Elliptic curve isogeny class with LMFDB label 34.a (Cremona label 34a)

• Label: 34.a
• Number of curves: $4$
• Conductor: $34$
• CM: no
• Rank: $0$

Elliptic curves in class 34.a

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
34.a1	34a4	$[1, 0, 0, -113, -329]$	$159661140625/48275138$	$48275138$	$[2]$	$12$	$0.17949$
34.a2	34a3	$[1, 0, 0, -103, -411]$	$120920208625/19652$	$19652$	$[2]$	$6$	$-0.16709$
34.a3	34a2	$[1, 0, 0, -43, 105]$	$8805624625/2312$	$2312$	$[6]$	$4$	$-0.36982$
34.a4	34a1	$[1, 0, 0, -3, 1]$	$3048625/1088$	$1088$	$[6]$	$2$	$-0.71639$	$\Gamma_0(N)$-optimal

Rank

The elliptic curves in class 34.a have rank $0$.

Complex multiplication

The elliptic curves in class 34.a do not have complex multiplication.

Modular form 34.2.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.

$\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)$

Isogeny graph

The vertices are labelled with LMFDB labels.