Properties

Label 52800db
Number of curves 4
Conductor 52800
CM no
Rank 1
Graph

Related objects

Downloads

Learn more about

Show commands for: SageMath
sage: E = EllipticCurve("52800.ex1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 52800db

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
52800.ex3 52800db1 [0, 1, 0, -8833, 298463] [2] 110592 \(\Gamma_0(N)\)-optimal
52800.ex4 52800db2 [0, 1, 0, 7167, 1274463] [2] 221184  
52800.ex1 52800db3 [0, 1, 0, -128833, -17773537] [2] 331776  
52800.ex2 52800db4 [0, 1, 0, -64833, -35373537] [2] 663552  

Rank

sage: E.rank()
 

The elliptic curves in class 52800db have rank \(1\).

Modular form 52800.2.a.ex

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

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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.