| Label |
Polynomial |
Degree |
Signature |
Discriminant |
Ram. prime count |
Root discriminant |
CM field |
Galois |
Monogenic |
Galois group |
Class group |
Unit group torsion |
Unit group rank |
Regulator |
| 15.1.723352547563839.1 |
x15 - x14 - 2x13 + 2x12 - 2x11 + 2x10 + 5x9 - 5x8 + 4x7 - 5x6 - 4x5 + 5x4 - 2x3 + x2 + x + 1 |
$15$ |
[1,7] |
$-\,3^{3}\cdot 6653\cdot 4026880369$ |
$3$ |
$9.78640837431$ |
|
|
not computed |
15T104 |
trivial |
$2$ |
$7$ |
$11.7410590074$ |
| 15.3.1788527348449625.1 |
x15 - 2x14 + 4x13 - 9x12 + 13x11 - 15x10 + 18x9 - 23x8 + 33x7 - 44x6 + 48x5 - 44x4 + 30x3 - 16x2 + 6x - 1 |
$15$ |
[3,6] |
$5^{3}\cdot 7^{10}\cdot 37^{3}$ |
$3$ |
$10.3952045383$ |
|
|
not computed |
$S_5 \times C_3$ (as 15T24) |
trivial |
$2$ |
$8$ |
$26.5068203244$ |
| 15.3.2164169497031757.1 |
x15 - 7x14 + 23x13 - 45x12 + 54x11 - 32x10 - 14x9 + 55x8 - 72x7 + 69x6 - 57x5 + 39x4 - 21x3 + 9x2 - 4x + 1 |
$15$ |
[3,6] |
$3^{3}\cdot 69593\cdot 1151759887$ |
$3$ |
$10.5281666665$ |
|
|
✓ |
15T104 |
trivial |
$2$ |
$8$ |
$29.6657425505$ |
| 15.3.2354315214908549.1 |
x15 - x14 + x13 - x12 - x11 + 3x10 - 2x9 + 2x8 - 2x7 - x6 + 2x3 - x2 + 2x - 1 |
$15$ |
[3,6] |
$27765763\cdot 84792023$ |
$2$ |
$10.5874402875$ |
|
|
✓ |
15T104 |
trivial |
$2$ |
$8$ |
$31.1653663197$ |
| 15.3.2432060458605625.1 |
x15 - x14 - 2x13 + x12 + 2x11 - 4x10 - 4x9 + 3x8 + 4x7 - 2x6 - 3x5 + 5x4 + 5x3 - x2 - 4x - 1 |
$15$ |
[3,6] |
$5^{4}\cdot 19^{2}\cdot 47^{6}$ |
$3$ |
$10.6103967712$ |
|
|
not computed |
15T46 |
trivial |
$2$ |
$8$ |
$32.0155843928$ |
| 15.3.3276367268581097.1 |
x15 - 6x13 - x12 + 16x11 + 8x10 - 20x9 - 24x8 + 4x7 + 31x6 + 15x5 - 15x4 - 14x3 + x2 + 4x + 1 |
$15$ |
[3,6] |
$3276367268581097$ |
$1$ |
$10.8232952365$ |
|
|
not computed |
15T104 |
trivial |
$2$ |
$8$ |
$37.7909873347$ |
| 15.1.3703260525677583.1 |
x15 - 2x14 + x13 - x12 - 5x11 + 4x10 - 3x9 + 2x8 + 6x7 - 3x6 + 3x5 - 4x4 - 5x3 - 3x2 - 3x - 1 |
$15$ |
[1,7] |
$-\,3\cdot 13^{3}\cdot 561866260913$ |
$3$ |
$10.912031669$ |
|
|
not computed |
15T104 |
trivial |
$2$ |
$7$ |
$39.9823344692$ |
| 15.3.4864965285308625.1 |
x15 - 3x14 + 6x13 - 12x12 + 14x11 - 17x10 + 24x9 - 28x8 + 31x7 - 21x6 + 18x5 - 15x4 + 16x3 - 11x2 + 5x - 1 |
