Properties

Label 6534.bc
Number of curves $3$
Conductor $6534$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more about

Show commands for: SageMath
sage: E = EllipticCurve("bc1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 6534.bc

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
6534.bc1 6534ba3 [1, -1, 1, -14906, 932473] [] 24300  
6534.bc2 6534ba1 [1, -1, 1, -386, -2857] [] 2700 \(\Gamma_0(N)\)-optimal
6534.bc3 6534ba2 [1, -1, 1, 1429, -14957] [] 8100  

Rank

sage: E.rank()
 

The elliptic curves in class 6534.bc have rank \(0\).

Complex multiplication

The elliptic curves in class 6534.bc do not have complex multiplication.

Modular form 6534.2.a.bc

sage: E.q_eigenform(10)
 
\( q + q^{2} + q^{4} + 3q^{5} + q^{7} + q^{8} + 3q^{10} + 4q^{13} + q^{14} + q^{16} - 2q^{19} + O(q^{20}) \)

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.