Elliptic Curve Rank Leaderboard

curve #3604

y2 + xy + y = x3 − x2 − 68377821263899296852267x + 6886248400820680528377823128414459
a-invariants
[1, -1, 1, -68377821263899296852267, 6886248400820680528377823128414459]
rank (lower bound)
≥ 17
torsion subgroup
trivial
conductor (N)
3199991341836188371521276362329878718158175687790
discriminant (Δ)
-24672238085935922757468883416984274683524930274694737461594086400000
Faltings height
11.8680
naive height
169.3528
primes of bad reduction
2, 5, 7, 11, 31, 43, 101, 35627957, 693914587, 1248560577878553982360441
regulator
1218534680544749405.81763555708802496069346323552753443268406699297125097
submitted by
Michael Rubinstein
submitted at
last updated

Witness: 17 independent points log in to add more points →

Commentary

Specialization at t = -2 of a rank-17 elliptic K3 family (member P = 2G + theta of C546 in https://gist.github.com/7fff-zip/58764130a98380def8d555e30ba81344, in reduced coordinates y^2 = x^3 - 27*c4(t)*x - 54*c6(t), c4 = 229266544691230630042225 + 1148767151849671983980280*t + 1683055912133375613928320*t^2 + 437075683846550943081920*t^3 - 419700913360243030971880*t^4 - 413476672102570136085360*t^5 + 296474488499927445158320*t^6 + 353395116108885163700480*t^7 + 85386537915381926875456*t^8, c6 = -110117600739533363968141608029430025 - 832583143909661430864544305147730260*t - 2258777613778127645018144727033322776*t^2 - 2323066840605949954916562239379172800*t^3 + 4224411691620789521802920064397980*t^4 + 760246669056877381267793145815769720*t^5 - 982276963083748004851457103694787400*t^6 - 597764504390070426967497552771547104*t^7 + 374646738137646635315808548695924200*t^8 + 71041369628477641221666859558448960*t^9 - 272311587156276263196050039283673920*t^10 - 153971474450137833790103496028596480*t^11 - 25015849076229626982910761017951104*t^12), found by searching small-height t = a/b for small conductor, with points from a 2-descent (PARI ellrank).

last edited by Michael Rubinstein at · history

Log in to edit commentary.