| Label |
Class |
Class size |
Class degree |
Base field |
Field degree |
Field signature |
Conductor |
Conductor norm |
Discriminant norm |
Root analytic conductor |
Bad primes |
Rank |
Torsion |
CM |
CM |
Sato-Tate |
$\Q$-curve |
Base change |
Semistable |
Potentially good |
Nonmax $\ell$ |
mod-$\ell$ images |
$Ш_{\textrm{an}}$ |
Tamagawa |
Regulator |
Period |
Leading coeff |
j-invariant |
Weierstrass coefficients |
Weierstrass equation |
| 1.1-a1 |
1.1-a |
$16$ |
$60$ |
\(\Q(\sqrt{3}, \sqrt{5})\) |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$5.36154$ |
$\textsf{none}$ |
0 |
$\Z/4\Z$ |
$\textsf{potential}$ |
$-240$ |
$N(\mathrm{U}(1))$ |
✓ |
|
✓ |
✓ |
|
|
$1$ |
\( 1 \) |
$1$ |
$558.1508429$ |
0.581407128 |
\( -144059431778799259905 a^{3} + 127634233646510918145 a^{2} + 1150602705390880344330 a + 129315311353667976165 \) |
\( \bigl[-\frac{4}{7} a^{3} + \frac{6}{7} a^{2} + \frac{31}{7} a - \frac{20}{7}\) , \( \frac{1}{7} a^{3} + \frac{2}{7} a^{2} - \frac{20}{7} a - \frac{16}{7}\) , \( -\frac{4}{7} a^{3} + \frac{6}{7} a^{2} + \frac{31}{7} a - \frac{20}{7}\) , \( -\frac{233}{7} a^{3} + \frac{472}{7} a^{2} + \frac{1678}{7} a - \frac{2166}{7}\) , \( \frac{1595}{7} a^{3} - \frac{3502}{7} a^{2} - \frac{10207}{7} a + \frac{13582}{7}\bigr] \) |
${y}^2+\left(-\frac{4}{7}a^{3}+\frac{6}{7}a^{2}+\frac{31}{7}a-\frac{20}{7}\right){x}{y}+\left(-\frac{4}{7}a^{3}+\frac{6}{7}a^{2}+\frac{31}{7}a-\frac{20}{7}\right){y}={x}^{3}+\left(\frac{1}{7}a^{3}+\frac{2}{7}a^{2}-\frac{20}{7}a-\frac{16}{7}\right){x}^{2}+\left(-\frac{233}{7}a^{3}+\frac{472}{7}a^{2}+\frac{1678}{7}a-\frac{2166}{7}\right){x}+\frac{1595}{7}a^{3}-\frac{3502}{7}a^{2}-\frac{10207}{7}a+\frac{13582}{7}$ |
| 1.1-a2 |
1.1-a |
$16$ |
$60$ |
\(\Q(\sqrt{3}, \sqrt{5})\) |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$5.36154$ |
$\textsf{none}$ |
0 |
$\Z/4\Z$ |
$\textsf{potential}$ |
$-240$ |
$N(\mathrm{U}(1))$ |
✓ |
|
✓ |
✓ |
|
|
$1$ |
\( 1 \) |
$1$ |
$558.1508429$ |
0.581407128 |
\( -31035888523715366655 a^{3} + 135008746807261021695 a^{2} - 100030783575792584970 a - 13206284544416331285 \) |
\( \bigl[-\frac{4}{7} a^{3} + \frac{6}{7} a^{2} + \frac{31}{7} a - \frac{20}{7}\) , \( -a - 1\) , \( -\frac{1}{7} a^{3} + \frac{5}{7} a^{2} - \frac{1}{7} a - \frac{12}{7}\) , \( -\frac{2}{7} a^{3} - \frac{109}{7} a^{2} - \frac{268}{7} a - \frac{73}{7}\) , \( \frac{592}{7} a^{3} + \frac{421}{7} a^{2} - \frac{2390}{7} a - \frac{274}{7}\bigr] \) |
${y}^2+\left(-\frac{4}{7}a^{3}+\frac{6}{7}a^{2}+\frac{31}{7}a-\frac{20}{7}\right){x}{y}+\left(-\frac{1}{7}a^{3}+\frac{5}{7}a^{2}-\frac{1}{7}a-\frac{12}{7}\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-\frac{2}{7}a^{3}-\frac{109}{7}a^{2}-\frac{268}{7}a-\frac{73}{7}\right){x}+\frac{592}{7}a^{3}+\frac{421}{7}a^{2}-\frac{2390}{7}a-\frac{274}{7}$ |
| 1.1-a3 |
1.1-a |
$16$ |
$60$ |
\(\Q(\sqrt{3}, \sqrt{5})\) |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$5.36154$ |
$\textsf{none}$ |
0 |
$\Z/4\Z$ |
$\textsf{potential}$ |
$-15$ |
$N(\mathrm{U}(1))$ |
✓ |
|
✓ |
✓ |
|
|
$1$ |
\( 1 \) |
$1$ |
$558.1508429$ |
0.581407128 |
\( 24570 a^{3} - 36855 a^{2} - 147420 a - 15660 \) |
\( \bigl[-\frac{4}{7} a^{3} + \frac{6}{7} a^{2} + \frac{31}{7} a - \frac{20}{7}\) , \( -a - 1\) , \( -\frac{1}{7} a^{3} + \frac{5}{7} a^{2} - \frac{1}{7} a - \frac{12}{7}\) , \( \frac{3}{7} a^{3} + \frac{6}{7} a^{2} - \frac{18}{7} a - \frac{13}{7}\) , \( -\frac{2}{7} a^{3} - \frac{11}{7} a^{2} - \frac{2}{7} a - \frac{3}{7}\bigr] \) |
${y}^2+\left(-\frac{4}{7}a^{3}+\frac{6}{7}a^{2}+\frac{31}{7}a-\frac{20}{7}\right){x}{y}+\left(-\frac{1}{7}a^{3}+\frac{5}{7}a^{2}-\frac{1}{7}a-\frac{12}{7}\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(\frac{3}{7}a^{3}+\frac{6}{7}a^{2}-\frac{18}{7}a-\frac{13}{7}\right){x}-\frac{2}{7}a^{3}-\frac{11}{7}a^{2}-\frac{2}{7}a-\frac{3}{7}$ |
| 1.1-a4 |
1.1-a |
$16$ |
$60$ |
\(\Q(\sqrt{3}, \sqrt{5})\) |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$5.36154$ |
$\textsf{none}$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{potential}$ |
$-60$ |
$N(\mathrm{U}(1))$ |
✓ |
|
✓ |
✓ |
$2$ |
2Cs |
$1$ |
\( 1 \) |
$1$ |
$558.1508429$ |
0.581407128 |
\( 4729995270 a^{3} - 7094992905 a^{2} - 28379971620 a + 33881522940 \) |
