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SageMath
E = EllipticCurve("bg1")
E.isogeny_class()
Elliptic curves in class 338130bg
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 338130.bg1 | 338130bg1 | \([1, -1, 0, -1710027504, -27217355620352]\) | \(31427652507069423952801/654426190080\) | \(11515471585159611214080\) | \([2]\) | \(112066560\) | \(3.7625\) | \(\Gamma_0(N)\)-optimal |
| 338130.bg2 | 338130bg2 | \([1, -1, 0, -1708154784, -27279944544560]\) | \(-31324512477868037557921/143427974919699600\) | \(-2523799925401644026064579600\) | \([2]\) | \(224133120\) | \(4.1091\) |
Rank
sage: E.rank()
The elliptic curves in class 338130bg have rank \(1\).
Complex multiplication
The elliptic curves in class 338130bg do not have complex multiplication.Modular form 338130.2.a.bg
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.
