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SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 474320h
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 474320.h1 | 474320h1 | \([0, 0, 0, -12492403, 16994897458]\) | \(-5154200289/20\) | \(-836624107467653120\) | \([]\) | \(28224000\) | \(2.6522\) | \(\Gamma_0(N)\)-optimal |
| 474320.h2 | 474320h2 | \([0, 0, 0, 87114797, -161250194798]\) | \(1747829720511/1280000000\) | \(-53543942877929799680000000\) | \([]\) | \(197568000\) | \(3.6252\) |
Rank
sage: E.rank()
The elliptic curves in class 474320h have rank \(1\).
Complex multiplication
The elliptic curves in class 474320h do not have complex multiplication.Modular form 474320.2.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.
\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
