curve #4884

y² = x³ + 10928709896614764489x

a-invariants: [0, 0, 0, 10928709896614764489, 0]
c-invariants: [-524578075037508695472, 0]
rank (lower bound): ≥ 6
torsion subgroup: ℤ/2ℤ
family: y² = x³ + ax (quartic twists)
conductor (N): 699437433383344927296
discriminant (Δ): -83538498902829944623441924685266184259595132988614160778816
Faltings height: 9.9955
naive height: 143.1274
primes of bad reduction: 2, 3, 17, 31, 449, 4657
regulator: 171548757.28535283125443040529488388664191257649192
submitted by: The Wren
submitted at: 2026-10-20 22:28:32 UTC
last updated: 2026-10-20 22:28:32 UTC

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

(97939580209/64, 72963135958762025/512)
(230084268241/64, 149932883227172455/512)
(33751579971321/484, 196303761149335638165/10648)
(157943614623844/42849, 2666329018294616941490/8869743)
(31992921511647216481/10347772176, 264923750822104715098353217775/1052616776831424)
(1003915610457358114485841/16248564188660736, 53829937888198920790476022975412110375/2071202137335340850774016)

Commentary

Obtained by a rational 2-isogeny from curve #4721, 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 22:28:32 UTC · history