↑

Properties

Label 5610.bb
Number of curves $2$
Conductor $5610$
CM no
Rank $1$
Graph

Related objects

Downloads

Learn more

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

Elliptic curves in class 5610.bb

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
5610.bb1 5610bd2 \([1, 1, 1, -880, 8777]\) \(75370704203521/7497765000\) \(7497765000\) \([2]\) \(4608\) \(0.63133\)  
5610.bb2 5610bd1 \([1, 1, 1, -200, -1015]\) \(885012508801/137332800\) \(137332800\) \([2]\) \(2304\) \(0.28476\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 5610.bb have rank \(1\).

Complex multiplication

The elliptic curves in class 5610.bb do not have complex multiplication.

Modular form 5610.2.a.bb

sage: E.q_eigenform(10)
 
\(q + q^{2} - q^{3} + q^{4} + q^{5} - q^{6} - 2 q^{7} + q^{8} + q^{9} + q^{10} + q^{11} - q^{12} - 4 q^{13} - 2 q^{14} - q^{15} + q^{16} + q^{17} + q^{18} - 2 q^{19} + O(q^{20})\) 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.