Properties

Label 52800cd
Number of curves 2
Conductor 52800
CM no
Rank 0
Graph

Related objects

Downloads

Learn more about

Show commands for: SageMath
sage: E = EllipticCurve("52800.gl1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 52800cd

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
52800.gl2 52800cd1 [0, 1, 0, 267, -837] [2] 24576 \(\Gamma_0(N)\)-optimal
52800.gl1 52800cd2 [0, 1, 0, -1233, -8337] [2] 49152  

Rank

sage: E.rank()
 

The elliptic curves in class 52800cd have rank \(0\).

Modular form 52800.2.a.gl

sage: E.q_eigenform(10)
 
\( q + q^{3} + 2q^{7} + q^{9} - q^{11} - 2q^{13} - 4q^{17} + 6q^{19} + O(q^{20}) \)

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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.