Elliptic curve isogeny class with Cremona label 9680b (LMFDB label 9680.e)

• Label: 9680b
• Number of curves: $1$
• Conductor: $9680$
• CM: no
• Rank: $1$

Rank

The elliptic curve 9680b1 has rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(5\)	\(1 + T\)
\(11\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(3\)	\( 1 + 2 T + 3 T^{2}\)	1.3.c
\(7\)	\( 1 + 7 T^{2}\)	1.7.a
\(13\)	\( 1 + 6 T + 13 T^{2}\)	1.13.g
\(17\)	\( 1 + 6 T + 17 T^{2}\)	1.17.g
\(19\)	\( 1 + 19 T^{2}\)	1.19.a
\(23\)	\( 1 - 6 T + 23 T^{2}\)	1.23.ag
\(29\)	\( 1 + 29 T^{2}\)	1.29.a
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 9680b do not have complex multiplication.

Modular form 9680.2.a.b

Elliptic curves in class 9680b

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
9680.e1	9680b1	\([0, -1, 0, 27064, 29493136]\)	\(453962/78125\)	\(-377271630560000000\)	\([]\)	\(88704\)	\(2.0519\)	\(\Gamma_0(N)\)-optimal