Elliptic curve isogeny class with Cremona label 61050b (LMFDB label 61050.e)

• Label: 61050b
• Number of curves: $1$
• Conductor: $61050$
• CM: no
• Rank: $1$

Rank

The elliptic curve 61050b1 has rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1 + T\)
\(3\)	\(1 + T\)
\(5\)	\(1\)
\(11\)	\(1 + T\)
\(37\)	\(1 + T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(7\)	\( 1 + 4 T + 7 T^{2}\)	1.7.e
\(13\)	\( 1 + 4 T + 13 T^{2}\)	1.13.e
\(17\)	\( 1 + 2 T + 17 T^{2}\)	1.17.c
\(19\)	\( 1 + 2 T + 19 T^{2}\)	1.19.c
\(23\)	\( 1 - 2 T + 23 T^{2}\)	1.23.ac
\(29\)	\( 1 - 10 T + 29 T^{2}\)	1.29.ak
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 61050b do not have complex multiplication.

Modular form 61050.2.a.b

Elliptic curves in class 61050b

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
61050.e1	61050b1	\([1, 1, 0, -12375, -232875]\)	\(13415107060081/6329664000\)	\(98901000000000\)	\([]\)	\(207360\)	\(1.3796\)	\(\Gamma_0(N)\)-optimal