\( \bigl[-\frac{4}{7} a^{3} + \frac{6}{7} a^{2} + \frac{31}{7} a - \frac{13}{7}\) , \( a + 1\) , \( \frac{1}{7} a^{3} + \frac{2}{7} a^{2} - \frac{13}{7} a - \frac{2}{7}\) , \( -\frac{51}{7} a^{3} + \frac{80}{7} a^{2} + \frac{453}{7} a - \frac{458}{7}\) , \( -\frac{206}{7} a^{3} + \frac{393}{7} a^{2} + \frac{1579}{7} a - \frac{1940}{7}\bigr] \) |
${y}^2+\left(-\frac{4}{7}a^{3}+\frac{6}{7}a^{2}+\frac{31}{7}a-\frac{13}{7}\right){x}{y}+\left(\frac{1}{7}a^{3}+\frac{2}{7}a^{2}-\frac{13}{7}a-\frac{2}{7}\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-\frac{51}{7}a^{3}+\frac{80}{7}a^{2}+\frac{453}{7}a-\frac{458}{7}\right){x}-\frac{206}{7}a^{3}+\frac{393}{7}a^{2}+\frac{1579}{7}a-\frac{1940}{7}$ |
| 1.1-a5 |
1.1-a |
$16$ |
$60$ |
\(\Q(\sqrt{3}, \sqrt{5})\) |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$5.36154$ |
$\textsf{none}$ |
0 |
$\Z/4\Z$ |
$\textsf{potential}$ |
$-240$ |
$N(\mathrm{U}(1))$ |
✓ |
|
✓ |
✓ |
|
|
$1$ |
\( 1 \) |
$1$ |
$558.1508429$ |
0.581407128 |
\( 31035888523715366655 a^{3} + 41901081236114921730 a^{2} - 76879044467583358455 a - 9264209836663261215 \) |
\( \bigl[-\frac{4}{7} a^{3} + \frac{6}{7} a^{2} + \frac{31}{7} a - \frac{13}{7}\) , \( a + 1\) , \( \frac{1}{7} a^{3} + \frac{2}{7} a^{2} - \frac{13}{7} a - \frac{2}{7}\) , \( -\frac{6}{7} a^{3} - \frac{110}{7} a^{2} + \frac{568}{7} a - \frac{443}{7}\) , \( -\frac{593}{7} a^{3} + \frac{2083}{7} a^{2} + \frac{303}{7} a - \frac{2104}{7}\bigr] \) |
${y}^2+\left(-\frac{4}{7}a^{3}+\frac{6}{7}a^{2}+\frac{31}{7}a-\frac{13}{7}\right){x}{y}+\left(\frac{1}{7}a^{3}+\frac{2}{7}a^{2}-\frac{13}{7}a-\frac{2}{7}\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-\frac{6}{7}a^{3}-\frac{110}{7}a^{2}+\frac{568}{7}a-\frac{443}{7}\right){x}-\frac{593}{7}a^{3}+\frac{2083}{7}a^{2}+\frac{303}{7}a-\frac{2104}{7}$ |
| 1.1-a6 |
1.1-a |
$16$ |
$60$ |
\(\Q(\sqrt{3}, \sqrt{5})\) |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$5.36154$ |
$\textsf{none}$ |
0 |
$\Z/4\Z$ |
$\textsf{potential}$ |
$-15$ |
$N(\mathrm{U}(1))$ |
✓ |
|
✓ |
✓ |
|
|
$1$ |
\( 1 \) |
$1$ |
$558.1508429$ |
0.581407128 |
\( -24570 a^{3} + 36855 a^{2} + 147420 a - 175365 \) |
\( \bigl[-\frac{1}{7} a^{3} + \frac{5}{7} a^{2} + \frac{6}{7} a - \frac{19}{7}\) , \( \frac{1}{7} a^{3} - \frac{5}{7} a^{2} - \frac{6}{7} a + \frac{19}{7}\) , \( -\frac{2}{7} a^{3} + \frac{3}{7} a^{2} + \frac{12}{7} a - \frac{10}{7}\) , \( -\frac{6}{7} a^{3} + \frac{16}{7} a^{2} - \frac{34}{7} a + \frac{33}{7}\) , \( \frac{31}{7} a^{3} - \frac{92}{7} a^{2} + \frac{38}{7} a + \frac{29}{7}\bigr] \) |
${y}^2+\left(-\frac{1}{7}a^{3}+\frac{5}{7}a^{2}+\frac{6}{7}a-\frac{19}{7}\right){x}{y}+\left(-\frac{2}{7}a^{3}+\frac{3}{7}a^{2}+\frac{12}{7}a-\frac{10}{7}\right){y}={x}^{3}+\left(\frac{1}{7}a^{3}-\frac{5}{7}a^{2}-\frac{6}{7}a+\frac{19}{7}\right){x}^{2}+\left(-\frac{6}{7}a^{3}+\frac{16}{7}a^{2}-\frac{34}{7}a+\frac{33}{7}\right){x}+\frac{31}{7}a^{3}-\frac{92}{7}a^{2}+\frac{38}{7}a+\frac{29}{7}$ |
| 1.1-a7 |
1.1-a |
$16$ |
$60$ |
\(\Q(\sqrt{3}, \sqrt{5})\) |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$5.36154$ |
$\textsf{none}$ |
0 |
$\Z/4\Z$ |
$\textsf{potential}$ |
$-240$ |
$N(\mathrm{U}(1))$ |
✓ |
|
✓ |
✓ |
|
|
$1$ |
\( 1 \) |
$1$ |
$558.1508429$ |
0.581407128 |
\( 144059431778799259905 a^{3} - 304544061689886861570 a^{2} - 973692877347504400905 a + 1263492818612259978735 \) |
\( \bigl[-\frac{4}{7} a^{3} + \frac{6}{7} a^{2} + \frac{31}{7} a - \frac{13}{7}\) , \( \frac{5}{7} a^{3} - \frac{4}{7} a^{2} - \frac{44}{7} a + \frac{18}{7}\) , \( \frac{1}{7} a^{3} + \frac{2}{7} a^{2} - \frac{13}{7} a - \frac{2}{7}\) , \( \frac{229}{7} a^{3} - \frac{228}{7} a^{2} - \frac{1899}{7} a - \frac{206}{7}\) , \( -\frac{1772}{7} a^{3} + \frac{1461}{7} a^{2} + \frac{13894}{7} a + \frac{1563}{7}\bigr] \) |
${y}^2+\left(-\frac{4}{7}a^{3}+\frac{6}{7}a^{2}+\frac{31}{7}a-\frac{13}{7}\right){x}{y}+\left(\frac{1}{7}a^{3}+\frac{2}{7}a^{2}-\frac{13}{7}a-\frac{2}{7}\right){y}={x}^{3}+\left(\frac{5}{7}a^{3}-\frac{4}{7}a^{2}-\frac{44}{7}a+\frac{18}{7}\right){x}^{2}+\left(\frac{229}{7}a^{3}-\frac{228}{7}a^{2}-\frac{1899}{7}a-\frac{206}{7}\right){x}-\frac{1772}{7}a^{3}+\frac{1461}{7}a^{2}+\frac{13894}{7}a+\frac{1563}{7}$ |
| 1.1-a8 |
1.1-a |
$16$ |
$60$ |
\(\Q(\sqrt{3}, \sqrt{5})\) |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$5.36154$ |
$\textsf{none}$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-240$ |
$N(\mathrm{U}(1))$ |
✓ |
|
✓ |
✓ |
|
|
$4$ |
\( 1 \) |
$1$ |
$34.88442768$ |
