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SageMath
E = EllipticCurve("fg1")
E.isogeny_class()
Elliptic curves in class 296208.fg
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 296208.fg1 | 296208fg3 | \([0, 0, 0, -1580139, 764523738]\) | \(82483294977/17\) | \(89927497617408\) | \([2]\) | \(2949120\) | \(2.0648\) | |
| 296208.fg2 | 296208fg2 | \([0, 0, 0, -99099, 11859210]\) | \(20346417/289\) | \(1528767459495936\) | \([2, 2]\) | \(1474560\) | \(1.7182\) | |
| 296208.fg3 | 296208fg1 | \([0, 0, 0, -11979, -215622]\) | \(35937/17\) | \(89927497617408\) | \([2]\) | \(737280\) | \(1.3716\) | \(\Gamma_0(N)\)-optimal |
| 296208.fg4 | 296208fg4 | \([0, 0, 0, -11979, 31983930]\) | \(-35937/83521\) | \(-441813795794325504\) | \([2]\) | \(2949120\) | \(2.0648\) |
Rank
sage: E.rank()
The elliptic curves in class 296208.fg have rank \(1\).
Complex multiplication
The elliptic curves in class 296208.fg do not have complex multiplication.Modular form 296208.2.a.fg
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.
