Properties

Label 15680dk
Number of curves 4
Conductor 15680
CM no
Rank 0
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("15680.cc1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 15680dk

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
15680.cc3 15680dk1 [0, 0, 0, -392, 2744] [2] 4608 \(\Gamma_0(N)\)-optimal
15680.cc2 15680dk2 [0, 0, 0, -1372, -16464] [2, 2] 9216  
15680.cc1 15680dk3 [0, 0, 0, -20972, -1168944] [2] 18432  
15680.cc4 15680dk4 [0, 0, 0, 2548, -93296] [2] 18432  

Rank

sage: E.rank()
 

The elliptic curves in class 15680dk have rank \(0\).

Modular form 15680.2.a.cc

sage: E.q_eigenform(10)
 
\( q + q^{5} - 3q^{9} + 4q^{11} - 2q^{13} - 2q^{17} - 4q^{19} + O(q^{20}) \)

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.

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.