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SageMath
E = EllipticCurve("u1")
E.isogeny_class()
Elliptic curves in class 481338u
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
481338.u1 | 481338u1 | \([1, -1, 0, -20811357, -35316029435]\) | \(771864882375147625/29358565696512\) | \(37915647212827423024128\) | \([2]\) | \(32768000\) | \(3.1006\) | \(\Gamma_0(N)\)-optimal |
481338.u2 | 481338u2 | \([1, -1, 0, 8635203, -127265857691]\) | \(55138849409108375/5449537181735712\) | \(-7037902716086203871408928\) | \([2]\) | \(65536000\) | \(3.4472\) |
Rank
sage: E.rank()
The elliptic curves in class 481338u have rank \(0\).
Complex multiplication
The elliptic curves in class 481338u do not have complex multiplication.Modular form 481338.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.