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SageMath
E = EllipticCurve("bt1")
E.isogeny_class()
Elliptic curves in class 202800.bt
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 202800.bt1 | 202800jl2 | \([0, -1, 0, -18084408, 20747559312]\) | \(4234737878642/1247410125\) | \(192672333377316000000000\) | \([2]\) | \(15482880\) | \(3.1737\) | |
| 202800.bt2 | 202800jl1 | \([0, -1, 0, 3040592, 2157559312]\) | \(40254822716/49359375\) | \(-3811972407750000000000\) | \([2]\) | \(7741440\) | \(2.8272\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 202800.bt have rank \(1\).
Complex multiplication
The elliptic curves in class 202800.bt do not have complex multiplication.Modular form 202800.2.a.bt
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
