Properties

Label 16560.cb
Number of curves $2$
Conductor $16560$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("cb1")
 
E.isogeny_class()
 

Elliptic curves in class 16560.cb

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
16560.cb1 16560bf2 \([0, 0, 0, -90207, 10427994]\) \(16110654114672/330625\) \(1665969120000\) \([2]\) \(46080\) \(1.4645\)  
16560.cb2 16560bf1 \([0, 0, 0, -5832, 151119]\) \(69657034752/8984375\) \(2829431250000\) \([2]\) \(23040\) \(1.1179\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 16560.cb have rank \(0\).

Complex multiplication

The elliptic curves in class 16560.cb do not have complex multiplication.

Modular form 16560.2.a.cb

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