Elliptic curve isogeny class with LMFDB label 80586.a (Cremona label 80586j)

• Label: 80586.a
• Number of curves: $1$
• Conductor: $80586$
• CM: no
• Rank: $1$

Rank

The elliptic curve 80586.a1 has rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1 + T\)
\(3\)	\(1\)
\(11\)	\(1\)
\(37\)	\(1 + T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 + 4 T + 5 T^{2}\)	1.5.e
\(7\)	\( 1 - T + 7 T^{2}\)	1.7.ab
\(13\)	\( 1 - 3 T + 13 T^{2}\)	1.13.ad
\(17\)	\( 1 - 3 T + 17 T^{2}\)	1.17.ad
\(19\)	\( 1 - 5 T + 19 T^{2}\)	1.19.af
\(23\)	\( 1 + 5 T + 23 T^{2}\)	1.23.f
\(29\)	\( 1 - 4 T + 29 T^{2}\)	1.29.ae
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 80586.a do not have complex multiplication.

Modular form 80586.2.a.a

Elliptic curves in class 80586.a

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
80586.a1	80586j1	\([1, -1, 0, 1611, -1648971]\)	\(357911/909312\)	\(-1174347321827328\)	\([]\)	\(594880\)	\(1.5706\)	\(\Gamma_0(N)\)-optimal