Elliptic Curve Isogeny Class with LMFDB label 30.a (Cremona label 30a)

• Label: 30.a
• Number of curves: 8
• Conductor: 30
• CM: no
• Rank: 0

Elliptic curves in class 30.a

LMFDB label	Cremona label	Weierstrass coefficients	Torsion structure	Modular degree	Optimality
30.a1	30a7	[1, 0, 1, -5334, -150368]	[2]	24
30.a2	30a8	[1, 0, 1, -454, -544]	[2]	24
30.a3	30a6	[1, 0, 1, -334, -2368]	[2, 2]	12
30.a4	30a5	[1, 0, 1, -289, 1862]	[6]	8
30.a5	30a4	[1, 0, 1, -69, -194]	[6]	8
30.a6	30a2	[1, 0, 1, -19, 26]	[2, 6]	4
30.a7	30a3	[1, 0, 1, -14, -64]	[2]	6
30.a8	30a1	[1, 0, 1, 1, 2]	[6]	2	\(\Gamma_0(N)\)-optimal

Rank

The elliptic curves in class 30.a have rank \(0\).

Modular form 30.2.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 LMFDB numbering.

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

Isogeny graph

The vertices are labelled with LMFDB labels.