Elliptic Curve Rank Leaderboard

curve #687

y2 + y = x3 − 36274357x + 72401493396
a-invariants
[0, 0, 1, -36274357, 72401493396]
rank (lower bound)
≥ 11
torsion subgroup
trivial
conductor (N)
19274162508860687844797
discriminant (Δ)
790240662863288201636677
Faltings height
3.3099
naive height
63.8335
primes of bad reduction
41, 541, 868949213690126137
regulator
4584691.38947998281581387138938011818619383151782838814959200
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 quite 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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