Properties

Label 574.i
Number of curves 2
Conductor 574
CM no
Rank 0
Graph

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Show commands for: SageMath

sage: E = EllipticCurve("574.i1")
sage: E.isogeny_class()

Elliptic curves in class 574.i

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
574.i1 574j2 [1, 1, 1, -15785, -769911] 1 600  
574.i2 574j1 [1, 1, 1, -175, 789] 5 120 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()

The elliptic curves in class 574.i have rank \(0\).

Modular form 574.2.a.i

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

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 LMFDB numbering.

\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.