Properties

Label 6930n
Number of curves 4
Conductor 6930
CM no
Rank 0
Graph

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Show commands for: SageMath

sage: E = EllipticCurve("6930.l1")
sage: E.isogeny_class()

Elliptic curves in class 6930n

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
6930.l3 6930n1 [1, -1, 0, -8919, 225693] 2 20480 \(\Gamma_0(N)\)-optimal
6930.l2 6930n2 [1, -1, 0, -54999, -4778595] 4 40960  
6930.l1 6930n3 [1, -1, 0, -871479, -312918147] 2 81920  
6930.l4 6930n4 [1, -1, 0, 24201, -17466435] 2 81920  

Rank

sage: E.rank()

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

Modular form 6930.2.a.l

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

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 Cremona numbering.

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.