Elliptic curve isogeny class with Cremona label 8624g (LMFDB label 8624.i)

• Label: 8624g
• Number of curves: $1$
• Conductor: $8624$
• CM: no
• Rank: $1$

Rank

The elliptic curve 8624g1 has rank \(1\).

L-function data

Bad L-factors:

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

Good L-factors:

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

See L-function page for more information

Complex multiplication

The elliptic curves in class 8624g do not have complex multiplication.

Modular form 8624.2.a.g

Elliptic curves in class 8624g

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
8624.i1	8624g1	\([0, -1, 0, -184, 848]\)	\(6902546/1331\)	\(133568512\)	\([]\)	\(2304\)	\(0.27630\)	\(\Gamma_0(N)\)-optimal