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SageMath
E = EllipticCurve("n1")
E.isogeny_class()
Elliptic curves in class 212160.n
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
212160.n1 | 212160hg1 | \([0, -1, 0, -29921, -1476255]\) | \(11301253512121/2899962000\) | \(760207638528000\) | \([2]\) | \(884736\) | \(1.5648\) | \(\Gamma_0(N)\)-optimal |
212160.n2 | 212160hg2 | \([0, -1, 0, 73759, -9542559]\) | \(169286748026759/247257562500\) | \(-64817086464000000\) | \([2]\) | \(1769472\) | \(1.9113\) |
Rank
sage: E.rank()
The elliptic curves in class 212160.n have rank \(2\).
Complex multiplication
The elliptic curves in class 212160.n do not have complex multiplication.Modular form 212160.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.