$15$ |
[3,6] |
$3^{9}\cdot 5^{3}\cdot 7^{11}$ |
$3$ |
$11.1123347675$ |
|
|
not computed |
$S_5 \times C_3$ (as 15T24) |
trivial |
$2$ |
$8$ |
$50.4138149085$ |
| 15.1.5976545641547631.1 |
x15 - 2x14 + 5x13 - 10x12 + 13x11 - 20x10 + 23x9 - 22x8 + 22x7 - 20x6 + 18x5 - 20x4 + 21x3 - 15x2 + 6x - 1 |
$15$ |
[1,7] |
$-\,3\cdot 195479\cdot 10191283363$ |
$3$ |
$11.2658340433$ |
|
|
not computed |
15T104 |
trivial |
$2$ |
$7$ |
$50.8430332143$ |
| 15.3.6114596477365737.1 |
x15 - 3x14 + 5x13 - 2x12 - 8x11 + 18x10 - 18x9 + 20x7 - 27x6 + 15x5 + 3x4 - 11x3 + 10x2 - 5x + 1 |
$15$ |
[3,6] |
$3^{4}\cdot 15601\cdot 4838718377$ |
$3$ |
$11.2829982327$ |
|
|
✓ |
15T104 |
trivial |
$2$ |
$8$ |
$53.4601866446$ |
| 15.1.6401597515801839.1 |
x15 - x14 - x13 + 2x12 - 4x11 - x10 + 3x9 + 3x8 + 12x7 - 2x6 - 14x5 + 7x4 + 11x3 - 6x2 + 1 |
$15$ |
[1,7] |
$-\,3^{9}\cdot 13^{3}\cdot 23^{6}$ |
$3$ |
$11.3175535402$ |
|
|
not computed |
$S_5 \times S_3$ (as 15T29) |
trivial |
$2$ |
$7$ |
$46.8775403574$ |
| 15.5.8565893077528823.1 |
x15 - 6x13 + 9x11 - 18x10 + x9 + 32x8 - 17x7 - 19x6 + 24x5 + 3x4 - 15x3 + 3x2 + 4x - 1 |
$15$ |
[5,5] |
$-\,23^{5}\cdot 191^{4}$ |
$2$ |
$11.5394429204$ |
|
|
not computed |
$C_5\times C_5^2:S_3$ (as 15T32) |
trivial |
$2$ |
$9$ |
$87.8024975924$ |
| 15.5.10496055636998343.1 |
x15 - 4x14 + 6x13 - x12 - 11x11 + 18x10 - 10x9 - 9x8 + 19x7 - 12x6 - 3x5 + 9x4 - 5x3 - x2 + 3x - 1 |
$15$ |
[5,5] |
$-\,3^{5}\cdot 157\cdot 2377\cdot 115742009$ |
$4$ |
$11.6968362025$ |
|
|
✓ |
15T104 |
trivial |
$2$ |
$9$ |
$99.2990074596$ |
| 15.3.10544075126076649.1 |
x15 - 6x14 + 11x13 - x12 - 10x11 - 13x10 + 18x9 + 40x8 - 30x7 - 64x6 + 42x5 + 47x4 - 27x3 - 19x2 + 9x + 1 |
$15$ |
[3,6] |
$37^{2}\cdot 43^{2}\cdot 1609^{3}$ |
$3$ |
$11.7003961458$ |
|
|
not computed |
15T78 |
trivial |
$2$ |
$8$ |
$73.2403388939$ |
| 15.3.11354350039657729.1 |
x15 - 4x14 + 5x13 + x12 - 7x11 + x10 + 7x9 - 2x8 - 8x7 + 22x6 - 37x5 + 35x4 - 20x3 + 11x2 - 7x + 1 |
$15$ |
[3,6] |
$13^{2}\cdot 127^{2}\cdot 1609^{3}$ |
$3$ |
$11.7582895867$ |
|
|
not computed |
15T78 |
trivial |
$2$ |
$8$ |
$79.4890458165$ |
| 15.3.12853809661090929.1 |
x15 - x14 - x13 + 3x12 - x10 - 4x9 + 4x8 + 2x7 - 7x6 - x5 + 2x4 - x3 + 2x + 1 |
