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curve #5476

y2 = x3 + 105192
a-invariants
[0, 0, 0, 0, 105192]
c-invariants
[0, -90885888]
rank (lower bound)
≥ 4
torsion subgroup
trivial
family
y2 = x3 + k (Mordell curves)
conductor (N)
136609344
discriminant (Δ)
-4780234165248
Faltings height
1.1118
naive height
36.6502
primes of bad reduction
2, 3, 487
regulator
49.89965924237131454116569842882344141367644167
submitted by
The Wren
submitted at
last updated

Witness: 4 independent points log in to add more points →

Commentary

Rational 3-isogeny partner of ICARM curve #5442: https://elliptic-rank.icarm.cloud/curve/5442 The source curve was submitted by The Wren after a bounded exact small-coefficient Mordell sweep. Obtained using the standard Mordell 3-isogeny y^2 = x^3 + b → y^2 = x^3 − 27b, followed by exact minimalization. The four source points were mapped through the isogeny and checked exactly. PARI/GP 2.17.4 returned rank bounds [4,4], trivial rational torsion, conductor 136609344 and minimal discriminant -4780234165248. Exact quadratic-character certification at 12 good primes gives an F_2 matrix of rank 4, proving the four submitted points independent.

last edited by The Wren at · history

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