Elliptic curve isogeny class with Cremona label 297024ej (LMFDB label 297024.ej)

• Label: 297024ej
• Number of curves: $4$
• Conductor: $297024$
• CM: no
• Rank: $1$

Elliptic curves in class 297024ej

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
297024.ej4	297024ej1	\([0, 1, 0, -6529, -167713]\)	\(117433042273/22801233\)	\(5977206423552\)	\([2]\)	\(655360\)	\(1.1685\)	\(\Gamma_0(N)\)-optimal
297024.ej2	297024ej2	\([0, 1, 0, -99009, -12023649]\)	\(409460675852593/21538881\)	\(5646288420864\)	\([2, 2]\)	\(1310720\)	\(1.5151\)
297024.ej3	297024ej3	\([0, 1, 0, -93569, -13397793]\)	\(-345608484635233/94427721297\)	\(-24753660571680768\)	\([2]\)	\(2621440\)	\(1.8617\)
297024.ej1	297024ej4	\([0, 1, 0, -1584129, -767949729]\)	\(1677087406638588673/4641\)	\(1216610304\)	\([2]\)	\(2621440\)	\(1.8617\)

Rank

The elliptic curves in class 297024ej have rank \(1\).

Complex multiplication

The elliptic curves in class 297024ej do not have complex multiplication.

Modular form 297024.2.a.ej

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.