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SageMath
E = EllipticCurve("u1")
E.isogeny_class()
Elliptic curves in class 317900.u
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
317900.u1 | 317900u2 | \([0, 0, 0, -85255, 9580350]\) | \(88723728/11\) | \(8496424288000\) | \([2]\) | \(983040\) | \(1.5040\) | |
317900.u2 | 317900u1 | \([0, 0, 0, -5780, 122825]\) | \(442368/121\) | \(5841291698000\) | \([2]\) | \(491520\) | \(1.1574\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 317900.u have rank \(0\).
Complex multiplication
The elliptic curves in class 317900.u do not have complex multiplication.Modular form 317900.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.