Properties

Label 546.f
Number of curves 2
Conductor 546
CM no
Rank 0
Graph

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Show commands for: SageMath

sage: E = EllipticCurve("546.f1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 546.f

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
546.f1 546f2 [1, 0, 0, -3674496, -2711401518] [] 8232  
546.f2 546f1 [1, 0, 0, 714, -82908] [7] 1176 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 546.f have rank \(0\).

Modular form 546.2.a.f

sage: E.q_eigenform(10)
 
\( q + q^{2} + q^{3} + q^{4} - q^{5} + q^{6} + q^{7} + q^{8} + q^{9} - q^{10} + 5q^{11} + q^{12} - q^{13} + q^{14} - q^{15} + q^{16} - 3q^{17} + q^{18} - q^{19} + O(q^{20}) \)

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.

\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.