Elliptic curve isogeny class with LMFDB label 25168.e (Cremona label 25168d)

• Label: 25168.e
• Number of curves: $1$
• Conductor: $25168$
• CM: no
• Rank: $2$

Rank

The elliptic curve 25168.e1 has rank \(2\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(11\)	\(1\)
\(13\)	\(1 + T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(3\)	\( 1 + T + 3 T^{2}\)	1.3.b
\(5\)	\( 1 + 4 T + 5 T^{2}\)	1.5.e
\(7\)	\( 1 + 2 T + 7 T^{2}\)	1.7.c
\(17\)	\( 1 + 3 T + 17 T^{2}\)	1.17.d
\(19\)	\( 1 + 19 T^{2}\)	1.19.a
\(23\)	\( 1 - T + 23 T^{2}\)	1.23.ab
\(29\)	\( 1 - 5 T + 29 T^{2}\)	1.29.af
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 25168.e do not have complex multiplication.

Modular form 25168.2.a.e

Elliptic curves in class 25168.e

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
25168.e1	25168d1	\([0, -1, 0, -40, -64]\)	\(58564/13\)	\(1610752\)	\([]\)	\(3840\)	\(-0.095716\)	\(\Gamma_0(N)\)-optimal