Properties

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

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Show commands: SageMath
sage: E = EllipticCurve("bt1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 116886.bt

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
116886.bt1 116886bu2 \([1, 0, 0, -1941573928, -32929197342832]\) \(3776104682692733708238625/3408048\) \(730545355674288\) \([]\) \(27371520\) \(3.5321\)  
116886.bt2 116886bu1 \([1, 0, 0, -23975608, -45150141376]\) \(7110352307247726625/6866458324992\) \(1471886322978419453952\) \([3]\) \(9123840\) \(2.9828\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 116886.2.a.bt

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