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SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 20216.h
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 20216.h1 | 20216b3 | \([0, 0, 0, -107939, -13649410]\) | \(1443468546/7\) | \(674449750016\) | \([2]\) | \(48384\) | \(1.4702\) | |
| 20216.h2 | 20216b4 | \([0, 0, 0, -21299, 946542]\) | \(11090466/2401\) | \(231336264255488\) | \([2]\) | \(48384\) | \(1.4702\) | |
| 20216.h3 | 20216b2 | \([0, 0, 0, -6859, -205770]\) | \(740772/49\) | \(2360574125056\) | \([2, 2]\) | \(24192\) | \(1.1236\) | |
| 20216.h4 | 20216b1 | \([0, 0, 0, 361, -13718]\) | \(432/7\) | \(-84306218752\) | \([2]\) | \(12096\) | \(0.77704\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 20216.h have rank \(0\).
Complex multiplication
The elliptic curves in class 20216.h do not have complex multiplication.Modular form 20216.2.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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
