Elliptic curve isogeny class with LMFDB label 8624.y (Cremona label 8624t)

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

Rank

The elliptic curves in class 8624.y 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 \(\mathbb{F}_p\)
\(3\)	\( 1 - 2 T + 3 T^{2}\)	1.3.ac
\(5\)	\( 1 + 2 T + 5 T^{2}\)	1.5.c
\(13\)	\( 1 - 2 T + 13 T^{2}\)	1.13.ac
\(17\)	\( 1 + 17 T^{2}\)	1.17.a
\(19\)	\( 1 - 2 T + 19 T^{2}\)	1.19.ac
\(23\)	\( 1 + 23 T^{2}\)	1.23.a
\(29\)	\( 1 - 6 T + 29 T^{2}\)	1.29.ag
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

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

Modular form 8624.2.a.y

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 8624.y

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
8624.y1	8624t2	\([0, -1, 0, -44704, 1440384]\)	\(59776471/29282\)	\(4839974175432704\)	\([2]\)	\(43008\)	\(1.7029\)
8624.y2	8624t1	\([0, -1, 0, 10176, 167168]\)	\(704969/484\)	\(-79999573147648\)	\([2]\)	\(21504\)	\(1.3564\)	\(\Gamma_0(N)\)-optimal