Properties

Label 62790w
Number of curves 8
Conductor 62790
CM no
Rank 1
Graph

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Show commands for: SageMath

sage: E = EllipticCurve("62790.v1")
sage: E.isogeny_class()

Elliptic curves in class 62790w

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
62790.v7 62790w1 [1, 0, 1, -134368, 149877806] 6 1658880 \(\Gamma_0(N)\)-optimal
62790.v6 62790w2 [1, 0, 1, -5134368, 4453877806] 12 3317760  
62790.v8 62790w3 [1, 0, 1, 1206257, -3990069694] 2 4976640  
62790.v5 62790w4 [1, 0, 1, -8239368, -1567338194] 6 6635520  
62790.v3 62790w5 [1, 0, 1, -82029368, 285951093806] 6 6635520  
62790.v4 62790w6 [1, 0, 1, -31561743, -65240015294] 4 9953280  
62790.v1 62790w7 [1, 0, 1, -498774543, -4287535531454] 2 19906560  
62790.v2 62790w8 [1, 0, 1, -88636943, 237190054466] 2 19906560  

Rank

sage: E.rank()

The elliptic curves in class 62790w have rank \(1\).

Modular form None

sage: E.q_eigenform(10)
\( q - q^{2} + q^{3} + q^{4} + q^{5} - q^{6} + q^{7} - q^{8} + q^{9} - q^{10} + q^{12} + q^{13} - q^{14} + q^{15} + q^{16} + 6q^{17} - q^{18} - 4q^{19} + O(q^{20}) \)

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.