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SageMath
E = EllipticCurve("ff1")
E.isogeny_class()
Elliptic curves in class 117600ff
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 117600.p3 | 117600ff1 | \([0, -1, 0, -7758, 91512]\) | \(438976/225\) | \(26471025000000\) | \([2, 2]\) | \(294912\) | \(1.2678\) | \(\Gamma_0(N)\)-optimal |
| 117600.p4 | 117600ff2 | \([0, -1, 0, 28992, 679512]\) | \(2863288/1875\) | \(-1764735000000000\) | \([2]\) | \(589824\) | \(1.6144\) | |
| 117600.p2 | 117600ff3 | \([0, -1, 0, -69008, -6890988]\) | \(38614472/405\) | \(381182760000000\) | \([2]\) | \(589824\) | \(1.6144\) | |
| 117600.p1 | 117600ff4 | \([0, -1, 0, -99633, 12127137]\) | \(14526784/15\) | \(112943040000000\) | \([2]\) | \(589824\) | \(1.6144\) |
Rank
sage: E.rank()
The elliptic curves in class 117600ff have rank \(1\).
Complex multiplication
The elliptic curves in class 117600ff do not have complex multiplication.Modular form 117600.2.a.ff
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 2 & 2 \\ 2 & 1 & 4 & 4 \\ 2 & 4 & 1 & 4 \\ 2 & 4 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
