Properties

Label 4830bc
Number of curves 8
Conductor 4830
CM no
Rank 0
Graph

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Show commands for: SageMath

sage: E = EllipticCurve("4830.be1")
sage: E.isogeny_class()

Elliptic curves in class 4830bc

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
4830.be7 4830bc1 [1, 0, 0, -3082736, -2078064384] 6 165888 \(\Gamma_0(N)\)-optimal
4830.be6 4830bc2 [1, 0, 0, -4393456, -140558080] 12 331776  
4830.be3 4830bc3 [1, 0, 0, -249518576, -1517079678720] 2 497664  
4830.be5 4830bc4 [1, 0, 0, -47316976, 124844147456] 6 663552  
4830.be8 4830bc5 [1, 0, 0, 17558544, -1119617280] 6 663552  
4830.be2 4830bc6 [1, 0, 0, -249518896, -1517075593024] 4 995328  
4830.be1 4830bc7 [1, 0, 0, -253899016, -1461052982200] 2 1990656  
4830.be4 4830bc8 [1, 0, 0, -245143896, -1572836718024] 2 1990656  

Rank

sage: E.rank()

The elliptic curves in class 4830bc have rank \(0\).

Modular form 4830.2.a.be

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

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.