Elliptic curve isogeny class with LMFDB label 126400.e (Cremona label 126400ba)

• Label: 126400.e
• Number of curves: $1$
• Conductor: $126400$
• CM: no
• Rank: $2$

Rank

The elliptic curve 126400.e1 has rank \(2\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(5\)	\(1\)
\(79\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(3\)	\( 1 + 3 T + 3 T^{2}\)	1.3.d
\(7\)	\( 1 - 3 T + 7 T^{2}\)	1.7.ad
\(11\)	\( 1 - 2 T + 11 T^{2}\)	1.11.ac
\(13\)	\( 1 + 5 T + 13 T^{2}\)	1.13.f
\(17\)	\( 1 + 6 T + 17 T^{2}\)	1.17.g
\(19\)	\( 1 + 19 T^{2}\)	1.19.a
\(23\)	\( 1 - 2 T + 23 T^{2}\)	1.23.ac
\(29\)	\( 1 + 6 T + 29 T^{2}\)	1.29.g
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 126400.e do not have complex multiplication.

Modular form 126400.2.a.e

Elliptic curves in class 126400.e

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
126400.e1	126400ba1	\([0, 0, 0, -13900, 454000]\)	\(72511713/20224\)	\(82837504000000\)	\([]\)	\(663552\)	\(1.3779\)	\(\Gamma_0(N)\)-optimal