Elliptic curve isogeny class with LMFDB label 145008.e (Cremona label 145008b)

• Label: 145008.e
• Number of curves: $1$
• Conductor: $145008$
• CM: no
• Rank: $2$

Rank

The elliptic curve 145008.e1 has rank \(2\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1\)
\(19\)	\(1 - T\)
\(53\)	\(1 + T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 + 3 T + 5 T^{2}\)	1.5.d
\(7\)	\( 1 + 3 T + 7 T^{2}\)	1.7.d
\(11\)	\( 1 - 2 T + 11 T^{2}\)	1.11.ac
\(13\)	\( 1 + 2 T + 13 T^{2}\)	1.13.c
\(17\)	\( 1 + 2 T + 17 T^{2}\)	1.17.c
\(23\)	\( 1 + 3 T + 23 T^{2}\)	1.23.d
\(29\)	\( 1 + 9 T + 29 T^{2}\)	1.29.j
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 145008.e do not have complex multiplication.

Modular form 145008.2.a.e

Elliptic curves in class 145008.e

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
145008.e1	145008b1	\([0, 0, 0, -130044, 18026399]\)	\(20851973263409152/31889679021\)	\(371961216100944\)	\([]\)	\(729600\)	\(1.6954\)	\(\Gamma_0(N)\)-optimal