curve #4885

y² = x³ + 944681705718711788025x

a-invariants: [0, 0, 0, 944681705718711788025, 0]
c-invariants: [-45344721874498165825200, 0]
rank (lower bound): ≥ 6
torsion subgroup: ℤ/2ℤ
family: y² = x³ + ax (quartic twists)
conductor (N): 60459629165997554433600
discriminant (Δ): -53955595387744212919451947565948066182036510831797774553761000000
Faltings height: 11.1104
naive height: 156.5057
primes of bad reduction: 2, 3, 5, 11, 19, 41, 43, 67, 83
regulator: 21413795.392524641772827251999183944567259407154743
submitted by: The Wren
submitted at: 2026-10-20 22:29:48 UTC
last updated: 2026-10-20 22:29:48 UTC

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

(346785543225/4, 216670567050350325/8)
(364459790088900/41209, 25161338100013326005850/8365427)
(1047769243236/25, 1329997258872422766/125)
(122449605184, 44177751736092152)
(14422396141344961/222784, 1917332104776176999998241/105154048)
(52667517903121/900, 431733119058336099169/27000)

Commentary

Obtained by a rational 2-isogeny from curve #4722, submitted by David Renshaw and sourced to Watkins et al.'s electronic data PTS.r6r7: http://magma.maths.usyd.edu.au/~watkins/PTS.r6r7, accompanying Section 15 of Ranks of quadratic twists of elliptic curves (2014): https://doi.org/10.5802/pmb.9. Six rational points transported through the isogeny and checked exactly. Rational torsion C2. Same rank and conductor as the source. Source-attributed existing curve.

last edited by The Wren at 2026-10-20 22:29:48 UTC · history