Elliptic Curve Isogeny Class with LMFDB label 630.f (Cremona label 630f)

• Label: 630.f
• Number of curves: 8
• Conductor: 630
• CM: no
• Rank: 0

Elliptic curves in class 630.f

LMFDB label	Cremona label	Weierstrass coefficients	Torsion structure	Modular degree	Optimality
630.f1	630f7	[1, -1, 0, -58059, -3373137]	[6]	4608
630.f2	630f4	[1, -1, 0, -51849, -4531275]	[2]	1536
630.f3	630f6	[1, -1, 0, -24309, 1426113]	[2, 6]	2304
630.f4	630f3	[1, -1, 0, -24129, 1448685]	[6]	1152
630.f5	630f2	[1, -1, 0, -3249, -69795]	[2, 2]	768
630.f6	630f5	[1, -1, 0, -729, -177147]	[2]	1536
630.f7	630f1	[1, -1, 0, -369, 1053]	[2]	384	\(\Gamma_0(N)\)-optimal
630.f8	630f8	[1, -1, 0, 6561, 4778595]	[6]	4608

Rank

The elliptic curves in class 630.f have rank \(0\).

Modular form 630.2.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.

\(\left(\begin{array}{rrrrrrrr} 1 & 3 & 2 & 4 & 6 & 12 & 12 & 4 \\ 3 & 1 & 6 & 12 & 2 & 4 & 4 & 12 \\ 2 & 6 & 1 & 2 & 3 & 6 & 6 & 2 \\ 4 & 12 & 2 & 1 & 6 & 12 & 3 & 4 \\ 6 & 2 & 3 & 6 & 1 & 2 & 2 & 6 \\ 12 & 4 & 6 & 12 & 2 & 1 & 4 & 3 \\ 12 & 4 & 6 & 3 & 2 & 4 & 1 & 12 \\ 4 & 12 & 2 & 4 & 6 & 3 & 12 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with LMFDB labels.