Properties

Label 46546a
Number of curves 4
Conductor 46546
CM no
Rank 0
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("46546.a1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 46546a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
46546.a4 46546a1 [1, 0, 1, -4136, 63030] [2] 102816 \(\Gamma_0(N)\)-optimal
46546.a3 46546a2 [1, 0, 1, -58896, 5495222] [2] 205632  
46546.a2 46546a3 [1, 0, 1, -141036, -20395306] [2] 308448  
46546.a1 46546a4 [1, 0, 1, -154726, -16200690] [2] 616896  

Rank

sage: E.rank()
 

The elliptic curves in class 46546a have rank \(0\).

Modular form 46546.2.a.a

sage: E.q_eigenform(10)
 
\( q - q^{2} - 2q^{3} + q^{4} + 2q^{6} - 4q^{7} - q^{8} + q^{9} + 6q^{11} - 2q^{12} - 2q^{13} + 4q^{14} + q^{16} + q^{17} - q^{18} + 4q^{19} + O(q^{20}) \)

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.