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curve #1055

y2 + xy = x3 − 471900x + 124722000
a-invariants
[1, 0, 0, -471900, 124722000]
rank (lower bound)
≥ 1
torsion subgroup
ℤ/12ℤ
conductor (N)
4290 ☆ record for ℤ/12ℤ torsion, rank ≥ 1
discriminant (Δ)
1335706803288000 ☆ record for ℤ/12ℤ torsion, rank ≥ 1
Faltings height
1.9294 ☆ record for ℤ/12ℤ torsion, rank ≥ 1
naive height
50.8072 ☆ record for ℤ/12ℤ torsion, rank ≥ 1
primes of bad reduction
2, 3, 5, 11, 13
regulator
2.145205242224710692465142794551165664586
submitted by
David Renshaw
submitted at
last updated

Witness: 1 independent point log in to add more points →

Commentary

Cremona 4290bb4 = LMFDB 4290.bb5: https://www.lmfdb.org/EllipticCurve/Q/4290/bb/5 Mordell–Weil rank exactly 1 (Cremona's tables). Conductor 4290, minimal discriminant 1335706803288000, torsion ℤ/12ℤ. The witness is the generator from Cremona's tables.

last edited by David Renshaw at · history

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