Properties

Label 134640.bw
Number of curves $2$
Conductor $134640$
CM no
Rank $1$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("bw1")
 
E.isogeny_class()
 

Elliptic curves in class 134640.bw

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
134640.bw1 134640ci2 \([0, 0, 0, -1693443, 847722242]\) \(179865548102096641/119964240000\) \(358211301212160000\) \([2]\) \(2064384\) \(2.3071\)  
134640.bw2 134640ci1 \([0, 0, 0, -126723, 7646978]\) \(75370704203521/35157196800\) \(104978827129651200\) \([2]\) \(1032192\) \(1.9605\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 134640.bw have rank \(1\).

Complex multiplication

The elliptic curves in class 134640.bw do not have complex multiplication.

Modular form 134640.2.a.bw

sage: E.q_eigenform(10)
 
\(q - q^{5} + 2 q^{7} - q^{11} - 4 q^{13} - q^{17} + 6 q^{19} + O(q^{20})\) 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.