$15$ |
[3,6] |
$3\cdot 4284603220363643$ |
$2$ |
$11.855925391$ |
|
|
not computed |
15T104 |
trivial |
$2$ |
$8$ |
$108.091851993$ |
| 15.3.15315650494266781.1 |
x15 - 2x14 + x13 - x12 + 7x11 - 5x10 - 10x9 + 7x8 + 16x7 - 15x6 - 19x5 + 27x4 - 2x3 - 11x2 + 6x - 1 |
$15$ |
[3,6] |
$127^{2}\cdot 9829^{3}$ |
$2$ |
$11.9952424328$ |
|
|
not computed |
15T78 |
trivial |
$2$ |
$8$ |
$87.5727798613$ |
| 15.3.16680932154277329.1 |
x15 - 2x14 + 6x13 - 14x12 + 23x11 - 35x10 + 44x9 - 41x8 + 25x7 - 4x6 - 20x5 + 34x4 - 30x3 + 17x2 - 6x + 1 |
$15$ |
[3,6] |
$3\cdot 47\cdot 103\cdot 11057\cdot 103878739$ |
$5$ |
$12.063722938$ |
|
|
not computed |
15T104 |
trivial |
$2$ |
$8$ |
$124.641970008$ |
| 15.3.19664802801826816.1 |
x15 - 5x14 + 14x13 - 23x12 + 19x11 + 7x10 - 41x9 + 47x8 - 10x7 - 39x6 + 50x5 - 18x4 - 16x3 + 21x2 - 9x + 1 |
$15$ |
[3,6] |
$2^{10}\cdot 79^{7}$ |
$2$ |
$12.1968019833$ |
|
|
not computed |
$D_5\times S_3$ (as 15T7) |
trivial |
$2$ |
$8$ |
$103.698212623$ |
| 15.3.21643467887730481.1 |
x15 - x14 - x13 + x12 - 7x11 - 2x10 + 18x9 + 12x8 - 17x7 + 7x6 - 11x5 - 21x4 + 22x3 - 11x2 - 2x - 1 |
$15$ |
[3,6] |
$13^{2}\cdot 47^{6}\cdot 109^{2}$ |
$3$ |
$12.2750081706$ |
|
|
not computed |
15T46 |
trivial |
$2$ |
$8$ |
$116.633322592$ |
| 15.3.23713122135310336.1 |
x15 - 5x14 + 10x13 - 5x12 - 15x11 + 29x10 - 8x9 - 31x8 + 36x7 - 24x5 + 12x4 + 9x3 - 9x2 + 1 |
$15$ |
[3,6] |
$2^{18}\cdot 67^{6}$ |
$2$ |
$12.3499703768$ |
|
|
not computed |
$A_5$ (as 15T5) |
trivial |
$2$ |
$8$ |
$133.707274982$ |
| 15.1.24118280788986467.1 |
x15 - 2x14 + 6x12 - 13x11 + 13x10 - x9 - 21x8 + 40x7 - 41x6 + 29x5 - 18x4 + 13x3 - 7x2 + x + 1 |
$15$ |
[1,7] |
$-\,59^{6}\cdot 83^{3}$ |
$2$ |
$12.3639267417$ |
|
|
not computed |
$S_5 \times S_3$ (as 15T29) |
trivial |
$2$ |
$7$ |
$81.1679989991$ |
| 15.3.31123779291971584.1 |
x15 + x13 - x12 - 5x11 - 4x10 - 5x9 - x8 + 4x7 + 2x6 - 2x5 - 4x4 - 5x3 - 4x2 - 3x - 1 |
$15$ |
[3,6] |
$2^{18}\cdot 587^{4}$ |
$2$ |
$12.5759119634$ |
|
|
not computed |
$S_6$ (as 15T28) |
trivial |
$2$ |
$8$ |
$152.23669177$ |
| 15.5.35351257235385344.1 |
x15 - 3x13 - 5x12 + 8x11 + x10 + 14x9 - 13x8 - 17x7 + 4x6 + x5 + 22x4 - 2x3 - 8x2 - 3x - 1 |
$15$ |
[5,5] |
