↑

Properties

Label 86490.bw
Number of curves $2$
Conductor $86490$
CM no
Rank $1$
Graph

Related objects

Downloads

Learn more

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

Elliptic curves in class 86490.bw

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
86490.bw1 86490bw1 \([1, -1, 1, -684893, -256004379]\) \(-1482713947827/325058560\) \(-7789248050595102720\) \([]\) \(1935360\) \(2.3456\) \(\Gamma_0(N)\)-optimal
86490.bw2 86490bw2 \([1, -1, 1, 4850467, 1537698277]\) \(722458663317/476656000\) \(-8326577327815796688000\) \([]\) \(5806080\) \(2.8950\)  

Rank

sage: E.rank()
 

The elliptic curves in class 86490.bw have rank \(1\).

Complex multiplication

The elliptic curves in class 86490.bw do not have complex multiplication.

Modular form 86490.2.a.bw

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{4} - q^{5} - q^{7} + q^{8} - q^{10} - 3 q^{11} + 4 q^{13} - q^{14} + q^{16} + 6 q^{17} - q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)
 

The vertices are labelled with LMFDB labels.