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SageMath
E = EllipticCurve("n1")
E.isogeny_class()
Elliptic curves in class 160080.n
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 160080.n1 | 160080by2 | \([0, -1, 0, -38064981, 90268717725]\) | \(1489157481162281146384384/2616603057861328125\) | \(10717606125000000000000\) | \([]\) | \(13996800\) | \(3.1204\) | |
| 160080.n2 | 160080by1 | \([0, -1, 0, -1984341, -958023459]\) | \(210966209738334797824/25153051046653125\) | \(103026897087091200000\) | \([]\) | \(4665600\) | \(2.5711\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 160080.n have rank \(0\).
Complex multiplication
The elliptic curves in class 160080.n do not have complex multiplication.Modular form 160080.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
