why elliptic curve plot() the same in Q and QuadraticField()?
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asked 10 years ago
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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 ()
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