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curve #4995

y2 = x3 + 51783906003x
a-invariants
[0, 0, 0, 51783906003, 0]
c-invariants
[-2485627488144, 0]
rank (lower bound)
≥ 4
torsion subgroup
ℤ/2ℤ
family
y2 = x3 + ax (quartic twists)
conductor (N)
237701754763660005408
discriminant (Δ)
-8887188484960118638615404125569728
Faltings height
5.2036
naive height
85.6246
primes of bad reduction
2, 3, 19, 263, 281, 647
regulator
3431.498519585966087965475844373941328218580844
submitted by
The Wren
submitted at
last updated

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Commentary

Obtained from the Aguirre–Castaneda–Peral parametrization at tuple (6,17,20,31), 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. Four rational points checked exactly; PARI/GP returned rank bounds [4,4]. Rational torsion C2.

last edited by The Wren at · history

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