$-\,2^{10}\cdot 11^{13}$ |
$2$ |
$12.6831459743$ |
|
|
not computed |
$S_3 \times C_5$ (as 15T4) |
trivial |
$2$ |
$9$ |
$211.33204879$ |
| 15.3.39671359416303616.1 |
x15 - 7x14 + 24x13 - 47x12 + 46x11 + 18x10 - 150x9 + 296x8 - 383x7 + 371x6 - 282x5 + 171x4 - 83x3 + 31x2 - 8x + 1 |
$15$ |
[3,6] |
$2^{18}\cdot 73^{6}$ |
$2$ |
$12.7810089465$ |
|
|
not computed |
$A_5$ (as 15T5) |
trivial |
$2$ |
$8$ |
$170.85154758$ |
| 15.1.44543599279432079.1 |
x15 - 4x14 + 4x13 + 4x12 - 5x11 - 13x10 + 20x9 + 4x8 - 15x7 - 13x6 + 27x5 - 4x4 - 8x3 - 2x2 + 6x - 1 |
$15$ |
[1,7] |
$-\,239^{7}$ |
$1$ |
$12.8800936408$ |
|
|
not computed |
$D_{15}$ (as 15T2) |
trivial |
$2$ |
$7$ |
$124.657592501$ |
| 15.3.47090024679574321.1 |
x15 - x12 - x11 - x8 - 2x7 + 2x5 + 3x4 + 2x3 - x - 1 |
$15$ |
[3,6] |
$14731^{4}$ |
$1$ |
$12.9279181717$ |
|
|
✓ |
$S_6$ (as 15T28) |
trivial |
$2$ |
$8$ |
$175.688399353$ |
| 15.3.57352136505929721.1 |
x15 - 2x14 + 4x13 - 10x12 + 22x11 - 33x10 + 40x9 - 63x8 + 81x7 - 81x6 + 63x5 - 69x4 + 57x3 - 24x2 + 3 |
$15$ |
[3,6] |
$3^{18}\cdot 23^{6}$ |
$2$ |
$13.0989546953$ |
|
|
not computed |
15T53 |
trivial |
$2$ |
$8$ |
$279.393832589$ |
| 15.1.57477829056511319.1 |
x15 - 2x14 + 3x13 - 3x12 - 3x11 + 6x10 - 14x9 + 4x8 - 9x7 - 7x6 + 7x5 - 15x4 + 4x3 - 4x2 + 2x - 1 |
$15$ |
[1,7] |
$-\,1609^{3}\cdot 13798511$ |
$2$ |
$13.1008665794$ |
|
|
not computed |
15T93 |
trivial |
$2$ |
$7$ |
$145.805581456$ |
| 15.3.59463924292145152.1 |
x15 - x14 - 6x13 + 15x12 - 9x11 - 13x10 + 30x9 - 31x8 + 24x7 - 14x6 + 10x5 - 18x4 + 27x3 - 21x2 + 8x - 1 |
$15$ |
[3,6] |
$2^{12}\cdot 13^{9}\cdot 37^{2}$ |
$3$ |
$13.1305697532$ |
|
|
not computed |
15T56 |
trivial |
$2$ |
$8$ |
$226.669584518$ |
| 15.1.59770508839234803.1 |
x15 - 2x12 + 3x9 - 3x6 + x3 - 1 |
$15$ |
[1,7] |
$-\,3^{15}\cdot 1609^{3}$ |
$2$ |
$13.1350721761$ |
|
|
✓ |
15T70 |
trivial |
$2$ |
$7$ |
$146.289665433$ |
| 15.1.59770508839234803.2 |
x15 - x9 - x6 + x3 + 1 |
$15$ |
[1,7] |
$-\,3^{15}\cdot 1609^{3}$ |
$2$ |
$13.1350721761$ |
|
|
✓ |
15T70 |
trivial |
$2$ |
$7$ |
$158.627231153$ |
| 15.3.69184806150882304.1 |
x15 + x13 - 3x12 - 3x11 - 5x10 - 2x9 + 3x8 + 7x7 + 4x6 + x5 + x4 + 3x3 + x2 - 1 |
$15$ |
[3,6] |
$2^{10}\cdot 47^{4}\cdot 61^{4}$ |
