Properties

Label 39600.bs
Number of curves 2
Conductor 39600
CM no
Rank 0
Graph

Related objects

Downloads

Learn more about

Show commands for: SageMath
sage: E = EllipticCurve("39600.bs1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 39600.bs

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
39600.bs1 39600dx2 [0, 0, 0, -2775, -26750] [2] 49152  
39600.bs2 39600dx1 [0, 0, 0, 600, -3125] [2] 24576 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 39600.bs have rank \(0\).

Modular form 39600.2.a.bs

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

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 LMFDB 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 LMFDB labels.