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SageMath
E = EllipticCurve("x1")
E.isogeny_class()
Elliptic curves in class 4560.x
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 4560.x1 | 4560bc3 | \([0, 1, 0, -7879680, -8516182860]\) | \(13209596798923694545921/92340\) | \(378224640\) | \([2]\) | \(92160\) | \(2.1806\) | |
| 4560.x2 | 4560bc4 | \([0, 1, 0, -498560, -129737292]\) | \(3345930611358906241/165622259047500\) | \(678388773058560000\) | \([4]\) | \(92160\) | \(2.1806\) | |
| 4560.x3 | 4560bc2 | \([0, 1, 0, -492480, -133188300]\) | \(3225005357698077121/8526675600\) | \(34925263257600\) | \([2, 2]\) | \(46080\) | \(1.8341\) | |
| 4560.x4 | 4560bc1 | \([0, 1, 0, -30400, -2142412]\) | \(-758575480593601/40535043840\) | \(-166031539568640\) | \([2]\) | \(23040\) | \(1.4875\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 4560.x have rank \(0\).
Complex multiplication
The elliptic curves in class 4560.x do not have complex multiplication.Modular form 4560.2.a.x
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.