0.581407128 |
\( -31035888523715366655 a^{3} + 135008746807261021695 a^{2} - 100030783575792584970 a - 13206284544416331285 \) |
\( \bigl[-\frac{1}{7} a^{3} + \frac{5}{7} a^{2} + \frac{6}{7} a - \frac{12}{7}\) , \( -\frac{2}{7} a^{3} + \frac{3}{7} a^{2} + \frac{19}{7} a - \frac{17}{7}\) , \( -\frac{1}{7} a^{3} + \frac{5}{7} a^{2} - \frac{1}{7} a - \frac{12}{7}\) , \( \frac{1}{7} a^{3} - \frac{117}{7} a^{2} - \frac{279}{7} a - \frac{65}{7}\) , \( -\frac{591}{7} a^{3} - \frac{426}{7} a^{2} + \frac{2398}{7} a + \frac{265}{7}\bigr] \) |
${y}^2+\left(-\frac{1}{7}a^{3}+\frac{5}{7}a^{2}+\frac{6}{7}a-\frac{12}{7}\right){x}{y}+\left(-\frac{1}{7}a^{3}+\frac{5}{7}a^{2}-\frac{1}{7}a-\frac{12}{7}\right){y}={x}^{3}+\left(-\frac{2}{7}a^{3}+\frac{3}{7}a^{2}+\frac{19}{7}a-\frac{17}{7}\right){x}^{2}+\left(\frac{1}{7}a^{3}-\frac{117}{7}a^{2}-\frac{279}{7}a-\frac{65}{7}\right){x}-\frac{591}{7}a^{3}-\frac{426}{7}a^{2}+\frac{2398}{7}a+\frac{265}{7}$ |
| 1.1-a9 |
1.1-a |
$16$ |
$60$ |
\(\Q(\sqrt{3}, \sqrt{5})\) |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$5.36154$ |
$\textsf{none}$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{potential}$ |
$-60$ |
$N(\mathrm{U}(1))$ |
✓ |
|
✓ |
✓ |
$2$ |
2Cs |
$1$ |
\( 1 \) |
$1$ |
$558.1508429$ |
0.581407128 |
\( -4729995270 a^{3} + 7094992905 a^{2} + 28379971620 a + 3136553685 \) |
\( \bigl[-\frac{4}{7} a^{3} + \frac{6}{7} a^{2} + \frac{31}{7} a - \frac{20}{7}\) , \( \frac{1}{7} a^{3} + \frac{2}{7} a^{2} - \frac{20}{7} a - \frac{16}{7}\) , \( -\frac{4}{7} a^{3} + \frac{6}{7} a^{2} + \frac{31}{7} a - \frac{20}{7}\) , \( -\frac{38}{7} a^{3} + \frac{57}{7} a^{2} + \frac{368}{7} a - \frac{421}{7}\) , \( -\frac{59}{7} a^{3} + \frac{1}{7} a^{2} + \frac{956}{7} a - \frac{1002}{7}\bigr] \) |
${y}^2+\left(-\frac{4}{7}a^{3}+\frac{6}{7}a^{2}+\frac{31}{7}a-\frac{20}{7}\right){x}{y}+\left(-\frac{4}{7}a^{3}+\frac{6}{7}a^{2}+\frac{31}{7}a-\frac{20}{7}\right){y}={x}^{3}+\left(\frac{1}{7}a^{3}+\frac{2}{7}a^{2}-\frac{20}{7}a-\frac{16}{7}\right){x}^{2}+\left(-\frac{38}{7}a^{3}+\frac{57}{7}a^{2}+\frac{368}{7}a-\frac{421}{7}\right){x}-\frac{59}{7}a^{3}+\frac{1}{7}a^{2}+\frac{956}{7}a-\frac{1002}{7}$ |
| 1.1-a10 |
1.1-a |
$16$ |
$60$ |
\(\Q(\sqrt{3}, \sqrt{5})\) |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$5.36154$ |
$\textsf{none}$ |
0 |
$\Z/4\Z$ |
$\textsf{potential}$ |
$-15$ |
$N(\mathrm{U}(1))$ |
✓ |
|
✓ |
✓ |
|
|
$1$ |
\( 1 \) |
$1$ |
$558.1508429$ |
0.581407128 |
\( 24570 a^{3} - 36855 a^{2} - 147420 a - 15660 \) |
\( \bigl[-\frac{1}{7} a^{3} + \frac{5}{7} a^{2} + \frac{6}{7} a - \frac{12}{7}\) , \( -\frac{2}{7} a^{3} + \frac{3}{7} a^{2} + \frac{19}{7} a - \frac{17}{7}\) , \( -\frac{1}{7} a^{3} + \frac{5}{7} a^{2} - \frac{1}{7} a - \frac{12}{7}\) , \( \frac{6}{7} a^{3} - \frac{2}{7} a^{2} - \frac{29}{7} a - \frac{5}{7}\) , \( \frac{3}{7} a^{3} + \frac{6}{7} a^{2} + \frac{10}{7} a - \frac{6}{7}\bigr] \) |
${y}^2+\left(-\frac{1}{7}a^{3}+\frac{5}{7}a^{2}+\frac{6}{7}a-\frac{12}{7}\right){x}{y}+\left(-\frac{1}{7}a^{3}+\frac{5}{7}a^{2}-\frac{1}{7}a-\frac{12}{7}\right){y}={x}^{3}+\left(-\frac{2}{7}a^{3}+\frac{3}{7}a^{2}+\frac{19}{7}a-\frac{17}{7}\right){x}^{2}+\left(\frac{6}{7}a^{3}-\frac{2}{7}a^{2}-\frac{29}{7}a-\frac{5}{7}\right){x}+\frac{3}{7}a^{3}+\frac{6}{7}a^{2}+\frac{10}{7}a-\frac{6}{7}$ |
| 1.1-a11 |
1.1-a |
$16$ |
$60$ |
\(\Q(\sqrt{3}, \sqrt{5})\) |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$5.36154$ |
$\textsf{none}$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-240$ |
$N(\mathrm{U}(1))$ |
✓ |
|
✓ |
✓ |
|
|
$4$ |
\( 1 \) |
$1$ |
$34.88442768$ |
0.581407128 |
\( -144059431778799259905 a^{3} + 127634233646510918145 a^{2} + 1150602705390880344330 a + 129315311353667976165 \) |
\( \bigl[-\frac{1}{7} a^{3} + \frac{5}{7} a^{2} + \frac{6}{7} a - \frac{12}{7}\) , \( -\frac{3}{7} a^{3} + \frac{1}{7} a^{2} + \frac{32}{7} a - \frac{8}{7}\) , \( -\frac{1}{7} a^{3} + \frac{5}{7} a^{2} + \frac{6}{7} a - \frac{12}{7}\) , \( -\frac{233}{7} a^{3} + \frac{465}{7} a^{2} + \frac{1678}{7} a - \frac{2138}{7}\) , \( -\frac{1597}{7} a^{3} + \frac{3505}{7} a^{2} + \frac{10219}{7} a - \frac{13606}{7}\bigr] \) |
