Elliptic curve isogeny class with Cremona label 2574e (LMFDB label 2574.i)

• Label: 2574e
• Number of curves: $1$
• Conductor: $2574$
• CM: no
• Rank: $0$

Rank

The elliptic curve 2574e1 has rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1 + T\)
\(3\)	\(1\)
\(11\)	\(1 - T\)
\(13\)	\(1 + T\)

Good L-factors:

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

See L-function page for more information

Complex multiplication

The elliptic curves in class 2574e do not have complex multiplication.

Modular form 2574.2.a.e

Elliptic curves in class 2574e

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
2574.i1	2574e1	\([1, -1, 0, -414, -3308]\)	\(-10779215329/658944\)	\(-480370176\)	\([]\)	\(1152\)	\(0.42053\)	\(\Gamma_0(N)\)-optimal