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SageMath
E = EllipticCurve("m1")
E.isogeny_class()
Elliptic curves in class 8550.m
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 8550.m1 | 8550i3 | \([1, -1, 0, -19242, 8268916]\) | \(-69173457625/2550136832\) | \(-29047652352000000\) | \([]\) | \(77760\) | \(1.8392\) | |
| 8550.m2 | 8550i1 | \([1, -1, 0, -3492, -78584]\) | \(-413493625/152\) | \(-1731375000\) | \([]\) | \(8640\) | \(0.74058\) | \(\Gamma_0(N)\)-optimal |
| 8550.m3 | 8550i2 | \([1, -1, 0, 2133, -302459]\) | \(94196375/3511808\) | \(-40001688000000\) | \([]\) | \(25920\) | \(1.2899\) |
Rank
sage: E.rank()
The elliptic curves in class 8550.m have rank \(1\).
Complex multiplication
The elliptic curves in class 8550.m do not have complex multiplication.Modular form 8550.2.a.m
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.
\(\left(\begin{array}{rrr} 1 & 9 & 3 \\ 9 & 1 & 3 \\ 3 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
