Properties

Label 20160.bs
Number of curves $3$
Conductor $20160$
CM no
Rank $1$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("bs1")
 
E.isogeny_class()
 

Elliptic curves in class 20160.bs

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
20160.bs1 20160bq3 \([0, 0, 0, -4728, 130898]\) \(-250523582464/13671875\) \(-637875000000\) \([]\) \(25920\) \(1.0233\)  
20160.bs2 20160bq1 \([0, 0, 0, -48, -142]\) \(-262144/35\) \(-1632960\) \([]\) \(2880\) \(-0.075270\) \(\Gamma_0(N)\)-optimal
20160.bs3 20160bq2 \([0, 0, 0, 312, 362]\) \(71991296/42875\) \(-2000376000\) \([]\) \(8640\) \(0.47404\)  

Rank

sage: E.rank()
 

The elliptic curves in class 20160.bs have rank \(1\).

Complex multiplication

The elliptic curves in class 20160.bs do not have complex multiplication.

Modular form 20160.2.a.bs

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

\(\left(\begin{array}{rrr} 1 & 9 & 3 \\ 9 & 1 & 3 \\ 3 & 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.