Elliptic curves over $\Q$ of conductor 53176

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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
53176.a1	53176b1	53176.a	53176b	$1$	$1$	\( 2^{3} \cdot 17^{2} \cdot 23 \)	\( - 2^{4} \cdot 17^{6} \cdot 23 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$46$	$2$	$0$	$3.801023503$	$1$		$2$	$110592$	$1.029743$	$-1149984000/23$	$0.95837$	$3.73436$	$[0, 0, 0, -15895, -771341]$	\(y^2=x^3-15895x-771341\)	46.2.0.a.1	$[(1003, 31501)]$
53176.b1	53176e1	53176.b	53176e	$1$	$1$	\( 2^{3} \cdot 17^{2} \cdot 23 \)	\( - 2^{11} \cdot 17^{7} \cdot 23^{3} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$3128$	$2$	$0$	$1$	$1$		$0$	$414720$	$1.752621$	$13935742/206839$	$0.84475$	$4.06921$	$[0, -1, 0, 18400, 4763116]$	\(y^2=x^3-x^2+18400x+4763116\)	3128.2.0.?	$[]$
53176.c1	53176g1	53176.c	53176g	$1$	$1$	\( 2^{3} \cdot 17^{2} \cdot 23 \)	\( - 2^{4} \cdot 17^{8} \cdot 23^{3} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$46$	$2$	$0$	$0.688361274$	$1$		$4$	$304128$	$1.885715$	$-12685358647552/3516263$	$0.89775$	$4.58985$	$[0, -1, 0, -353832, 81148417]$	\(y^2=x^3-x^2-353832x+81148417\)	46.2.0.a.1	$[(108, 6647)]$
53176.d1	53176a2	53176.d	53176a	$2$	$2$	\( 2^{3} \cdot 17^{2} \cdot 23 \)	\( 2^{11} \cdot 17^{6} \cdot 23^{2} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.6.0.6	2B	$184$	$12$	$0$	$1.941356224$	$1$		$3$	$110592$	$1.287060$	$2315250/529$	$0.89506$	$3.60974$	$[0, 0, 0, -10115, 304606]$	\(y^2=x^3-10115x+304606\)	2.3.0.a.1, 8.6.0.b.1, 92.6.0.?, 184.12.0.?	$[(102, 578)]$
53176.d2	53176a1	53176.d	53176a	$2$	$2$	\( 2^{3} \cdot 17^{2} \cdot 23 \)	\( - 2^{10} \cdot 17^{6} \cdot 23 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.6.0.1	2B	$184$	$12$	$0$	$3.882712448$	$1$		$3$	$55296$	$0.940486$	$13500/23$	$0.90383$	$3.13435$	$[0, 0, 0, 1445, 29478]$	\(y^2=x^3+1445x+29478\)	2.3.0.a.1, 8.6.0.c.1, 46.6.0.a.1, 184.12.0.?	$[(111, 1248)]$
53176.e1	53176c1	53176.e	53176c	$1$	$1$	\( 2^{3} \cdot 17^{2} \cdot 23 \)	\( - 2^{4} \cdot 17^{6} \cdot 23 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$46$	$2$	$0$	$1$	$1$		$0$	$39424$	$0.676488$	$-562432/23$	$0.75822$	$3.04008$	$[0, 1, 0, -1252, 17233]$	\(y^2=x^3+x^2-1252x+17233\)	46.2.0.a.1	$[]$
53176.f1	53176d1	53176.f	53176d	$1$	$1$	\( 2^{3} \cdot 17^{2} \cdot 23 \)	\( - 2^{4} \cdot 17^{6} \cdot 23 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$46$	$2$	$0$	$1$	$1$		$0$	$40960$	$0.588546$	$-256/23$	$0.98486$	$2.79087$	$[0, 1, 0, -96, 4517]$	\(y^2=x^3+x^2-96x+4517\)	46.2.0.a.1	$[]$
53176.g1	53176f2	53176.g	53176f	$2$	$2$	\( 2^{3} \cdot 17^{2} \cdot 23 \)	\( 2^{11} \cdot 17^{8} \cdot 23^{4} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.6.0.6	2B	$136$	$12$	$0$	$1$	$25$	$5$	$1$	$1511424$	$2.325962$	$1517600157122/80874049$	$0.89665$	$4.84057$	$[0, -1, 0, -878656, -301771092]$	\(y^2=x^3-x^2-878656x-301771092\)	2.3.0.a.1, 8.6.0.b.1, 68.6.0.c.1, 136.12.0.?	$[]$
53176.g2	53176f1	53176.g	53176f	$2$	$2$	\( 2^{3} \cdot 17^{2} \cdot 23 \)	\( 2^{10} \cdot 17^{7} \cdot 23^{2} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.6.0.1	2B	$136$	$12$	$0$	$1$	$25$	$5$	$1$	$755712$	$1.979391$	$2916972108004/8993$	$0.89490$	$4.83692$	$[0, -1, 0, -867096, -310487332]$	\(y^2=x^3-x^2-867096x-310487332\)	2.3.0.a.1, 8.6.0.c.1, 34.6.0.a.1, 136.12.0.?	$[]$

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