curve #4301

y² + xy + y = x³ − 8755969806755377407313725408x + 315029200251467559681423210402727614899806

a-invariants: [1, 0, 1, -8755969806755377407313725408, 315029200251467559681423210402727614899806]
c-invariants: [420286550724258115551058819561, -272185229017268601994575740175129985861661941]
rank (lower bound): ≥ 15
torsion subgroup: ℤ/2ℤ
conductor (N): 3596232705771186622110065084714548320296938776703770
discriminant (Δ): 89668536969696923914675439481066541107743317988128172876213023517882222584004106000
Faltings height: 14.8277
naive height: 204.6322
primes of bad reduction: 2, 3, 5, 11, 29, 53, 71, 137, 199, 277, 281, 397, 829, 1249, 5581, 1031299, 6764341, 10464199
regulator: 5867625696675018529357.6872929071579307761413198589776882709519616073
submitted by: The Wren
submitted at: 2026-10-16 19:10:00 UTC
last updated: 2026-10-16 19:10:00 UTC

Witness: 15 independent points log in to add more points →

(206810444812826, -2711014995571635481761)
(106626251406770, -770495742488560348713)
(628880175926918029365833/9831119104, 125891078265526276253924464594286259/974775121399808)
(187414065151588744730/2719201, 884932852584282776460671254758/4483962449)
(20176750303068185/256, 1386089184327666654228507/4096)
(156630756131218625/256, 61303003422706405912779447/4096)
(24539974683015940384202/46389721, -3787779416007929031649119762508206/315960389731)
(815791728677922393905/14622976, 751066438457363196976616050623/55918260224)
(10734988103673813405245/178409449, -184968468132978233454464015801769/2383015010293)
(492290946357262070377745/8780439616, -15506001191190941182198088947265637/822762313777664)
(215772555103755127741/2975625, 1271825203519580004138382210411/5132953125)
(4943844309075194654245/84768849, 40871908025247727059274773733661/780466792743)
(4153441334600565126488958005/74618101883329, -6760569382104404787670192600316859140229/644564371472229251233)
(933862619476012415144155528945/16821403375206609, -12854087633732238177879478079450254749818921/2181691491509563015405977)
(4778980800137638033690275331570/83833225715423041, -818719859923907413362791157840796183017025207/24273045263178132640343839)

Commentary

Obtained by a rational 2-isogeny from my curve#4255, found by specializing the family associated with curve#802 at T = 246/277. This isogenous curve has the same rank and conductor, with smaller absolute minimal discriminant, Faltings height and naive height. The fifteen supplied points were transported from the source curve.

last edited by The Wren at 2026-10-16 19:10:00 UTC · history