Properties

Label 112.b
Number of curves 4
Conductor \(112\)
CM no
Rank \(0\)
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("112.b1")
sage: E.isogeny_class()

Elliptic curves in class 112.b

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
112.b1 112b3 [0, 0, 0, -299, -1990] 2 16  
112.b2 112b4 [0, 0, 0, -59, 138] 4 16  
112.b3 112b2 [0, 0, 0, -19, -30] 4 8  
112.b4 112b1 [0, 0, 0, 1, -2] 2 4 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()

The elliptic curves in class 112.b have rank \(0\).

Modular form 112.2.1.b

sage: E.q_eigenform(10)
\( q + 2q^{5} + q^{7} - 3q^{9} + 4q^{11} + 2q^{13} - 6q^{17} - 8q^{19} + O(q^{20}) \)

Isogeny matrix

sage: E.isogeny_class().matrix()

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

Isogeny graph

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