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SageMath
E = EllipticCurve("do1")
E.isogeny_class()
Elliptic curves in class 14400.do
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 14400.do1 | 14400cy4 | \([0, 0, 0, -348300, 20682000]\) | \(57960603/31250\) | \(2519424000000000000\) | \([2]\) | \(221184\) | \(2.2220\) | |
| 14400.do2 | 14400cy2 | \([0, 0, 0, -204300, -35542000]\) | \(8527173507/200\) | \(22118400000000\) | \([2]\) | \(73728\) | \(1.6727\) | |
| 14400.do3 | 14400cy1 | \([0, 0, 0, -12300, -598000]\) | \(-1860867/320\) | \(-35389440000000\) | \([2]\) | \(36864\) | \(1.3261\) | \(\Gamma_0(N)\)-optimal |
| 14400.do4 | 14400cy3 | \([0, 0, 0, 83700, 2538000]\) | \(804357/500\) | \(-40310784000000000\) | \([2]\) | \(110592\) | \(1.8754\) |
Rank
sage: E.rank()
The elliptic curves in class 14400.do have rank \(0\).
Complex multiplication
The elliptic curves in class 14400.do do not have complex multiplication.Modular form 14400.2.a.do
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.
\(\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
