Elliptic curves over $\Q$ of conductor 1656

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Label	Cremona label	Class	Cremona class	Class size	Class degree	Conductor	Discriminant	Rank	Torsion	$\textrm{End}^0(E_{\overline\Q})$	CM	Sato-Tate	Semistable	Potentially good	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
1656.a1	1656g2	1656.a	1656g	$2$	$2$	\( 2^{3} \cdot 3^{2} \cdot 23 \)	\( 2^{10} \cdot 3^{7} \cdot 23^{2} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$276$	$12$	$0$	$0.825883932$	$1$		$7$	$1024$	$0.483531$	$19307236/1587$	$1.01848$	$4.08776$	$[0, 0, 0, -507, 4070]$	\(y^2=x^3-507x+4070\)	2.3.0.a.1, 12.6.0.a.1, 92.6.0.?, 276.12.0.?	$[(19, 36)]$
1656.a2	1656g1	1656.a	1656g	$2$	$2$	\( 2^{3} \cdot 3^{2} \cdot 23 \)	\( - 2^{8} \cdot 3^{8} \cdot 23 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$276$	$12$	$0$	$0.412941966$	$1$		$11$	$512$	$0.136958$	$21296/207$	$0.81409$	$3.35434$	$[0, 0, 0, 33, 290]$	\(y^2=x^3+33x+290\)	2.3.0.a.1, 12.6.0.b.1, 46.6.0.a.1, 276.12.0.?	$[(1, 18)]$
1656.b1	1656a3	1656.b	1656a	$4$	$4$	\( 2^{3} \cdot 3^{2} \cdot 23 \)	\( 2^{10} \cdot 3^{9} \cdot 23^{4} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.8	2B	$552$	$48$	$0$	$1$	$1$		$1$	$3072$	$1.168377$	$45989074372/7555707$	$0.96263$	$5.13680$	$[0, 0, 0, -6771, -181474]$	\(y^2=x^3-6771x-181474\)	2.3.0.a.1, 4.12.0-4.c.1.2, 12.24.0-12.h.1.1, 184.24.0.?, 552.48.0.?	$[ ]$
1656.b2	1656a2	1656.b	1656a	$4$	$4$	\( 2^{3} \cdot 3^{2} \cdot 23 \)	\( 2^{8} \cdot 3^{12} \cdot 23^{2} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.1	2Cs	$276$	$48$	$0$	$1$	$1$		$3$	$1536$	$0.821804$	$4135597648/385641$	$1.11158$	$4.62480$	$[0, 0, 0, -1911, 29450]$	\(y^2=x^3-1911x+29450\)	2.6.0.a.1, 4.12.0-2.a.1.1, 12.24.0-12.a.1.2, 92.24.0.?, 276.48.0.?	$[ ]$
1656.b3	1656a1	1656.b	1656a	$4$	$4$	\( 2^{3} \cdot 3^{2} \cdot 23 \)	\( 2^{4} \cdot 3^{9} \cdot 23 \)	$0$	$\Z/4\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.7	2B	$552$	$48$	$0$	$1$	$1$		$3$	$768$	$0.475230$	$61604313088/621$	$1.06623$	$4.61515$	$[0, 0, 0, -1866, 31025]$	\(y^2=x^3-1866x+31025\)	2.3.0.a.1, 4.12.0-4.c.1.1, 24.24.0-24.ba.1.8, 138.6.0.?, 184.24.0.?, $\ldots$	$[ ]$
1656.b4	1656a4	1656.b	1656a	$4$	$4$	\( 2^{3} \cdot 3^{2} \cdot 23 \)	\( - 2^{10} \cdot 3^{18} \cdot 23 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.6	2B	$552$	$48$	$0$	$1$	$1$		$1$	$3072$	$1.168377$	$1640689628/12223143$	$0.98661$	$5.02092$	$[0, 0, 0, 2229, 139574]$	\(y^2=x^3+2229x+139574\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.5, 12.12.0-4.c.1.1, 24.24.0-24.ba.1.12, $\ldots$	$[ ]$
