Properties

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

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Show commands: SageMath
E = EllipticCurve("bl1")
 
E.isogeny_class()
 

Elliptic curves in class 86640bl

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
86640.m2 86640bl1 \([0, -1, 0, 8544, 896256]\) \(129205871/729000\) \(-389136420864000\) \([]\) \(311040\) \(1.4816\) \(\Gamma_0(N)\)-optimal
86640.m1 86640bl2 \([0, -1, 0, -511296, 141045120]\) \(-27692833539889/35156250\) \(-18766224000000000\) \([]\) \(933120\) \(2.0309\)  

Rank

sage: E.rank()
 

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

Complex multiplication

The elliptic curves in class 86640bl do not have complex multiplication.

Modular form 86640.2.a.bl

sage: E.q_eigenform(10)
 
\(q - q^{3} - q^{5} + q^{7} + q^{9} + 3 q^{11} + 2 q^{13} + q^{15} - 6 q^{17} + O(q^{20})\) Copy content 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.