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816 bytes, as of the version from 2026-11-02 11:01 (current). Recorded here, not run.
"""Independent conductor-27 elliptic L-value control for the t=24 row.
Tao--Guo v2 Theorem 1.5 gives Ntilde(24)=-3L'(C_24,0).
The weight-two completed L-function gives L'(0)=27 L(2)/(4*pi^2).
"""
import numberdb.sage as numberdb
from sage.libs.pari import pari
from sage.rings.real_mpfr import RealField
import json
E=pari.ellinit([0,-27*24**2,0,216*24**3*(24-27),-432*24**4*(24-27)**2])
conductor=int(pari.ellglobalred(E)[0]);assert conductor==27
rows=[]
for digits in [145,195]:
bits=numberdb.bits(digits,losing=32)
pari.set_real_precision_bits(bits)
L=pari.lfuncreate(E)
value=pari.lfun(L,2,precision=bits)
R=RealField(bits);v=-R(81)/(4*R.pi()**2)*R(value)
rows.append({'working_digits':digits,'L2':str(R(value)),'modified_24':str(v)})
print(json.dumps({'conductor':conductor,'evaluations':rows},indent=2))