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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 52800.f
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 52800.f1 | 52800ff4 | \([0, -1, 0, -3152033, 2122175937]\) | \(3382175663521924/59189241375\) | \(60609783168000000000\) | \([2]\) | \(2359296\) | \(2.5925\) | |
| 52800.f2 | 52800ff2 | \([0, -1, 0, -402033, -47574063]\) | \(28071778927696/12404390625\) | \(3175524000000000000\) | \([2, 2]\) | \(1179648\) | \(2.2459\) | |
| 52800.f3 | 52800ff1 | \([0, -1, 0, -341533, -76674563]\) | \(275361373935616/148240125\) | \(2371842000000000\) | \([2]\) | \(589824\) | \(1.8993\) | \(\Gamma_0(N)\)-optimal |
| 52800.f4 | 52800ff3 | \([0, -1, 0, 1379967, -355860063]\) | \(283811208976796/217529296875\) | \(-222750000000000000000\) | \([2]\) | \(2359296\) | \(2.5925\) |
Rank
sage: E.rank()
The elliptic curves in class 52800.f have rank \(1\).
Complex multiplication
The elliptic curves in class 52800.f do not have complex multiplication.Modular form 52800.2.a.f
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.
