Properties

Label 67760ba
Number of curves $4$
Conductor $67760$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("67760.ba1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 67760ba

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
67760.ba4 67760ba1 [0, 0, 0, 4477, -183678] [2] 122880 \(\Gamma_0(N)\)-optimal
67760.ba3 67760ba2 [0, 0, 0, -34243, -1972542] [2, 2] 245760  
67760.ba2 67760ba3 [0, 0, 0, -169763, 25158562] [2] 491520  
67760.ba1 67760ba4 [0, 0, 0, -518243, -143590942] [2] 491520  

Rank

sage: E.rank()
 

The elliptic curves in class 67760ba have rank \(1\).

Modular form 67760.2.a.ba

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

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 Cremona numbering.

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.