g2c_columns = SearchColumns([
LinkCol("label", "g2c.label", "Label", url_for_curve_label, default=True),
ProcessedLinkCol(
"class",
"g2c.isogeny_class",
"Class",
lambda v: url_for_isogeny_class_label(class_from_curve_label(v)),
class_from_curve_label,
default=True,
orig="label"),
ProcessedCol("eqn",
"g2c.minimal_equation",
"Equation",
lambda v: min_eqn_pretty(literal_eval(v)),
default=True,
mathmode=True),
ProcessedCol("st_group",
"g2c.st_group",
"Sato-Tate",
lambda v: st_link_by_name(1, 4, v),
default=True,
align="center"),
CheckCol("is_simple_geom",
"ag.geom_simple",
r"\(\overline{\Q}\)-simple",
default=True),
CheckCol("is_gl2_type", "g2c.gl2type", r"\(\GL_2\)", default=True),
MathCol("analytic_rank", "g2c.analytic_rank", "Rank*", default=True)
])
shortcuts={
"jump": genus2_jump,
"download": G2C_download()
},
projection=[
"label",
"eqn",
"st_group",
"is_gl2_type",
"is_simple_geom",
"analytic_rank",
],
cleaners={
"class": lambda v: class_from_curve_label(v["label"]),
"equation_formatted":
lambda v: min_eqn_pretty(literal_eval(v.pop("eqn"))),
"st_group_link": lambda v: st_link_by_name(1, 4, v.pop("st_group")),
},
bread=lambda: get_bread("Search results"),
learnmore=learnmore_list,
credit=lambda: credit_string,
url_for_label=lambda label: url_for(".by_label", label=label),
)
def genus2_curve_search(info, query):
parse_ints(info, query, 'abs_disc', 'absolute discriminant')
parse_bool(info, query, 'is_gl2_type', 'is of GL2-type')
parse_bool(info, query, 'has_square_sha', 'has square Sha')
parse_bool(info, query, 'locally_solvable', 'is locally solvable')
parse_bool(info, query, 'is_simple_geom', 'is geometrically simple')
parse_ints(info, query, 'cond', 'conductor')
if info.get('analytic_sha') == "None":
CheckCol("is_simple_geom", "ag.geom_simple", r"\(\overline{\Q}\)-simple", short_title="Qbar-simple"),
MathCol("aut_grp_tex", "g2c.aut_grp", r"\(\Aut(X)\)", short_title="Q-automorphisms"),
MathCol("geom_aut_grp_tex", "g2c.geom_aut_grp", r"\(\Aut(X_{\overline{\Q}})\)", short_title="Qbar-automorphisms"),
MathCol("num_rat_pts", "g2c.all_rational_points", r"$\Q$-points", short_title="Q-points*"),
MathCol("num_rat_wpts", "g2c.num_rat_wpts", r"$\Q$-Weierstrass points", short_title="Q-Weierstrass points"),
CheckCol("locally_solvable", "g2c.locally_solvable", "Locally solvable"),
CheckCol("has_square_sha", "g2c.analytic_sha", "Square ле*"),
MathCol("analytic_sha", "g2c.analytic_sha", "Analytic ле*"),
ProcessedCol("tamagawa_product", "g2c.tamagawa", "Tamagawa", lambda v: web_latex(factor(v)), short_title="Tamagawa product", align="center"),
ProcessedCol("regulator", "g2c.regulator", "Regulator", lambda v: r"\(%.6f\)"%v, align="right"),
ProcessedCol("real_period", "g2c.real_period", "Real period", lambda v: r"\(%.6f\)"%v, align="right"),
ProcessedCol("leading_coeff", "g2c.bsd_invariants", "Leading coefficient", lambda v: r"\(%.6f\)"%v, align="right"),
ProcessedCol("igusa_clebsch_inv", "g2c.igusa_clebsch_invariants", "Igusa-Clebsch invariants", lambda v: v.replace("'",""), short_title="Igusa-Clebsch invariants", mathmode=True),
ProcessedCol("igusa_inv", "g2c.igusa_invariants", "Igusa invariants", lambda v: v.replace("'",""), short_title="Igusa invariants", mathmode=True),
ProcessedCol("g2_inv", "g2c.g2_invariants", "G2-invariants", lambda v: v.replace("'",""), short_title="G2-invariants", mathmode=True),
ProcessedCol("eqn", "g2c.minimal_equation", "Equation", lambda v: min_eqn_pretty(literal_eval(v)), default=True, mathmode=True),
])
@search_wrap(
table=db.g2c_curves,
title="Genus 2 curve search results",
err_title="Genus 2 curves search input error",
shortcuts={"jump": genus2_jump, "download": G2C_download()},
columns=g2c_columns,
bread=lambda: get_bread("Search results"),
learnmore=learnmore_list,
url_for_label=lambda label: url_for(".by_label", label=label),
)
def genus2_curve_search(info, query):
parse_ints(info, query, "abs_disc", "absolute discriminant")
parse_bool(info, query, "is_gl2_type", "is of GL2-type")