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.