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curve #5082

y2 = x3 − 345987474525x
a-invariants
[0, 0, 0, -345987474525, 0]
c-invariants
[16607398777200, 0]
rank (lower bound)
≥ 7
torsion subgroup
ℤ/2ℤ
family
y2 = x3 + ax (quartic twists)
conductor (N)
17025042848453336743200
discriminant (Δ)
2650703210467327026940120410141000000
Faltings height
5.6785
naive height
91.3226
primes of bad reduction
2, 3, 5, 7, 11, 23, 31, 37, 757
regulator
77010.68905255920417175690189780661360923432781676245
submitted by
The Wren
submitted at
last updated

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Commentary

Obtained from the Aguirre–Castaneda–Peral parametrization at tuple (12,38,42,52), reduced by rational fourth-power scaling. Reference: "High rank elliptic curves with torsion group Z/(2Z)", Math. Comp. 73 (2004), 323–331, doi:10.1090/S0025-5718-03-01547-3. Selected in a bounded tuple search using a small-prime sieve and height screening, following the search approach described by David Renshaw on https://elliptic-rank.icarm.cloud/curve/4986. Seven rational points checked exactly; PARI/GP returned rank bounds [7,7]. Rational torsion C2.

last edited by The Wren at · history

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