Elliptic curve isogeny class with LMFDB label 97344.b (Cremona label 97344cz)

• Label: 97344.b
• Number of curves: $1$
• Conductor: $97344$
• CM: no
• Rank: $2$

Rank

The elliptic curve 97344.b1 has rank \(2\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1\)
\(13\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 + 4 T + 5 T^{2}\)	1.5.e
\(7\)	\( 1 + 3 T + 7 T^{2}\)	1.7.d
\(11\)	\( 1 + 2 T + 11 T^{2}\)	1.11.c
\(17\)	\( 1 + 6 T + 17 T^{2}\)	1.17.g
\(19\)	\( 1 + 4 T + 19 T^{2}\)	1.19.e
\(23\)	\( 1 - 8 T + 23 T^{2}\)	1.23.ai
\(29\)	\( 1 + 4 T + 29 T^{2}\)	1.29.e
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 97344.b do not have complex multiplication.

Modular form 97344.2.a.b

Elliptic curves in class 97344.b

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
97344.b1	97344cz1	\([0, 0, 0, 78, 650]\)	\(6656/27\)	\(-212891328\)	\([]\)	\(46080\)	\(0.28068\)	\(\Gamma_0(N)\)-optimal