Elliptic curve isogeny class with LMFDB label 268770.y (Cremona label 268770y)

• Label: 268770.y
• Number of curves: $4$
• Conductor: $268770$
• CM: no
• Rank: $0$

Elliptic curves in class 268770.y

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
268770.y1	268770y3	\([1, 0, 1, -1915643, 1020338318]\)	\(32208729120020809/658986840\)	\(15906340320591960\)	\([2]\)	\(5898240\)	\(2.2283\)
268770.y2	268770y2	\([1, 0, 1, -123843, 14780158]\)	\(8702409880009/1120910400\)	\(27056052122817600\)	\([2, 2]\)	\(2949120\)	\(1.8818\)
268770.y3	268770y1	\([1, 0, 1, -31363, -1903234]\)	\(141339344329/17141760\)	\(413760414781440\)	\([2]\)	\(1474560\)	\(1.5352\)	\(\Gamma_0(N)\)-optimal
268770.y4	268770y4	\([1, 0, 1, 188277, 77329006]\)	\(30579142915511/124675335000\)	\(-3009359501160615000\)	\([2]\)	\(5898240\)	\(2.2283\)

Rank

The elliptic curves in class 268770.y have rank \(0\).

Complex multiplication

The elliptic curves in class 268770.y do not have complex multiplication.

Modular form 268770.2.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 LMFDB 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 LMFDB labels.