Elliptic Curve Isogeny Class with Cremona label 7623p (LMFDB label 7623.g)

• Label: 7623p
• Number of curves: 6
• Conductor: 7623
• CM: no
• Rank: 0

Elliptic curves in class 7623p

LMFDB label	Cremona label	Weierstrass coefficients	Torsion order	Modular degree	Optimality
7623.g6	7623p1	[1, -1, 1, 1066, -3220]	2	5120	\(\Gamma_0(N)\)-optimal
7623.g5	7623p2	[1, -1, 1, -4379, -22822]	4	10240
7623.g2	7623p3	[1, -1, 1, -53384, -4727302]	4	20480
7623.g3	7623p4	[1, -1, 1, -42494, 3361790]	2	20480
7623.g1	7623p5	[1, -1, 1, -853799, -303442180]	2	40960
7623.g4	7623p6	[1, -1, 1, -37049, -7687204]	2	40960

Rank

The elliptic curves in class 7623p have rank \(0\).

Modular form 7623.2.a.g

Isogeny matrix

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

\(\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 4 & 8 & 8 \\ 2 & 1 & 2 & 2 & 4 & 4 \\ 4 & 2 & 1 & 4 & 2 & 2 \\ 4 & 2 & 4 & 1 & 8 & 8 \\ 8 & 4 & 2 & 8 & 1 & 4 \\ 8 & 4 & 2 & 8 & 4 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.