Elliptic Curve Isogeny Class with LMFDB label 12615.f (Cremona label 12615f)

• Label: 12615.f
• Number of curves: 8
• Conductor: 12615
• CM: no
• Rank: 1

Elliptic curves in class 12615.f

LMFDB label	Cremona label	Weierstrass coefficients	Torsion structure	Modular degree	Optimality
12615.f1	12615f7	[1, 0, 1, -1816578, -942537797]	[2]	100352
12615.f2	12615f5	[1, 0, 1, -113553, -14729777]	[2, 2]	50176
12615.f3	12615f8	[1, 0, 1, -92528, -20347657]	[2]	100352
12615.f4	12615f4	[1, 0, 1, -67298, 6714041]	[2]	25088
12615.f5	12615f3	[1, 0, 1, -8428, -138427]	[2, 2]	25088
12615.f6	12615f2	[1, 0, 1, -4223, 103781]	[2, 2]	12544
12615.f7	12615f1	[1, 0, 1, -18, 4543]	[2]	6272	\(\Gamma_0(N)\)-optimal
12615.f8	12615f6	[1, 0, 1, 29417, -1031569]	[2]	50176

Rank

The elliptic curves in class 12615.f have rank \(1\).

Modular form 12615.2.a.f

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 LMFDB numbering.

\(\left(\begin{array}{rrrrrrrr} 1 & 2 & 4 & 16 & 4 & 8 & 16 & 8 \\ 2 & 1 & 2 & 8 & 2 & 4 & 8 & 4 \\ 4 & 2 & 1 & 16 & 4 & 8 & 16 & 8 \\ 16 & 8 & 16 & 1 & 4 & 2 & 4 & 8 \\ 4 & 2 & 4 & 4 & 1 & 2 & 4 & 2 \\ 8 & 4 & 8 & 2 & 2 & 1 & 2 & 4 \\ 16 & 8 & 16 & 4 & 4 & 2 & 1 & 8 \\ 8 & 4 & 8 & 8 & 2 & 4 & 8 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with LMFDB labels.