Elliptic curve isogeny class with LMFDB label 78400.hv (Cremona label 78400hf)

• Label: 78400.hv
• Number of curves: $1$
• Conductor: $78400$
• CM: no
• Rank: $1$

Rank

The elliptic curve 78400.hv1 has rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(5\)	\(1\)
\(7\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(3\)	\( 1 - T + 3 T^{2}\)	1.3.ab
\(11\)	\( 1 + T + 11 T^{2}\)	1.11.b
\(13\)	\( 1 - 6 T + 13 T^{2}\)	1.13.ag
\(17\)	\( 1 - 7 T + 17 T^{2}\)	1.17.ah
\(19\)	\( 1 + T + 19 T^{2}\)	1.19.b
\(23\)	\( 1 + 8 T + 23 T^{2}\)	1.23.i
\(29\)	\( 1 - 6 T + 29 T^{2}\)	1.29.ag
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 78400.hv do not have complex multiplication.

Modular form 78400.2.a.hv

Isogeny graph

Elliptic curves in class 78400.hv

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
78400.hv1	78400hf1	\([0, 1, 0, -32993, -2327137]\)	\(-10303010/49\)	\(-18890099916800\)	\([]\)	\(221184\)	\(1.3970\)	\(\Gamma_0(N)\)-optimal