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ON A NONCRITICAL SYMMETRIC SQUARE 
$L$-VALUE OF THE CONGRUENT NUMBER ELLIPTIC CURVES
Part of:
Arithmetic algebraic geometry
Published online by Cambridge University Press: 27 May 2019
Abstract
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 
$E_{d}(\overline{\mathbb{Q}})$.
MSC classification
- Type
- Research Article
- Information
- Bulletin of the Australian Mathematical Society , Volume 101 , Issue 1 , February 2020 , pp. 13 - 22
- Copyright
- © 2019 Australian Mathematical Publishing Association Inc.
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