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SageMath
E = EllipticCurve("n1")
E.isogeny_class()
Elliptic curves in class 179088.n
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
179088.n1 | 179088bh1 | \([0, -1, 0, -2492896, -1514524928]\) | \(-418288977642645996769/122877464621184\) | \(-503306095088369664\) | \([]\) | \(3161088\) | \(2.3757\) | \(\Gamma_0(N)\)-optimal |
179088.n2 | 179088bh2 | \([0, -1, 0, 13833344, 66885734272]\) | \(71473535169369644529791/513262758348672548034\) | \(-2102324258196162756747264\) | \([]\) | \(22127616\) | \(3.3487\) |
Rank
sage: E.rank()
The elliptic curves in class 179088.n have rank \(0\).
Complex multiplication
The elliptic curves in class 179088.n do not have complex multiplication.Modular form 179088.2.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 LMFDB numbering.
\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.