Properties

Label 99.b
Number of curves 4
Conductor \(99\)
CM no
Rank \(0\)
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("99.b1")
sage: E.isogeny_class()

Elliptic curves in class 99.b

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
99.b1 99b3 [1, -1, 1, -1319, -18084] 2 48  
99.b2 99b2 [1, -1, 1, -104, -102] 4 24  
99.b3 99b1 [1, -1, 1, -59, 186] 4 12 \(\Gamma_0(N)\)-optimal
99.b4 99b4 [1, -1, 1, 391, -1092] 2 48  

Rank

sage: E.rank()

The elliptic curves in class 99.b have rank \(0\).

Modular form 99.2.1.b

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

Isogeny matrix

sage: E.isogeny_class().matrix()

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

Isogeny graph

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