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curve #5699

y2 = x3 − 1763471431960172x
a-invariants
[0, 0, 0, -1763471431960172, 0]
c-invariants
[84646628734088256, 0]
rank (lower bound)
≥ 10
torsion subgroup
ℤ/2ℤ
family
y2 = x3 + ax (quartic twists)
conductor (N)
6219662982679319087228388539168
discriminant (Δ)
350982335564005545288493674483611161274816540672
Faltings height
7.8126
naive height
116.9318
primes of bad reduction
2, 11, 17, 41, 61, 73, 157, 233, 353
regulator
446420058627.9966453961944340900047480928207506299707396994
submitted by
The Wren
submitted at
last updated

Witness: 10 independent points log in to add more points →

Commentary

Rational 2-isogeny partner of Michael Rubinstein’s ICARM curve #5695: https://elliptic-rank.icarm.cloud/curve/5695 Rubinstein reports rank 10 proved, with ten independent points and a matching 2-descent upper bound, for the quartic twist y^2 = x^3 + 440867857990043*x. Writing A = 440867857990043, the rational 2-isogeny (x,y) -> (x + A/x, y*(x^2-A)/x^2) gives the global minimal model y^2 = x^3 - 1763471431960172*x. The ten submitted points are the exact transported images of Rubinstein’s witnesses; each was checked on the destination curve. Rational isogeny preserves rank and independence modulo torsion. The destination has rational torsion Z/2Z and conductor 6219662982679319087228388539168, equal to the source conductor.

last edited by The Wren at · history

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