curve #471

y² + xy = x³ − 1074823784146380656x + 428719158724371531410862336

a-invariants: [1, 0, 0, -1074823784146380656, 428719158724371531410862336]
rank (lower bound): ≥ 14
torsion subgroup: trivial
conductor (N): 26259581507169921361816476153125499685328670
discriminant (Δ): 66257033241903953545157666376524076784274994640281600
Faltings height: 9.0899
naive height: 136.1697
primes of bad reduction: 2, 3, 5, 13, 331, 1097, 55098185820203, 3365513002778618976293
regulator: 15024385522048.3492377558448956016474396248950653065438032197990204
submitted by: Alexandar Slavov
submitted at: 2026-08-31 17:21:34 UTC
last updated: 2026-08-31 17:21:34 UTC

Witness: 14 independent points log in to add more points →

(758267514496, -660288174551206928)
(475326460, -5022186872156)
(587698720, -178427158064)
(808242946, 9379921263922)
(608563720, -43329540656)
(5833765581/16, 591075512003313/64)
(-1181857124, 6943609832032)
(-9814610435/16, -1873790360956151/64)
(546770716, 2120713770592)
(99376916440/169, 303411464395768/2197)
(3233937280/9, -254580942974128/27)
(98253282071896/172225, -78757483748777652176/71473375)
(917001096, 14635201672872)
(8691943216, 804832066978192)

Commentary

This curve was found by Aleksandar Lyubomirov Slavov, a 17-year-old independent researcher and high-school student from Bulgaria, as the specialization (T=3) of the Mestre/Fermigier quartic construction with sextuple (348,-600,-216,492,876,-900). It was identified during a computational search over specializations using multi-bound Mestre–Nagao screening and exact rational-point search. Four additional non-obvious quartic points were found. Exact eclib saturation and the ICARM verifier certify the displayed 14 rational points as independent, establishing rank ≥14.

last edited by Alexandar Slavov at 2026-08-31 17:21:34 UTC · history