Elliptic curve isogeny class with Cremona label 247962g (LMFDB label 247962.g)

• Label: 247962g
• Number of curves: $4$
• Conductor: $247962$
• CM: no
• Rank: $1$

Elliptic curves in class 247962g

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
247962.g4	247962g1	\([1, 1, 0, 103890, 9310644]\)	\(5137417856375/4510142208\)	\(-108863868745412352\)	\([2]\)	\(2985984\)	\(1.9566\)	\(\Gamma_0(N)\)-optimal
247962.g3	247962g2	\([1, 1, 0, -520350, 82097028]\)	\(645532578015625/252306960048\)	\(6090076657338843312\)	\([2]\)	\(5971968\)	\(2.3031\)
247962.g2	247962g3	\([1, 1, 0, -1079565, -576972963]\)	\(-5764706497797625/2612665516032\)	\(-63063394167143006208\)	\([2]\)	\(8957952\)	\(2.5059\)
247962.g1	247962g4	\([1, 1, 0, -18835725, -31469140131]\)	\(30618029936661765625/3678951124992\)	\(88800936627122024448\)	\([2]\)	\(17915904\)	\(2.8524\)

Rank

The elliptic curves in class 247962g have rank \(1\).

Complex multiplication

The elliptic curves in class 247962g do not have complex multiplication.

Modular form 247962.2.a.g

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.

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.