Elliptic curve isogeny class with LMFDB label 51376.s (Cremona label 51376n)

• Label: 51376.s
• Number of curves: $1$
• Conductor: $51376$
• CM: no
• Rank: $2$

Rank

The elliptic curve 51376.s1 has rank \(2\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(13\)	\(1\)
\(19\)	\(1 + T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(3\)	\( 1 - T + 3 T^{2}\)	1.3.ab
\(5\)	\( 1 + T + 5 T^{2}\)	1.5.b
\(7\)	\( 1 + T + 7 T^{2}\)	1.7.b
\(11\)	\( 1 + 11 T^{2}\)	1.11.a
\(17\)	\( 1 + 3 T + 17 T^{2}\)	1.17.d
\(23\)	\( 1 + 6 T + 23 T^{2}\)	1.23.g
\(29\)	\( 1 + 8 T + 29 T^{2}\)	1.29.i
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 51376.s do not have complex multiplication.

Modular form 51376.2.a.s

Elliptic curves in class 51376.s

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
51376.s1	51376n1	\([0, 1, 0, 33744, -1075372]\)	\(214921799/150176\)	\(-2969071076900864\)	\([]\)	\(161280\)	\(1.6574\)	\(\Gamma_0(N)\)-optimal