# Echidna DatabasesDatabases for Elliptic Curves and Higher Dimensional Analogues

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

## Interactive Interfaces

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.
Atkin modular polynomials

## 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.
 Atkin-Lehner dimensions: tables of genera of modular curves $X_0(N)$ and dimensions of Atkin-Lehner eigenspaces of weight $2$ forms.