Elliptic curve isogeny class with LMFDB label 1530.b (Cremona label 1530c)

• Label: 1530.b
• Number of curves: $8$
• Conductor: $1530$
• CM: no
• Rank: $0$

Elliptic curves in class 1530.b

LMFDB label	Cremona label	Weierstrass coefficients	Torsion structure	Modular degree	Optimality
1530.b1	1530c7	[1, -1, 0, -1021230, 397475626]	[2]	16384
1530.b2	1530c3	[1, -1, 0, -195840, -33309104]	[2]	4096
1530.b3	1530c5	[1, -1, 0, -64980, 5986876]	[2, 2]	8192
1530.b4	1530c4	[1, -1, 0, -12960, -453200]	[2, 2]	4096
1530.b5	1530c2	[1, -1, 0, -12240, -518144]	[2, 2]	2048
1530.b6	1530c1	[1, -1, 0, -720, -8960]	[2]	1024	\(\Gamma_0(N)\)-optimal
1530.b7	1530c6	[1, -1, 0, 27540, -2745500]	[2]	8192
1530.b8	1530c8	[1, -1, 0, 58950, 26038750]	[2]	16384

Rank

The elliptic curves in class 1530.b have rank \(0\).

Complex multiplication

The elliptic curves in class 1530.b do not have complex multiplication.

Modular form 1530.2.a.b

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.

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

Isogeny graph

The vertices are labelled with LMFDB labels.