Elliptic curve isogeny class with LMFDB label 7623.i (Cremona label 7623f)

• Label: 7623.i
• Number of curves: $3$
• Conductor: $7623$
• CM: no
• Rank: $1$

Elliptic curves in class 7623.i

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
7623.i1	7623f1	\([0, 0, 1, -97284, 11679192]\)	\(-78843215872/539\)	\(-696101235291\)	\([]\)	\(24000\)	\(1.4533\)	\(\Gamma_0(N)\)-optimal
7623.i2	7623f2	\([0, 0, 1, -53724, 22160817]\)	\(-13278380032/156590819\)	\(-202232026977976611\)	\([]\)	\(72000\)	\(2.0026\)
7623.i3	7623f3	\([0, 0, 1, 479886, -573614748]\)	\(9463555063808/115539436859\)	\(-149215481859696469371\)	\([]\)	\(216000\)	\(2.5519\)

Rank

The elliptic curves in class 7623.i have rank \(1\).

Complex multiplication

The elliptic curves in class 7623.i do not have complex multiplication.

Modular form 7623.2.a.i

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.