Elliptic curve isogeny class with Cremona label 17600by (LMFDB label 17600.t)

• Label: 17600by
• Number of curves: $2$
• Conductor: $17600$
• CM: no
• Rank: $0$

Elliptic curves in class 17600by

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
17600.t2	17600by1	\([0, 1, 0, -408, 2938]\)	\(7529536/275\)	\(275000000\)	\([2]\)	\(9216\)	\(0.38895\)	\(\Gamma_0(N)\)-optimal
17600.t1	17600by2	\([0, 1, 0, -1033, -8937]\)	\(1906624/605\)	\(38720000000\)	\([2]\)	\(18432\)	\(0.73552\)

Rank

The elliptic curves in class 17600by have rank \(0\).

Complex multiplication

The elliptic curves in class 17600by do not have complex multiplication.

Modular form 17600.2.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.