Elliptic curves over $\Q$ of conductor 78

Conductor	j-invariant	Rank	Torsion	Complex multiplication
Bad$\ p$	Discriminant	Regulator	Analytic order of Ш	Galois image
Isogeny class size	Isogeny class degree	Cyclic isogeny degree	$p\ $div$\ $|Ш|	Nonmax$\ \ell$
Curves per isogeny class	Reduction	Integral points	Faltings height

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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	Regulator	$Ш_{\textrm{an}}$	Ш primes	Integral points	Modular degree	Faltings height	j-invariant	Weierstrass coefficients	Weierstrass equation
78.a1	78a4	78.a	78a	$4$	$4$	\( 2 \cdot 3 \cdot 13 \)	\( 2^{4} \cdot 3^{5} \cdot 13^{4} \)	$0$	$\Z/4\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	4.12.0.7	2B	$1$	$1$		$2$	$160$	$0.968078$	$986551739719628473/111045168$	$[1, 1, 0, -20739, 1140957]$	\(y^2+xy=x^3+x^2-20739x+1140957\)
78.a2	78a3	78.a	78a	$4$	$4$	\( 2 \cdot 3 \cdot 13 \)	\( 2^{4} \cdot 3^{20} \cdot 13 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	4.12.0.8	2B	$1$	$1$		$0$	$160$	$0.968078$	$1416134368422073/725251155408$	$[1, 1, 0, -2339, -15747]$	\(y^2+xy=x^3+x^2-2339x-15747\)
78.a3	78a2	78.a	78a	$4$	$4$	\( 2 \cdot 3 \cdot 13 \)	\( 2^{8} \cdot 3^{10} \cdot 13^{2} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	4.12.0.1	2Cs	$1$	$1$		$2$	$80$	$0.621504$	$242702053576633/2554695936$	$[1, 1, 0, -1299, 17325]$	\(y^2+xy=x^3+x^2-1299x+17325\)
78.a4	78a1	78.a	78a	$4$	$4$	\( 2 \cdot 3 \cdot 13 \)	\( - 2^{16} \cdot 3^{5} \cdot 13 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	8.12.0.6	2B	$1$	$1$		$1$	$40$	$0.274930$	$-822656953/207028224$	$[1, 1, 0, -19, 685]$	\(y^2+xy=x^3+x^2-19x+685\)