Properties

Label 54760.e
Number of curves 4
Conductor 54760
CM no
Rank 0
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("54760.e1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 54760.e

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
54760.e1 54760c4 [0, 0, 0, -146483, -21578178] [2] 202752  
54760.e2 54760c2 [0, 0, 0, -9583, -303918] [2, 2] 101376  
54760.e3 54760c1 [0, 0, 0, -2738, 50653] [2] 50688 \(\Gamma_0(N)\)-optimal
54760.e4 54760c3 [0, 0, 0, 17797, -1722202] [2] 202752  

Rank

sage: E.rank()
 

The elliptic curves in class 54760.e have rank \(0\).

Modular form 54760.2.a.e

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 LMFDB 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 LMFDB labels.