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Properties

Label 86190.k
Number of curves $2$
Conductor $86190$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("k1")
 
E.isogeny_class()
 

Elliptic curves in class 86190.k

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
86190.k1 86190k1 \([1, 1, 0, -781628, 250778832]\) \(4980061835533/313344000\) \(3322856251533312000\) \([2]\) \(2515968\) \(2.3050\) \(\Gamma_0(N)\)-optimal
86190.k2 86190k2 \([1, 1, 0, 624452, 1055337808]\) \(2539391358707/46818000000\) \(-496481451645114000000\) \([2]\) \(5031936\) \(2.6516\)  

Rank

sage: E.rank()
 

The elliptic curves in class 86190.k have rank \(0\).

Complex multiplication

The elliptic curves in class 86190.k do not have complex multiplication.

Modular form 86190.2.a.k

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