Elliptic curve isogeny class with Cremona label 1290h (LMFDB label 1290.f)

• Label: 1290h
• Number of curves: $1$
• Conductor: $1290$
• CM: no
• Rank: $0$

Rank

The elliptic curve 1290h1 has rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1 + T\)
\(3\)	\(1 - T\)
\(5\)	\(1 - T\)
\(43\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(7\)	\( 1 - 2 T + 7 T^{2}\)	1.7.ac
\(11\)	\( 1 + 6 T + 11 T^{2}\)	1.11.g
\(13\)	\( 1 - 2 T + 13 T^{2}\)	1.13.ac
\(17\)	\( 1 + 17 T^{2}\)	1.17.a
\(19\)	\( 1 - 2 T + 19 T^{2}\)	1.19.ac
\(23\)	\( 1 - 6 T + 23 T^{2}\)	1.23.ag
\(29\)	\( 1 - 6 T + 29 T^{2}\)	1.29.ag
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 1290h do not have complex multiplication.

Modular form 1290.2.a.h

Elliptic curves in class 1290h

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
1290.f1	1290h1	\([1, 0, 1, 120229952, -3351306510322]\)	\(192203697666261893287480365959/4963160303408775168000000000\)	\(-4963160303408775168000000000\)	\([]\)	\(1068480\)	\(3.9945\)	\(\Gamma_0(N)\)-optimal