Properties

Label 67760bt
Number of curves 4
Conductor 67760
CM no
Rank 0
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("67760.cd1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 67760bt

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
67760.cd3 67760bt1 [0, -1, 0, -108456, 267570800] [2] 1658880 \(\Gamma_0(N)\)-optimal
67760.cd2 67760bt2 [0, -1, 0, -6923176, 6951448176] [2] 3317760  
67760.cd4 67760bt3 [0, -1, 0, 975704, -7207061904] [2] 4976640  
67760.cd1 67760bt4 [0, -1, 0, -50560616, -134439928720] [2] 9953280  

Rank

sage: E.rank()
 

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

Modular form 67760.2.a.cd

sage: E.q_eigenform(10)
 
\( q + 2q^{3} - q^{5} + q^{7} + q^{9} + 4q^{13} - 2q^{15} - 4q^{19} + O(q^{20}) \)

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 Cremona numbering.

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.