Properties

Label 574i
Number of curves 2
Conductor 574
CM no
Rank 1
Graph

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Show commands for: SageMath

sage: E = EllipticCurve("574.g1")
sage: E.isogeny_class()

Elliptic curves in class 574i

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
574.g2 574i1 [1, -1, 1, -19353, 958713] 7 3528 \(\Gamma_0(N)\)-optimal
574.g1 574i2 [1, -1, 1, -9611313, -11466507927] 1 24696  

Rank

sage: E.rank()

The elliptic curves in class 574i have rank \(1\).

Modular form 574.2.a.g

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

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 Cremona 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 Cremona labels.