Elliptic curve isogeny class with Cremona label 25688c (LMFDB label 25688.i)

• Label: 25688c
• Number of curves: $1$
• Conductor: $25688$
• CM: no
• Rank: $2$

Rank

The elliptic curve 25688c1 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 \(\mathbb{F}_p\)
\(3\)	\( 1 + 2 T + 3 T^{2}\)	1.3.c
\(5\)	\( 1 - T + 5 T^{2}\)	1.5.ab
\(7\)	\( 1 - 3 T + 7 T^{2}\)	1.7.ad
\(11\)	\( 1 - 3 T + 11 T^{2}\)	1.11.ad
\(17\)	\( 1 - 5 T + 17 T^{2}\)	1.17.af
\(23\)	\( 1 + 23 T^{2}\)	1.23.a
\(29\)	\( 1 - 2 T + 29 T^{2}\)	1.29.ac
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

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

Modular form 25688.2.a.c

Elliptic curves in class 25688c

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
25688.i1	25688c1	\([0, 1, 0, -27096, -4602064]\)	\(-101306/361\)	\(-7840203312441344\)	\([]\)	\(104832\)	\(1.7357\)	\(\Gamma_0(N)\)-optimal