$3$ |
$13.2637822009$ |
|
|
not computed |
$S_6$ (as 15T28) |
trivial |
$2$ |
$8$ |
$273.665310463$ |
| 15.1.69378727128301847.1 |
x15 - 2x14 + 2x13 - 2x12 + 2x11 - 4x10 + 3x9 + 2x8 + x7 - 5x6 + 3x5 + 3x4 + 6x3 + 2x2 - 1 |
$15$ |
[1,7] |
$-\,23^{5}\cdot 47^{6}$ |
$2$ |
$13.266257472$ |
|
|
not computed |
$D_5\times S_3$ (as 15T7) |
trivial |
$2$ |
$7$ |
$185.949282778$ |
| 15.5.77595502265817783.1 |
x15 - 3x13 - 2x12 + x11 + 12x10 + 3x9 - 15x8 - 10x7 - 4x6 + 20x5 + 7x4 - 3x3 - 7x2 - 4x + 1 |
$15$ |
[5,5] |
$-\,3\cdot 13^{3}\cdot 11772948303113$ |
$3$ |
$13.3656198083$ |
|
|
not computed |
15T104 |
trivial |
$2$ |
$9$ |
$416.964032767$ |
| 15.1.96318312824155136.1 |
x15 - 6x14 + 19x13 - 39x12 + 58x11 - 67x10 + 68x9 - 69x8 + 65x7 - 52x6 + 33x5 - 20x4 + 12x3 - 4x2 + 3x - 1 |
$15$ |
[1,7] |
$-\,2^{10}\cdot 11^{7}\cdot 13^{6}$ |
$3$ |
$13.5596118481$ |
|
|
not computed |
$D_5\times S_3$ (as 15T7) |
trivial |
$2$ |
$7$ |
$226.323474369$ |
| 15.3.98765528526263521.1 |
x15 - 3x14 + 7x13 - 12x12 + 8x11 - 2x10 - 17x9 + 36x8 - 49x7 + 54x6 - 41x5 + 30x4 - 17x3 + 8x2 - 5x + 3 |
$15$ |
[3,6] |
$13^{3}\cdot 31^{6}\cdot 37^{3}$ |
$3$ |
$13.5823116986$ |
|
|
not computed |
$S_5 \times S_3$ (as 15T29) |
trivial |
$2$ |
$8$ |
$363.728980494$ |
| 15.3.126064044311049216.1 |
x15 - 4x14 + 3x13 + 15x12 - 40x11 + 23x10 + 52x9 - 111x8 + 83x7 - 67x5 + 86x4 - 62x3 + 26x2 - 7x + 1 |
$15$ |
[3,6] |
$2^{10}\cdot 3^{5}\cdot 47^{7}$ |
$3$ |
$13.8050955127$ |
|
|
not computed |
$D_5\times S_3$ (as 15T7) |
trivial |
$2$ |
$8$ |
$280.863045663$ |
| 15.3.137631064560062464.1 |
x15 - x14 - 2x13 + 3x12 + 11x11 - 5x10 - 14x9 - 5x8 - 10x7 + 22x6 + 14x5 + 2x4 - 13x3 - 5x2 + 1 |
$15$ |
[3,6] |
$2^{12}\cdot 23^{6}\cdot 61^{3}$ |
$3$ |
$13.8861258816$ |
|
|
not computed |
$S_5 \times S_3$ (as 15T29) |
trivial |
$2$ |
$8$ |
$381.090214491$ |
| 15.3.146928604515779584.1 |
x15 - 2x14 - 3x13 + 9x12 - x11 - 5x10 + 4x9 - x8 + x7 - x5 - x4 + 7x3 - x2 + 1 |
$15$ |
[3,6] |
$2^{10}\cdot 3461^{4}$ |
$2$ |
$13.9467737903$ |
|
|
not computed |
$S_6$ (as 15T28) |
trivial |
$2$ |
$8$ |
$470.017972215$ |
| 15.1.154669958288795403.1 |
x15 - x12 + 2x9 - 3x6 + 3x3 - 1 |
$15$ |
[1,7] |
$-\,3^{15}\cdot 47^{6}$ |
