Properties

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

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Show commands: SageMath
sage: E = EllipticCurve("f1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 546.f

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
546.f1 546f2 \([1, 0, 0, -3674496, -2711401518]\) \(-5486773802537974663600129/2635437714\) \(-2635437714\) \([]\) \(8232\) \(2.0465\)  
546.f2 546f1 \([1, 0, 0, 714, -82908]\) \(40251338884511/2997011332224\) \(-2997011332224\) \([7]\) \(1176\) \(1.0736\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

The elliptic curves in class 546.f do not have complex multiplication.

Modular form 546.2.a.f

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

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.