Elliptic curves over $\Q$ of conductor 65

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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
65.a1	65a1	65.a	65a	$2$	$2$	\( 5 \cdot 13 \)	\( 5 \cdot 13 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	8.12.0.22	2B	$520$	$48$	$0$	$0.375514098$	$1$		$7$	$2$	$-0.961616$	$117649/65$	$0.95681$	$2.79693$	$[1, 0, 0, -1, 0]$	\(y^2+xy=x^3-x\)	2.3.0.a.1, 4.6.0.b.1, 8.12.0-4.b.1.2, 130.6.0.?, 260.24.0.?, $\ldots$	$[(1, 0)]$
65.a2	65a2	65.a	65a	$2$	$2$	\( 5 \cdot 13 \)	\( - 5^{2} \cdot 13^{2} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	8.12.0.37	2B	$520$	$48$	$0$	$0.187757049$	$1$		$12$	$4$	$-0.615042$	$6967871/4225$	$0.89914$	$3.77464$	$[1, 0, 0, 4, 1]$	\(y^2+xy=x^3+4x+1\)	2.3.0.a.1, 4.6.0.a.1, 8.12.0-4.a.1.1, 260.12.0.?, 520.48.0.?	$[(1, 2)]$

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