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SageMath
sage: E = EllipticCurve("v1")
sage: E.isogeny_class()
Elliptic curves in class 97461.v
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 97461.v1 | 97461k4 | \([1, -1, 0, -10915641, -13878310608]\) | \(1677087406638588673/4641\) | \(398040567561\) | \([2]\) | \(1966080\) | \(2.3442\) | |
| 97461.v2 | 97461k2 | \([1, -1, 0, -682236, -216714933]\) | \(409460675852593/21538881\) | \(1847306274050601\) | \([2, 2]\) | \(983040\) | \(1.9976\) | |
| 97461.v3 | 97461k3 | \([1, -1, 0, -644751, -241612470]\) | \(-345608484635233/94427721297\) | \(-8098699370512778937\) | \([2]\) | \(1966080\) | \(2.3442\) | |
| 97461.v4 | 97461k1 | \([1, -1, 0, -44991, -2982960]\) | \(117433042273/22801233\) | \(1955573308427193\) | \([2]\) | \(491520\) | \(1.6511\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 97461.v have rank \(0\).
Complex multiplication
The elliptic curves in class 97461.v do not have complex multiplication.Modular form 97461.2.a.v
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.
