Properties

Label 15680co
Number of curves $2$
Conductor $15680$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("co1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 15680co

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
15680.y2 15680co1 [0, -1, 0, 159, 1] [] 4608 \(\Gamma_0(N)\)-optimal
15680.y1 15680co2 [0, -1, 0, -2081, -38975] [] 13824  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 15680.2.a.co

sage: E.q_eigenform(10)
 
\(q - q^{3} - q^{5} - 2q^{9} - 6q^{11} - 4q^{13} + q^{15} - 2q^{19} + O(q^{20})\)  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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.