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05-28-15, 10:23 PM
You may have noticed some new types of WUs for the decic search. We are taking a temporary detour to search for a special type of field. This search is exploratory in nature, and not a complete search (which would take way too long). Once this special field is found we will return to the search over {2,5}.
The new search is for a particular A5 extension of Q(?421), ramified only at 2. Its existence is known from general theory applied to the 2-torsion points of the Jacobian of a special abelian surface. Due to its geometric origins, it has very limited ramification. On the other hand, it has non-solvable Galois group. This combination is difficult to find, and would provide a good example illustrating the general theory. Having the field explicitly would allow further computations to be done, such as computing the root discriminant of the Galois closure of the field, and computing Frobenius elements for many large primes.
More... (http://numberfields.asu.edu/NumberFields/forum_thread.php?id=234)
The new search is for a particular A5 extension of Q(?421), ramified only at 2. Its existence is known from general theory applied to the 2-torsion points of the Jacobian of a special abelian surface. Due to its geometric origins, it has very limited ramification. On the other hand, it has non-solvable Galois group. This combination is difficult to find, and would provide a good example illustrating the general theory. Having the field explicitly would allow further computations to be done, such as computing the root discriminant of the Galois closure of the field, and computing Frobenius elements for many large primes.
More... (http://numberfields.asu.edu/NumberFields/forum_thread.php?id=234)