Elliptic curve isogeny class with Cremona label 114240gr (LMFDB label 114240.dm)

• Label: 114240gr
• Number of curves: $4$
• Conductor: $114240$
• CM: no
• Rank: $1$

Elliptic curves in class 114240gr

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
114240.dm4	114240gr1	\([0, -1, 0, -11585, 1094625]\)	\(-656008386769/1581036975\)	\(-414459356774400\)	\([2]\)	\(393216\)	\(1.4930\)	\(\Gamma_0(N)\)-optimal
114240.dm3	114240gr2	\([0, -1, 0, -244865, 46677537]\)	\(6193921595708449/6452105625\)	\(1691380776960000\)	\([2, 2]\)	\(786432\)	\(1.8395\)
114240.dm2	114240gr3	\([0, -1, 0, -305345, 21917025]\)	\(12010404962647729/6166198828125\)	\(1616432025600000000\)	\([2]\)	\(1572864\)	\(2.1861\)
114240.dm1	114240gr4	\([0, -1, 0, -3916865, 2985011937]\)	\(25351269426118370449/27551475\)	\(7222453862400\)	\([2]\)	\(1572864\)	\(2.1861\)

Rank

The elliptic curves in class 114240gr have rank \(1\).

Complex multiplication

The elliptic curves in class 114240gr do not have complex multiplication.

Modular form 114240.2.a.gr

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.