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SageMath
E = EllipticCurve("br1")
E.isogeny_class()
Elliptic curves in class 408135br
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 408135.br3 | 408135br1 | \([1, 0, 1, -47324, 3946997]\) | \(2428257525121/8150625\) | \(39341510105625\) | \([2]\) | \(1179648\) | \(1.4729\) | \(\Gamma_0(N)\)-optimal |
| 408135.br2 | 408135br2 | \([1, 0, 1, -68449, 68447]\) | \(7347774183121/4251692025\) | \(20522105331498225\) | \([2, 2]\) | \(2359296\) | \(1.8195\) | |
| 408135.br4 | 408135br3 | \([1, 0, 1, 273776, 616007]\) | \(470166844956479/272118787605\) | \(-1313465413080902445\) | \([2]\) | \(4718592\) | \(2.1661\) | |
| 408135.br1 | 408135br4 | \([1, 0, 1, -748674, -248621813]\) | \(9614816895690721/34652610405\) | \(167261531776347645\) | \([2]\) | \(4718592\) | \(2.1661\) |
Rank
sage: E.rank()
The elliptic curves in class 408135br have rank \(1\).
Complex multiplication
The elliptic curves in class 408135br do not have complex multiplication.Modular form 408135.2.a.br
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.
