Elliptic curve isogeny class with Cremona label 9240c (LMFDB label 9240.f)

• Label: 9240c
• Number of curves: $4$
• Conductor: $9240$
• CM: no
• Rank: $1$

Elliptic curves in class 9240c

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
9240.f4	9240c1	\([0, -1, 0, -71, -6180]\)	\(-2508888064/1037680875\)	\(-16602894000\)	\([2]\)	\(7680\)	\(0.64020\)	\(\Gamma_0(N)\)-optimal
9240.f3	9240c2	\([0, -1, 0, -5516, -154284]\)	\(72516235474384/833765625\)	\(213444000000\)	\([2, 2]\)	\(15360\)	\(0.98678\)
9240.f1	9240c3	\([0, -1, 0, -88016, -10021284]\)	\(73639964854838596/9904125\)	\(10141824000\)	\([2]\)	\(30720\)	\(1.3333\)
9240.f2	9240c4	\([0, -1, 0, -10136, 146940]\)	\(112477694831716/56396484375\)	\(57750000000000\)	\([2]\)	\(30720\)	\(1.3333\)

Rank

The elliptic curves in class 9240c have rank \(1\).

Complex multiplication

The elliptic curves in class 9240c do not have complex multiplication.

Modular form 9240.2.a.c

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.