${y}^2+\left(-\frac{1}{7}a^{3}+\frac{5}{7}a^{2}+\frac{6}{7}a-\frac{12}{7}\right){x}{y}+\left(-\frac{1}{7}a^{3}+\frac{5}{7}a^{2}+\frac{6}{7}a-\frac{12}{7}\right){y}={x}^{3}+\left(-\frac{3}{7}a^{3}+\frac{1}{7}a^{2}+\frac{32}{7}a-\frac{8}{7}\right){x}^{2}+\left(-\frac{233}{7}a^{3}+\frac{465}{7}a^{2}+\frac{1678}{7}a-\frac{2138}{7}\right){x}-\frac{1597}{7}a^{3}+\frac{3505}{7}a^{2}+\frac{10219}{7}a-\frac{13606}{7}$ |
| 1.1-a12 |
1.1-a |
$16$ |
$60$ |
\(\Q(\sqrt{3}, \sqrt{5})\) |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$5.36154$ |
$\textsf{none}$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{potential}$ |
$-60$ |
$N(\mathrm{U}(1))$ |
✓ |
|
✓ |
✓ |
$2$ |
2Cs |
$1$ |
\( 1 \) |
$1$ |
$558.1508429$ |
0.581407128 |
\( -4729995270 a^{3} + 7094992905 a^{2} + 28379971620 a + 3136553685 \) |
\( \bigl[\frac{1}{7} a^{3} + \frac{2}{7} a^{2} - \frac{13}{7} a - \frac{9}{7}\) , \( -\frac{1}{7} a^{3} - \frac{2}{7} a^{2} + \frac{13}{7} a + \frac{9}{7}\) , \( -\frac{2}{7} a^{3} + \frac{3}{7} a^{2} + \frac{12}{7} a - \frac{3}{7}\) , \( \frac{3}{7} a^{3} - \frac{281}{7} a^{2} + \frac{332}{7} a + \frac{43}{7}\) , \( -\frac{579}{7} a^{3} + \frac{1397}{7} a^{2} - \frac{726}{7} a - \frac{102}{7}\bigr] \) |
${y}^2+\left(\frac{1}{7}a^{3}+\frac{2}{7}a^{2}-\frac{13}{7}a-\frac{9}{7}\right){x}{y}+\left(-\frac{2}{7}a^{3}+\frac{3}{7}a^{2}+\frac{12}{7}a-\frac{3}{7}\right){y}={x}^{3}+\left(-\frac{1}{7}a^{3}-\frac{2}{7}a^{2}+\frac{13}{7}a+\frac{9}{7}\right){x}^{2}+\left(\frac{3}{7}a^{3}-\frac{281}{7}a^{2}+\frac{332}{7}a+\frac{43}{7}\right){x}-\frac{579}{7}a^{3}+\frac{1397}{7}a^{2}-\frac{726}{7}a-\frac{102}{7}$ |
| 1.1-a13 |
1.1-a |
$16$ |
$60$ |
\(\Q(\sqrt{3}, \sqrt{5})\) |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$5.36154$ |
$\textsf{none}$ |
0 |
$\Z/4\Z$ |
$\textsf{potential}$ |
$-15$ |
$N(\mathrm{U}(1))$ |
✓ |
|
✓ |
✓ |
|
|
$1$ |
\( 1 \) |
$1$ |
$558.1508429$ |
0.581407128 |
\( -24570 a^{3} + 36855 a^{2} + 147420 a - 175365 \) |
\( \bigl[-\frac{1}{7} a^{3} + \frac{5}{7} a^{2} + \frac{6}{7} a - \frac{19}{7}\) , \( -\frac{1}{7} a^{3} + \frac{5}{7} a^{2} + \frac{6}{7} a - \frac{19}{7}\) , \( -\frac{2}{7} a^{3} + \frac{3}{7} a^{2} + \frac{12}{7} a - \frac{10}{7}\) , \( -\frac{45}{7} a^{3} + \frac{64}{7} a^{2} + \frac{347}{7} a - \frac{120}{7}\) , \( 19 a^{3} - 22 a^{2} - 146 a + 25\bigr] \) |
${y}^2+\left(-\frac{1}{7}a^{3}+\frac{5}{7}a^{2}+\frac{6}{7}a-\frac{19}{7}\right){x}{y}+\left(-\frac{2}{7}a^{3}+\frac{3}{7}a^{2}+\frac{12}{7}a-\frac{10}{7}\right){y}={x}^{3}+\left(-\frac{1}{7}a^{3}+\frac{5}{7}a^{2}+\frac{6}{7}a-\frac{19}{7}\right){x}^{2}+\left(-\frac{45}{7}a^{3}+\frac{64}{7}a^{2}+\frac{347}{7}a-\frac{120}{7}\right){x}+19a^{3}-22a^{2}-146a+25$ |
| 1.1-a14 |
1.1-a |
$16$ |
$60$ |
\(\Q(\sqrt{3}, \sqrt{5})\) |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$5.36154$ |
$\textsf{none}$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-240$ |
$N(\mathrm{U}(1))$ |
✓ |
|
✓ |
✓ |
|
|
$4$ |
\( 1 \) |
$1$ |
$34.88442768$ |
0.581407128 |
\( 144059431778799259905 a^{3} - 304544061689886861570 a^{2} - 973692877347504400905 a + 1263492818612259978735 \) |
\( \bigl[\frac{1}{7} a^{3} + \frac{2}{7} a^{2} - \frac{13}{7} a - \frac{2}{7}\) , \( -\frac{3}{7} a^{3} + \frac{1}{7} a^{2} + \frac{32}{7} a - \frac{8}{7}\) , \( -\frac{3}{7} a^{3} + \frac{8}{7} a^{2} + \frac{18}{7} a - \frac{29}{7}\) , \( 32 a^{3} - 32 a^{2} - 264 a - 35\) , \( \frac{1997}{7} a^{3} - \frac{1683}{7} a^{2} - \frac{15755}{7} a - \frac{1824}{7}\bigr] \) |
${y}^2+\left(\frac{1}{7}a^{3}+\frac{2}{7}a^{2}-\frac{13}{7}a-\frac{2}{7}\right){x}{y}+\left(-\frac{3}{7}a^{3}+\frac{8}{7}a^{2}+\frac{18}{7}a-\frac{29}{7}\right){y}={x}^{3}+\left(-\frac{3}{7}a^{3}+\frac{1}{7}a^{2}+\frac{32}{7}a-\frac{8}{7}\right){x}^{2}+\left(32a^{3}-32a^{2}-264a-35\right){x}+\frac{1997}{7}a^{3}-\frac{1683}{7}a^{2}-\frac{15755}{7}a-\frac{1824}{7}$ |
| 1.1-a15 |
1.1-a |
$16$ |
$60$ |
\(\Q(\sqrt{3}, \sqrt{5})\) |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$5.36154$ |
$\textsf{none}$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{potential}$ |
$-60$ |
$N(\mathrm{U}(1))$ |
✓ |
|
✓ |
✓ |
$2$ |
2Cs |
$1$ |
\( 1 \) |
$1$ |
$558.1508429$ |
0.581407128 |
\( 4729995270 a^{3} - 7094992905 a^{2} - 28379971620 a + 33881522940 \) |
\( \bigl[\frac{1}{7} a^{3} + \frac{2}{7} a^{2} - \frac{13}{7} a - \frac{2}{7}\) , \( \frac{2}{7} a^{3} - \frac{3}{7} a^{2} - \frac{19}{7} a + \frac{3}{7}\) , \( -\frac{3}{7} a^{3} + \frac{8}{7} a^{2} + \frac{18}{7} a - \frac{29}{7}\) , \( -\frac{46}{7} a^{3} + \frac{76}{7} a^{2} + \frac{402}{7} a - \frac{475}{7}\) , \( \frac{156}{7} a^{3} - \frac{311}{7} a^{2} - \frac{1139}{7} a + \frac{1438}{7}\bigr] \) |
