Properties

Label 116886.u
Number of curves $2$
Conductor $116886$
CM no
Rank $1$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("u1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 116886.u

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
116886.u1 116886j2 \([1, 0, 1, -3688772954056, 2726910926533633046]\) \(-3133382230165522315000208250857964625/153574604080128\) \(-272066779178795639808\) \([]\) \(1077753600\) \(5.3134\)  
116886.u2 116886j1 \([1, 0, 1, -45540006856, 3740684175189014]\) \(-5895856113332931416918127084625/215771481613620039647232\) \(-382252341738906331057489969152\) \([]\) \(359251200\) \(4.7641\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 116886.u have rank \(1\).

Complex multiplication

The elliptic curves in class 116886.u do not have complex multiplication.

Modular form 116886.2.a.u

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.