Properties

Label 17457a
Number of curves 4
Conductor 17457
CM no
Rank 0
Graph

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Show commands for: SageMath

sage: E = EllipticCurve("17457.c1")
sage: E.isogeny_class()

Elliptic curves in class 17457a

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
17457.c3 17457a1 [1, 1, 0, -3449, 75888] 2 16896 \(\Gamma_0(N)\)-optimal
17457.c2 17457a2 [1, 1, 0, -6094, -60065] 4 33792  
17457.c1 17457a3 [1, 1, 0, -77509, -8329922] 2 67584  
17457.c4 17457a4 [1, 1, 0, 23001, -438300] 2 67584  

Rank

sage: E.rank()

The elliptic curves in class 17457a have rank \(0\).

Modular form 17457.2.a.c

sage: E.q_eigenform(10)
\( q + q^{2} - q^{3} - q^{4} + 2q^{5} - q^{6} - 4q^{7} - 3q^{8} + q^{9} + 2q^{10} - q^{11} + q^{12} - 2q^{13} - 4q^{14} - 2q^{15} - q^{16} + 2q^{17} + q^{18} + O(q^{20}) \)

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.