Elliptic curve isogeny class with LMFDB label 580.a (Cremona label 580a)

• Label: 580.a
• Number of curves: $2$
• Conductor: $580$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 580.a have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(5\)	\(1 + T\)
\(29\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(3\)	\( 1 + 3 T^{2}\)	1.3.a
\(7\)	\( 1 + 7 T^{2}\)	1.7.a
\(11\)	\( 1 + 2 T + 11 T^{2}\)	1.11.c
\(13\)	\( 1 + 2 T + 13 T^{2}\)	1.13.c
\(17\)	\( 1 + 17 T^{2}\)	1.17.a
\(19\)	\( 1 + 2 T + 19 T^{2}\)	1.19.c
\(23\)	\( 1 + 8 T + 23 T^{2}\)	1.23.i
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 580.a do not have complex multiplication.

Modular form 580.2.a.a

Isogeny matrix

The \((i,j)\)-th entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the LMFDB numbering.

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with LMFDB labels, and the \( \Gamma_0(N) \)-optimal curve is highlighted in blue.

Elliptic curves in class 580.a

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
580.a1	580a1	\([0, 0, 0, -8, -7]\)	\(3538944/725\)	\(11600\)	\([2]\)	\(24\)	\(-0.50465\)	\(\Gamma_0(N)\)-optimal
580.a2	580a2	\([0, 0, 0, 17, -42]\)	\(2122416/4205\)	\(-1076480\)	\([2]\)	\(48\)	\(-0.15807\)