Elliptic curve isogeny class with Cremona label 78400hx (LMFDB label 78400.ei)

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

Rank

The elliptic curve 78400hx1 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
\(11\)	\( 1 + 11 T^{2}\)	1.11.a
\(13\)	\( 1 + 2 T + 13 T^{2}\)	1.13.c
\(17\)	\( 1 - 2 T + 17 T^{2}\)	1.17.ac
\(19\)	\( 1 - 6 T + 19 T^{2}\)	1.19.ag
\(23\)	\( 1 - 3 T + 23 T^{2}\)	1.23.ad
\(29\)	\( 1 + 7 T + 29 T^{2}\)	1.29.h
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

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

Modular form 78400.2.a.hx

Elliptic curves in class 78400hx

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
78400.ei1	78400hx1	\([0, -1, 0, -80033, 8118937]\)	\(12544\)	\(4519603984000000\)	\([]\)	\(376320\)	\(1.7474\)	\(\Gamma_0(N)\)-optimal