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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 (6 matches)

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Label	Cremona label	Class	Cremona class	Class size	Class degree	Conductor	Discriminant	Rank	Torsion	$\textrm{End}^0(E_{\overline\Q})$	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
56.a1	56a4	56.a	56a	$4$	$4$	$2^{3} \cdot 7$	$2^{11} \cdot 7$	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.103	2B	$56$	$48$	$0$	$1$	$1$		$1$	$8$	$-0.002033$	$1443468546/7$	$1.04654$	$7.13352$	$[0, 0, 0, -299, 1990]$	$y^2=x^3-299x+1990$	2.3.0.a.1, 4.6.0.c.1, 8.24.0-8.p.1.7, 28.12.0-4.c.1.1, 56.48.0-56.bp.1.3	$[]$
56.a2	56a3	56.a	56a	$4$	$4$	$2^{3} \cdot 7$	$2^{11} \cdot 7^{4}$	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.58	2B	$56$	$48$	$0$	$1$	$1$		$1$	$8$	$-0.002033$	$11090466/2401$	$1.11706$	$5.92401$	$[0, 0, 0, -59, -138]$	$y^2=x^3-59x-138$	2.3.0.a.1, 4.12.0-4.c.1.2, 8.24.0-8.k.1.1, 56.48.0-56.v.1.8	$[]$
56.a3	56a2	56.a	56a	$4$	$4$	$2^{3} \cdot 7$	$2^{10} \cdot 7^{2}$	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.1	2Cs	$56$	$48$	$0$	$1$	$1$		$3$	$4$	$-0.348607$	$740772/49$	$1.06534$	$5.07954$	$[0, 0, 0, -19, 30]$	$y^2=x^3-19x+30$	2.6.0.a.1, 4.12.0-2.a.1.1, 8.24.0-8.a.1.2, 28.24.0-28.b.1.1, 56.48.0-56.d.1.3	$[]$
56.a4	56a1	56.a	56a	$4$	$4$	$2^{3} \cdot 7$	$- 2^{8} \cdot 7$	$0$	$\Z/4\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.50	2B	$56$	$48$	$0$	$1$	$1$		$3$	$2$	$-0.695180$	$432/7$	$0.89152$	$3.70389$	$[0, 0, 0, 1, 2]$	$y^2=x^3+x+2$	2.3.0.a.1, 4.12.0-4.c.1.1, 8.24.0-8.p.1.1, 14.6.0.b.1, 28.24.0-28.g.1.2, $\ldots$	$[]$
56.b1	56b2	56.b	56b	$2$	$2$	$2^{3} \cdot 7$	$2^{11} \cdot 7^{2}$	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.6.0.6	2B	$56$	$12$	$0$	$1$	$1$		$1$	$8$	$-0.234669$	$3543122/49$	$1.08036$	$5.64054$	$[0, -1, 0, -40, -84]$	$y^2=x^3-x^2-40x-84$	2.3.0.a.1, 8.6.0.b.1, 28.6.0.c.1, 56.12.0.k.1	$[]$
56.b2	56b1	56.b	56b	$2$	$2$	$2^{3} \cdot 7$	$- 2^{10} \cdot 7$	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.6.0.1	2B	$56$	$12$	$0$	$1$	$1$		$1$	$4$	$-0.581243$	$-4/7$	$1.03482$	$4.05739$	$[0, -1, 0, 0, -4]$	$y^2=x^3-x^2-4$	2.3.0.a.1, 8.6.0.c.1, 14.6.0.b.1, 56.12.0.n.1	$[]$

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