The Tamagawa number of an elliptic curve defined over a number field at a prime of is the index , where is the completion of at and is the subgroup of consisting of all points whose reduction modulo is smooth.
The Tamagawa number of at is usually denoted . It is a positive integer, and equal to if has good reduction at and may be computed in general using Tate's algorithm.
The product of the Tamagawa numbers over all primes is a positive integer known as the Tamagawa product.
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- Last edited by Andrew Sutherland on 2019-03-09 15:02:36
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- ec.analytic_sha_order
- ec.bsdconjecture
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- ec.q.bsdconjecture
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- lmfdb/ecnf/templates/ecnf-curve.html (line 442)
- lmfdb/elliptic_curves/templates/bhkssw.html (line 47)
- lmfdb/elliptic_curves/templates/ec-curve.html (line 288)
- 2019-03-09 15:02:36 by Andrew Sutherland (Reviewed)