Elliptic curves over $\Q$ of conductor 78

Results (4 matches)

 

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
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	$312$	$48$	$0$	$1$	$1$		$2$	$160$	$0.968078$	$986551739719628473/111045168$	$1.06555$	$9.51016$	$[1, 1, 0, -20739, 1140957]$	\(y^2+xy=x^3+x^2-20739x+1140957\)	2.3.0.a.1, 4.12.0-4.c.1.1, 12.24.0-12.h.1.2, 104.24.0.?, 312.48.0.?	$[]$
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	$312$	$48$	$0$	$1$	$1$		$0$	$160$	$0.968078$	$1416134368422073/725251155408$	$1.07849$	$8.00758$	$[1, 1, 0, -2339, -15747]$	\(y^2+xy=x^3+x^2-2339x-15747\)	2.3.0.a.1, 4.12.0-4.c.1.2, 24.24.0-24.ba.1.16, 26.6.0.b.1, 52.24.0-52.g.1.1, $\ldots$	$[]$
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	$156$	$48$	$0$	$1$	$1$		$2$	$80$	$0.621504$	$242702053576633/2554695936$	$1.10395$	$7.60272$	$[1, 1, 0, -1299, 17325]$	\(y^2+xy=x^3+x^2-1299x+17325\)	2.6.0.a.1, 4.12.0-2.a.1.1, 12.24.0-12.a.1.1, 52.24.0-52.b.1.2, 156.48.0.?	$[]$
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	$312$	$48$	$0$	$1$	$1$		$1$	$40$	$0.274930$	$-822656953/207028224$	$1.08584$	$6.10676$	$[1, 1, 0, -19, 685]$	\(y^2+xy=x^3+x^2-19x+685\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.5, 12.12.0-4.c.1.2, 24.24.0-24.ba.1.4, $\ldots$	$[]$