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SageMath
E = EllipticCurve("br1")
E.isogeny_class()
Elliptic curves in class 171600br
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 171600.ga4 | 171600br1 | \([0, 1, 0, 437592, 240715188]\) | \(144794100308831/474439680000\) | \(-30364139520000000000\) | \([2]\) | \(3538944\) | \(2.4215\) | \(\Gamma_0(N)\)-optimal |
| 171600.ga3 | 171600br2 | \([0, 1, 0, -4170408, 2830411188]\) | \(125337052492018849/18404100000000\) | \(1177862400000000000000\) | \([2, 2]\) | \(7077888\) | \(2.7680\) | |
| 171600.ga1 | 171600br3 | \([0, 1, 0, -64170408, 197830411188]\) | \(456612868287073618849/12544848030000\) | \(802870273920000000000\) | \([2]\) | \(14155776\) | \(3.1146\) | |
| 171600.ga2 | 171600br4 | \([0, 1, 0, -17898408, -26355316812]\) | \(9908022260084596129/1047363281250000\) | \(67031250000000000000000\) | \([2]\) | \(14155776\) | \(3.1146\) |
Rank
sage: E.rank()
The elliptic curves in class 171600br have rank \(0\).
Complex multiplication
The elliptic curves in class 171600br do not have complex multiplication.Modular form 171600.2.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.
