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

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

Elliptic curves in class 630.h

LMFDB label	Cremona label	Weierstrass coefficients	Torsion structure	Modular degree	Optimality
630.h1	630i7	[1, -1, 1, -3161093, 2164026557]	[6]	9216
630.h2	630i6	[1, -1, 1, -197573, 33848381]	[2, 6]	4608
630.h3	630i8	[1, -1, 1, -183173, 38980541]	[6]	9216
630.h4	630i4	[1, -1, 1, -39218, 2946557]	[2]	3072
630.h5	630i3	[1, -1, 1, -13253, 449597]	[6]	2304
630.h6	630i2	[1, -1, 1, -5198, -74419]	[2, 2]	1536
630.h7	630i1	[1, -1, 1, -4478, -114163]	[2]	768	\(\Gamma_0(N)\)-optimal
630.h8	630i5	[1, -1, 1, 17302, -560419]	[2]	3072

Rank

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

Modular form 630.2.a.h

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.

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

Isogeny graph

The vertices are labelled with LMFDB labels.