Properties

Label 4851j
Number of curves 4
Conductor 4851
CM no
Rank 1
Graph

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Show commands for: SageMath

sage: E = EllipticCurve("4851.b1")
sage: E.isogeny_class()

Elliptic curves in class 4851j

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
4851.b3 4851j1 [1, -1, 1, -2876, -58138] 2 3456 \(\Gamma_0(N)\)-optimal
4851.b2 4851j2 [1, -1, 1, -5081, 45056] 4 6912  
4851.b1 4851j3 [1, -1, 1, -64616, 6331952] 2 13824  
4851.b4 4851j4 [1, -1, 1, 19174, 336116] 2 13824  

Rank

sage: E.rank()

The elliptic curves in class 4851j have rank \(1\).

Modular form 4851.2.a.b

sage: E.q_eigenform(10)
\( q - q^{2} - q^{4} - 2q^{5} + 3q^{8} + 2q^{10} - q^{11} + 2q^{13} - q^{16} - 2q^{17} + O(q^{20}) \)

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.

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.