Hello Jack,
typically you want
sage: E = EllipticCurve("11a1")
sage: m = 5
sage: ms = E.modular_symbol()
sage: chi = DirichletGroup(m).0
sage: chi
Dirichlet character modulo 5 of conductor 5 mapping 2 |--> zeta4
sage: sum( (chi^2)(a) * ms(a/m) for a in [1..(m-1)] )
5
The symbol ms is already divided by the correct period of E. In
particular ms(0) is L(E,1)/Omega. See the documentation in
ell_modular_symbols.py .
Don't hestitate to ask me directly for more help, I have done a lot of
such sums recently.
Chris.
On Aug 31, 9:35 pm, jack <[email protected]> wrote:
> I appreciated your previous responses on this subject. I would now
> like to apply these modular symbols to elliptic curves. In
> particular, I want to compute the algebraic value of a twisted L-
> function by applying Birch's theorem in [MTT]
>
> That is L(E,1,chi)^{alg} = sum_{a mod,m) chi(a)*{a,m}/Omega
>
> For this to work, the modular symbols need to translate to real
> numbers and I don't see the appropriate functions to perform this.
>
> Best Wishes,
> Jack Fearnley
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