Elliptic curve isogeny class with LMFDB label 13650.by (Cremona label 13650bw)

• Label: 13650.by
• Number of curves: $4$
• Conductor: $13650$
• CM: no
• Rank: $1$

Elliptic curves in class 13650.by

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
13650.by1	13650bw3	\([1, 1, 1, -48913, 4142531]\)	\(828279937799497/193444524\)	\(3022570687500\)	\([2]\)	\(49152\)	\(1.3854\)
13650.by2	13650bw2	\([1, 1, 1, -3413, 47531]\)	\(281397674377/96589584\)	\(1509212250000\)	\([2, 2]\)	\(24576\)	\(1.0388\)
13650.by3	13650bw1	\([1, 1, 1, -1413, -20469]\)	\(19968681097/628992\)	\(9828000000\)	\([2]\)	\(12288\)	\(0.69221\)	\(\Gamma_0(N)\)-optimal
13650.by4	13650bw4	\([1, 1, 1, 10087, 344531]\)	\(7264187703863/7406095788\)	\(-115720246687500\)	\([2]\)	\(49152\)	\(1.3854\)

Rank

The elliptic curves in class 13650.by have rank \(1\).

Complex multiplication

The elliptic curves in class 13650.by do not have complex multiplication.

Modular form 13650.2.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 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.