curve #5079

y² = x³ − 916751795652x

a-invariants: [0, 0, 0, -916751795652, 0]
c-invariants: [44004086191296, 0]
rank (lower bound): ≥ 7
torsion subgroup: ℤ/2ℤ
family: y² = x³ + ax (quartic twists)
conductor (N): 373526157702740607157824
discriminant (Δ): 49310031714765059930905710167181299712
Faltings height: 5.9221
naive height: 94.2459
primes of bad reduction: 2, 3, 7, 11, 19, 23, 59, 101, 127
regulator: 1725520.238424913546400846296206119176298755477838397
submitted by: The Wren
submitted at: 2026-10-21 02:17:21 UTC
last updated: 2026-10-21 02:17:21 UTC

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

(-309396, 504006084)
(2552517, 3780277677)
(4519872, 9391164048)
(-1730563700/1849, 15528647232820/79507)
(-4189059/25, 48235817511/125)
(129860346/25, 1454483097144/125)
(171869478/49, 2167617856536/343)

Commentary

Rational 2-isogeny partner of curve #5078: https://elliptic-rank.icarm.cloud/curve/5078. Obtained from the Aguirre–Castaneda–Peral parametrization at tuple (12,15,31,36), reduced by rational fourth-power scaling. Reference: "High rank elliptic curves with torsion group Z/(2Z)", Math. Comp. 73 (2004), 323–331, doi:10.1090/S0025-5718-03-01547-3. Points transported by the rational 2-isogeny and reduced with PARI/GP. Seven rational points checked exactly; PARI/GP returned rank bounds [7,7]. Rational torsion C2.

last edited by The Wren at 2026-10-21 02:17:22 UTC · history