Elliptic curve isogeny class with Cremona label 57a (LMFDB label 57.a)

• Label: 57a
• Number of curves: $1$
• Conductor: $57$
• CM: no
• Rank: $1$

Rank

The elliptic curve 57a1 has rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(3\)	\(1 + T\)
\(19\)	\(1 + T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(2\)	\( 1 + 2 T + 2 T^{2}\)	1.2.c
\(5\)	\( 1 + 3 T + 5 T^{2}\)	1.5.d
\(7\)	\( 1 + 5 T + 7 T^{2}\)	1.7.f
\(11\)	\( 1 - T + 11 T^{2}\)	1.11.ab
\(13\)	\( 1 - 2 T + 13 T^{2}\)	1.13.ac
\(17\)	\( 1 + T + 17 T^{2}\)	1.17.b
\(23\)	\( 1 + 4 T + 23 T^{2}\)	1.23.e
\(29\)	\( 1 + 2 T + 29 T^{2}\)	1.29.c
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 57a do not have complex multiplication.

Modular form 57.2.a.a

Elliptic curves in class 57a

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
57.a1	57a1	\([0, -1, 1, -2, 2]\)	\(-1404928/171\)	\(-171\)	\([]\)	\(4\)	\(-0.83655\)	\(\Gamma_0(N)\)-optimal