Properties

Label 88270u
Number of curves 2
Conductor 88270
CM no
Rank 0
Graph

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Show commands for: SageMath

sage: E = EllipticCurve("88270.k1")
sage: E.isogeny_class()

Elliptic curves in class 88270u

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
88270.k2 88270u1 [1, -1, 1, 2810783433, 57129831452559] 7 285815040 \(\Gamma_0(N)\)-optimal
88270.k1 88270u2 [1, -1, 1, -938726820567, -350077314766040241] 1 2000705280  

Rank

sage: E.rank()

The elliptic curves in class 88270u have rank \(0\).

Modular form 88270.2.a.k

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

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.