Properties

Label 1617j
Number of curves 4
Conductor 1617
CM no
Rank 0
Graph

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Show commands for: SageMath

sage: E = EllipticCurve("1617.j1")
sage: E.isogeny_class()

Elliptic curves in class 1617j

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
1617.j3 1617j1 [1, 0, 1, -320, 2153] 2 432 \(\Gamma_0(N)\)-optimal
1617.j2 1617j2 [1, 0, 1, -565, -1669] 4 864  
1617.j1 1617j3 [1, 0, 1, -7180, -234517] 2 1728  
1617.j4 1617j4 [1, 0, 1, 2130, -12449] 2 1728  

Rank

sage: E.rank()

The elliptic curves in class 1617j have rank \(0\).

Modular form 1617.2.a.j

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

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.