Elliptic curve isogeny class with Cremona label 13520t (LMFDB label 13520.y)

• Label: 13520t
• Number of curves: $4$
• Conductor: $13520$
• CM: no
• Rank: $0$

Elliptic curves in class 13520t

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
13520.y2	13520t1	\([0, -1, 0, -87936, -9948160]\)	\(3803721481/26000\)	\(514035851264000\)	\([2]\)	\(96768\)	\(1.6568\)	\(\Gamma_0(N)\)-optimal
13520.y3	13520t2	\([0, -1, 0, -33856, -22105344]\)	\(-217081801/10562500\)	\(-208827064576000000\)	\([2]\)	\(193536\)	\(2.0033\)
13520.y1	13520t3	\([0, -1, 0, -561136, 155482560]\)	\(988345570681/44994560\)	\(889569882763427840\)	\([2]\)	\(290304\)	\(2.2061\)
13520.y4	13520t4	\([0, -1, 0, 304144, 590891456]\)	\(157376536199/7722894400\)	\(-152686330658691481600\)	\([2]\)	\(580608\)	\(2.5526\)

Rank

The elliptic curves in class 13520t have rank \(0\).

Complex multiplication

The elliptic curves in class 13520t do not have complex multiplication.

Modular form 13520.2.a.t

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.

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.