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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 5550g
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
5550.j2 | 5550g1 | \([1, 1, 0, -54185, 4961925]\) | \(-140754878313089741/4409857671168\) | \(-551232208896000\) | \([2]\) | \(40320\) | \(1.6051\) | \(\Gamma_0(N)\)-optimal |
5550.j1 | 5550g2 | \([1, 1, 0, -873385, 313800325]\) | \(589429221475670903501/552712568832\) | \(69089071104000\) | \([2]\) | \(80640\) | \(1.9517\) |
Rank
sage: E.rank()
The elliptic curves in class 5550g have rank \(0\).
Complex multiplication
The elliptic curves in class 5550g do not have complex multiplication.Modular form 5550.2.a.g
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.