Properties

Label 4018.f
Number of curves 2
Conductor 4018
CM no
Rank 0
Graph

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Show commands for: SageMath

sage: E = EllipticCurve("4018.f1")
sage: E.isogeny_class()

Elliptic curves in class 4018.f

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
4018.f1 4018c2 [1, 1, 0, -114391, 14839637] 1 17280  
4018.f2 4018c1 [1, 1, 0, -3896, -69152] 1 5760 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()

The elliptic curves in class 4018.f have rank \(0\).

Modular form 4018.2.a.f

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

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.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.