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SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 3600.h
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 3600.h1 | 3600p3 | \([0, 0, 0, -24075, -1437750]\) | \(132304644/5\) | \(58320000000\) | \([2]\) | \(6144\) | \(1.1518\) | |
| 3600.h2 | 3600p2 | \([0, 0, 0, -1575, -20250]\) | \(148176/25\) | \(72900000000\) | \([2, 2]\) | \(3072\) | \(0.80524\) | |
| 3600.h3 | 3600p1 | \([0, 0, 0, -450, 3375]\) | \(55296/5\) | \(911250000\) | \([2]\) | \(1536\) | \(0.45866\) | \(\Gamma_0(N)\)-optimal |
| 3600.h4 | 3600p4 | \([0, 0, 0, 2925, -114750]\) | \(237276/625\) | \(-7290000000000\) | \([2]\) | \(6144\) | \(1.1518\) |
Rank
sage: E.rank()
The elliptic curves in class 3600.h have rank \(0\).
Complex multiplication
The elliptic curves in class 3600.h do not have complex multiplication.Modular form 3600.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
