Properties

Label 15680.dr
Number of curves $2$
Conductor $15680$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("dr1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 15680.dr

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
15680.dr1 15680ba1 \([0, 0, 0, -8428, -297808]\) \(-5154200289/20\) \(-256901120\) \([]\) \(23040\) \(0.82690\) \(\Gamma_0(N)\)-optimal
15680.dr2 15680ba2 \([0, 0, 0, 58772, 2825648]\) \(1747829720511/1280000000\) \(-16441671680000000\) \([]\) \(161280\) \(1.7999\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 15680.2.a.dr

sage: E.q_eigenform(10)
 
\(q + 3q^{3} - q^{5} + 6q^{9} + 2q^{11} - 3q^{15} + 4q^{17} - 6q^{19} + O(q^{20})\)  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 LMFDB numbering.

\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.