1656.c1	1656e1	1656.c	1656e	$1$	$1$	\( 2^{3} \cdot 3^{2} \cdot 23 \)	\( - 2^{4} \cdot 3^{6} \cdot 23 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$46$	$2$	$0$	$0.481927265$	$1$		$4$	$336$	$0.162443$	$-1149984000/23$	$0.95837$	$4.07807$	$[0, 0, 0, -495, 4239]$	\(y^2=x^3-495x+4239\)	46.2.0.a.1	$[(13, 1)]$
1656.d1	1656d2	1656.d	1656d	$2$	$2$	\( 2^{3} \cdot 3^{2} \cdot 23 \)	\( 2^{10} \cdot 3^{13} \cdot 23^{2} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$276$	$12$	$0$	$7.386021547$	$1$		$3$	$7168$	$1.718628$	$10963069081334500/1156923$	$1.02886$	$6.80725$	$[0, 0, 0, -419835, -104704666]$	\(y^2=x^3-419835x-104704666\)	2.3.0.a.1, 12.6.0.a.1, 92.6.0.?, 276.12.0.?	$[(13315, 1534572)]$
1656.d2	1656d1	1656.d	1656d	$2$	$2$	\( 2^{3} \cdot 3^{2} \cdot 23 \)	\( - 2^{8} \cdot 3^{20} \cdot 23 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$276$	$12$	$0$	$3.693010773$	$1$		$5$	$3584$	$1.372053$	$-10627137250000/110008287$	$1.04721$	$5.68647$	$[0, 0, 0, -26175, -1644478]$	\(y^2=x^3-26175x-1644478\)	2.3.0.a.1, 12.6.0.b.1, 46.6.0.a.1, 276.12.0.?	$[(193, 702)]$
1656.e1	1656f2	1656.e	1656f	$2$	$2$	\( 2^{3} \cdot 3^{2} \cdot 23 \)	\( 2^{11} \cdot 3^{6} \cdot 23^{2} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.6.0.6	2B	$184$	$12$	$0$	$2.584062255$	$1$		$3$	$768$	$0.419759$	$2315250/529$	$0.89506$	$3.89513$	$[0, 0, 0, -315, -1674]$	\(y^2=x^3-315x-1674\)	2.3.0.a.1, 8.6.0.b.1, 92.6.0.?, 184.12.0.?	$[(30, 126)]$
1656.e2	1656f1	1656.e	1656f	$2$	$2$	\( 2^{3} \cdot 3^{2} \cdot 23 \)	\( - 2^{10} \cdot 3^{6} \cdot 23 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.6.0.1	2B	$184$	$12$	$0$	$1.292031127$	$1$		$7$	$384$	$0.073185$	$13500/23$	$0.90383$	$3.19722$	$[0, 0, 0, 45, -162]$	\(y^2=x^3+45x-162\)	2.3.0.a.1, 8.6.0.c.1, 46.6.0.a.1, 184.12.0.?	$[(6, 18)]$
1656.f1	1656c3	1656.f	1656c	$4$	$4$	\( 2^{3} \cdot 3^{2} \cdot 23 \)	\( 2^{11} \cdot 3^{7} \cdot 23 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.7	2B	$552$	$48$	$0$	$7.762964760$	$1$		$1$	$2048$	$1.011965$	$1378334691074/69$	$1.07977$	$5.68906$	$[0, 0, 0, -26499, -1660322]$	\(y^2=x^3-26499x-1660322\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.3, 24.24.0-24.y.1.8, 184.24.0.?, $\ldots$	$[(4706/5, 18396/5)]$
