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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
3332.a1	3332c1	3332.a	3332c	$1$	$1$	$2^{2} \cdot 7^{2} \cdot 17$	$- 2^{8} \cdot 7^{4} \cdot 17$	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$68$	$2$	$0$	$1$	$1$		$0$	$2304$	$0.227250$	$-7260624/17$	$1.18988$	$3.59138$	$[0, 0, 0, -343, -2450]$	$y^2=x^3-343x-2450$	68.2.0.a.1	$[]$
3332.b1	3332b1	3332.b	3332b	$1$	$1$	$2^{2} \cdot 7^{2} \cdot 17$	$- 2^{8} \cdot 7^{8} \cdot 17$	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$68$	$2$	$0$	$1$	$1$		$0$	$2016$	$0.681629$	$14000/17$	$0.64708$	$3.79137$	$[0, -1, 0, 572, -5704]$	$y^2=x^3-x^2+572x-5704$	68.2.0.a.1	$[]$
3332.c1	3332e1	3332.c	3332e	$1$	$1$	$2^{2} \cdot 7^{2} \cdot 17$	$- 2^{8} \cdot 7^{2} \cdot 17^{7}$	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$68$	$2$	$0$	$1$	$1$		$0$	$8064$	$1.142326$	$-728871512656/410338673$	$0.94414$	$4.61469$	$[0, -1, 0, -4356, -153992]$	$y^2=x^3-x^2-4356x-153992$	68.2.0.a.1	$[]$
3332.d1	3332a1	3332.d	3332a	$1$	$1$	$2^{2} \cdot 7^{2} \cdot 17$	$- 2^{8} \cdot 7^{8} \cdot 17^{7}$	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$68$	$2$	$0$	$1$	$1$		$0$	$56448$	$2.115280$	$-728871512656/410338673$	$0.94414$	$6.05409$	$[0, 1, 0, -213460, 53246164]$	$y^2=x^3+x^2-213460x+53246164$	68.2.0.a.1	$[]$
3332.e1	3332d1	3332.e	3332d	$1$	$1$	$2^{2} \cdot 7^{2} \cdot 17$	$- 2^{8} \cdot 7^{2} \cdot 17$	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$68$	$2$	$0$	$1$	$1$		$0$	$288$	$-0.291326$	$14000/17$	$0.64708$	$2.35197$	$[0, 1, 0, 12, 20]$	$y^2=x^3+x^2+12x+20$	68.2.0.a.1	$[]$
3332.f1	3332f1	3332.f	3332f	$1$	$1$	$2^{2} \cdot 7^{2} \cdot 17$	$- 2^{8} \cdot 7^{10} \cdot 17$	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$68$	$2$	$0$	$1$	$1$		$0$	$16128$	$1.200205$	$-7260624/17$	$1.18988$	$5.03078$	$[0, 0, 0, -16807, 840350]$	$y^2=x^3-16807x+840350$	68.2.0.a.1	$[]$

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