Echidna Databases
Databases for Elliptic Curves and Higher Dimensional Analogues

Consult the Echidna Algorithms page for Magma and Sage interfaces to the data hosted here.

Interactive Interfaces

Atkin modular polynomials
Access to individual Atkin modular polynomials.
Complex multiplication class invariants in genus 1
Hilbert class polynomials: an interactive interface to Hilbert class polynomials on $X(1) = X_0(1)$.
Weber class polynomials: an interactive interface to Weber class polynomials on $X$, where $X(48) \rightarrow X \rightarrow X(1)$.
Dedekind eta class polynomials: an interactive interface to Dedekind eta class polynomials on $X_0(p)$.
Atkin class polynomials: an interactive interface to Atkin class polynomials on $X_0^+(p) = X_0(p)/(w_p)$.
Complex multiplication class invariants in genus 2
Complex multiplication of abelian surfaces, an interface to databases of quartic CM fields, subschemes of Igusa CM invariants, and genus 2 curves over finite fields.

Static Databases

The following database files are available for use with the Echidna Algorithms (see Echidna Algorithms); each tarball expands into subdirectories of share/dbs/ alongside the Echidna Algorithms in share/src/.
Brandt modules
ModBrdt_brdt.tgz Brandt modules source data files: Brandt module theta series.
ModBrdt_quat.tgz Brandt modules source data files: quaternion ideal class representations.
ModBrdt_dcmp.tgz Brandt modules source data files: decompositions.
ModBrdt_hcke.tgz Brandt modules source data files: Hecke operators.
ModBrdt_proj.tgz Brandt modules source data files: projections.
Complex multiplication class polynomials in genus 1
PolCM_Cls.tgz Hilbert class polynomials source data files.
PolCM_Atk.tgz Atkin class polynomials source data files.
PolCM_Eta.tgz Dedekind eta class polynomials source data files.
PolCM_Wbr.tgz Weber class polynomials source data files.
Complex multiplication class invariants in genus 2
CrvG2: Ordinary genus 2 curves source data files (source pool for canonical lifting algorithms).
FldCM: Quartic CM field source data files.
IgusaLIX: Source files for Defining polynomials of CM Igusa invariants ('LIX' representation).
Modular polynomials defining X0(N)
PolMod_Cls.tgz Classical modular polynomials source data files (levels N < 30). And of higher levels: [030-060] [060-090] [090-120]
The classical database gives all (composite) levels up to $16$, the prime power levels up to $49$, and prime levels up to $113$.
PolMod_Eta.tgz Dedekind eta modular polynomials source data files (levels $N < 200$). And of higher levels: [200-400] [400-700]
The Dedekind eta database gives all prime levels up to $200$, plus the prime squares $4$, $9$, $25$, and incomplete data for primes up to $700$.
Above level $400$, the database consists only of primes $N = 1 \bmod 12$.
PolMod_Atk.tgz Atkin modular polynomials source data files (levels $N < 500$). And of higher levels: [500-600] [600-700] [700-800] [800-900]
Divisors of supersingular points.
DivSS.tgz Divisors of supersingular points source data files.
Genera of ternary quadratic forms.
SymGen.tgz Data files for genera of ternary quadratic forms.

Static Tables

Atkin-Lehner dimensions: tables of genera of modular curves $X_0(N)$ and dimensions of Atkin-Lehner eigenspaces of weight $2$ forms.
This work has been supported by the Australian Partnership for Advanced Computing (APAC) Merit Allocation Scheme Modular Curve Invariants 2004-2006. Initial database compilation was carried out in 2000 at the Mathematical Sciences Research Institute, through a network of Linux machines, and a 2002 Major Equipment Grant from the University of Sydney provided hardware for extension of this work.
David Kohel (David.Kohel@univ-amu.fr) Institut de Mathématiques de Marseille
Valid HTML 4.0!