Properties

Label 6930.bk
Number of curves $2$
Conductor $6930$
CM no
Rank $0$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("bk1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 6930.bk

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
6930.bk1 6930bj2 \([1, -1, 1, -662, 6711]\) \(43949604889/42350\) \(30873150\) \([2]\) \(3072\) \(0.35829\)  
6930.bk2 6930bj1 \([1, -1, 1, -32, 159]\) \(-4826809/10780\) \(-7858620\) \([2]\) \(1536\) \(0.011719\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 6930.bk have rank \(0\).

Complex multiplication

The elliptic curves in class 6930.bk do not have complex multiplication.

Modular form 6930.2.a.bk

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{4} + q^{5} + q^{7} + q^{8} + q^{10} + q^{11} + 2q^{13} + q^{14} + q^{16} - 2q^{17} + 6q^{19} + O(q^{20})\)  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.