Elliptic curve isogeny class with LMFDB label 21.a (Cremona label 21a)

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

Elliptic curves in class 21.a

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
21.a1	21a5	$[1, 0, 0, -784, -8515]$	$53297461115137/147$	$147$	$[2]$	$4$	$0.074205$
21.a2	21a2	$[1, 0, 0, -49, -136]$	$13027640977/21609$	$21609$	$[2, 2]$	$2$	$-0.27237$
21.a3	21a3	$[1, 0, 0, -39, 90]$	$6570725617/45927$	$45927$	$[8]$	$2$	$-0.27237$
21.a4	21a6	$[1, 0, 0, -34, -217]$	$-4354703137/17294403$	$-17294403$	$[2]$	$4$	$0.074205$
21.a5	21a1	$[1, 0, 0, -4, -1]$	$7189057/3969$	$3969$	$[2, 4]$	$1$	$-0.61894$	$\Gamma_0(N)$-optimal
21.a6	21a4	$[1, 0, 0, 1, 0]$	$103823/63$	$-63$	$[4]$	$2$	$-0.96552$

Rank

The elliptic curves in class 21.a have rank $0$.

Complex multiplication

The elliptic curves in class 21.a do not have complex multiplication.

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 LMFDB numbering.

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

Isogeny graph

The vertices are labelled with LMFDB labels.