Elliptic curve isogeny class with LMFDB label 588.f (Cremona label 588d)

• Label: 588.f
• Number of curves: $1$
• Conductor: $588$
• CM: no
• Rank: $0$

Rank

The elliptic curve 588.f1 has rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1 - T\)
\(7\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 - 2 T + 5 T^{2}\)	1.5.ac
\(11\)	\( 1 - 2 T + 11 T^{2}\)	1.11.ac
\(13\)	\( 1 - 3 T + 13 T^{2}\)	1.13.ad
\(17\)	\( 1 + 8 T + 17 T^{2}\)	1.17.i
\(19\)	\( 1 - T + 19 T^{2}\)	1.19.ab
\(23\)	\( 1 - 8 T + 23 T^{2}\)	1.23.ai
\(29\)	\( 1 - 4 T + 29 T^{2}\)	1.29.ae
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 588.f do not have complex multiplication.

Modular form 588.2.a.f

Elliptic curves in class 588.f

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
588.f1	588d1	\([0, 1, 0, 6403, 44463]\)	\(401408/243\)	\(-17572220289792\)	\([]\)	\(1260\)	\(1.2307\)	\(\Gamma_0(N)\)-optimal