Properties

Label 13200by
Number of curves $2$
Conductor $13200$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("by1")
 
E.isogeny_class()
 

Elliptic curves in class 13200by

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
13200.y1 13200by1 \([0, -1, 0, -9333, -360963]\) \(-56197120/3267\) \(-5227200000000\) \([]\) \(25920\) \(1.1967\) \(\Gamma_0(N)\)-optimal
13200.y2 13200by2 \([0, -1, 0, 50667, -660963]\) \(8990228480/5314683\) \(-8503492800000000\) \([]\) \(77760\) \(1.7460\)  

Rank

sage: E.rank()
 

The elliptic curves in class 13200by have rank \(0\).

Complex multiplication

The elliptic curves in class 13200by do not have complex multiplication.

Modular form 13200.2.a.by

sage: E.q_eigenform(10)
 
\(q - q^{3} + q^{7} + q^{9} + q^{11} - q^{13} - 6 q^{17} + 7 q^{19} + O(q^{20})\) Copy content Toggle raw display

Isogeny matrix

sage: E.isogeny_class().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.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)
 

The vertices are labelled with Cremona labels.