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SageMath
E = EllipticCurve("u1")
E.isogeny_class()
Elliptic curves in class 283920.u
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
283920.u1 | 283920u2 | \([0, -1, 0, -338056, 83823856]\) | \(-36522255042169/4741632000\) | \(-554703878356992000\) | \([]\) | \(3732480\) | \(2.1381\) | |
283920.u2 | 283920u1 | \([0, -1, 0, 26984, -281360]\) | \(18573478391/11022480\) | \(-1289474258042880\) | \([]\) | \(1244160\) | \(1.5888\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 283920.u have rank \(0\).
Complex multiplication
The elliptic curves in class 283920.u do not have complex multiplication.Modular form 283920.2.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 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.