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SageMath
E = EllipticCurve("n1")
E.isogeny_class()
Elliptic curves in class 17600n
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
17600.ch1 | 17600n1 | \([0, 1, 0, -1633, 68863]\) | \(-117649/440\) | \(-1802240000000\) | \([]\) | \(18432\) | \(1.0373\) | \(\Gamma_0(N)\)-optimal |
17600.ch2 | 17600n2 | \([0, 1, 0, 14367, -1643137]\) | \(80062991/332750\) | \(-1362944000000000\) | \([]\) | \(55296\) | \(1.5866\) |
Rank
sage: E.rank()
The elliptic curves in class 17600n have rank \(0\).
Complex multiplication
The elliptic curves in class 17600n do not have complex multiplication.Modular form 17600.2.a.n
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.