Elliptic curve isogeny class with Cremona label 348075s (LMFDB label 348075.s)

• Label: 348075s
• Number of curves: $4$
• Conductor: $348075$
• CM: no
• Rank: $2$

Elliptic curves in class 348075s

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
348075.s4	348075s1	\([1, -1, 1, -22955, 1096922]\)	\(117433042273/22801233\)	\(259720294640625\)	\([2]\)	\(1310720\)	\(1.4828\)	\(\Gamma_0(N)\)-optimal
348075.s2	348075s2	\([1, -1, 1, -348080, 79126922]\)	\(409460675852593/21538881\)	\(245341316390625\)	\([2, 2]\)	\(2621440\)	\(1.8294\)
348075.s1	348075s3	\([1, -1, 1, -5569205, 5060080172]\)	\(1677087406638588673/4641\)	\(52863890625\)	\([2]\)	\(5242880\)	\(2.1760\)
348075.s3	348075s4	\([1, -1, 1, -328955, 88192172]\)	\(-345608484635233/94427721297\)	\(-1075590762898640625\)	\([2]\)	\(5242880\)	\(2.1760\)

Rank

The elliptic curves in class 348075s have rank \(2\).

Complex multiplication

The elliptic curves in class 348075s do not have complex multiplication.

Modular form 348075.2.a.s

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.