Elliptic curve isogeny class with Cremona label 264992a (LMFDB label 264992.a)

• Label: 264992a
• Number of curves: $1$
• Conductor: $264992$
• CM: no
• Rank: $1$

Rank

The elliptic curve 264992a1 has rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(7\)	\(1\)
\(13\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(3\)	\( 1 + 3 T + 3 T^{2}\)	1.3.d
\(5\)	\( 1 + 3 T + 5 T^{2}\)	1.5.d
\(11\)	\( 1 - 4 T + 11 T^{2}\)	1.11.ae
\(17\)	\( 1 + 5 T + 17 T^{2}\)	1.17.f
\(19\)	\( 1 + 6 T + 19 T^{2}\)	1.19.g
\(23\)	\( 1 + 6 T + 23 T^{2}\)	1.23.g
\(29\)	\( 1 + 4 T + 29 T^{2}\)	1.29.e
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 264992a do not have complex multiplication.

Modular form 264992.2.a.a

Elliptic curves in class 264992a

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
264992.a1	264992a1	\([0, 0, 0, -4459, -115934]\)	\(-74088\)	\(-132339124736\)	\([]\)	\(653184\)	\(0.94135\)	\(\Gamma_0(N)\)-optimal