Elliptic curve isogeny class with LMFDB label 8624.l (Cremona label 8624n)

• Label: 8624.l
• Number of curves: $2$
• Conductor: $8624$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 8624.l have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(7\)	\(1\)
\(11\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(3\)	\( 1 + T + 3 T^{2}\)	1.3.b
\(5\)	\( 1 + 5 T^{2}\)	1.5.a
\(13\)	\( 1 - 5 T + 13 T^{2}\)	1.13.af
\(17\)	\( 1 - 6 T + 17 T^{2}\)	1.17.ag
\(19\)	\( 1 + 2 T + 19 T^{2}\)	1.19.c
\(23\)	\( 1 + 6 T + 23 T^{2}\)	1.23.g
\(29\)	\( 1 - 3 T + 29 T^{2}\)	1.29.ad
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 8624.l do not have complex multiplication.

Modular form 8624.2.a.l

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.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

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

Elliptic curves in class 8624.l

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
8624.l1	8624n2	\([0, -1, 0, -4451568, 3616561600]\)	\(413160293352625/42592\)	\(1005708919570432\)	\([]\)	\(120960\)	\(2.3084\)
8624.l2	8624n1	\([0, -1, 0, -61168, 3789248]\)	\(1071912625/360448\)	\(8511123418513408\)	\([]\)	\(40320\)	\(1.7591\)	\(\Gamma_0(N)\)-optimal