Properties

Label 67760bo
Number of curves $3$
Conductor $67760$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("bo1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 67760bo

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
67760.k2 67760bo1 \([0, -1, 0, -2581, 56861]\) \(-262144/35\) \(-253970984960\) \([]\) \(64800\) \(0.92094\) \(\Gamma_0(N)\)-optimal
67760.k3 67760bo2 \([0, -1, 0, 16779, -148355]\) \(71991296/42875\) \(-311114456576000\) \([]\) \(194400\) \(1.4703\)  
67760.k1 67760bo3 \([0, -1, 0, -254261, -51537539]\) \(-250523582464/13671875\) \(-99207416000000000\) \([]\) \(583200\) \(2.0196\)  

Rank

sage: E.rank()
 

The elliptic curves in class 67760bo have rank \(0\).

Complex multiplication

The elliptic curves in class 67760bo do not have complex multiplication.

Modular form 67760.2.a.bo

sage: E.q_eigenform(10)
 
\(q - q^{3} - q^{5} + q^{7} - 2q^{9} - 5q^{13} + q^{15} - 3q^{17} + 2q^{19} + O(q^{20})\)  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.

\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.