Elliptic curve isogeny class with Cremona label 41280ca (LMFDB label 41280.b)

• Label: 41280ca
• Number of curves: $1$
• Conductor: $41280$
• CM: no
• Rank: $2$

Rank

The elliptic curve 41280ca1 has rank \(2\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1 - T\)
\(5\)	\(1 + T\)
\(43\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(7\)	\( 1 + T + 7 T^{2}\)	1.7.b
\(11\)	\( 1 - 4 T + 11 T^{2}\)	1.11.ae
\(13\)	\( 1 - 5 T + 13 T^{2}\)	1.13.af
\(17\)	\( 1 + 8 T + 17 T^{2}\)	1.17.i
\(19\)	\( 1 - 5 T + 19 T^{2}\)	1.19.af
\(23\)	\( 1 - 8 T + 23 T^{2}\)	1.23.ai
\(29\)	\( 1 - 3 T + 29 T^{2}\)	1.29.ad
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 41280ca do not have complex multiplication.

Modular form 41280.2.a.ca

Elliptic curves in class 41280ca

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
41280.b1	41280ca1	\([0, -1, 0, -72001, 7460335]\)	\(-645008376471556096/783675\)	\(-50155200\)	\([]\)	\(92160\)	\(1.1890\)	\(\Gamma_0(N)\)-optimal