Properties

Label 6930i
Number of curves 6
Conductor 6930
CM no
Rank 0
Graph

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Show commands for: SageMath

sage: E = EllipticCurve("6930.d1")
sage: E.isogeny_class()

Elliptic curves in class 6930i

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
6930.d5 6930i1 [1, -1, 0, -2995650, -2337570284] 2 368640 \(\Gamma_0(N)\)-optimal
6930.d4 6930i2 [1, -1, 0, -50181570, -136808005100] 4 737280  
6930.d1 6930i3 [1, -1, 0, -802898370, -8756469168620] 2 1474560  
6930.d3 6930i4 [1, -1, 0, -52439490, -123820900844] 4 1474560  
6930.d2 6930i5 [1, -1, 0, -236147490, 1278495746356] 2 2949120  
6930.d6 6930i6 [1, -1, 0, 95141790, -694989970700] 2 2949120  

Rank

sage: E.rank()

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

Modular form 6930.2.a.d

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

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.

\(\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 4 & 8 & 8 \\ 2 & 1 & 2 & 2 & 4 & 4 \\ 4 & 2 & 1 & 4 & 8 & 8 \\ 4 & 2 & 4 & 1 & 2 & 2 \\ 8 & 4 & 8 & 2 & 1 & 4 \\ 8 & 4 & 8 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.