Properties

Label 114c
Number of curves 4
Conductor 114
CM no
Rank 0
Graph

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Show commands for: SageMath

sage: E = EllipticCurve("114.b1")
sage: E.isogeny_class()

Elliptic curves in class 114c

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
114.b4 114c1 [1, 1, 1, -352, -2431] 4 60 \(\Gamma_0(N)\)-optimal
114.b2 114c2 [1, 1, 1, -5472, -158079] 4 120  
114.b1 114c3 [1, 1, 1, -87552, -10007679] 2 240  
114.b3 114c4 [1, 1, 1, -5312, -167551] 2 240  

Rank

sage: E.rank()

The elliptic curves in class 114c have rank \(0\).

Modular form 114.2.a.b

sage: E.q_eigenform(10)
\( q + q^{2} - q^{3} + q^{4} + 2q^{5} - q^{6} + q^{8} + q^{9} + 2q^{10} - 4q^{11} - q^{12} + 2q^{13} - 2q^{15} + q^{16} - 6q^{17} + q^{18} - q^{19} + O(q^{20}) \)

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 Cremona 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 Cremona labels.