Elliptic curve isogeny class with Cremona label 112896by (LMFDB label 112896.o)

• Label: 112896by
• Number of curves: $2$
• Conductor: $112896$
• CM: no
• Rank: $1$

Elliptic curves in class 112896by

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
112896.o1	112896by1	\([0, 0, 0, -8526, 216776]\)	\(1560896/441\)	\(19365303992832\)	\([2]\)	\(294912\)	\(1.2564\)	\(\Gamma_0(N)\)-optimal
112896.o2	112896by2	\([0, 0, 0, 22344, 1426880]\)	\(438976/567\)	\(-1593487871410176\)	\([2]\)	\(589824\)	\(1.6030\)

Rank

The elliptic curves in class 112896by have rank \(1\).

Complex multiplication

The elliptic curves in class 112896by do not have complex multiplication.

Modular form 112896.2.a.by

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.

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

Isogeny graph

The vertices are labelled with Cremona labels.