Properties

Label 15680cl
Number of curves $3$
Conductor $15680$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("cl1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 15680cl

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
15680.ba2 15680cl1 [0, -1, 0, -261, 1891] [] 4608 \(\Gamma_0(N)\)-optimal
15680.ba3 15680cl2 [0, -1, 0, 1699, -5165] [] 13824  
15680.ba1 15680cl3 [0, -1, 0, -25741, -1654309] [] 41472  

Rank

sage: E.rank()
 

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

Complex multiplication

The elliptic curves in class 15680cl do not have complex multiplication.

Modular form 15680.2.a.cl

sage: E.q_eigenform(10)
 
\(q - q^{3} - q^{5} - 2q^{9} - 3q^{11} + 5q^{13} + q^{15} - 3q^{17} - 2q^{19} + O(q^{20})\)  Toggle raw display

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.

\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.