Elliptic curve isogeny class with Cremona label 344760y (LMFDB label 344760.y)

• Label: 344760y
• Number of curves: $4$
• Conductor: $344760$
• CM: no
• Rank: $2$

Elliptic curves in class 344760y

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
344760.y3	344760y1	\([0, -1, 0, -160775, 20395452]\)	\(5951163357184/1129312125\)	\(87215582860146000\)	\([2]\)	\(3317760\)	\(1.9682\)	\(\Gamma_0(N)\)-optimal
344760.y2	344760y2	\([0, -1, 0, -776780, -244733100]\)	\(41948679809104/3291890625\)	\(4067667787716000000\)	\([2, 2]\)	\(6635520\)	\(2.3147\)
344760.y4	344760y3	\([0, -1, 0, 774640, -1101737508]\)	\(10400706415004/112060546875\)	\(-553876332750000000000\)	\([2]\)	\(13271040\)	\(2.6613\)
344760.y1	344760y4	\([0, -1, 0, -12184280, -16365812100]\)	\(40472803590982276/281883375\)	\(1393251544473984000\)	\([2]\)	\(13271040\)	\(2.6613\)

Rank

The elliptic curves in class 344760y have rank \(2\).

Complex multiplication

The elliptic curves in class 344760y do not have complex multiplication.

Modular form 344760.2.a.y

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.