Properties

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

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

Elliptic curves in class 116886k

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
116886.s2 116886k1 \([1, 0, 1, -469241, -123900856]\) \(-6449916994998625/8532911772\) \(-15116573711716092\) \([2]\) \(1290240\) \(2.0110\) \(\Gamma_0(N)\)-optimal
116886.s1 116886k2 \([1, 0, 1, -7510231, -7922501380]\) \(26444015547214434625/46191222\) \(81830567437542\) \([2]\) \(2580480\) \(2.3575\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 116886.2.a.k

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