Elliptic curve isogeny class with LMFDB label 35131.e (Cremona label 35131a)

• Label: 35131.e
• Number of curves: $1$
• Conductor: $35131$
• CM: no
• Rank: $1$

Rank

The elliptic curve 35131.e1 has rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(19\)	\(1 + T\)
\(43\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(2\)	\( 1 - T + 2 T^{2}\)	1.2.ab
\(3\)	\( 1 + 2 T + 3 T^{2}\)	1.3.c
\(5\)	\( 1 - 2 T + 5 T^{2}\)	1.5.ac
\(7\)	\( 1 + 3 T + 7 T^{2}\)	1.7.d
\(11\)	\( 1 - 3 T + 11 T^{2}\)	1.11.ad
\(13\)	\( 1 + 2 T + 13 T^{2}\)	1.13.c
\(17\)	\( 1 + 3 T + 17 T^{2}\)	1.17.d
\(23\)	\( 1 + T + 23 T^{2}\)	1.23.b
\(29\)	\( 1 + 29 T^{2}\)	1.29.a
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 35131.e do not have complex multiplication.

Modular form 35131.2.a.e

Elliptic curves in class 35131.e

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
35131.e1	35131a1	\([1, 0, 1, -172879690, 874896991611]\)	\(-48888643731442873/6859\)	\(-80169365704065259\)	\([]\)	\(2394756\)	\(3.0971\)	\(\Gamma_0(N)\)-optimal