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SageMath
E = EllipticCurve("lx1")
E.isogeny_class()
Elliptic curves in class 100800lx
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 100800.gp3 | 100800lx1 | \([0, 0, 0, -50700, -2774000]\) | \(4826809/1680\) | \(5016453120000000\) | \([2]\) | \(589824\) | \(1.7142\) | \(\Gamma_0(N)\)-optimal |
| 100800.gp2 | 100800lx2 | \([0, 0, 0, -338700, 73834000]\) | \(1439069689/44100\) | \(131681894400000000\) | \([2, 2]\) | \(1179648\) | \(2.0608\) | |
| 100800.gp4 | 100800lx3 | \([0, 0, 0, 93300, 249226000]\) | \(30080231/9003750\) | \(-26885053440000000000\) | \([2]\) | \(2359296\) | \(2.4073\) | |
| 100800.gp1 | 100800lx4 | \([0, 0, 0, -5378700, 4801354000]\) | \(5763259856089/5670\) | \(16930529280000000\) | \([2]\) | \(2359296\) | \(2.4073\) |
Rank
sage: E.rank()
The elliptic curves in class 100800lx have rank \(1\).
Complex multiplication
The elliptic curves in class 100800lx do not have complex multiplication.Modular form 100800.2.a.lx
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.
