Properties

Label 50025g
Number of curves 2
Conductor 50025
CM no
Rank 1
Graph

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Show commands for: SageMath

sage: E = EllipticCurve("50025.c1")
sage: E.isogeny_class()

Elliptic curves in class 50025g

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
50025.c1 50025g1 [1, 1, 1, -9338, 343406] 2 41472 \(\Gamma_0(N)\)-optimal
50025.c2 50025g2 [1, 1, 1, -8713, 392156] 2 82944  

Rank

sage: E.rank()

The elliptic curves in class 50025g have rank \(1\).

Modular form 50025.2.a.c

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

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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.