Properties

Label 46546.a
Number of curves $4$
Conductor $46546$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("a1")
 
E.isogeny_class()
 

Elliptic curves in class 46546.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
46546.a1 46546a4 \([1, 0, 1, -154726, -16200690]\) \(159661140625/48275138\) \(123860796464719442\) \([2]\) \(616896\) \(1.9849\)  
46546.a2 46546a3 \([1, 0, 1, -141036, -20395306]\) \(120920208625/19652\) \(50421655389668\) \([2]\) \(308448\) \(1.6384\)  
46546.a3 46546a2 \([1, 0, 1, -58896, 5495222]\) \(8805624625/2312\) \(5931959457608\) \([2]\) \(205632\) \(1.4356\)  
46546.a4 46546a1 \([1, 0, 1, -4136, 63030]\) \(3048625/1088\) \(2791510332992\) \([2]\) \(102816\) \(1.0891\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 46546.a have rank \(0\).

Complex multiplication

The elliptic curves in class 46546.a do not have complex multiplication.

Modular form 46546.2.a.a

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

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.