Properties

Label 39600.bl
Number of curves 3
Conductor 39600
CM no
Rank 0
Graph

Related objects

Downloads

Learn more about

Show commands for: SageMath
sage: E = EllipticCurve("39600.bl1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 39600.bl

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
39600.bl1 39600dy3 [0, 0, 0, -28153200, -57496282000] [] 840000  
39600.bl2 39600dy2 [0, 0, 0, -37200, -5002000] [] 168000  
39600.bl3 39600dy1 [0, 0, 0, -1200, 38000] [] 33600 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Modular form 39600.2.a.bl

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

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.

\(\left(\begin{array}{rrr} 1 & 5 & 25 \\ 5 & 1 & 5 \\ 25 & 5 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.