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$182$	$2$	$0$	$0.362508900$	$1$	$4$	$192$	$0.002399$	$-135834624/15379$	$0.86662$	$3.35704$	$[0, 0, 0, -68, 236]$	$y^2=x^3-68x+236$	182.2.0.?	$[(1, 13)]$
1456.i1	1456i3	1456.i	1456i	$4$	$4$	$ 2^{4} \cdot 7 \cdot 13 $	$ 2^{17} \cdot 7^{3} \cdot 13^{8} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.24.0.101	2B	$56$	$48$	$0$	$6.357395233$	$1$	$1$	$17280$	$2.143154$	$22868021811807457713/8953460393696$	$1.08758$	$7.26222$	$[0, 0, 0, -946139, -354106230]$	$y^2=x^3-946139x-354106230$	2.3.0.a.1, 4.6.0.c.1, 8.24.0-8.p.1.5, 28.12.0-4.c.1.2, 56.48.0-56.bp.1.7	$[(-14169/5, 34146/5)]$
1456.i2	1456i4	1456.i	1456i	$4$	$4$	$ 2^{4} \cdot 7 \cdot 13 $	$ 2^{17} \cdot 7^{12} \cdot 13^{2} $	$1$	$\Z/4\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.24.0.49	2B	$56$	$48$	$0$	$1.589348808$	$1$	$7$	$17280$	$2.143154$	$3389174547561866673/74853681183008$	$1.05145$	$7.00010$	$[0, 0, 0, -500699, 133740682]$	$y^2=x^3-500699x+133740682$	2.3.0.a.1, 4.12.0-4.c.1.1, 8.24.0-8.k.1.2, 56.48.0-56.v.1.3	$[(-771, 7840)]$
1456.i3	1456i2	1456.i	1456i	$4$	$4$	$ 2^{4} \cdot 7 \cdot 13 $	$ 2^{22} \cdot 7^{6} \cdot 13^{4} $	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.24.0.2	2Cs	$56$	$48$	$0$	$3.178697616$	$1$	$7$	$8640$	$1.796581$	$8511781274893233/3440817243136$	$1.08472$	$6.17812$	$[0, 0, 0, -68059, -3752310]$	$y^2=x^3-68059x-3752310$	2.6.0.a.1, 4.12.0-2.a.1.1, 8.24.0-8.a.1.1, 28.24.0-28.b.1.2, 56.48.0-56.d.1.1	$[(-65, 630)]$
1456.i4	1456i1	1456.i	1456i	$4$	$4$	$ 2^{4} \cdot 7 \cdot 13 $	$ - 2^{32} \cdot 7^{3} \cdot 13^{2} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.24.0.60	2B	$56$	$48$	$0$	$1.589348808$	$1$	$7$	$4320$	$1.450006$	$71903073502287/60782804992$	$1.03131$	$5.52267$	$[0, 0, 0, 13861, -426358]$	$y^2=x^3+13861x-426358$	2.3.0.a.1, 4.12.0-4.c.1.2, 8.24.0-8.p.1.3, 14.6.0.b.1, 28.24.0-28.g.1.1, $\ldots$	$[(31, 182)]$
1456.j1	1456a1	1456.j	1456a	$1$	$1$	$ 2^{4} \cdot 7 \cdot 13 $	$ - 2^{11} \cdot 7 \cdot 13 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$728$	$2$	$0$	$0.267954550$	$1$	$6$	$96$	$-0.301737$	$-31250/91$	$0.83978$	$2.71457$	$[0, 1, 0, -8, 20]$	$y^2=x^3+x^2-8x+20$	728.2.0.?	$[(2, 4)]$
1456.k1	1456h3	1456.k	1456h	$3$	$9$	$ 2^{4} \cdot 7 \cdot 13 $	$ - 2^{12} \cdot 7^{9} \cdot 13 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	9.12.0.1	3B	$3276$	$144$	$3$	$4.303018462$	$1$	$2$	$2592$	$1.053251$	$-178643795968/524596891$	$1.15023$	$4.94690$	$[0, -1, 0, -1877, 77789]$	$y^2=x^3-x^2-1877x+77789$	3.4.0.a.1, 9.12.0.a.1, 12.8.0-3.a.1.2, 36.24.0-9.a.1.1, 117.36.0.?, $\ldots$	$[(-20, 327)]$
1456.k2	1456h1	1456.k	1456h	$3$	$9$	$ 2^{4} \cdot 7 \cdot 13 $	$ - 2^{12} \cdot 7 \cdot 13 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	9.12.0.1	3B	$3276$	$144$	$3$	$4.303018462$	$1$	$2$	$288$	$-0.045361$	$-43614208/91$	$0.87141$	$3.55769$	$[0, -1, 0, -117, -451]$	$y^2=x^3-x^2-117x-451$	3.4.0.a.1, 9.12.0.a.1, 12.8.0-3.a.1.1, 36.24.0-9.a.1.2, 117.36.0.?, $\ldots$	$[(68, 549)]$
1456.k3	1456h2	1456.k	1456h	$3$	$9$	$ 2^{4} \cdot 7 \cdot 13 $	$ - 2^{12} \cdot 7^{3} \cdot 13^{3} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.12.0.1	3Cs	$3276$	$144$	$3$	$1.434339487$	$1$	$2$	$864$	$0.503945$	$224755712/753571$	$0.95798$	$3.99750$	$[0, -1, 0, 203, -2499]$	$y^2=x^3-x^2+203x-2499$	3.12.0.a.1, 12.24.0-3.a.1.1, 117.36.0.?, 182.2.0.?, 468.72.0.?, $\ldots$	$[(12, 39)]$
1456.l1	1456b1	1456.l	1456b	$1$	$1$	$ 2^{4} \cdot 7 \cdot 13 $	$ - 2^{8} \cdot 7^{3} \cdot 13 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$182$	$2$	$0$	$2.650071309$	$1$	$2$	$192$	$-0.158746$	$-1024/4459$	$0.96270$	$2.93854$	$[0, -1, 0, -1, -51]$	$y^2=x^3-x^2-x-51$	182.2.0.?	$[(12, 39)]$
1456.m1	1456m1	1456.m	1456m	$1$	$1$	$ 2^{4} \cdot 7 \cdot 13 $	$ - 2^{8} \cdot 7 \cdot 13 $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$182$	$2$	$0$	$1$	$1$	$0$	$96$	$-0.469602$	$-65536/91$	$0.78564$	$2.45202$	$[0, -1, 0, -5, -7]$	$y^2=x^3-x^2-5x-7$	182.2.0.?	$[]$

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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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