curve #4902

y² = x³ + 35966339144319973217284x

a-invariants: [0, 0, 0, 35966339144319973217284, 0]
c-invariants: [-1726384278927358714429632, 0]
rank (lower bound): ≥ 6
torsion subgroup: ℤ/2ℤ
family: y² = x³ + ax (quartic twists)
conductor (N): 287730713154559785738272
discriminant (Δ): -2977615931182250720359024961552204639161073593917072431934478205587456
Faltings height: 12.0203
naive height: 167.4242
primes of bad reduction: 2, 17, 73, 233, 353, 929
regulator: 398962827.47176892088493678974256679248764016339211
submitted by: The Wren
submitted at: 2026-10-20 22:33:29 UTC
last updated: 2026-10-20 22:33:29 UTC

Witness: 6 independent points log in to add more points →

(18588937397121/1024, 841116018755078360385/32768)
(2023106576867998493472225/305384292661504, 82426907426117936297982513025006695855/5336666249564362452992)
(382714316884608200109121/18504705024, 236771988316249880300779808313464735/2517232033824768)
(10832174026764487929/411116176, 259072889593282954069467726195/8335791584576)
(1934078816380827894577849/718800765411600, 189599609718432561433158418917367128493/19271379169037085336000)
(189048070127331859223349025/27554926986445824, 71898115505121885703832444236202358844465/4574028822225986591096832)

Commentary

Obtained by a rational 2-isogeny from curve #4724, submitted by David Renshaw and sourced to Watkins et al.'s electronic data PTS.r6r7: http://magma.maths.usyd.edu.au/~watkins/PTS.r6r7, accompanying Section 15 of Ranks of quadratic twists of elliptic curves (2014): https://doi.org/10.5802/pmb.9. Six rational points transported through the isogeny and checked exactly. Rational torsion C2. Same rank and conductor as the source. Source-attributed existing curve.

last edited by The Wren at 2026-10-20 22:33:29 UTC · history