Properties

Label 37.b
Number of curves 3
Conductor \(37\)
CM no
Rank \(0\)
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("37.b1")
sage: E.isogeny_class()

Elliptic curves in class 37.b

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
37.b1 37b2 [0, 1, 1, -1873, -31833] 1 6  
37.b2 37b1 [0, 1, 1, -23, -50] 3 2 \(\Gamma_0(N)\)-optimal
37.b3 37b3 [0, 1, 1, -3, 1] 3 6  

Rank

sage: E.rank()

The elliptic curves in class 37.b have rank \(0\).

Modular form 37.2.1.b

sage: E.q_eigenform(10)
\( q + q^{3} - 2q^{4} - q^{7} - 2q^{9} + 3q^{11} - 2q^{12} - 4q^{13} + 4q^{16} + 6q^{17} + 2q^{19} + O(q^{20}) \)

Isogeny matrix

sage: E.isogeny_class().matrix()

\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)

Isogeny graph

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