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SageMath
E = EllipticCurve("t1")
E.isogeny_class()
Elliptic curves in class 59290.t
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
59290.t1 | 59290bw2 | \([1, 1, 0, -2644457, -1656311411]\) | \(23560326604350529/1375000\) | \(119358922375000\) | \([]\) | \(933120\) | \(2.1660\) | |
59290.t2 | 59290bw1 | \([1, 1, 0, -35697, -1835819]\) | \(57954303169/17036800\) | \(1478904791795200\) | \([]\) | \(311040\) | \(1.6167\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 59290.t have rank \(0\).
Complex multiplication
The elliptic curves in class 59290.t do not have complex multiplication.Modular form 59290.2.a.t
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.