Properties

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

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Show commands for: SageMath

sage: E = EllipticCurve("114.c1")
sage: E.isogeny_class()

Elliptic curves in class 114a

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
114.c3 114a1 [1, 0, 0, -8, 0] 6 12 \(\Gamma_0(N)\)-optimal
114.c4 114a2 [1, 0, 0, 32, 8] 6 24  
114.c1 114a3 [1, 0, 0, -428, -3444] 2 36  
114.c2 114a4 [1, 0, 0, -418, -3610] 2 72  

Rank

sage: E.rank()

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

Modular form 114.2.a.c

sage: E.q_eigenform(10)
\( q + q^{2} + q^{3} + q^{4} + q^{6} - 4q^{7} + q^{8} + q^{9} + q^{12} - 4q^{13} - 4q^{14} + q^{16} + 6q^{17} + q^{18} + q^{19} + O(q^{20}) \)

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.

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.