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SageMath
E = EllipticCurve("fl1")
E.isogeny_class()
Elliptic curves in class 228800.fl
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 228800.fl1 | 228800de4 | \([0, -1, 0, -37449633, 88222371137]\) | \(1418098748958579169/8307406250\) | \(34027136000000000000\) | \([2]\) | \(21233664\) | \(2.9374\) | |
| 228800.fl2 | 228800de3 | \([0, -1, 0, -2297633, 1432083137]\) | \(-327495950129089/26547449500\) | \(-108738353152000000000\) | \([2]\) | \(10616832\) | \(2.5909\) | |
| 228800.fl3 | 228800de2 | \([0, -1, 0, -665633, 4659137]\) | \(7962857630209/4606058600\) | \(18866416025600000000\) | \([2]\) | \(7077888\) | \(2.3881\) | |
| 228800.fl4 | 228800de1 | \([0, -1, 0, 166367, 499137]\) | \(124326214271/71980480\) | \(-294832046080000000\) | \([2]\) | \(3538944\) | \(2.0416\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 228800.fl have rank \(0\).
Complex multiplication
The elliptic curves in class 228800.fl do not have complex multiplication.Modular form 228800.2.a.fl
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
