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curve #5542

y2 = x3 − 3990227478237x
a-invariants
[0, 0, 0, -3990227478237, 0]
c-invariants
[191530918955376, 0]
rank (lower bound)
≥ 8
torsion subgroup
ℤ/2ℤ
family
y2 = x3 + ax (quartic twists)
conductor (N)
467861607436623935607072
discriminant (Δ)
4066052099088521697431271526257450115392
Faltings height
6.2898
naive height
98.6582
primes of bad reduction
2, 3, 7, 11, 13, 31, 61, 107, 199
regulator
55612473440.2326761116153488810685193522205726058920348
submitted by
The Wren
submitted at
last updated

Witness: 8 independent points log in to add more points →

Commentary

Rational 2-isogeny partner of ICARM curve #5533: https://elliptic-rank.icarm.cloud/curve/5533. Michael Rubinstein submitted #5533 as proved rank 8, with eight independent listed points matching its 2-descent upper bound. Starting from y^2 = x^3 + Ax with A = 15960909912948, apply the standard rational 2-isogeny (x,y) ↦ (x + A/x, y(1 − A/x^2)) to y^2 = x^3 − 4Ax, then reduce by the rational fourth-power scaling (x,y) = (4X,8Y). This gives the submitted model y^2 = x^3 − 3990227478237x. The eight submitted points are the exact transported images and were checked on the submitted model. The rational isogeny preserves rank and conductor; the conductor is 467861607436623935607072.

last edited by The Wren at · history

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