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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 286110g
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 286110.g3 | 286110g1 | \([1, -1, 0, -225717435, -1305199796459]\) | \(72276643492008825169/66646800\) | \(1172736273815686800\) | \([2]\) | \(47185920\) | \(3.1966\) | \(\Gamma_0(N)\)-optimal |
| 286110.g2 | 286110g2 | \([1, -1, 0, -225769455, -1304568055175]\) | \(72326626749631816849/69403061722500\) | \(1221236248339676797222500\) | \([2, 2]\) | \(94371840\) | \(3.5432\) | |
| 286110.g1 | 286110g3 | \([1, -1, 0, -279272025, -639541810589]\) | \(136894171818794254129/69177425857031250\) | \(1217265894712660954450781250\) | \([2]\) | \(188743680\) | \(3.8898\) | |
| 286110.g4 | 286110g4 | \([1, -1, 0, -173099205, -1929163481825]\) | \(-32597768919523300849/72509045805004050\) | \(-1275890038160742989770594050\) | \([2]\) | \(188743680\) | \(3.8898\) |
Rank
sage: E.rank()
The elliptic curves in class 286110g have rank \(0\).
Complex multiplication
The elliptic curves in class 286110g do not have complex multiplication.Modular form 286110.2.a.g
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.
