Elliptic curve isogeny class with LMFDB label 5100.s (Cremona label 5100m)

• Label: 5100.s
• Number of curves: $1$
• Conductor: $5100$
• CM: no
• Rank: $0$

Rank

The elliptic curve 5100.s1 has rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1 - T\)
\(5\)	\(1\)
\(17\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(7\)	\( 1 - T + 7 T^{2}\)	1.7.ab
\(11\)	\( 1 - 3 T + 11 T^{2}\)	1.11.ad
\(13\)	\( 1 - 2 T + 13 T^{2}\)	1.13.ac
\(19\)	\( 1 - T + 19 T^{2}\)	1.19.ab
\(23\)	\( 1 - 2 T + 23 T^{2}\)	1.23.ac
\(29\)	\( 1 - 5 T + 29 T^{2}\)	1.29.af
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 5100.s do not have complex multiplication.

Modular form 5100.2.a.s

Elliptic curves in class 5100.s

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
5100.s1	5100m1	\([0, 1, 0, -158, -9687]\)	\(-1755904/159375\)	\(-39843750000\)	\([]\)	\(2880\)	\(0.71361\)	\(\Gamma_0(N)\)-optimal