Elliptic curve isogeny class with Cremona label 130050ek (LMFDB label 130050.b)

• Label: 130050ek
• Number of curves: $1$
• Conductor: $130050$
• CM: no
• Rank: $0$

Rank

The elliptic curve 130050ek1 has rank \(0\).

L-function data

Bad L-factors:

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

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(7\)	\( 1 + 3 T + 7 T^{2}\)	1.7.d
\(11\)	\( 1 + 11 T^{2}\)	1.11.a
\(13\)	\( 1 + T + 13 T^{2}\)	1.13.b
\(19\)	\( 1 + 19 T^{2}\)	1.19.a
\(23\)	\( 1 + 4 T + 23 T^{2}\)	1.23.e
\(29\)	\( 1 + 4 T + 29 T^{2}\)	1.29.e
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 130050ek do not have complex multiplication.

Modular form 130050.2.a.ek

Elliptic curves in class 130050ek

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
130050.b1	130050ek1	\([1, -1, 0, 3529503, 413549901]\)	\(11053587253415/6565418768\)	\(-2888174954395371229200\)	\([]\)	\(11612160\)	\(2.8072\)	\(\Gamma_0(N)\)-optimal