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SageMath
sage: E = EllipticCurve("e1")
sage: E.isogeny_class()
Elliptic curves in class 12882e
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 12882.e1 | 12882e1 | \([1, 1, 0, -494883, -79253235]\) | \(13403946614821979039929/5057590268826067968\) | \(5057590268826067968\) | \([2]\) | \(632320\) | \(2.2885\) | \(\Gamma_0(N)\)-optimal |
| 12882.e2 | 12882e2 | \([1, 1, 0, 1548157, -563453715]\) | \(410363075617640914325831/374944243169850027552\) | \(-374944243169850027552\) | \([2]\) | \(1264640\) | \(2.6351\) |
Rank
sage: E.rank()
The elliptic curves in class 12882e have rank \(1\).
Complex multiplication
The elliptic curves in class 12882e do not have complex multiplication.Modular form 12882.2.a.e
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.
