Properties

Label 4730k
Number of curves 2
Conductor 4730
CM no
Rank 1
Graph

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Show commands for: SageMath

sage: E = EllipticCurve("4730.d1")
sage: E.isogeny_class()

Elliptic curves in class 4730k

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
4730.d1 4730k1 [1, -1, 1, -5582262, 5077966149] 7 219520 \(\Gamma_0(N)\)-optimal
4730.d2 4730k2 [1, -1, 1, 40144188, -96077802411] 1 1536640  

Rank

sage: E.rank()

The elliptic curves in class 4730k have rank \(1\).

Modular form 4730.2.a.d

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

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.