Properties

Label 52983.e
Number of curves 6
Conductor 52983
CM no
Rank 0
Graph

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Show commands for: SageMath

sage: E = EllipticCurve("52983.e1")
sage: E.isogeny_class()

Elliptic curves in class 52983.e

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
52983.e1 52983a6 [1, -1, 1, -5934254, 5565613650] 2 802816  
52983.e2 52983a4 [1, -1, 1, -371039, 86959518] 4 401408  
52983.e3 52983a3 [1, -1, 1, -295349, -61332330] 2 401408  
52983.e4 52983a5 [1, -1, 1, -257504, 141093006] 2 802816  
52983.e5 52983a2 [1, -1, 1, -30434, 445848] 4 200704  
52983.e6 52983a1 [1, -1, 1, 7411, 52260] 2 100352 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()

The elliptic curves in class 52983.e have rank \(0\).

Modular form 52983.2.a.e

sage: E.q_eigenform(10)
\( q - q^{2} - q^{4} + 2q^{5} - q^{7} + 3q^{8} - 2q^{10} + 4q^{11} - 2q^{13} + q^{14} - q^{16} - 6q^{17} - 4q^{19} + O(q^{20}) \)

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 LMFDB numbering.

\(\left(\begin{array}{rrrrrr} 1 & 2 & 8 & 4 & 4 & 8 \\ 2 & 1 & 4 & 2 & 2 & 4 \\ 8 & 4 & 1 & 8 & 2 & 4 \\ 4 & 2 & 8 & 1 & 4 & 8 \\ 4 & 2 & 2 & 4 & 1 & 2 \\ 8 & 4 & 4 & 8 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.