Properties

Label 86640.db
Number of curves $2$
Conductor $86640$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("86640.db1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 86640.db

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
86640.db1 86640dd2 [0, 1, 0, -154124016, -734647036716] [2] 28016640  
86640.db2 86640dd1 [0, 1, 0, -13651696, -988203820] [2] 14008320 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 86640.db have rank \(1\).

Modular form 86640.2.a.db

sage: E.q_eigenform(10)
 
\( q + q^{3} - q^{5} + 4q^{7} + q^{9} - 6q^{11} + 4q^{13} - q^{15} + 6q^{17} + O(q^{20}) \)

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.