Elliptic curve isogeny class with LMFDB label 37.a (Cremona label 37a)

• Label: 37.a
• Number of curves: $1$
• Conductor: $37$
• CM: no
• Rank: $1$

Rank

The elliptic curve 37.a1 has rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(37\)	\(1 + T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(2\)	\( 1 + 2 T + 2 T^{2}\)	1.2.c
\(3\)	\( 1 + 3 T + 3 T^{2}\)	1.3.d
\(5\)	\( 1 + 2 T + 5 T^{2}\)	1.5.c
\(7\)	\( 1 + T + 7 T^{2}\)	1.7.b
\(11\)	\( 1 + 5 T + 11 T^{2}\)	1.11.f
\(13\)	\( 1 + 2 T + 13 T^{2}\)	1.13.c
\(17\)	\( 1 + 17 T^{2}\)	1.17.a
\(19\)	\( 1 + 19 T^{2}\)	1.19.a
\(23\)	\( 1 - 2 T + 23 T^{2}\)	1.23.ac
\(29\)	\( 1 - 6 T + 29 T^{2}\)	1.29.ag
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 37.a do not have complex multiplication.

Modular form 37.2.a.a

Elliptic curves in class 37.a

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
37.a1	37a1	\([0, 0, 1, -1, 0]\)	\(110592/37\)	\(37\)	\([]\)	\(2\)	\(-0.99654\)	\(\Gamma_0(N)\)-optimal