Elliptic curve isogeny class with Cremona label 342a (LMFDB label 342.e)

• Label: 342a
• Number of curves: $3$
• Conductor: $342$
• CM: no
• Rank: $0$

Elliptic curves in class 342a

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
342.e2	342a1	$[1, -1, 1, -140, -601]$	$-413493625/152$	$-110808$	$[]$	$60$	$-0.064137$	$\Gamma_0(N)$-optimal
342.e3	342a2	$[1, -1, 1, 85, -2437]$	$94196375/3511808$	$-2560108032$	$[3]$	$180$	$0.48517$
342.e1	342a3	$[1, -1, 1, -770, 66305]$	$-69173457625/2550136832$	$-1859049750528$	$[3]$	$540$	$1.0345$

Rank

The elliptic curves in class 342a have rank $0$.

Complex multiplication

The elliptic curves in class 342a do not have complex multiplication.

Modular form 342.2.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.

$\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)$

Isogeny graph

The vertices are labelled with Cremona labels.