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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 457776f
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
457776.f2 | 457776f1 | \([0, 0, 0, -70227, -1326510]\) | \(19683/11\) | \(21406095265370112\) | \([2]\) | \(3932160\) | \(1.8238\) | \(\Gamma_0(N)\)-optimal* |
457776.f1 | 457776f2 | \([0, 0, 0, -694467, 221527170]\) | \(19034163/121\) | \(235467047919071232\) | \([2]\) | \(7864320\) | \(2.1704\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 457776f have rank \(1\).
Complex multiplication
The elliptic curves in class 457776f do not have complex multiplication.Modular form 457776.2.a.f
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.