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SageMath
E = EllipticCurve("be1")
E.isogeny_class()
Elliptic curves in class 8550be
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 8550.v3 | 8550be1 | \([1, -1, 1, -5820980, -5453749353]\) | \(-1914980734749238129/20440940544000\) | \(-232835088384000000000\) | \([2]\) | \(552960\) | \(2.7245\) | \(\Gamma_0(N)\)-optimal |
| 8550.v2 | 8550be2 | \([1, -1, 1, -93372980, -347256757353]\) | \(7903870428425797297009/886464000000\) | \(10097379000000000000\) | \([2]\) | \(1105920\) | \(3.0711\) | |
| 8550.v4 | 8550be3 | \([1, -1, 1, 19235020, -28401589353]\) | \(69096190760262356111/70568821500000000\) | \(-803822982398437500000000\) | \([2]\) | \(1658880\) | \(3.2738\) | |
| 8550.v1 | 8550be4 | \([1, -1, 1, -104226980, -261497845353]\) | \(10993009831928446009969/3767761230468750000\) | \(42917155265808105468750000\) | \([2]\) | \(3317760\) | \(3.6204\) |
Rank
sage: E.rank()
The elliptic curves in class 8550be have rank \(0\).
Complex multiplication
The elliptic curves in class 8550be do not have complex multiplication.Modular form 8550.2.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 Cremona numbering.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
