Elliptic curve isogeny class with LMFDB label 2057.c (Cremona label 2057a)

• Label: 2057.c
• Number of curves: $1$
• Conductor: $2057$
• CM: no
• Rank: $1$

Rank

The elliptic curve 2057.c1 has rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(11\)	\(1\)
\(17\)	\(1 + T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(2\)	\( 1 + 2 T^{2}\)	1.2.a
\(3\)	\( 1 - 2 T + 3 T^{2}\)	1.3.ac
\(5\)	\( 1 + 5 T^{2}\)	1.5.a
\(7\)	\( 1 + 3 T + 7 T^{2}\)	1.7.d
\(13\)	\( 1 - 6 T + 13 T^{2}\)	1.13.ag
\(19\)	\( 1 + 6 T + 19 T^{2}\)	1.19.g
\(23\)	\( 1 - 6 T + 23 T^{2}\)	1.23.ag
\(29\)	\( 1 + 9 T + 29 T^{2}\)	1.29.j
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 2057.c do not have complex multiplication.

Modular form 2057.2.a.c

Elliptic curves in class 2057.c

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
2057.c1	2057a1	\([0, -1, 1, 37, 76]\)	\(4096000/4913\)	\(-6539203\)	\([]\)	\(360\)	\(-0.0060196\)	\(\Gamma_0(N)\)-optimal