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SageMath
E = EllipticCurve("be1")
E.isogeny_class()
Elliptic curves in class 106722.be
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 106722.be1 | 106722dn4 | \([1, -1, 0, -12087378, 16171409106]\) | \(1285429208617/614922\) | \(93431196463825194282\) | \([2]\) | \(5898240\) | \(2.7869\) | |
| 106722.be2 | 106722dn3 | \([1, -1, 0, -6751278, -6637857066]\) | \(223980311017/4278582\) | \(650087385763700318742\) | \([2]\) | \(5898240\) | \(2.7869\) | |
| 106722.be3 | 106722dn2 | \([1, -1, 0, -881568, 162788940]\) | \(498677257/213444\) | \(32430663235377340164\) | \([2, 2]\) | \(2949120\) | \(2.4403\) | |
| 106722.be4 | 106722dn1 | \([1, -1, 0, 185652, 18714240]\) | \(4657463/3696\) | \(-561569926153720176\) | \([2]\) | \(1474560\) | \(2.0937\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 106722.be have rank \(0\).
Complex multiplication
The elliptic curves in class 106722.be do not have complex multiplication.Modular form 106722.2.a.be
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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
