Elliptic curve isogeny class with LMFDB label 51425.r (Cremona label 51425c)

• Label: 51425.r
• Number of curves: $1$
• Conductor: $51425$
• CM: no
• Rank: $2$

Rank

The elliptic curve 51425.r1 has rank \(2\).

L-function data

Bad L-factors:

Prime	L-Factor
\(5\)	\(1\)
\(11\)	\(1\)
\(17\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(2\)	\( 1 + 2 T^{2}\)	1.2.a
\(3\)	\( 1 + 2 T + 3 T^{2}\)	1.3.c
\(7\)	\( 1 - 3 T + 7 T^{2}\)	1.7.ad
\(13\)	\( 1 + 6 T + 13 T^{2}\)	1.13.g
\(19\)	\( 1 + 6 T + 19 T^{2}\)	1.19.g
\(23\)	\( 1 + 6 T + 23 T^{2}\)	1.23.g
\(29\)	\( 1 + 9 T + 29 T^{2}\)	1.29.j
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 51425.r do not have complex multiplication.

Modular form 51425.2.a.r

Elliptic curves in class 51425.r

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
51425.r1	51425c1	\([0, 1, 1, 917, 11369]\)	\(4096000/4913\)	\(-102175046875\)	\([]\)	\(51840\)	\(0.79870\)	\(\Gamma_0(N)\)-optimal