Elliptic Curve Rank Leaderboard

curve #686

y2 = x3 − 127265047x + 551353318330
a-invariants
[0, 0, 0, -127265047, 551353318330]
rank (lower bound)
≥ 11
torsion subgroup
trivial
conductor (N)
18597723997878981667496
discriminant (Δ)
595127167932127413359872
Faltings height
3.4373
naive height
67.5990
primes of bad reduction
2, 431, 5393771461101792827
regulator
4550641.01475868708712299052195683486836946771091304033912667
submitted by
NDElkies
submitted at
last updated

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Commentary

from the searches earlier this year that found Curves 157, 158, 244 of ranks 12, 13, 14; this rank-11 curve now appears also in M.Rubinstein's github tables. It is not quite a record but has N very close to the curve (#50) from Elkies-Watkins 2004, and is one of several curves with N smaller than the second-smallest N from that paper (66484354768372183177742, for [1, -1, 0, -38099014, 115877816224]).

last edited by NDElkies at · history

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