Elliptic curve isogeny class with Cremona label 115a (LMFDB label 115.a)

• Label: 115a
• Number of curves: $1$
• Conductor: $115$
• CM: no
• Rank: $0$

Rank

The elliptic curve 115a1 has rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(5\)	\(1 + T\)
\(23\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(2\)	\( 1 - 2 T + 2 T^{2}\)	1.2.ac
\(3\)	\( 1 + 3 T^{2}\)	1.3.a
\(7\)	\( 1 - T + 7 T^{2}\)	1.7.ab
\(11\)	\( 1 - 2 T + 11 T^{2}\)	1.11.ac
\(13\)	\( 1 + 2 T + 13 T^{2}\)	1.13.c
\(17\)	\( 1 - 3 T + 17 T^{2}\)	1.17.ad
\(19\)	\( 1 + 2 T + 19 T^{2}\)	1.19.c
\(29\)	\( 1 - 7 T + 29 T^{2}\)	1.29.ah
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 115a do not have complex multiplication.

Modular form 115.2.a.a

Isogeny graph

Elliptic curves in class 115a

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
115.a1	115a1	\([0, 0, 1, 7, -11]\)	\(37933056/71875\)	\(-71875\)	\([]\)	\(10\)	\(-0.38348\)	\(\Gamma_0(N)\)-optimal