Elliptic Curve Isogeny Class with Cremona label 15a (LMFDB label 15.a)

• Label: 15a
• Number of curves: 8
• Conductor: 15
• CM: no
• Rank: 0

Elliptic curves in class 15a

LMFDB label	Cremona label	Weierstrass coefficients	Torsion structure	Modular degree	Optimality
15.a5	15a1	[1, 1, 1, -10, -10]	[2, 4]	1	\(\Gamma_0(N)\)-optimal
15.a2	15a2	[1, 1, 1, -135, -660]	[2, 2]	2
15.a6	15a3	[1, 1, 1, -5, 2]	[2, 4]	2
15.a8	15a4	[1, 1, 1, 35, -28]	[8]	2
15.a1	15a5	[1, 1, 1, -2160, -39540]	[2]	4
15.a3	15a6	[1, 1, 1, -110, -880]	[2]	4
15.a4	15a7	[1, 1, 1, -80, 242]	[4]	4
15.a7	15a8	[1, 1, 1, 0, 0]	[4]	4

Rank

The elliptic curves in class 15a have rank \(0\).

Modular form 15.2.a.a

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.

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

Isogeny graph

The vertices are labelled with Cremona labels.