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SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 1872.h
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 1872.h1 | 1872q3 | \([0, 0, 0, -10011, -385526]\) | \(37159393753/1053\) | \(3144241152\) | \([2]\) | \(2048\) | \(0.92409\) | |
| 1872.h2 | 1872q4 | \([0, 0, 0, -2811, 51946]\) | \(822656953/85683\) | \(255848067072\) | \([4]\) | \(2048\) | \(0.92409\) | |
| 1872.h3 | 1872q2 | \([0, 0, 0, -651, -5510]\) | \(10218313/1521\) | \(4541681664\) | \([2, 2]\) | \(1024\) | \(0.57751\) | |
| 1872.h4 | 1872q1 | \([0, 0, 0, 69, -470]\) | \(12167/39\) | \(-116453376\) | \([2]\) | \(512\) | \(0.23094\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 1872.h have rank \(0\).
Complex multiplication
The elliptic curves in class 1872.h do not have complex multiplication.Modular form 1872.2.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.
