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Properties

Label 66270.n
Number of curves $2$
Conductor $66270$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("n1")
 
E.isogeny_class()
 

Elliptic curves in class 66270.n

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
66270.n1 66270p2 \([1, 1, 1, -65392187626, -6436336642975927]\) \(27632526176252046076847/46132031250\) \(51627761958004131705468750\) \([2]\) \(181923840\) \(4.6247\)  
66270.n2 66270p1 \([1, 1, 1, -4085744356, -100634524526431]\) \(-6739948204520897807/8716961002500\) \(-9755416690746195113843917500\) \([2]\) \(90961920\) \(4.2781\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 66270.n have rank \(1\).

Complex multiplication

The elliptic curves in class 66270.n do not have complex multiplication.

Modular form 66270.2.a.n

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.