Properties

Label 15680.de
Number of curves 4
Conductor 15680
CM no
Rank 1
Graph

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Show commands for: SageMath

sage: E = EllipticCurve("15680.de1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 15680.de

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
15680.de1 15680cp3 [0, -1, 0, -8101, -277899] [2] 17280  
15680.de2 15680cp4 [0, -1, 0, -7121, -348655] [2] 34560  
15680.de3 15680cp1 [0, -1, 0, -261, 1205] [2] 5760 \(\Gamma_0(N)\)-optimal
15680.de4 15680cp2 [0, -1, 0, 719, 7281] [2] 11520  

Rank

sage: E.rank()
 

The elliptic curves in class 15680.de have rank \(1\).

Modular form 15680.2.a.de

sage: E.q_eigenform(10)
 
\( q + 2q^{3} - q^{5} + q^{9} + 2q^{13} - 2q^{15} + 6q^{17} + 4q^{19} + O(q^{20}) \)

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 LMFDB 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 LMFDB labels.