why elliptic curve plot() the same in Q and QuadraticField()?

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asked
2014-10-28 05:59:14 -0500

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```
sage: E = EllipticCurve([0,0,0,-15,22])
sage: show(E)
sage: K1.<a> = QuadraticField(3)
sage: E1 = EllipticCurve(K1,[0,0,0,-15,22])
sage: show(E1)
sage: E.torsion_subgroup()
Torsion Subgroup isomorphic to Z/6 associated to the Elliptic Curve defined by y^2 = x^3 - 15*x + 22 over Rational Field
sage: E1.torsion_subgroup()
Torsion Subgroup isomorphic to Z/2 + Z/6 associated to the Elliptic Curve defined by y^2 = x^3 + (-15)*x + 22 over Number Field in a with defining polynomial x^2 - 3
sage: table(E1.torsion_subgroup().list(),frame="true").transpose()
+----------------------------+
| (0 : 1 : 0) |
+----------------------------+
| (-2*a + 5 : -6*a + 12 : 1) |
+----------------------------+
| (3 : 2 : 1) |
+----------------------------+
| (-2*a - 1 : 0 : 1) |
+----------------------------+
| (3 : -2 : 1) |
+----------------------------+
| (-2*a + 5 : 6*a - 12 : 1) |
+----------------------------+
| (2 : 0 : 1) |
+----------------------------+
| (2*a + 5 : 6*a + 12 : 1) |
+----------------------------+
| (-1 : 6 : 1) |
+----------------------------+
| (2*a - 1 : 0 : 1) |
+----------------------------+
| (-1 : -6 : 1) |
+----------------------------+
| (2*a + 5 : -6*a - 12 : 1) |
+----------------------------+
sage: E.plot()
sage: E1.plot()
```