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SageMath
E = EllipticCurve("br1")
E.isogeny_class()
Elliptic curves in class 18480.br
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 18480.br1 | 18480ci3 | \([0, -1, 0, -788480, 269747712]\) | \(13235378341603461121/9240\) | \(37847040\) | \([2]\) | \(73728\) | \(1.6671\) | |
| 18480.br2 | 18480ci2 | \([0, -1, 0, -49280, 4227072]\) | \(3231355012744321/85377600\) | \(349706649600\) | \([2, 2]\) | \(36864\) | \(1.3205\) | |
| 18480.br3 | 18480ci4 | \([0, -1, 0, -47360, 4569600]\) | \(-2868190647517441/527295615000\) | \(-2159802839040000\) | \([4]\) | \(73728\) | \(1.6671\) | |
| 18480.br4 | 18480ci1 | \([0, -1, 0, -3200, 61440]\) | \(885012508801/127733760\) | \(523197480960\) | \([2]\) | \(18432\) | \(0.97396\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 18480.br have rank \(1\).
Complex multiplication
The elliptic curves in class 18480.br do not have complex multiplication.Modular form 18480.2.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 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.
