Elliptic curve isogeny class with LMFDB label 308.a (Cremona label 308a)

• Label: 308.a
• Number of curves: $1$
• Conductor: $308$
• CM: no
• Rank: $1$

Rank

The elliptic curve 308.a1 has rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(7\)	\(1 + T\)
\(11\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(3\)	\( 1 + T + 3 T^{2}\)	1.3.b
\(5\)	\( 1 + T + 5 T^{2}\)	1.5.b
\(13\)	\( 1 + 4 T + 13 T^{2}\)	1.13.e
\(17\)	\( 1 + 6 T + 17 T^{2}\)	1.17.g
\(19\)	\( 1 + 2 T + 19 T^{2}\)	1.19.c
\(23\)	\( 1 - T + 23 T^{2}\)	1.23.ab
\(29\)	\( 1 - 2 T + 29 T^{2}\)	1.29.ac
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 308.a do not have complex multiplication.

Modular form 308.2.a.a

Elliptic curves in class 308.a

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
308.a1	308a1	\([0, -1, 0, -21, 49]\)	\(-4194304/539\)	\(-137984\)	\([]\)	\(24\)	\(-0.28020\)	\(\Gamma_0(N)\)-optimal