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SageMath
E = EllipticCurve("br1")
E.isogeny_class()
Elliptic curves in class 87120br
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 87120.er2 | 87120br1 | \([0, 0, 0, 3993, -2254714]\) | \(16/5\) | \(-2200248149425920\) | \([2]\) | \(304128\) | \(1.6231\) | \(\Gamma_0(N)\)-optimal |
| 87120.er1 | 87120br2 | \([0, 0, 0, -235587, -42839566]\) | \(821516/25\) | \(44004962988518400\) | \([2]\) | \(608256\) | \(1.9697\) |
Rank
sage: E.rank()
The elliptic curves in class 87120br have rank \(1\).
Complex multiplication
The elliptic curves in class 87120br do not have complex multiplication.Modular form 87120.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
