2007
DOI: 10.1216/rmjm/1181068772
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Explicit Equations of Some Elliptic Modular Surfaces

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Cited by 13 publications
(26 citation statements)
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“…Because of the fibration over P 1 C , the j-function will explicitly depend on the projective coordinate of this base Riemann sphere and can thus be treated as a rational map from the base P 1 C to its range P 1 . All of these j-functions are given in [10] and certain simplifications, in [7,19]. Generalizing [7,11], we find the nice fact that Proposition 2.1.…”
Section: Modular Surfaces Ramification Data and J-functionsmentioning
confidence: 73%
“…Because of the fibration over P 1 C , the j-function will explicitly depend on the projective coordinate of this base Riemann sphere and can thus be treated as a rational map from the base P 1 C to its range P 1 . All of these j-functions are given in [10] and certain simplifications, in [7,19]. Generalizing [7,11], we find the nice fact that Proposition 2.1.…”
Section: Modular Surfaces Ramification Data and J-functionsmentioning
confidence: 73%
“…The recurrence for this example is (16) (n + 1) 2 u n+1 = (10n 2 + 2)u n−1 − 9(n − 1) 2 u n−3 u 0 = 1, u 1 = 0, u 2 = 3, u 3 = 0, u 4 = 15.…”
Section: Further Boundsmentioning
confidence: 98%
“…Next, consider the elliptic family associated to Γ(8; 4, 1, 2). From [16] we know that the defining equation is y 2 = x 3 − 2(8t 4 − 16t 3 + 16t 2 − 8t + 1)x 2 + (2t − 1) 4 (8t 2 − 8t + 1)x.…”
Section: Asymptotic Behaviormentioning
confidence: 99%
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“…We also include a reference, but naturally the given models are far from unique. Other models may be found in [Elkies 2008b;Schütt 2007a;Top and Yui 2007] [Elkies 2008b, §5] For d = −8, −12, it was shown in [Schütt 2007a, §7] that the named fibrations are defined over ‫.ޑ‬ To obtain Picard rank 20 over ‫,ޑ‬ it suffices to apply a quadratic twist as in Example 8 such that the fibre of type I 4 or I 3 , respectively, becomes split-multiplicative.…”
Section: Existence Of K3 Surfaces Of Picard Rank 20 Over ‫ޑ‬mentioning
confidence: 99%