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SageMath
E = EllipticCurve("br1")
E.isogeny_class()
Elliptic curves in class 82110.br
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 82110.br1 | 82110br4 | \([1, 0, 0, -1545324081, 23381332267545]\) | \(408114879566277798087624787060369/6337051947007316223570000\) | \(6337051947007316223570000\) | \([2]\) | \(42270720\) | \(3.8938\) | |
| 82110.br2 | 82110br2 | \([1, 0, 0, -99474081, 342290857545]\) | \(108856287578506661479816660369/12378655769859332100000000\) | \(12378655769859332100000000\) | \([2, 2]\) | \(21135360\) | \(3.5473\) | |
| 82110.br3 | 82110br1 | \([1, 0, 0, -23891361, -39265829559]\) | \(1508156412264989366576166289/206783323792550830080000\) | \(206783323792550830080000\) | \([2]\) | \(10567680\) | \(3.2007\) | \(\Gamma_0(N)\)-optimal |
| 82110.br4 | 82110br3 | \([1, 0, 0, 137052399, 1723179753081]\) | \(284697489670284592032089987951/1447497023154543457031250000\) | \(-1447497023154543457031250000\) | \([2]\) | \(42270720\) | \(3.8938\) |
Rank
sage: E.rank()
The elliptic curves in class 82110.br have rank \(1\).
Complex multiplication
The elliptic curves in class 82110.br do not have complex multiplication.Modular form 82110.2.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.
