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SageMath
E = EllipticCurve("eo1")
E.isogeny_class()
Elliptic curves in class 286650.eo
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 286650.eo1 | 286650eo1 | \([1, -1, 0, -1361817, 633032091]\) | \(-86806489/3510\) | \(-11293669412323593750\) | \([]\) | \(6967296\) | \(2.4238\) | \(\Gamma_0(N)\)-optimal |
| 286650.eo2 | 286650eo2 | \([1, -1, 0, 6741558, 1921468716]\) | \(10531168151/6591000\) | \(-21207001452029859375000\) | \([]\) | \(20901888\) | \(2.9731\) |
Rank
sage: E.rank()
The elliptic curves in class 286650.eo have rank \(0\).
Complex multiplication
The elliptic curves in class 286650.eo do not have complex multiplication.Modular form 286650.2.a.eo
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
