Elliptic curve isogeny class with LMFDB label 9450.e (Cremona label 9450g)

• Label: 9450.e
• Number of curves: $3$
• Conductor: $9450$
• CM: no
• Rank: $1$

Elliptic curves in class 9450.e

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
9450.e1	9450g3	\([1, -1, 0, -1208817, 511853341]\)	\(-51449278832786523/125440\)	\(-476280000000\)	\([]\)	\(93312\)	\(1.9071\)
9450.e2	9450g1	\([1, -1, 0, -14442, 752716]\)	\(-789657671907/117649000\)	\(-49633171875000\)	\([]\)	\(31104\)	\(1.3578\)	\(\Gamma_0(N)\)-optimal
9450.e3	9450g2	\([1, -1, 0, 95808, -2469034]\)	\(316238809797/191406250\)	\(-58866394042968750\)	\([]\)	\(93312\)	\(1.9071\)

Rank

The elliptic curves in class 9450.e have rank \(1\).

Complex multiplication

The elliptic curves in class 9450.e do not have complex multiplication.

Modular form 9450.2.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 LMFDB numbering.

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

Isogeny graph

The vertices are labelled with LMFDB labels.