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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 20097g
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 20097.b3 | 20097g1 | \([1, -1, 1, -446, -3468]\) | \(13430356633/180873\) | \(131856417\) | \([2]\) | \(6656\) | \(0.36477\) | \(\Gamma_0(N)\)-optimal |
| 20097.b2 | 20097g2 | \([1, -1, 1, -851, 4146]\) | \(93391282153/44876601\) | \(32715042129\) | \([2, 2]\) | \(13312\) | \(0.71134\) | |
| 20097.b1 | 20097g3 | \([1, -1, 1, -11246, 461526]\) | \(215751695207833/163381911\) | \(119105413119\) | \([4]\) | \(26624\) | \(1.0579\) | |
| 20097.b4 | 20097g4 | \([1, -1, 1, 3064, 29202]\) | \(4365111505607/3058314567\) | \(-2229511319343\) | \([2]\) | \(26624\) | \(1.0579\) |
Rank
sage: E.rank()
The elliptic curves in class 20097g have rank \(1\).
Complex multiplication
The elliptic curves in class 20097g do not have complex multiplication.Modular form 20097.2.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.
