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Properties

Label 858k
Number of curves 2
Conductor 858
CM no
Rank 0
Graph

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Show commands for: SageMath

sage: E = EllipticCurve("858.k1")
sage: E.isogeny_class()

Elliptic curves in class 858k

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
858.k1 858k1 [1, 0, 0, -5774401, 5346023177] 7 35280 \(\Gamma_0(N)\)-optimal
858.k2 858k2 [1, 0, 0, 16353089, -335543012233] 1 246960  

Rank

sage: E.rank()

The elliptic curves in class 858k have rank \(0\).

Modular form 858.2.a.k

sage: E.q_eigenform(10)
\( q + q^{2} + q^{3} + q^{4} - q^{5} + q^{6} + q^{7} + q^{8} + q^{9} - q^{10} + q^{11} + q^{12} - q^{13} + q^{14} - q^{15} + q^{16} + 4q^{17} + q^{18} + 6q^{19} + O(q^{20}) \)

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.

\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.