curve #3812

y² = x³ + x² − 456694416047078541143859945x + 3927020559401597982755740295478917690043

a-invariants: [0, 1, 0, -456694416047078541143859945, 3927020559401597982755740295478917690043]
rank (lower bound): ≥ 21
torsion subgroup: trivial
conductor (N): 2150360671794370298557152011892777004225695617569693378821603621480
discriminant (Δ): -565913754280706720436803906391168575845598371842566865883758666782910326220000000
Faltings height: 14.2537
naive height: 195.8605
primes of bad reduction: 2, 3, 5, 11, 13, 17, 190278919009708672015334851, 3521776109602953751079450752033469
regulator: 21799544380309647641.779401272018502946794144243641714792887275063014387250001900
submitted by: 7fff-zip
submitted at: 2026-10-03 04:55:12 UTC
last updated: 2026-10-03 04:55:12 UTC

(52186687958391, 349601927590852900470)
(1115086093520151, -37229177724898796036790)
(-97901733960723/4, 168358315762046725731/8)
(-697966394283291/289, -347953507636003222560750/4913)
(179899765824846, -2396670704236935503445)
(-47996427888312771/2209, 6222863921578184926869750/103823)
(143446773136505659629/26569, -1718038049720110049719305885510/4330747)
(71206773317349/4, 303415049460352508775/8)
(-14458821846025881/625, 717927135041966836010778/15625)
(-2993225122156539/121, -12391701159108163485870/1331)
(889117793968778349/7225, 826534592978961752063196282/614125)
(522269639567799/49, -5637942541184393391930/343)
(324521888278453971/961, -184508695661337582786918810/29791)
(42614094724437, 248698489082499961950)
(96132783692373, -921105856452193307298)
(13592522065371, -15188830003686910230)
(17490142669770069/1369, 675159981195558234640770/50653)
(-223192758423341/9, 29169794364106084370/27)
(-1587138479186511/64, -602476377069234184695/512)
(-24797723879163, 1791623938719456270)
(-870775728972409067601/35129329, 860956091110597322256593539050/208211532983)

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