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Properties

Label 66270.r
Number of curves $2$
Conductor $66270$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("r1")
 
E.isogeny_class()
 

Elliptic curves in class 66270.r

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
66270.r1 66270v2 \([1, 1, 1, -29602620, 61980763407]\) \(27632526176252046076847/46132031250\) \(4789565880468750\) \([2]\) \(3870720\) \(2.6996\)  
66270.r2 66270v1 \([1, 1, 1, -1849590, 968502255]\) \(-6739948204520897807/8716961002500\) \(-905021042162557500\) \([2]\) \(1935360\) \(2.3530\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 66270.r have rank \(0\).

Complex multiplication

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

Modular form 66270.2.a.r

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.