Properties

Label 546.b
Number of curves $4$
Conductor $546$
CM no
Rank $1$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("b1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 546.b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
546.b1 546c3 \([1, 0, 1, -1957, 33140]\) \(828279937799497/193444524\) \(193444524\) \([4]\) \(384\) \(0.58064\)  
546.b2 546c2 \([1, 0, 1, -137, 380]\) \(281397674377/96589584\) \(96589584\) \([2, 2]\) \(192\) \(0.23407\)  
546.b3 546c1 \([1, 0, 1, -57, -164]\) \(19968681097/628992\) \(628992\) \([2]\) \(96\) \(-0.11250\) \(\Gamma_0(N)\)-optimal
546.b4 546c4 \([1, 0, 1, 403, 2756]\) \(7264187703863/7406095788\) \(-7406095788\) \([2]\) \(384\) \(0.58064\)  

Rank

sage: E.rank()
 

The elliptic curves in class 546.b have rank \(1\).

Complex multiplication

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

Modular form 546.2.a.b

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