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SageMath
E = EllipticCurve("fo1")
E.isogeny_class()
Elliptic curves in class 234234.fo
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 234234.fo1 | 234234fo4 | \([1, -1, 1, -61215719, -184334440507]\) | \(7209828390823479793/49509306\) | \(174210561598939866\) | \([2]\) | \(14155776\) | \(2.9080\) | |
| 234234.fo2 | 234234fo3 | \([1, -1, 1, -5334179, -401991235]\) | \(4770223741048753/2740574865798\) | \(9643380710580124786278\) | \([2]\) | \(14155776\) | \(2.9080\) | |
| 234234.fo3 | 234234fo2 | \([1, -1, 1, -3828389, -2875703047]\) | \(1763535241378513/4612311396\) | \(16229541948464200356\) | \([2, 2]\) | \(7077888\) | \(2.5614\) | |
| 234234.fo4 | 234234fo1 | \([1, -1, 1, -147569, -79752175]\) | \(-100999381393/723148272\) | \(-2544573470377930992\) | \([2]\) | \(3538944\) | \(2.2149\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 234234.fo have rank \(1\).
Complex multiplication
The elliptic curves in class 234234.fo do not have complex multiplication.Modular form 234234.2.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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
