ON A NONCRITICAL SYMMETRIC SQUARE -VALUE OF THE CONGRUENT NUMBER ELLIPTIC CURVES
2019 ◽
Vol 101
(1)
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pp. 13-22
Keyword(s):
The congruent number elliptic curves are defined by $E_{d}:y^{2}=x^{3}-d^{2}x$, where $d\in \mathbb{N}$. We give a simple proof of a formula for $L(\operatorname{Sym}^{2}(E_{d}),3)$ in terms of the determinant of the elliptic trilogarithm evaluated at some degree zero divisors supported on the torsion points on $E_{d}(\overline{\mathbb{Q}})$.
Keyword(s):
2018 ◽
Vol 30
(3)
◽
pp. 893-915
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1986 ◽
Vol 79
◽
pp. 119-122
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1984 ◽
Vol 96
◽
pp. 139-165
◽
Keyword(s):
2010 ◽
Vol 53
(4)
◽
pp. 661-666
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Keyword(s):