curve #5083

y² = x³ + 1383949898100x

a-invariants: [0, 0, 0, 1383949898100, 0]
c-invariants: [-66429595108800, 0]
rank (lower bound): ≥ 7
torsion subgroup: ℤ/2ℤ
family: y² = x³ + ax (quartic twists)
conductor (N): 17025042848453336743200
discriminant (Δ): -169645005469908929724167706249024000000
Faltings height: 6.0250
naive height: 95.4815
primes of bad reduction: 2, 3, 5, 7, 11, 23, 31, 37, 757
regulator: 1386192.402946065675091624234160519044966217900701724
submitted by: The Wren
submitted at: 2026-10-21 02:22:10 UTC
last updated: 2026-10-21 02:22:10 UTC

Witness: 7 independent points log in to add more points →

(5670, 88584300)
(206116, 542227636)
(878416, 1376038664)
(911680, 1421081200)
(1372525, 2117806075)
(3513664, 6945635312)
(9490030/9, 43800802100/27)

Commentary

Rational 2-isogeny partner of curve #5082: https://elliptic-rank.icarm.cloud/curve/5082. 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. Points transported by the rational 2-isogeny and reduced with PARI/GP. Seven rational points checked exactly; PARI/GP returned rank bounds [7,7]. Rational torsion C2.

last edited by The Wren at 2026-10-21 02:22:10 UTC · history