Elliptic curve isogeny class with LMFDB label 2646.e (Cremona label 2646n)

• Label: 2646.e
• Number of curves: $1$
• Conductor: $2646$
• CM: no
• Rank: $1$

Rank

The elliptic curve 2646.e1 has rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1 + T\)
\(3\)	\(1\)
\(7\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 + T + 5 T^{2}\)	1.5.b
\(11\)	\( 1 + T + 11 T^{2}\)	1.11.b
\(13\)	\( 1 - 2 T + 13 T^{2}\)	1.13.ac
\(17\)	\( 1 + 6 T + 17 T^{2}\)	1.17.g
\(19\)	\( 1 - 5 T + 19 T^{2}\)	1.19.af
\(23\)	\( 1 - 3 T + 23 T^{2}\)	1.23.ad
\(29\)	\( 1 - 2 T + 29 T^{2}\)	1.29.ac
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 2646.e do not have complex multiplication.

Modular form 2646.2.a.e

Elliptic curves in class 2646.e

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
2646.e1	2646n1	\([1, -1, 0, -129075, 17999477]\)	\(-33268701/256\)	\(-1830021227322624\)	\([]\)	\(16128\)	\(1.7581\)	\(\Gamma_0(N)\)-optimal