Properties

Label 14.a
Number of curves 6
Conductor \(14\)
CM False
Rank \(0\)
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("14.a1")
sage: E.isogeny_class()

Elliptic curves in class 14.a

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
14.a1 14a5 [1, 0, 1, -2731, -55146] 2 6  
14.a2 14a3 [1, 0, 1, -171, -874] 2 3  
14.a3 14a2 [1, 0, 1, -36, -70] 6 2  
14.a4 14a6 [1, 0, 1, -11, 12] 6 6  
14.a5 14a4 [1, 0, 1, -1, 0] 6 3  
14.a6 14a1 [1, 0, 1, 4, -6] 6 1 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()

The elliptic curves in class 14.a have rank \(0\).

Modular form 14.2.1.a

sage: E.q_eigenform(10)
\( q - q^{2} - 2q^{3} + q^{4} + 2q^{6} + q^{7} - q^{8} + q^{9} + O(q^{10}) \)

Isogeny matrix

sage: E.isogeny_class().matrix()

\(\left(\begin{array}{rrrrrr} 1 & 2 & 3 & 9 & 18 & 6 \\ 2 & 1 & 6 & 18 & 9 & 3 \\ 3 & 6 & 1 & 3 & 6 & 2 \\ 9 & 18 & 3 & 1 & 2 & 6 \\ 18 & 9 & 6 & 2 & 1 & 3 \\ 6 & 3 & 2 & 6 & 3 & 1 \end{array}\right)\)

Isogeny graph

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