$2$ |
$13.9945970392$ |
|
|
✓ |
$C_3^4:D_{10}$ (as 15T43) |
trivial |
$2$ |
$7$ |
$255.941349852$ |
| 15.1.154669958288795403.2 |
x15 - 2x12 + 2x9 - x6 + 1 |
$15$ |
[1,7] |
$-\,3^{15}\cdot 47^{6}$ |
$2$ |
$13.9945970392$ |
|
|
✓ |
$C_3^4:D_{10}$ (as 15T43) |
trivial |
$2$ |
$7$ |
$288.777984962$ |
| 15.5.154972454814106259.1 |
x15 - x14 - 2x13 + x12 + x11 - x10 + 2x9 - 15x8 + 8x7 + 28x6 - 34x5 - 7x4 + 27x3 - 7x2 - 3x + 1 |
$15$ |
[5,5] |
$-\,11^{13}\cdot 67^{2}$ |
$2$ |
$13.9964200427$ |
|
|
not computed |
15T44 |
trivial |
$2$ |
$9$ |
$492.79424719$ |
| 15.1.196421600341796875.1 |
x15 - x10 + 1 |
$15$ |
[1,7] |
$-\,5^{15}\cdot 23^{5}$ |
$2$ |
$14.2193348993$ |
|
|
✓ |
$C_5^2:(C_4\times S_3)$ (as 15T27) |
trivial |
$2$ |
$7$ |
$358.947276162$ |
| 15.3.334095024862954369.1 |
x15 - 2x14 + 3x13 - 5x12 + x11 - 19x10 + 16x9 - 26x8 + 55x7 - 78x6 + 88x5 - 54x4 + 39x3 - 52x2 + 21x - 1 |
$15$ |
[3,6] |
$7^{12}\cdot 17^{6}$ |
$2$ |
$14.731874164$ |
|
|
not computed |
$D_5\times C_3$ (as 15T3) |
trivial |
$2$ |
$8$ |
$678.185779099$ |
| 15.3.351730374981194881.1 |
x15 - 2x14 + x12 - 6x11 + 27x9 - 37x8 + 44x7 - 34x6 + 14x5 - 15x4 - 8x3 + 9x - 1 |
$15$ |
[3,6] |
$7^{12}\cdot 71^{4}$ |
$2$ |
$14.7824808479$ |
|
|
not computed |
$C_5^3:C_6$ (as 15T30) |
trivial |
$2$ |
$8$ |
$694.485336338$ |
| 15.5.388863829589238784.1 |
x15 - 3x14 + 2x13 - x12 + 5x11 - 22x9 + 33x8 - 22x7 + 22x6 - 22x5 - 9x4 + 38x3 - 29x2 + 9x - 1 |
$15$ |
[5,5] |
$-\,2^{10}\cdot 11^{14}$ |
$2$ |
$14.8817214018$ |
|
|
not computed |
$S_3 \times C_5$ (as 15T4) |
trivial |
$2$ |
$9$ |
$803.578266232599$ |
| 15.1.426781883555301359.1 |
x15 - x - 1 |
$15$ |
[1,7] |
$-\,52489\cdot 418511\cdot 19428121$ |
$3$ |
$14.9743184596$ |
|
|
✓ |
15T104 |
trivial |
$2$ |
$7$ |
$501.532588967$ |
| 15.1.449005897206417391.1 |
x15 + x - 1 |
$15$ |
[1,7] |
$-\,7334881\cdot 61215157711$ |
$2$ |
$15.0250803442$ |
|
|
✓ |
15T104 |
trivial |
$2$ |
$7$ |
$548.874139448$ |
| 15.1.677952124826430464.1 |
x15 - x14 + 4x13 + 4x11 - 2x10 - 6x9 - 12x8 - 25x7 + 19x6 - 6x5 + 28x4 + 32x3 - 36x2 + 4x + 4 |
$15$ |
[1,7] |
$-\,2^{10}\cdot 131^{7}$ |
$2$ |
$15.4435309131$ |
|
|
|
$D_{15}$ (as 15T2) |
trivial |
$2$ |
$7$ |
$1343.20606196$ |
