Elliptic curve isogeny class with Cremona label 122304cg (LMFDB label 122304.m)

• Label: 122304cg
• Number of curves: $1$
• Conductor: $122304$
• CM: no
• Rank: $1$

Rank

The elliptic curve 122304cg1 has rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1 + T\)
\(7\)	\(1\)
\(13\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 + 5 T^{2}\)	1.5.a
\(11\)	\( 1 + 11 T^{2}\)	1.11.a
\(17\)	\( 1 + 2 T + 17 T^{2}\)	1.17.c
\(19\)	\( 1 - 2 T + 19 T^{2}\)	1.19.ac
\(23\)	\( 1 + 8 T + 23 T^{2}\)	1.23.i
\(29\)	\( 1 + 6 T + 29 T^{2}\)	1.29.g
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 122304cg do not have complex multiplication.

Modular form 122304.2.a.cg

Elliptic curves in class 122304cg

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
122304.m1	122304cg1	\([0, -1, 0, 383, 2689]\)	\(68921/78\)	\(-7013400576\)	\([]\)	\(61440\)	\(0.57569\)	\(\Gamma_0(N)\)-optimal