Properties

Label 67240e
Number of curves 4
Conductor 67240
CM no
Rank 0
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("67240.g1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 67240e

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
67240.g3 67240e1 [0, 0, 0, -3362, 68921] [2] 69120 \(\Gamma_0(N)\)-optimal
67240.g2 67240e2 [0, 0, 0, -11767, -413526] [2, 2] 138240  
67240.g4 67240e3 [0, 0, 0, 21853, -2343314] [2] 276480  
67240.g1 67240e4 [0, 0, 0, -179867, -29360346] [2] 276480  

Rank

sage: E.rank()
 

The elliptic curves in class 67240e have rank \(0\).

Modular form 67240.2.a.g

sage: E.q_eigenform(10)
 
\( q + q^{5} + 4q^{7} - 3q^{9} - 4q^{11} + 2q^{13} - 2q^{17} - 4q^{19} + O(q^{20}) \)

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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.