Elliptic curve isogeny class with Cremona label 1620e (LMFDB label 1620.d)

• Label: 1620e
• Number of curves: $2$
• Conductor: $1620$
• CM: no
• Rank: $1$

Elliptic curves in class 1620e

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
1620.d2	1620e1	$[0, 0, 0, -72, 36]$	$221184/125$	$23328000$	$[3]$	$432$	$0.10377$	$\Gamma_0(N)$-optimal
1620.d1	1620e2	$[0, 0, 0, -3672, -85644]$	$362225664/5$	$75582720$	$[]$	$1296$	$0.65307$

Rank

The elliptic curves in class 1620e have rank $1$.

Complex multiplication

The elliptic curves in class 1620e do not have complex multiplication.

Modular form 1620.2.a.e

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.

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

Isogeny graph

The vertices are labelled with Cremona labels.