SELF-POINTS ON ELLIPTIC CURVES OF PRIME CONDUCTOR
2009 ◽
Vol 05
(05)
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pp. 911-932
Keyword(s):
Let E be an elliptic curve of conductor p. Given a cyclic subgroup C of order p in E[p], we construct a modular point PC on E, called self-point, as the image of (E,C) on X0(p) under the modular parametrization X0(p) → E. We prove that the point is of infinite order in the Mordell–Weil group of E over the field of definition of C. One can deduce a lower bound on the growth of the rank of the Mordell–Weil group in its PGL 2(ℤp)-tower inside ℚ(E[p∞]).
2013 ◽
Vol 357
(1)
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pp. 279-305
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1997 ◽
Vol 49
(4)
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pp. 749-771
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2016 ◽
Vol 164
(1)
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pp. 67-98
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2000 ◽
Vol 62
(2)
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pp. 303-306
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2020 ◽
Vol 102
(2)
◽
pp. 177-185
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2012 ◽
Vol 154
(2)
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pp. 303-324
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2019 ◽
Vol 15
(08)
◽
pp. 1547-1563
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