Elliptic curve isogeny class with LMFDB label 357.a (Cremona label 357d)

• Label: 357.a
• Number of curves: $1$
• Conductor: $357$
• CM: no
• Rank: $1$

Rank

The elliptic curve 357.a1 has rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(3\)	\(1 - T\)
\(7\)	\(1 - T\)
\(17\)	\(1 + T\)

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
\(11\)	\( 1 + 3 T + 11 T^{2}\)	1.11.d
\(13\)	\( 1 - T + 13 T^{2}\)	1.13.ab
\(19\)	\( 1 + 7 T + 19 T^{2}\)	1.19.h
\(23\)	\( 1 - T + 23 T^{2}\)	1.23.ab
\(29\)	\( 1 + 10 T + 29 T^{2}\)	1.29.k
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 357.a do not have complex multiplication.

Modular form 357.2.a.a

Elliptic curves in class 357.a

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
357.a1	357d1	\([0, 1, 1, -42, 110]\)	\(-8390176768/1821771\)	\(-1821771\)	\([]\)	\(112\)	\(-0.077806\)	\(\Gamma_0(N)\)-optimal