Properties

Label 6930bl
Number of curves 8
Conductor 6930
CM no
Rank 0
Graph

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Show commands for: SageMath

sage: E = EllipticCurve("6930.bl1")
sage: E.isogeny_class()

Elliptic curves in class 6930bl

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
6930.bl6 6930bl1 [1, -1, 1, -2578802, -1593306511] 2 110592 \(\Gamma_0(N)\)-optimal
6930.bl5 6930bl2 [1, -1, 1, -2581682, -1589567119] 4 221184  
6930.bl4 6930bl3 [1, -1, 1, -2751737, -1367291239] 6 331776  
6930.bl3 6930bl4 [1, -1, 1, -3939962, 265300049] 2 442368  
6930.bl7 6930bl5 [1, -1, 1, -1269482, -3205147759] 2 442368  
6930.bl2 6930bl6 [1, -1, 1, -14548217, 20191955609] 12 663552  
6930.bl1 6930bl7 [1, -1, 1, -229211897, 1335736852121] 6 1327104  
6930.bl8 6930bl8 [1, -1, 1, 11371783, 84297299609] 6 1327104  

Rank

sage: E.rank()

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

Modular form 6930.2.a.bl

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

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.

\(\left(\begin{array}{rrrrrrrr} 1 & 2 & 3 & 4 & 4 & 6 & 12 & 12 \\ 2 & 1 & 6 & 2 & 2 & 3 & 6 & 6 \\ 3 & 6 & 1 & 12 & 12 & 2 & 4 & 4 \\ 4 & 2 & 12 & 1 & 4 & 6 & 3 & 12 \\ 4 & 2 & 12 & 4 & 1 & 6 & 12 & 3 \\ 6 & 3 & 2 & 6 & 6 & 1 & 2 & 2 \\ 12 & 6 & 4 & 3 & 12 & 2 & 1 & 4 \\ 12 & 6 & 4 & 12 & 3 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.