Elliptic curve isogeny class with LMFDB label 25688.l (Cremona label 25688b)

• Label: 25688.l
• Number of curves: $1$
• Conductor: $25688$
• CM: no
• Rank: $1$

Rank

The elliptic curve 25688.l1 has rank \(1\).

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 \(\mathbb{F}_p\)
\(3\)	\( 1 - 2 T + 3 T^{2}\)	1.3.ac
\(5\)	\( 1 + 5 T^{2}\)	1.5.a
\(7\)	\( 1 - 2 T + 7 T^{2}\)	1.7.ac
\(11\)	\( 1 - 4 T + 11 T^{2}\)	1.11.ae
\(17\)	\( 1 + 3 T + 17 T^{2}\)	1.17.d
\(23\)	\( 1 - T + 23 T^{2}\)	1.23.ab
\(29\)	\( 1 + 2 T + 29 T^{2}\)	1.29.c
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 25688.l do not have complex multiplication.

Modular form 25688.2.a.l

Elliptic curves in class 25688.l

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
25688.l1	25688b1	\([0, -1, 0, -1408, -20931]\)	\(-4000000/247\)	\(-19075549168\)	\([]\)	\(13440\)	\(0.72702\)	\(\Gamma_0(N)\)-optimal