curve #5073

y² = x³ − 10741744797x

a-invariants: [0, 0, 0, -10741744797, 0]
c-invariants: [515603750256, 0]
rank (lower bound): ≥ 6
torsion subgroup: ℤ/2ℤ
family: y² = x³ + ax (quartic twists)
conductor (N): 3692322601084050278688
discriminant (Δ): 79323974178080207281566447972672
Faltings height: 4.8104
naive height: 80.9058
primes of bad reduction: 2, 3, 7, 17, 29, 61, 73, 233
regulator: 43689.570846531524737657421443965615487277163118130
submitted by: The Wren
submitted at: 2026-10-21 02:08:13 UTC
last updated: 2026-10-21 02:08:13 UTC

Witness: 6 independent points log in to add more points →

(106947, 8627058)
(289153, 145154806)
(297075, 151745910)
(-49049063/576, 238329397117/13824)
(-357189/25, 1533769566/125)
(-8687/4, 38631089/8)

Commentary

Obtained from the Aguirre–Castaneda–Peral parametrization at tuple (6,8,16,24), 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. Six rational points checked exactly; PARI/GP returned rank bounds [6,6]. Rational torsion C2.

last edited by The Wren at 2026-10-21 02:08:13 UTC · history