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<pics/wiles1.eps> <pics/hecke_in_front.eps>
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[]\OT1/lcmss/m/n/19.907 All of the quan-ti-ties in the BSD con-jec-ture, []\OT1
/lcmss/bx/n/19.907 ex-cept[] \OT1/lcmss/m/n/19.907 for $#[](\OML/lcmm/m/it/19.9
07 E=\U/msb/m/n/20.74 Q\OT1/lcmss/m/n/19.907 )$,

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\OT1/lcmss/m/n/19.907 four op-ti-mal curves with con-jec-turally non-triv-ial $
[](\OML/lcmm/m/it/19.907 E\OT1/lcmss/m/n/19.907 )$: 571A,
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[]\OT1/lcmss/m/n/19.907 Using MAGMA's \OT1/lcmtt/m/n/19.907 FourDescent \OT1/lc
mss/m/n/19.907 com-mand, we com-pute $[][](\OML/lcmm/m/it/19.907 E=\U/msb/m/n/2
0.74 Q\OT1/lcmss/m/n/19.907 )$
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[30]
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[]\OT1/lcmss/m/n/19.907 If $\OML/lcmm/m/it/19.907 E\OT1/lcmss/m/n/19.907 (\OML/
lcmm/m/it/19.907 K\OT1/lcmss/m/n/19.907 )$ too dif-fi-cult to com-pute, can som
e-times use the Cremona-
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[31]
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[]\OT1/lcmss/m/n/19.907 In many cases with $\OML/lcmm/m/it/19.907 r[] \OT1/lcms
s/m/n/19.907 = 1$, there is a big Tam-a-gawa number---
[32] [33]

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[34] (./bsd.aux)

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(see the transcript file for additional information)
Output written on bsd.dvi (34 pages, 32488 bytes).
Transcript written on bsd.log.