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 \(0\).

Complex multiplication

The elliptic curves in class 630.h do not have complex multiplication.

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.