Properties

Label 4851.b
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 4851.b

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

Rank

sage: E.rank()
 

The elliptic curves in class 4851.b 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 LMFDB 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 LMFDB labels.