Elliptic curve isogeny class with Cremona label 96824e (LMFDB label 96824.g)

• Label: 96824e
• Number of curves: $1$
• Conductor: $96824$
• CM: no
• Rank: $2$

Rank

The elliptic curve 96824e1 has rank \(2\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(7\)	\(1\)
\(13\)	\(1 - T\)
\(19\)	\(1 + T\)

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
\(11\)	\( 1 + 11 T^{2}\)	1.11.a
\(17\)	\( 1 + 3 T + 17 T^{2}\)	1.17.d
\(23\)	\( 1 - T + 23 T^{2}\)	1.23.ab
\(29\)	\( 1 + 29 T^{2}\)	1.29.a
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 96824e do not have complex multiplication.

Modular form 96824.2.a.e

Elliptic curves in class 96824e

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
96824.g1	96824e1	\([0, 0, 0, 49, -1029]\)	\(6912/247\)	\(-464948848\)	\([]\)	\(28800\)	\(0.34304\)	\(\Gamma_0(N)\)-optimal