Properties

Label 66654.l
Number of curves $4$
Conductor $66654$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("l1")
 
E.isogeny_class()
 

Elliptic curves in class 66654.l

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
66654.l1 66654v4 \([1, -1, 0, -851500188, -9563471523270]\) \(632678989847546725777/80515134\) \(8689045361500567854\) \([2]\) \(16220160\) \(3.4940\)  
66654.l2 66654v3 \([1, -1, 0, -60888528, -103543708266]\) \(231331938231569617/90942310746882\) \(9814327122144990588263442\) \([2]\) \(16220160\) \(3.4940\)  
66654.l3 66654v2 \([1, -1, 0, -53223318, -149392395360]\) \(154502321244119857/55101928644\) \(5946498921480817192164\) \([2, 2]\) \(8110080\) \(3.1475\)  
66654.l4 66654v1 \([1, -1, 0, -2851938, -3023239356]\) \(-23771111713777/22848457968\) \(-2465763613139997879408\) \([2]\) \(4055040\) \(2.8009\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 66654.l have rank \(0\).

Complex multiplication

The elliptic curves in class 66654.l do not have complex multiplication.

Modular form 66654.2.a.l

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

\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.