..nodoctest

Broker-Lauter-Streng

x.__init__(...) initializes x; see help(type(x)) for signature

recip.bls.cosets_of_GammaN_iter(p)

Returns exactly one representative of every left coset of Gamma_0(N) in Sp_4(ZZ).

recip.bls.count_nn_endomorphisms(Z, p)

Gives a lower bound (hopefully tight) on the number of (p,p)-endomorphisms for the input prime p.

recip.bls.humbert8()

Gives an equation for the Humbert surface of discriminant 8, due to David Gruenewald.

See also http://echidna.maths.usyd.edu.au/~davidg/thesis.html which contains this surface with respect to other invariants.

recip.bls.ic_from_Cab(a, b)

recip.bls.ic_on_humb8(ic)

recip.bls.ideal_power(I, n)

Returns I^n if I is principal. (because I**n is too slow in Sage 5.4.1)

recip.bls.is_polarized_product(Z, info=False, reduce=True)

Returns True or False. If True, then we know Z is a polarized product of CM elliptic curves. If False, then likely it is not (no proof!). If info is True, then returns information on the elliptic curves. If reduce is True, then reduce first (use reduce=False if already reduced).

recip.bls.j_from_Cab(a, b)

recip.bls.j_from_a()

recip.bls.lower_root(ideal, n)

recip.bls.mult_ic(ic, d)

recip.bls.nn_isogenous_matrices_iter(Z, p)

Returns all Sp_4(ZZ)-classes of period matrices that are (p,p)-isogenous to Z.

recip.bls.nn_isogenous_matrices_iter2(Z, p)

Returns all Sp_4(ZZ)-classes of period matrices that are (p,p)-isogenous to Z.

recip.bls.recognize_all_from_article(bound=2, print_results=False)

Returns a list of pairs ((a1,a2),l). Here a1, a2 runs over the numbers a1 and a2 from the article, and each l is itself a list. The elements of l are triples (Z, o0, o1), where the Z are period matrices.

recip.bls.recognize_matrix(Z, bound=2)

Tries to write Z as a polarized product of CM elliptic curves. If that fails, tries this for all (p,p)-isogenous varieties for p below the given bound.

recip.bls.reduce_ic(ic)