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Properties

Label 105966bd
Number of curves $2$
Conductor $105966$
CM no
Rank $0$
Graph

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

Elliptic curves in class 105966bd

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
105966.bb2 105966bd1 \([1, -1, 0, -10229661, 9101174917]\) \(11194326053/3096576\) \(32748487961824570392576\) \([2]\) \(13095936\) \(3.0277\) \(\Gamma_0(N)\)-optimal
105966.bb1 105966bd2 \([1, -1, 0, -150710301, 712094393605]\) \(35796701971493/4572288\) \(48355189256131592220288\) \([2]\) \(26191872\) \(3.3743\)  

Rank

sage: E.rank()
 

The elliptic curves in class 105966bd have rank \(0\).

Complex multiplication

The elliptic curves in class 105966bd do not have complex multiplication.

Modular form 105966.2.a.bd

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{4} + 2 q^{5} + q^{7} - q^{8} - 2 q^{10} + 4 q^{11} + 4 q^{13} - q^{14} + q^{16} + 8 q^{17} - 4 q^{19} + O(q^{20})\) 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 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.