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Rational and Elliptic Parametrizations ofQ-Curves

✍ Scribed by Josep González; Joan-C. Lario

Publisher
Elsevier Science
Year
1998
Tongue
English
Weight
359 KB
Volume
72
Category
Article
ISSN
0022-314X

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✦ Synopsis

We describe explicit parametrizations of the rational points of X*(N), the algebraic curve obtained as quotient of the modular curve X 0 (N) by the group B(N) generated by the Atkin Lehner involutions, whenever N is square-free and the curve is rational or elliptic. By taking into account the moduli interpretation of X*(N), along with a standard ``boundedness'' conjecture, we obtain all the Q -isogeny classes of Q-curves except for a finite set. 1998 Academic Press '(z) '( pz)+ 24Â( p&1, 12)

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