Genus 2 Curves Database | Igusa CM Invariants Database | Quartic CM Fields Database |
A quartic CM field field K is represented by invariants [D,A,B], where K = Q[x]/(x4+Ax2+B), and D is the discriminant of the totally real quadratic subfield (hence A2-4B = m2D for some m).
K | Quartic invariants | Cl(OK) | Igusa invariants | Kr | Reflex invariants | Cl(OKr) | Igusa invariants |
1) | [5, 853, 153401] | C56 | 19618) | [153401, 451, 12500] | C56 | ||
2) | [5, 1889, 812069] | C56 | ---) | [812069, 1733, 547805] | C7 x C56 | ||
3) | [5, 1385, 469205] | C2 x C2 x C14 | ---) | [469205, 925, 96605] | C2 x C4 x C112 | ||
4) | [5, 1098, 270981] | C56 | 18473) | [30109, 549, 7605] | C2 x C28 | ||
5) | [5, 861, 184129] | C2 x C28 | ---) | [184129, 607, 46080] | C4 x C56 | ||
6) | [5, 1309, 361669] | C2 x C2 x C14 | 6263) | [61, 693, 29645] | C2 x C28 | ||
7) | [5, 1021, 260509] | C56 | ---) | [260509, 777, 85805] | C280 | ||
8) | [5, 279, 18409] | C2 x C28 | ---) |