Elliptic curve isogeny class with Cremona label 73920ed (LMFDB label 73920.g)

• Label: 73920ed
• Number of curves: $4$
• Conductor: $73920$
• CM: no
• Rank: $0$

Elliptic curves in class 73920ed

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
73920.g3	73920ed1	\([0, -1, 0, -28476, 1858626]\)	\(39902117402149696/11253263175\)	\(720208843200\)	\([2]\)	\(147456\)	\(1.2563\)	\(\Gamma_0(N)\)-optimal
73920.g2	73920ed2	\([0, -1, 0, -32121, 1356345]\)	\(894838079076544/326869475625\)	\(1338857372160000\)	\([2, 2]\)	\(294912\)	\(1.6029\)
73920.g4	73920ed3	\([0, -1, 0, 98559, 9484641]\)	\(3231158304084472/3064088671875\)	\(-100404057600000000\)	\([2]\)	\(589824\)	\(1.9495\)
73920.g1	73920ed4	\([0, -1, 0, -221121, -38976255]\)	\(36489314991346568/1012845712725\)	\(33188928314572800\)	\([2]\)	\(589824\)	\(1.9495\)

Rank

The elliptic curves in class 73920ed have rank \(0\).

Complex multiplication

The elliptic curves in class 73920ed do not have complex multiplication.

Modular form 73920.2.a.ed

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.

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.