1656.f2	1656c4	1656.f	1656c	$4$	$4$	\( 2^{3} \cdot 3^{2} \cdot 23 \)	\( 2^{11} \cdot 3^{7} \cdot 23^{4} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.8	2B	$552$	$48$	$0$	$1.940741190$	$1$		$3$	$2048$	$1.011965$	$1522096994/839523$	$1.08605$	$4.77049$	$[0, 0, 0, -2739, 11950]$	\(y^2=x^3-2739x+11950\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.4, 12.12.0-4.c.1.1, 24.24.0-24.s.1.4, $\ldots$	$[(-42, 230)]$
1656.f3	1656c2	1656.f	1656c	$4$	$4$	\( 2^{3} \cdot 3^{2} \cdot 23 \)	\( 2^{10} \cdot 3^{8} \cdot 23^{2} \)	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.1	2Cs	$552$	$48$	$0$	$3.881482380$	$1$		$5$	$1024$	$0.665391$	$676449508/4761$	$0.99194$	$4.56756$	$[0, 0, 0, -1659, -25850]$	\(y^2=x^3-1659x-25850\)	2.6.0.a.1, 8.12.0-2.a.1.1, 12.12.0-2.a.1.1, 24.24.0-24.b.1.2, 92.12.0.?, $\ldots$	$[(122, 1260)]$
1656.f4	1656c1	1656.f	1656c	$4$	$4$	\( 2^{3} \cdot 3^{2} \cdot 23 \)	\( - 2^{8} \cdot 3^{10} \cdot 23 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.12	2B	$552$	$48$	$0$	$1.940741190$	$1$		$5$	$512$	$0.318818$	$-35152/1863$	$0.89850$	$3.66052$	$[0, 0, 0, -39, -902]$	\(y^2=x^3-39x-902\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.2, 12.12.0-4.c.1.2, 24.24.0-24.y.1.2, $\ldots$	$[(14, 36)]$
1656.g1	1656i1	1656.g	1656i	$1$	$1$	\( 2^{3} \cdot 3^{2} \cdot 23 \)	\( - 2^{4} \cdot 3^{6} \cdot 23 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$46$	$2$	$0$	$1$	$1$		$0$	$240$	$-0.190813$	$-562432/23$	$0.75822$	$3.05883$	$[0, 0, 0, -39, -97]$	\(y^2=x^3-39x-97\)	46.2.0.a.1	$[ ]$
1656.h1	1656h2	1656.h	1656h	$2$	$2$	\( 2^{3} \cdot 3^{2} \cdot 23 \)	\( 2^{11} \cdot 3^{9} \cdot 23^{2} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$552$	$12$	$0$	$1$	$1$		$1$	$1536$	$0.986779$	$80919167474/14283$	$0.96612$	$5.30655$	$[0, 0, 0, -10299, 402230]$	\(y^2=x^3-10299x+402230\)	2.3.0.a.1, 24.6.0.a.1, 92.6.0.?, 552.12.0.?	$[ ]$
1656.h2	1656h1	1656.h	1656h	$2$	$2$	\( 2^{3} \cdot 3^{2} \cdot 23 \)	\( - 2^{10} \cdot 3^{12} \cdot 23 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$552$	$12$	$0$	$1$	$1$		$1$	$768$	$0.640205$	$-28756228/16767$	$0.89435$	$4.23553$	$[0, 0, 0, -579, 7598]$	\(y^2=x^3-579x+7598\)	2.3.0.a.1, 24.6.0.d.1, 46.6.0.a.1, 552.12.0.?	$[ ]$
1656.i1	1656b1	1656.i	1656b	$1$	$1$	\( 2^{3} \cdot 3^{2} \cdot 23 \)	\( - 2^{4} \cdot 3^{6} \cdot 23 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$46$	$2$	$0$	$1$	$1$		$0$	$240$	$-0.278755$	$-256/23$	$0.98486$	$2.69299$	$[0, 0, 0, -3, -25]$	\(y^2=x^3-3x-25\)	46.2.0.a.1	$[ ]$

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