Properties

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

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Show commands: SageMath
sage: E = EllipticCurve("r1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 6930.r

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
6930.r1 6930r1 \([1, -1, 1, -263, -1573]\) \(74246873427/16940\) \(457380\) \([2]\) \(2048\) \(0.077890\) \(\Gamma_0(N)\)-optimal
6930.r2 6930r2 \([1, -1, 1, -233, -1969]\) \(-51603494067/35870450\) \(-968502150\) \([2]\) \(4096\) \(0.42446\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 6930.2.a.r

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.