Properties

Label 5586.bb
Number of curves $2$
Conductor $5586$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("bb1")
 
E.isogeny_class()
 

Elliptic curves in class 5586.bb

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
5586.bb1 5586z1 \([1, 0, 0, -17347, 700097]\) \(4906933498657/1032471552\) \(121469245621248\) \([2]\) \(23040\) \(1.4173\) \(\Gamma_0(N)\)-optimal
5586.bb2 5586z2 \([1, 0, 0, 37533, 4245345]\) \(49702082429663/94844496096\) \(-11158360121198304\) \([2]\) \(46080\) \(1.7639\)  

Rank

sage: E.rank()
 

The elliptic curves in class 5586.bb have rank \(0\).

Complex multiplication

The elliptic curves in class 5586.bb do not have complex multiplication.

Modular form 5586.2.a.bb

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{3} + q^{4} + 2 q^{5} + q^{6} + q^{8} + q^{9} + 2 q^{10} + 2 q^{11} + q^{12} + 6 q^{13} + 2 q^{15} + q^{16} + 4 q^{17} + q^{18} - q^{19} + O(q^{20})\) 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.