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curve #5703

y2 = x3 + 8902509668x
a-invariants
[0, 0, 0, 8902509668, 0]
c-invariants
[-427320464064, 0]
rank (lower bound)
≥ 7
torsion subgroup
ℤ/2ℤ
family
y2 = x3 + ax (quartic twists)
conductor (N)
937925188033532192 ☆ record for quartic twists, rank ≥ 7
discriminant (Δ)
-45156194597812520442313608040448
Faltings height
4.7634
naive height
80.3424
primes of bad reduction
2, 13, 29, 233, 1949
regulator
16575465.63976003275691686038856450608643594496944406
submitted by
The Wren
submitted at
last updated

Witness: 7 independent points log in to add more points →

Commentary

Rational 2-isogeny partner of Michael Rubinstein’s ICARM curve #5669: https://elliptic-rank.icarm.cloud/curve/5669 Rubinstein reports rank 7 proved, with seven independent points and a matching 2-descent upper bound, for the quartic twist y^2 = x^3 - 2225627417*x. Writing A = -2225627417, the rational 2-isogeny (x,y) -> (x + A/x, y*(x^2-A)/x^2) gives the global minimal model y^2 = x^3 + 8902509668*x. The seven 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 937925188033532192, equal to the source conductor.

last edited by The Wren at · history

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