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[]\OT1/cmr/m/n/10.95 For an el-lip-tic curve $\OML/cmm/m/it/10.95 E$ \OT1/cmr/m
/n/10.95 de-fined over a num-ber field $\OML/cmm/m/it/10.95 K$\OT1/cmr/m/n/10.9
5 , let $[][](\OML/cmm/m/it/10.95 E=K\OT1/cmr/m/n/10.95 ) = [](\OML/cmm/m/it/10
.95 H[]\OT1/cmr/m/n/10.95 (\OML/cmm/m/it/10.95 K; E\OT1/cmr/m/n/10.95 ) \OMS/cm
sy/m/n/10.95 !
 []


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LaTeX Warning: Citation `kolyvagin:weil' on page 3 undefined on input line 57.


Overfull \hbox (15.49132pt too wide) in paragraph at lines 57--59
\OML/cmm/m/it/10.95 E[] \OT1/cmr/m/n/10.95 : \OMS/cmsy/m/n/10.95 ^^@\OML/cmm/m/
it/10.95 Dy[] \OT1/cmr/m/n/10.95 = 4\OML/cmm/m/it/10.95 x[] \OMS/cmsy/m/n/10.95
 ^^@ \OT1/cmr/m/n/10.95 4\OML/cmm/m/it/10.95 x \OT1/cmr/m/n/10.95 + 1$ with $\O
ML/cmm/m/it/10.95 D \OMS/cmsy/m/n/10.95 2 f\OT1/cmr/m/n/10.95 7\OML/cmm/m/it/10
.95 ; \OT1/cmr/m/n/10.95 11\OML/cmm/m/it/10.95 ; \OT1/cmr/m/n/10.95 47\OML/cmm/
m/it/10.95 ; \OT1/cmr/m/n/10.95 71\OML/cmm/m/it/10.95 ; \OT1/cmr/m/n/10.95 83\O
ML/cmm/m/it/10.95 ; \OT1/cmr/m/n/10.95 84\OML/cmm/m/it/10.95 ; \OT1/cmr/m/n/10.
95 127\OML/cmm/m/it/10.95 ; \OT1/cmr/m/n/10.95 159\OML/cmm/m/it/10.95 ; \OT1/cm
r/m/n/10.95 164\OML/cmm/m/it/10.95 ; \OT1/cmr/m/n/10.95 219\OML/cmm/m/it/10.95 
; \OT1/cmr/m/n/10.95 231\OML/cmm/m/it/10.95 ; \OT1/cmr/m/n/10.95 263\OML/cmm/m/
it/10.95 ; \OT1/cmr/m/n/10.95 271\OML/cmm/m/it/10.95 ; [] 
 []


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[][]\OT1/cmr/bx/n/14.4 Weakening the Hy-pothe-ses for Triv-i-al-ity of $[]\OT1/
cmr/m/n/14.4 (\OML/cmm/m/it/14.4 E=K\OT1/cmr/m/n/14.4 )[\OML/cmm/m/it/14.4 p\OT
1/cmr/m/n/14.4 ]$ 
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Overfull \hbox (12.00082pt too wide) in paragraph at lines 186--186
[][]\OT1/cmr/m/n/10.95 Denote com-plex con-ju-ga-tion by $\OML/cmm/m/it/10.95 ^
^\$\OT1/cmr/m/n/10.95 . We will de-com-pose $\OML/cmm/m/it/10.95 E\OT1/cmr/m/n/
10.95 (\OML/cmm/m/it/10.95 K\OT1/cmr/m/n/10.95 )$ into its eigenspaces
 []


Overfull \hbox (5.53236pt too wide) in paragraph at lines 191--191
[]\OT1/cmr/m/n/10.95 In light of Don-nelly's ob-ser-va-tion, we can ap-ply Koly
-va-gin's re-sult that $[](\OML/cmm/m/it/10.95 E=K\OT1/cmr/m/n/10.95 )[\OML/cmm
/m/it/10.95 p\OT1/cmr/m/n/10.95 ] =
 []

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