${y}^2+\left(\frac{1}{7}a^{3}+\frac{2}{7}a^{2}-\frac{13}{7}a-\frac{2}{7}\right){x}{y}+\left(-\frac{3}{7}a^{3}+\frac{8}{7}a^{2}+\frac{18}{7}a-\frac{29}{7}\right){y}={x}^{3}+\left(\frac{2}{7}a^{3}-\frac{3}{7}a^{2}-\frac{19}{7}a+\frac{3}{7}\right){x}^{2}+\left(-\frac{46}{7}a^{3}+\frac{76}{7}a^{2}+\frac{402}{7}a-\frac{475}{7}\right){x}+\frac{156}{7}a^{3}-\frac{311}{7}a^{2}-\frac{1139}{7}a+\frac{1438}{7}$ |
| 1.1-a16 |
1.1-a |
$16$ |
$60$ |
\(\Q(\sqrt{3}, \sqrt{5})\) |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$5.36154$ |
$\textsf{none}$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-240$ |
$N(\mathrm{U}(1))$ |
✓ |
|
✓ |
✓ |
|
|
$4$ |
\( 1 \) |
$1$ |
$34.88442768$ |
0.581407128 |
\( 31035888523715366655 a^{3} + 41901081236114921730 a^{2} - 76879044467583358455 a - 9264209836663261215 \) |
\( \bigl[\frac{1}{7} a^{3} + \frac{2}{7} a^{2} - \frac{13}{7} a - \frac{2}{7}\) , \( \frac{2}{7} a^{3} - \frac{3}{7} a^{2} - \frac{19}{7} a + \frac{3}{7}\) , \( -\frac{3}{7} a^{3} + \frac{8}{7} a^{2} + \frac{18}{7} a - \frac{29}{7}\) , \( -\frac{1}{7} a^{3} - \frac{114}{7} a^{2} + \frac{517}{7} a - \frac{460}{7}\) , \( 84 a^{3} - 313 a^{2} + 36 a + 231\bigr] \) |
${y}^2+\left(\frac{1}{7}a^{3}+\frac{2}{7}a^{2}-\frac{13}{7}a-\frac{2}{7}\right){x}{y}+\left(-\frac{3}{7}a^{3}+\frac{8}{7}a^{2}+\frac{18}{7}a-\frac{29}{7}\right){y}={x}^{3}+\left(\frac{2}{7}a^{3}-\frac{3}{7}a^{2}-\frac{19}{7}a+\frac{3}{7}\right){x}^{2}+\left(-\frac{1}{7}a^{3}-\frac{114}{7}a^{2}+\frac{517}{7}a-\frac{460}{7}\right){x}+84a^{3}-313a^{2}+36a+231$ |
| 1.1-b1 |
1.1-b |
$12$ |
$90$ |
\(\Q(\sqrt{3}, \sqrt{5})\) |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$5.36154$ |
$\textsf{none}$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-180$ |
$N(\mathrm{U}(1))$ |
✓ |
|
✓ |
✓ |
$3$ |
3B.1.2 |
$9$ |
\( 1 \) |
$1$ |
$11.51826733$ |
0.431935025 |
\( \frac{320010540736506880}{7} a^{3} + \frac{432041363372270080}{7} a^{2} - \frac{792698580269972480}{7} a - \frac{95523117261563840}{7} \) |
\( \bigl[-\frac{2}{7} a^{3} + \frac{3}{7} a^{2} + \frac{19}{7} a - \frac{3}{7}\) , \( -\frac{3}{7} a^{3} + \frac{8}{7} a^{2} + \frac{18}{7} a - \frac{22}{7}\) , \( -\frac{1}{7} a^{3} + \frac{5}{7} a^{2} - \frac{1}{7} a - \frac{19}{7}\) , \( -\frac{51}{7} a^{3} + \frac{3}{7} a^{2} + \frac{75}{7} a + \frac{11}{7}\) , \( -32 a^{3} - 84 a^{2} + 120 a + 13\bigr] \) |
${y}^2+\left(-\frac{2}{7}a^{3}+\frac{3}{7}a^{2}+\frac{19}{7}a-\frac{3}{7}\right){x}{y}+\left(-\frac{1}{7}a^{3}+\frac{5}{7}a^{2}-\frac{1}{7}a-\frac{19}{7}\right){y}={x}^{3}+\left(-\frac{3}{7}a^{3}+\frac{8}{7}a^{2}+\frac{18}{7}a-\frac{22}{7}\right){x}^{2}+\left(-\frac{51}{7}a^{3}+\frac{3}{7}a^{2}+\frac{75}{7}a+\frac{11}{7}\right){x}-32a^{3}-84a^{2}+120a+13$ |
| 1.1-b2 |
1.1-b |
$12$ |
$90$ |
\(\Q(\sqrt{3}, \sqrt{5})\) |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$5.36154$ |
$\textsf{none}$ |
0 |
$\Z/6\Z$ |
$\textsf{potential}$ |
$-20$ |
$N(\mathrm{U}(1))$ |
✓ |
|
✓ |
✓ |
$3$ |
3Cs.1.1 |
$1$ |
\( 1 \) |
$1$ |
$932.9796544$ |
0.431935025 |
\( \frac{1131520}{7} a^{3} - \frac{1697280}{7} a^{2} - \frac{6789120}{7} a + \frac{8101440}{7} \) |
\( \bigl[-\frac{2}{7} a^{3} + \frac{3}{7} a^{2} + \frac{19}{7} a - \frac{3}{7}\) , \( -\frac{3}{7} a^{3} + \frac{8}{7} a^{2} + \frac{18}{7} a - \frac{22}{7}\) , \( -\frac{1}{7} a^{3} + \frac{5}{7} a^{2} - \frac{1}{7} a - \frac{19}{7}\) , \( -\frac{1}{7} a^{3} - \frac{2}{7} a^{2} + \frac{20}{7} a + \frac{16}{7}\) , \( -\frac{3}{7} a^{3} + \frac{8}{7} a^{2} + \frac{4}{7} a - \frac{15}{7}\bigr] \) |
${y}^2+\left(-\frac{2}{7}a^{3}+\frac{3}{7}a^{2}+\frac{19}{7}a-\frac{3}{7}\right){x}{y}+\left(-\frac{1}{7}a^{3}+\frac{5}{7}a^{2}-\frac{1}{7}a-\frac{19}{7}\right){y}={x}^{3}+\left(-\frac{3}{7}a^{3}+\frac{8}{7}a^{2}+\frac{18}{7}a-\frac{22}{7}\right){x}^{2}+\left(-\frac{1}{7}a^{3}-\frac{2}{7}a^{2}+\frac{20}{7}a+\frac{16}{7}\right){x}-\frac{3}{7}a^{3}+\frac{8}{7}a^{2}+\frac{4}{7}a-\frac{15}{7}$ |
| 1.1-b3 |
1.1-b |
$12$ |
$90$ |
\(\Q(\sqrt{3}, \sqrt{5})\) |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$5.36154$ |
$\textsf{none}$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-180$ |
$N(\mathrm{U}(1))$ |
✓ |
|
✓ |
✓ |
$3$ |
3B.1.2 |
$9$ |
\( 1 \) |
$1$ |
