Elliptic Curve Isogeny Class with Cremona label 21a (LMFDB label 21.a)

• Label: 21a
• Number of curves: 6
• Conductor: 21
• CM: no
• Rank: 0

Elliptic curves in class 21a

LMFDB label	Cremona label	Weierstrass coefficients	Torsion structure	Modular degree	Optimality
21.a5	21a1	[1, 0, 0, -4, -1]	[2, 4]	1	\(\Gamma_0(N)\)-optimal
21.a2	21a2	[1, 0, 0, -49, -136]	[2, 2]	2
21.a3	21a3	[1, 0, 0, -39, 90]	[8]	2
21.a6	21a4	[1, 0, 0, 1, 0]	[4]	2
21.a1	21a5	[1, 0, 0, -784, -8515]	[2]	4
21.a4	21a6	[1, 0, 0, -34, -217]	[2]	4

Rank

The elliptic curves in class 21a have rank \(0\).

Modular form 21.2.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 Cremona numbering.

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

Isogeny graph

The vertices are labelled with Cremona labels.