Properties

Label 116886.b
Number of curves $2$
Conductor $116886$
CM no
Rank $0$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("b1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 116886.b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
116886.b1 116886a2 \([1, 1, 0, -82161, -7293645]\) \(26013270347/5398974\) \(12730498277069034\) \([2]\) \(887040\) \(1.8053\)  
116886.b2 116886a1 \([1, 1, 0, 11009, -678575]\) \(62570773/121716\) \(-286999961157756\) \([2]\) \(443520\) \(1.4588\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 116886.b have rank \(0\).

Complex multiplication

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

Modular form 116886.2.a.b

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.