Elliptic curve isogeny class with Cremona label 121680cg (LMFDB label 121680.y)

• Label: 121680cg
• Number of curves: $1$
• Conductor: $121680$
• CM: no
• Rank: $2$

Rank

The elliptic curve 121680cg1 has rank \(2\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1\)
\(5\)	\(1 + T\)
\(13\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(7\)	\( 1 - 3 T + 7 T^{2}\)	1.7.ad
\(11\)	\( 1 + 6 T + 11 T^{2}\)	1.11.g
\(17\)	\( 1 + 6 T + 17 T^{2}\)	1.17.g
\(19\)	\( 1 + 19 T^{2}\)	1.19.a
\(23\)	\( 1 - 2 T + 23 T^{2}\)	1.23.ac
\(29\)	\( 1 + 8 T + 29 T^{2}\)	1.29.i
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 121680cg do not have complex multiplication.

Modular form 121680.2.a.cg

Elliptic curves in class 121680cg

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
121680.y1	121680cg1	\([0, 0, 0, 8112, 1748812]\)	\(1769472/40625\)	\(-1355367967200000\)	\([]\)	\(322560\)	\(1.5838\)	\(\Gamma_0(N)\)-optimal