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Properties

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

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Show commands: SageMath
E = EllipticCurve("bd1")
 
E.isogeny_class()
 

Elliptic curves in class 116886.bd

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
116886.bd1 116886bc2 \([1, 1, 1, -30282007, -64148871379]\) \(1733490909744055732873/99355964553216\) \(176015151919859890176\) \([2]\) \(10813440\) \(2.9484\)  
116886.bd2 116886bc1 \([1, 1, 1, -1784087, -1122871507]\) \(-354499561600764553/101902222098432\) \(-180526002482920292352\) \([2]\) \(5406720\) \(2.6019\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 116886.2.a.bd

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