↑

Properties

Label 139638.bd
Number of curves $2$
Conductor $139638$
CM no
Rank $1$
Graph

Related objects

Downloads

Learn more

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

Elliptic curves in class 139638.bd

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
139638.bd1 139638x1 \([1, 1, 1, -3451, 48101]\) \(1771561/612\) \(1570224562308\) \([2]\) \(411264\) \(1.0419\) \(\Gamma_0(N)\)-optimal
139638.bd2 139638x2 \([1, 1, 1, 10239, 349281]\) \(46268279/46818\) \(-120122179016562\) \([2]\) \(822528\) \(1.3885\)  

Rank

sage: E.rank()
 

The elliptic curves in class 139638.bd have rank \(1\).

Complex multiplication

The elliptic curves in class 139638.bd do not have complex multiplication.

Modular form 139638.2.a.bd

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