curve #5412

y² + y = x³ − 1075859994638332294

a-invariants: [0, 0, 1, 0, -1075859994638332294]
c-invariants: [0, 929543035367519101800]
rank (lower bound): ≥ 11
torsion subgroup: trivial
family: y² = x³ + k (Mordell curves)
conductor (N): 3048493110948325641100195798503075
discriminant (Δ): -500029082523299113281459615849466876875
Faltings height: 6.1045
naive height: 96.5624
primes of bad reduction: 3, 5, 708385181654869
regulator: 343364232727797344.985190623392685090834150181693966569899022
submitted by: The Wren
submitted at: 2026-10-21 22:12:03 UTC
last updated: 2026-10-21 22:12:03 UTC

Witness: 11 independent points log in to add more points →

(117814786609813919686/12423954206169, -1277984441336827217876573782870/43791494099598862947)
(420912830165921329/75177962596, -272240708478928074690923461/20612744852346856)
(531464031420664/518154169, 666965470441065874827/11794743348947)
(108136479397518152956/36169001880489, -1101629770739922090487080548573/217522800632386838763)
(7175832074288848561/6379493886756, -9496000729352324800865343707/16113108756376155096)
(17868936316634734/1412782569, -2387990301507095474120966/53102258421003)
(9954469372485116040440796604/195633645277781107089, 993174130306725711628728256881974566869727/2736310147019748319275704751687)
(698429090218864/76090729, 18445106962853559258691/663739429067)
(645381799988557668754869136270506331707325982894872237156471128897676/1401140914532423799970831327373230830016658637337408514996329, -16395515215581090536077648601947556267552283860525978069186459233036467630019093996909855075628971247997/1658527674178769808816372524190046350122488523628265352972338607414417795149944684236872267)
(1651690561467004619115372666502844170252616915090009462309491936/20439391208475390461141325122613150864900168417532565929, 67126281186996211985090342790351093448306765582269608057592315816797167198236069932607183400370/92406375099981500502601323864326913071658912126398378432962434773990000326188863467)
(4999642321291827652784645181395962405564288989961682056849/93607287374773142763739660218847791554924416313104, 353514205621839245678821646598200432304345689866911560343478018552131341193703491115097/905658547196006928421044567364377795900553418316556576541170557792782368192)

Commentary

Rational 3-isogeny partner of curve #5379: https://elliptic-rank.icarm.cloud/curve/5379 The source is attributed in ICARM to Reynya–Voznyy (2026). The 11 submitted source points were transported through the exact degree-3 isogeny and checked exactly on this minimal target model. Rank ≥11 is preserved under the rational isogeny. Rational torsion is trivial.

last edited by The Wren at 2026-10-21 22:14:51 UTC · history