Elliptic curve isogeny class with Cremona label 41262g (LMFDB label 41262.a)

• Label: 41262g
• Number of curves: $4$
• Conductor: $41262$
• CM: no
• Rank: $1$

Elliptic curves in class 41262g

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
41262.a4	41262g1	\([1, 1, 0, -10326, -8436780]\)	\(-822656953/207028224\)	\(-30647607187931136\)	\([2]\)	\(506880\)	\(1.8427\)	\(\Gamma_0(N)\)-optimal
41262.a3	41262g2	\([1, 1, 0, -687446, -217666860]\)	\(242702053576633/2554695936\)	\(378186684010447104\)	\([2, 2]\)	\(1013760\)	\(2.1893\)
41262.a2	41262g3	\([1, 1, 0, -1237606, 179218564]\)	\(1416134368422073/725251155408\)	\(107363199539100437712\)	\([2]\)	\(2027520\)	\(2.5358\)
41262.a1	41262g4	\([1, 1, 0, -10971206, -13991735004]\)	\(986551739719628473/111045168\)	\(16438670164034352\)	\([2]\)	\(2027520\)	\(2.5358\)

Rank

The elliptic curves in class 41262g have rank \(1\).

Complex multiplication

The elliptic curves in class 41262g do not have complex multiplication.

Modular form 41262.2.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.

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.