Properties

Label 86640.d
Number of curves $2$
Conductor $86640$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more about

Show commands for: SageMath
sage: E = EllipticCurve("86640.d1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 86640.d

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
86640.d1 86640bq2 [0, -1, 0, -21059416, -37190773520] [2] 3502080  
86640.d2 86640bq1 [0, -1, 0, -1305496, -590710544] [2] 1751040 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 86640.d have rank \(0\).

Modular form 86640.2.a.d

sage: E.q_eigenform(10)
 
\( q - q^{3} - q^{5} - 2q^{7} + q^{9} + 2q^{13} + q^{15} - 6q^{17} + O(q^{20}) \)

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.