Properties

Label 16560.bs
Number of curves $4$
Conductor $16560$
CM no
Rank $1$
Graph

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

Elliptic curves in class 16560.bs

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
16560.bs1 16560r3 \([0, 0, 0, -9507, 351106]\) \(63649751618/1164375\) \(1738402560000\) \([2]\) \(24576\) \(1.1435\)  
16560.bs2 16560r2 \([0, 0, 0, -1227, -8246]\) \(273671716/119025\) \(88851686400\) \([2, 2]\) \(12288\) \(0.79696\)  
16560.bs3 16560r1 \([0, 0, 0, -1047, -13034]\) \(680136784/345\) \(64385280\) \([2]\) \(6144\) \(0.45039\) \(\Gamma_0(N)\)-optimal
16560.bs4 16560r4 \([0, 0, 0, 4173, -61166]\) \(5382838942/4197615\) \(-6267005614080\) \([2]\) \(24576\) \(1.1435\)  

Rank

sage: E.rank()
 

The elliptic curves in class 16560.bs have rank \(1\).

Complex multiplication

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

Modular form 16560.2.a.bs

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

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.