Elliptic curve isogeny class with LMFDB label 75840.z (Cremona label 75840q)

• Label: 75840.z
• Number of curves: $1$
• Conductor: $75840$
• CM: no
• Rank: $1$

Rank

The elliptic curve 75840.z1 has rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1 + T\)
\(5\)	\(1 - T\)
\(79\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(7\)	\( 1 + T + 7 T^{2}\)	1.7.b
\(11\)	\( 1 - 5 T + 11 T^{2}\)	1.11.af
\(13\)	\( 1 - 5 T + 13 T^{2}\)	1.13.af
\(17\)	\( 1 + 3 T + 17 T^{2}\)	1.17.d
\(19\)	\( 1 + 4 T + 19 T^{2}\)	1.19.e
\(23\)	\( 1 + 9 T + 23 T^{2}\)	1.23.j
\(29\)	\( 1 + 3 T + 29 T^{2}\)	1.29.d
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 75840.z do not have complex multiplication.

Modular form 75840.2.a.z

Elliptic curves in class 75840.z

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
75840.z1	75840q1	\([0, -1, 0, -60, 342]\)	\(-379503424/479925\)	\(-30715200\)	\([]\)	\(23040\)	\(0.12997\)	\(\Gamma_0(N)\)-optimal