Properties

Label 17.a
Number of curves 4
Conductor \(17\)
CM False
Rank \(0\)
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("17.a1")
sage: E.isogeny_class()

Elliptic curves in class 17.a

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
17.a1 17a3 [1, -1, 1, -91, -310] 2 4  
17.a2 17a2 [1, -1, 1, -6, -4] 4 2  
17.a3 17a1 [1, -1, 1, -1, -14] 4 1 \(\Gamma_0(N)\)-optimal
17.a4 17a4 [1, -1, 1, -1, 0] 4 4  

Rank

sage: E.rank()

The elliptic curves in class 17.a have rank \(0\).

Modular form 17.2.1.a

sage: E.q_eigenform(10)
\( q - q^{2} - q^{4} - 2q^{5} + 4q^{7} + 3q^{8} - 3q^{9} + O(q^{10}) \)

Isogeny matrix

sage: E.isogeny_class().matrix()

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

Isogeny graph

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