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SageMath
E = EllipticCurve("u1")
E.isogeny_class()
Elliptic curves in class 417450u
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
417450.u2 | 417450u1 | \([1, 1, 0, -132255, -18564795]\) | \(5776556465785/1073088\) | \(47526021259200\) | \([]\) | \(2332800\) | \(1.6266\) | \(\Gamma_0(N)\)-optimal* |
417450.u1 | 417450u2 | \([1, 1, 0, -322830, 45049140]\) | \(84013940106985/28705554432\) | \(1271341017877708800\) | \([]\) | \(6998400\) | \(2.1759\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 417450u have rank \(1\).
Complex multiplication
The elliptic curves in class 417450u do not have complex multiplication.Modular form 417450.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.