Properties

Label 49098.b
Number of curves 2
Conductor 49098
CM no
Rank 2
Graph

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Show commands for: SageMath

sage: E = EllipticCurve("49098.b1")
sage: E.isogeny_class()

Elliptic curves in class 49098.b

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
49098.b1 49098e2 [1, 1, 0, -6101, 180405] 2 82944  
49098.b2 49098e1 [1, 1, 0, -221, 5181] 2 41472 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()

The elliptic curves in class 49098.b have rank \(2\).

Modular form None

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

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 LMFDB numbering.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.