$11.51826733$ |
0.431935025 |
\( \frac{1485394448522849280}{7} a^{3} - \frac{3140148847261304320}{7} a^{2} - \frac{10039731355286164480}{7} a + \frac{13027853817486391360}{7} \) |
\( \bigl[-\frac{2}{7} a^{3} + \frac{3}{7} a^{2} + \frac{19}{7} a - \frac{3}{7}\) , \( -\frac{5}{7} a^{3} + \frac{4}{7} a^{2} + \frac{44}{7} a - \frac{4}{7}\) , \( -\frac{3}{7} a^{3} + \frac{8}{7} a^{2} + \frac{18}{7} a - \frac{22}{7}\) , \( -\frac{243}{7} a^{3} + \frac{431}{7} a^{2} + \frac{1717}{7} a - \frac{1481}{7}\) , \( -\frac{845}{7} a^{3} + \frac{1943}{7} a^{2} + \frac{5553}{7} a - \frac{8663}{7}\bigr] \) |
${y}^2+\left(-\frac{2}{7}a^{3}+\frac{3}{7}a^{2}+\frac{19}{7}a-\frac{3}{7}\right){x}{y}+\left(-\frac{3}{7}a^{3}+\frac{8}{7}a^{2}+\frac{18}{7}a-\frac{22}{7}\right){y}={x}^{3}+\left(-\frac{5}{7}a^{3}+\frac{4}{7}a^{2}+\frac{44}{7}a-\frac{4}{7}\right){x}^{2}+\left(-\frac{243}{7}a^{3}+\frac{431}{7}a^{2}+\frac{1717}{7}a-\frac{1481}{7}\right){x}-\frac{845}{7}a^{3}+\frac{1943}{7}a^{2}+\frac{5553}{7}a-\frac{8663}{7}$ |
| 1.1-b4 |
1.1-b |
$12$ |
$90$ |
\(\Q(\sqrt{3}, \sqrt{5})\) |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$5.36154$ |
$\textsf{none}$ |
0 |
$\Z/6\Z$ |
$\textsf{potential}$ |
$-180$ |
$N(\mathrm{U}(1))$ |
✓ |
|
✓ |
✓ |
$3$ |
3B.1.1 |
$1$ |
\( 1 \) |
$1$ |
$932.9796544$ |
0.431935025 |
\( \frac{1485394448522849280}{7} a^{3} - \frac{3140148847261304320}{7} a^{2} - \frac{10039731355286164480}{7} a + \frac{13027853817486391360}{7} \) |
\( \bigl[-\frac{2}{7} a^{3} + \frac{3}{7} a^{2} + \frac{19}{7} a - \frac{3}{7}\) , \( \frac{1}{7} a^{3} + \frac{2}{7} a^{2} - \frac{6}{7} a - \frac{9}{7}\) , \( -\frac{1}{7} a^{3} + \frac{5}{7} a^{2} - \frac{1}{7} a - \frac{19}{7}\) , \( -\frac{227}{7} a^{3} + \frac{421}{7} a^{2} + \frac{1607}{7} a - \frac{1492}{7}\) , \( \frac{818}{7} a^{3} - \frac{2074}{7} a^{2} - \frac{5174}{7} a + \frac{9893}{7}\bigr] \) |
${y}^2+\left(-\frac{2}{7}a^{3}+\frac{3}{7}a^{2}+\frac{19}{7}a-\frac{3}{7}\right){x}{y}+\left(-\frac{1}{7}a^{3}+\frac{5}{7}a^{2}-\frac{1}{7}a-\frac{19}{7}\right){y}={x}^{3}+\left(\frac{1}{7}a^{3}+\frac{2}{7}a^{2}-\frac{6}{7}a-\frac{9}{7}\right){x}^{2}+\left(-\frac{227}{7}a^{3}+\frac{421}{7}a^{2}+\frac{1607}{7}a-\frac{1492}{7}\right){x}+\frac{818}{7}a^{3}-\frac{2074}{7}a^{2}-\frac{5174}{7}a+\frac{9893}{7}$ |
| 1.1-b5 |
1.1-b |
$12$ |
$90$ |
\(\Q(\sqrt{3}, \sqrt{5})\) |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$5.36154$ |
$\textsf{none}$ |
0 |
$\Z/6\Z$ |
$\textsf{potential}$ |
$-180$ |
$N(\mathrm{U}(1))$ |
✓ |
|
✓ |
✓ |
$3$ |
3B.1.1 |
$1$ |
\( 1 \) |
$1$ |
$932.9796544$ |
0.431935025 |
\( -\frac{1485394448522849280}{7} a^{3} + \frac{1316034498307243520}{7} a^{2} + \frac{11863845704240225280}{7} a + \frac{1333368063461771840}{7} \) |
\( \bigl[-\frac{2}{7} a^{3} + \frac{3}{7} a^{2} + \frac{19}{7} a - \frac{3}{7}\) , \( \frac{1}{7} a^{3} + \frac{2}{7} a^{2} - \frac{20}{7} a - \frac{2}{7}\) , \( -\frac{3}{7} a^{3} + \frac{8}{7} a^{2} + \frac{18}{7} a - \frac{22}{7}\) , \( \frac{223}{7} a^{3} - \frac{254}{7} a^{2} - \frac{1744}{7} a + \frac{282}{7}\) , \( -\frac{820}{7} a^{3} + \frac{383}{7} a^{2} + \frac{6887}{7} a + \frac{3453}{7}\bigr] \) |
${y}^2+\left(-\frac{2}{7}a^{3}+\frac{3}{7}a^{2}+\frac{19}{7}a-\frac{3}{7}\right){x}{y}+\left(-\frac{3}{7}a^{3}+\frac{8}{7}a^{2}+\frac{18}{7}a-\frac{22}{7}\right){y}={x}^{3}+\left(\frac{1}{7}a^{3}+\frac{2}{7}a^{2}-\frac{20}{7}a-\frac{2}{7}\right){x}^{2}+\left(\frac{223}{7}a^{3}-\frac{254}{7}a^{2}-\frac{1744}{7}a+\frac{282}{7}\right){x}-\frac{820}{7}a^{3}+\frac{383}{7}a^{2}+\frac{6887}{7}a+\frac{3453}{7}$ |
| 1.1-b6 |
1.1-b |
$12$ |
$90$ |
\(\Q(\sqrt{3}, \sqrt{5})\) |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$5.36154$ |
$\textsf{none}$ |
0 |
$\Z/6\Z$ |
$\textsf{potential}$ |
$-20$ |
$N(\mathrm{U}(1))$ |
✓ |
|
✓ |
✓ |
$3$ |
3Cs.1.1 |
$1$ |
\( 1 \) |
$1$ |
$932.9796544$ |
0.431935025 |
\( -\frac{1131520}{7} a^{3} + \frac{1697280}{7} a^{2} + \frac{6789120}{7} a + \frac{746560}{7} \) |
\( \bigl[-\frac{2}{7} a^{3} + \frac{3}{7} a^{2} + \frac{19}{7} a - \frac{3}{7}\) , \( \frac{1}{7} a^{3} - \frac{5}{7} a^{2} + \frac{1}{7} a + \frac{19}{7}\) , \( -\frac{3}{7} a^{3} + \frac{8}{7} a^{2} + \frac{18}{7} a - \frac{22}{7}\) , \( -a^{3} + 2 a^{2} + 6 a - 6\) , \( \frac{9}{7} a^{3} - \frac{17}{7} a^{2} - \frac{61}{7} a + \frac{52}{7}\bigr] \) |
