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SageMath
E = EllipticCurve("fo1")
E.isogeny_class()
Elliptic curves in class 193600.fo
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 193600.fo1 | 193600hx3 | \([0, 0, 0, -91318700, 17284366000]\) | \(46424454082884/26794860125\) | \(48607978698654848000000000\) | \([2]\) | \(53084160\) | \(3.6183\) | |
| 193600.fo2 | 193600hx2 | \([0, 0, 0, -61068700, -183031134000]\) | \(55537159171536/228765625\) | \(103749698404000000000000\) | \([2, 2]\) | \(26542080\) | \(3.2718\) | |
| 193600.fo3 | 193600hx1 | \([0, 0, 0, -61008200, -183413131000]\) | \(885956203616256/15125\) | \(428717762000000000\) | \([2]\) | \(13271040\) | \(2.9252\) | \(\Gamma_0(N)\)-optimal |
| 193600.fo4 | 193600hx4 | \([0, 0, 0, -31786700, -358898826000]\) | \(-1957960715364/29541015625\) | \(-53589720250000000000000000\) | \([2]\) | \(53084160\) | \(3.6183\) |
Rank
sage: E.rank()
The elliptic curves in class 193600.fo have rank \(0\).
Complex multiplication
The elliptic curves in class 193600.fo do not have complex multiplication.Modular form 193600.2.a.fo
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
