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SageMath
E = EllipticCurve("ox1")
E.isogeny_class()
Elliptic curves in class 388080.ox
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 388080.ox1 | 388080ox1 | \([0, 0, 0, -205947, -35966294]\) | \(74246873427/16940\) | \(220406987243520\) | \([2]\) | \(2359296\) | \(1.7440\) | \(\Gamma_0(N)\)-optimal |
| 388080.ox2 | 388080ox2 | \([0, 0, 0, -182427, -44494646]\) | \(-51603494067/35870450\) | \(-466711795488153600\) | \([2]\) | \(4718592\) | \(2.0906\) |
Rank
sage: E.rank()
The elliptic curves in class 388080.ox have rank \(1\).
Complex multiplication
The elliptic curves in class 388080.ox do not have complex multiplication.Modular form 388080.2.a.ox
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