${y}^2+\left(-\frac{2}{7}a^{3}+\frac{3}{7}a^{2}+\frac{19}{7}a-\frac{3}{7}\right){x}{y}+\left(-\frac{3}{7}a^{3}+\frac{8}{7}a^{2}+\frac{18}{7}a-\frac{22}{7}\right){y}={x}^{3}+\left(\frac{1}{7}a^{3}-\frac{5}{7}a^{2}+\frac{1}{7}a+\frac{19}{7}\right){x}^{2}+\left(-a^{3}+2a^{2}+6a-6\right){x}+\frac{9}{7}a^{3}-\frac{17}{7}a^{2}-\frac{61}{7}a+\frac{52}{7}$ |
| 1.1-b7 |
1.1-b |
$12$ |
$90$ |
\(\Q(\sqrt{3}, \sqrt{5})\) |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$5.36154$ |
$\textsf{none}$ |
0 |
$\Z/6\Z$ |
$\textsf{potential}$ |
$-180$ |
$N(\mathrm{U}(1))$ |
✓ |
|
✓ |
✓ |
$3$ |
3B.1.1 |
$1$ |
\( 1 \) |
$1$ |
$932.9796544$ |
0.431935025 |
\( -\frac{320010540736506880}{7} a^{3} + \frac{1392072985581790720}{7} a^{2} - \frac{1031415768684088320}{7} a - \frac{136169793422759360}{7} \) |
\( \bigl[-\frac{2}{7} a^{3} + \frac{3}{7} a^{2} + \frac{19}{7} a - \frac{3}{7}\) , \( -\frac{3}{7} a^{3} + \frac{1}{7} a^{2} + \frac{25}{7} a + \frac{6}{7}\) , \( -\frac{3}{7} a^{3} + \frac{8}{7} a^{2} + \frac{18}{7} a - \frac{22}{7}\) , \( \frac{39}{7} a^{3} - \frac{139}{7} a^{2} + \frac{165}{7} a + \frac{6}{7}\) , \( -26 a^{3} + 160 a^{2} - 124 a - 19\bigr] \) |
${y}^2+\left(-\frac{2}{7}a^{3}+\frac{3}{7}a^{2}+\frac{19}{7}a-\frac{3}{7}\right){x}{y}+\left(-\frac{3}{7}a^{3}+\frac{8}{7}a^{2}+\frac{18}{7}a-\frac{22}{7}\right){y}={x}^{3}+\left(-\frac{3}{7}a^{3}+\frac{1}{7}a^{2}+\frac{25}{7}a+\frac{6}{7}\right){x}^{2}+\left(\frac{39}{7}a^{3}-\frac{139}{7}a^{2}+\frac{165}{7}a+\frac{6}{7}\right){x}-26a^{3}+160a^{2}-124a-19$ |
| 1.1-b8 |
1.1-b |
$12$ |
$90$ |
\(\Q(\sqrt{3}, \sqrt{5})\) |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$5.36154$ |
$\textsf{none}$ |
0 |
$\Z/6\Z$ |
$\textsf{potential}$ |
$-180$ |
$N(\mathrm{U}(1))$ |
✓ |
|
✓ |
✓ |
$3$ |
3B.1.1 |
$1$ |
\( 1 \) |
$1$ |
$932.9796544$ |
0.431935025 |
\( \frac{320010540736506880}{7} a^{3} + \frac{432041363372270080}{7} a^{2} - \frac{792698580269972480}{7} a - \frac{95523117261563840}{7} \) |
\( \bigl[-\frac{2}{7} a^{3} + \frac{3}{7} a^{2} + \frac{19}{7} a - \frac{3}{7}\) , \( -\frac{1}{7} a^{3} - \frac{2}{7} a^{2} + \frac{20}{7} a + \frac{9}{7}\) , \( -\frac{3}{7} a^{3} + \frac{8}{7} a^{2} + \frac{18}{7} a - \frac{22}{7}\) , \( -\frac{59}{7} a^{3} + \frac{15}{7} a^{2} + \frac{123}{7} a - \frac{8}{7}\) , \( \frac{125}{7} a^{3} + \frac{418}{7} a^{2} - \frac{512}{7} a - \frac{82}{7}\bigr] \) |
${y}^2+\left(-\frac{2}{7}a^{3}+\frac{3}{7}a^{2}+\frac{19}{7}a-\frac{3}{7}\right){x}{y}+\left(-\frac{3}{7}a^{3}+\frac{8}{7}a^{2}+\frac{18}{7}a-\frac{22}{7}\right){y}={x}^{3}+\left(-\frac{1}{7}a^{3}-\frac{2}{7}a^{2}+\frac{20}{7}a+\frac{9}{7}\right){x}^{2}+\left(-\frac{59}{7}a^{3}+\frac{15}{7}a^{2}+\frac{123}{7}a-\frac{8}{7}\right){x}+\frac{125}{7}a^{3}+\frac{418}{7}a^{2}-\frac{512}{7}a-\frac{82}{7}$ |
| 1.1-b9 |
1.1-b |
$12$ |
$90$ |
\(\Q(\sqrt{3}, \sqrt{5})\) |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$5.36154$ |
$\textsf{none}$ |
0 |
$\Z/6\Z$ |
$\textsf{potential}$ |
$-20$ |
$N(\mathrm{U}(1))$ |
✓ |
|
✓ |
✓ |
$3$ |
3Cs.1.1 |
$1$ |
\( 1 \) |
$1$ |
$932.9796544$ |
0.431935025 |
\( \frac{1131520}{7} a^{3} - \frac{1697280}{7} a^{2} - \frac{6789120}{7} a + \frac{8101440}{7} \) |
\( \bigl[-\frac{2}{7} a^{3} + \frac{3}{7} a^{2} + \frac{19}{7} a - \frac{3}{7}\) , \( -\frac{1}{7} a^{3} - \frac{2}{7} a^{2} + \frac{20}{7} a + \frac{9}{7}\) , \( -\frac{3}{7} a^{3} + \frac{8}{7} a^{2} + \frac{18}{7} a - \frac{22}{7}\) , \( -\frac{9}{7} a^{3} + \frac{10}{7} a^{2} + \frac{68}{7} a - \frac{3}{7}\) , \( -\frac{6}{7} a^{3} + \frac{2}{7} a^{2} + \frac{64}{7} a - \frac{16}{7}\bigr] \) |
${y}^2+\left(-\frac{2}{7}a^{3}+\frac{3}{7}a^{2}+\frac{19}{7}a-\frac{3}{7}\right){x}{y}+\left(-\frac{3}{7}a^{3}+\frac{8}{7}a^{2}+\frac{18}{7}a-\frac{22}{7}\right){y}={x}^{3}+\left(-\frac{1}{7}a^{3}-\frac{2}{7}a^{2}+\frac{20}{7}a+\frac{9}{7}\right){x}^{2}+\left(-\frac{9}{7}a^{3}+\frac{10}{7}a^{2}+\frac{68}{7}a-\frac{3}{7}\right){x}-\frac{6}{7}a^{3}+\frac{2}{7}a^{2}+\frac{64}{7}a-\frac{16}{7}$ |
| 1.1-b10 |
1.1-b |
$12$ |
$90$ |
\(\Q(\sqrt{3}, \sqrt{5})\) |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$5.36154$ |
$\textsf{none}$ |
0 |
$\Z/6\Z$ |
$\textsf{potential}$ |
$-20$ |
$N(\mathrm{U}(1))$ |
✓ |
|
✓ |
✓ |
$3$ |
3Cs.1.1 |
$1$ |
\( 1 \) |
$1$ |
$932.9796544$ |
0.431935025 |
\( -\frac{1131520}{7} a^{3} + \frac{1697280}{7} a^{2} + \frac{6789120}{7} a + \frac{746560}{7} \) |
