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SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 1638.h
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 1638.h1 | 1638h2 | \([1, -1, 0, -33070464, 73207840986]\) | \(-5486773802537974663600129/2635437714\) | \(-1921234093506\) | \([]\) | \(65856\) | \(2.5959\) | |
| 1638.h2 | 1638h1 | \([1, -1, 0, 6426, 2238516]\) | \(40251338884511/2997011332224\) | \(-2184821261191296\) | \([]\) | \(9408\) | \(1.6229\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 1638.h have rank \(1\).
Complex multiplication
The elliptic curves in class 1638.h do not have complex multiplication.Modular form 1638.2.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 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.
