Properties

Label 546g
Number of curves $4$
Conductor $546$
CM no
Rank $0$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("g1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 546g

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
546.g3 546g1 \([1, 0, 0, -7, -7]\) \(38272753/4368\) \(4368\) \([2]\) \(48\) \(-0.56917\) \(\Gamma_0(N)\)-optimal
546.g2 546g2 \([1, 0, 0, -27, 45]\) \(2181825073/298116\) \(298116\) \([2, 2]\) \(96\) \(-0.22260\)  
546.g1 546g3 \([1, 0, 0, -417, 3243]\) \(8020417344913/187278\) \(187278\) \([2]\) \(192\) \(0.12397\)  
546.g4 546g4 \([1, 0, 0, 43, 255]\) \(8780064047/32388174\) \(-32388174\) \([2]\) \(192\) \(0.12397\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 546.2.a.g

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