Elliptic Curve Isogeny Class with LMFDB label 5415.j (Cremona label 5415k)

• Label: 5415.j
• Number of curves: 8
• Conductor: 5415
• CM: no
• Rank: 0

Elliptic curves in class 5415.j

LMFDB label	Cremona label	Weierstrass coefficients	Torsion structure	Modular degree	Optimality
5415.j1	5415k7	[1, 0, 1, -779768, 264965501]	[2]	27648
5415.j2	5415k5	[1, 0, 1, -48743, 4135781]	[2, 2]	13824
5415.j3	5415k8	[1, 0, 1, -39718, 5716961]	[2]	27648
5415.j4	5415k3	[1, 0, 1, -28888, -1892197]	[2]	6912
5415.j5	5415k4	[1, 0, 1, -3618, 38431]	[2, 2]	6912
5415.j6	5415k2	[1, 0, 1, -1813, -29437]	[2, 2]	3456
5415.j7	5415k1	[1, 0, 1, -8, -1279]	[2]	1728	\(\Gamma_0(N)\)-optimal
5415.j8	5415k6	[1, 0, 1, 12627, 291853]	[2]	13824

Rank

The elliptic curves in class 5415.j have rank \(0\).

Modular form 5415.2.a.j

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.