Properties

Label 43190.g
Number of curves 2
Conductor 43190
CM no
Rank 1
Graph

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Show commands for: SageMath

sage: E = EllipticCurve("43190.g1")
sage: E.isogeny_class()

Elliptic curves in class 43190.g

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
43190.g1 43190s2 [1, -1, 1, -1270782, -2412118701] 1 6108144  
43190.g2 43190s1 [1, -1, 1, -137832, 20026539] 7 872592 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()

The elliptic curves in class 43190.g have rank \(1\).

Modular form 43190.2.a.g

sage: E.q_eigenform(10)
\( q + q^{2} - 3q^{3} + q^{4} + q^{5} - 3q^{6} + q^{7} + q^{8} + 6q^{9} + q^{10} - 2q^{11} - 3q^{12} - 7q^{13} + q^{14} - 3q^{15} + q^{16} + 4q^{17} + 6q^{18} - q^{19} + O(q^{20}) \)

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.

\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.