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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 92400c
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 92400.h3 | 92400c1 | \([0, -1, 0, -169327383, 662879537262]\) | \(2147658844706816042407936/483688189481299210485\) | \(120922047370324802621250000\) | \([2]\) | \(22708224\) | \(3.7176\) | \(\Gamma_0(N)\)-optimal |
| 92400.h2 | 92400c2 | \([0, -1, 0, -889927508, -9648908251488]\) | \(19486220601593009351102416/1221175284018082695225\) | \(4884701136072330780900000000\) | \([2, 2]\) | \(45416448\) | \(4.0642\) | |
| 92400.h4 | 92400c3 | \([0, -1, 0, 707937992, -40494103863488]\) | \(2452389160534358561651516/45692546768053107181875\) | \(-731080748288849714910000000000\) | \([2]\) | \(90832896\) | \(4.4108\) | |
| 92400.h1 | 92400c4 | \([0, -1, 0, -14017395008, -638769660721488]\) | \(19037313645387618625546168804/82399233032965368135\) | \(1318387728527445890160000000\) | \([2]\) | \(90832896\) | \(4.4108\) |
Rank
sage: E.rank()
The elliptic curves in class 92400c have rank \(1\).
Complex multiplication
The elliptic curves in class 92400c do not have complex multiplication.Modular form 92400.2.a.c
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
