curve #4898

y² = x³ + 3853182641625660153321x

a-invariants: [0, 0, 0, 3853182641625660153321, 0]
c-invariants: [-184952766798031687359408, 0]
rank (lower bound): ≥ 6
torsion subgroup: ℤ/2ℤ
family: y² = x³ + ax (quartic twists)
conductor (N): 246603689064042249812544
discriminant (Δ): -3661329033028852273755752931343351827834791139955501474776057290304
Faltings height: 11.4618
naive height: 160.7232
primes of bad reduction: 2, 3, 7, 17, 41, 751, 5647
regulator: 1254511441.6403883663914029876584191253239188595990
submitted by: The Wren
submitted at: 2026-10-20 22:32:10 UTC
last updated: 2026-10-20 22:32:10 UTC

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

(2448883819972526049/223502500, 22046447373985553189634070407/3341362375000)
(1129113255738708100/41977441, 3017591670728171551404254410/271971840239)
(4061461916160000/786769, 3123164331419811066273600/697864103)
(333560026594117242623025/10786587078436, 432034885766681226600656405156979345/35426323222184884184)
(88920605851915945568400/59064066961, 26538261374151991793742441229990620/14354399257598791)
(2429734377423865421160328893609024/71635116158712758656225, 249774349637321841134351785092182978624993541368232/19172950639027770941798388235836625)

Commentary

Obtained by a rational 2-isogeny from curve #4726, 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 22:32:10 UTC · history