Properties

Label 6930.j
Number of curves $2$
Conductor $6930$
CM no
Rank $1$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("j1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 6930.j

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
6930.j1 6930l1 \([1, -1, 0, -54, 0]\) \(24137569/13860\) \(10103940\) \([2]\) \(1536\) \(0.033680\) \(\Gamma_0(N)\)-optimal
6930.j2 6930l2 \([1, -1, 0, 216, -162]\) \(1524845951/889350\) \(-648336150\) \([2]\) \(3072\) \(0.38025\)  

Rank

sage: E.rank()
 

The elliptic curves in class 6930.j have rank \(1\).

Complex multiplication

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

Modular form 6930.2.a.j

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