Properties

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

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Show commands: SageMath
sage: E = EllipticCurve("b1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 6534.b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
6534.b1 6534g3 \([1, -1, 0, -3471, 80603]\) \(-132651/2\) \(-69739270326\) \([]\) \(8100\) \(0.88374\)  
6534.b2 6534g2 \([1, -1, 0, -1656, -33984]\) \(-1167051/512\) \(-220410533376\) \([]\) \(8100\) \(0.88374\)  
6534.b3 6534g1 \([1, -1, 0, 159, 501]\) \(9261/8\) \(-382657176\) \([]\) \(2700\) \(0.33444\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 6534.2.a.b

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