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SageMath
E = EllipticCurve("u1")
E.isogeny_class()
Elliptic curves in class 422331u
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
422331.u2 | 422331u1 | \([1, 0, 0, -2173935, 1232426376]\) | \(2000852317801/2094417\) | \(1189355015251955097\) | \([2]\) | \(17418240\) | \(2.3856\) | \(\Gamma_0(N)\)-optimal |
422331.u1 | 422331u2 | \([1, 0, 0, -2712200, 575204811]\) | \(3885442650361/1996623837\) | \(1133821284924421501317\) | \([2]\) | \(34836480\) | \(2.7322\) |
Rank
sage: E.rank()
The elliptic curves in class 422331u have rank \(1\).
Complex multiplication
The elliptic curves in class 422331u do not have complex multiplication.Modular form 422331.2.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.