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Properties

Label 66066.cy
Number of curves $3$
Conductor $66066$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("cy1")
 
E.isogeny_class()
 

Elliptic curves in class 66066.cy

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
66066.cy1 66066cm3 \([1, 0, 0, -3152839, 2154541577]\) \(-1956469094246217097/36641439744\) \(-64912545634320384\) \([]\) \(2624400\) \(2.3504\)  
66066.cy2 66066cm2 \([1, 0, 0, -14704, 6570752]\) \(-198461344537/10417365504\) \(-18454998449631744\) \([]\) \(874800\) \(1.8011\)  
66066.cy3 66066cm1 \([1, 0, 0, 1631, -240943]\) \(270840023/14329224\) \(-25385094398664\) \([]\) \(291600\) \(1.2518\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 66066.cy have rank \(0\).

Complex multiplication

The elliptic curves in class 66066.cy do not have complex multiplication.

Modular form 66066.2.a.cy

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.