Properties

Label 546.d
Number of curves $3$
Conductor $546$
CM no
Rank $0$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("d1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 546.d

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
546.d1 546d3 \([1, 0, 1, -26057, -1621108]\) \(-1956469094246217097/36641439744\) \(-36641439744\) \([]\) \(1944\) \(1.1515\)  
546.d2 546d2 \([1, 0, 1, -122, -4948]\) \(-198461344537/10417365504\) \(-10417365504\) \([3]\) \(648\) \(0.60215\)  
546.d3 546d1 \([1, 0, 1, 13, 182]\) \(270840023/14329224\) \(-14329224\) \([3]\) \(216\) \(0.052847\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 546.2.a.d

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

\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.