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SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 70180h
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 70180.a1 | 70180h1 | \([0, 1, 0, -105996161, -420068239736]\) | \(4646415367355940880384/38478378125\) | \(1090668704472050000\) | \([2]\) | \(5644800\) | \(3.0489\) | \(\Gamma_0(N)\)-optimal |
| 70180.a2 | 70180h2 | \([0, 1, 0, -105922956, -420677363900]\) | \(-289799689905740628304/835751962890625\) | \(-379029909281402500000000\) | \([2]\) | \(11289600\) | \(3.3955\) |
Rank
sage: E.rank()
The elliptic curves in class 70180h have rank \(1\).
Complex multiplication
The elliptic curves in class 70180h do not have complex multiplication.Modular form 70180.2.a.h
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
