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SageMath
E = EllipticCurve("u1")
E.isogeny_class()
Elliptic curves in class 88270u
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
88270.k2 | 88270u1 | \([1, -1, 1, 2810783433, 57129831452559]\) | \(2455872791358451393794120395694399/2831226586844364800000000000000\) | \(-2831226586844364800000000000000\) | \([7]\) | \(285815040\) | \(4.5295\) | \(\Gamma_0(N)\)-optimal |
88270.k1 | 88270u2 | \([1, -1, 1, -938726820567, -350077314766040241]\) | \(-91483209224241436429962941197655681681601/1781546240931158951849152905279200\) | \(-1781546240931158951849152905279200\) | \([]\) | \(2000705280\) | \(5.5025\) |
Rank
sage: E.rank()
The elliptic curves in class 88270u have rank \(0\).
Complex multiplication
The elliptic curves in class 88270u do not have complex multiplication.Modular form 88270.2.a.u
sage: E.q_eigenform(10)
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.