\( \bigl[-\frac{2}{7} a^{3} + \frac{3}{7} a^{2} + \frac{19}{7} a - \frac{3}{7}\) , \( \frac{1}{7} a^{3} + \frac{2}{7} a^{2} - \frac{20}{7} a - \frac{2}{7}\) , \( -\frac{3}{7} a^{3} + \frac{8}{7} a^{2} + \frac{18}{7} a - \frac{22}{7}\) , \( -a^{3} + 3 a^{2} + 3 a - 9\) , \( -\frac{19}{7} a^{3} + \frac{39}{7} a^{2} + \frac{121}{7} a - \frac{137}{7}\bigr] \) |
${y}^2+\left(-\frac{2}{7}a^{3}+\frac{3}{7}a^{2}+\frac{19}{7}a-\frac{3}{7}\right){x}{y}+\left(-\frac{3}{7}a^{3}+\frac{8}{7}a^{2}+\frac{18}{7}a-\frac{22}{7}\right){y}={x}^{3}+\left(\frac{1}{7}a^{3}+\frac{2}{7}a^{2}-\frac{20}{7}a-\frac{2}{7}\right){x}^{2}+\left(-a^{3}+3a^{2}+3a-9\right){x}-\frac{19}{7}a^{3}+\frac{39}{7}a^{2}+\frac{121}{7}a-\frac{137}{7}$ |
| 1.1-b11 |
1.1-b |
$12$ |
$90$ |
\(\Q(\sqrt{3}, \sqrt{5})\) |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$5.36154$ |
$\textsf{none}$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-180$ |
$N(\mathrm{U}(1))$ |
✓ |
|
✓ |
✓ |
$3$ |
3B.1.2 |
$9$ |
\( 1 \) |
$1$ |
$11.51826733$ |
0.431935025 |
\( -\frac{320010540736506880}{7} a^{3} + \frac{1392072985581790720}{7} a^{2} - \frac{1031415768684088320}{7} a - \frac{136169793422759360}{7} \) |
\( \bigl[-\frac{2}{7} a^{3} + \frac{3}{7} a^{2} + \frac{19}{7} a - \frac{3}{7}\) , \( \frac{5}{7} a^{3} - \frac{4}{7} a^{2} - \frac{44}{7} a + \frac{11}{7}\) , \( -\frac{3}{7} a^{3} + \frac{8}{7} a^{2} + \frac{18}{7} a - \frac{22}{7}\) , \( \frac{47}{7} a^{3} - \frac{144}{7} a^{2} + \frac{96}{7} a + \frac{11}{7}\) , \( \frac{222}{7} a^{3} - \frac{1257}{7} a^{2} + \frac{1027}{7} a + \frac{109}{7}\bigr] \) |
${y}^2+\left(-\frac{2}{7}a^{3}+\frac{3}{7}a^{2}+\frac{19}{7}a-\frac{3}{7}\right){x}{y}+\left(-\frac{3}{7}a^{3}+\frac{8}{7}a^{2}+\frac{18}{7}a-\frac{22}{7}\right){y}={x}^{3}+\left(\frac{5}{7}a^{3}-\frac{4}{7}a^{2}-\frac{44}{7}a+\frac{11}{7}\right){x}^{2}+\left(\frac{47}{7}a^{3}-\frac{144}{7}a^{2}+\frac{96}{7}a+\frac{11}{7}\right){x}+\frac{222}{7}a^{3}-\frac{1257}{7}a^{2}+\frac{1027}{7}a+\frac{109}{7}$ |
| 1.1-b12 |
1.1-b |
$12$ |
$90$ |
\(\Q(\sqrt{3}, \sqrt{5})\) |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$5.36154$ |
$\textsf{none}$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-180$ |
$N(\mathrm{U}(1))$ |
✓ |
|
✓ |
✓ |
$3$ |
3B.1.2 |
$9$ |
\( 1 \) |
$1$ |
$11.51826733$ |
0.431935025 |
\( -\frac{1485394448522849280}{7} a^{3} + \frac{1316034498307243520}{7} a^{2} + \frac{11863845704240225280}{7} a + \frac{1333368063461771840}{7} \) |
\( \bigl[-\frac{2}{7} a^{3} + \frac{3}{7} a^{2} + \frac{19}{7} a - \frac{3}{7}\) , \( \frac{1}{7} a^{3} - \frac{5}{7} a^{2} + \frac{1}{7} a + \frac{19}{7}\) , \( -\frac{3}{7} a^{3} + \frac{8}{7} a^{2} + \frac{18}{7} a - \frac{22}{7}\) , \( \frac{223}{7} a^{3} - \frac{261}{7} a^{2} - \frac{1723}{7} a + \frac{303}{7}\) , \( \frac{1040}{7} a^{3} - \frac{636}{7} a^{2} - \frac{8592}{7} a - \frac{3193}{7}\bigr] \) |
${y}^2+\left(-\frac{2}{7}a^{3}+\frac{3}{7}a^{2}+\frac{19}{7}a-\frac{3}{7}\right){x}{y}+\left(-\frac{3}{7}a^{3}+\frac{8}{7}a^{2}+\frac{18}{7}a-\frac{22}{7}\right){y}={x}^{3}+\left(\frac{1}{7}a^{3}-\frac{5}{7}a^{2}+\frac{1}{7}a+\frac{19}{7}\right){x}^{2}+\left(\frac{223}{7}a^{3}-\frac{261}{7}a^{2}-\frac{1723}{7}a+\frac{303}{7}\right){x}+\frac{1040}{7}a^{3}-\frac{636}{7}a^{2}-\frac{8592}{7}a-\frac{3193}{7}$ |
| 16.1-a1 |
16.1-a |
$8$ |
$12$ |
\(\Q(\sqrt{3}, \sqrt{5})\) |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{8} \) |
$7.58237$ |
$(-2/7a^3+3/7a^2+19/7a-3/7)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{potential}$ |
$-12$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$2$ |
2Cs |
$1$ |
\( 1 \) |
$1$ |
$1252.456616$ |
1.304642309 |
\( 54000 \) |
\( \bigl[-\frac{3}{7} a^{3} + \frac{8}{7} a^{2} + \frac{18}{7} a - \frac{29}{7}\) , \( -\frac{3}{7} a^{3} + \frac{8}{7} a^{2} + \frac{18}{7} a - \frac{36}{7}\) , \( -\frac{2}{7} a^{3} + \frac{3}{7} a^{2} + \frac{19}{7} a - \frac{3}{7}\) , \( -2\) , \( -\frac{1}{7} a^{3} - \frac{2}{7} a^{2} + \frac{13}{7} a + \frac{2}{7}\bigr] \) |
${y}^2+\left(-\frac{3}{7}a^{3}+\frac{8}{7}a^{2}+\frac{18}{7}a-\frac{29}{7}\right){x}{y}+\left(-\frac{2}{7}a^{3}+\frac{3}{7}a^{2}+\frac{19}{7}a-\frac{3}{7}\right){y}={x}^{3}+\left(-\frac{3}{7}a^{3}+\frac{8}{7}a^{2}+\frac{18}{7}a-\frac{36}{7}\right){x}^{2}-2{x}-\frac{1}{7}a^{3}-\frac{2}{7}a^{2}+\frac{13}{7}a+\frac{2}{7}$ |
| 16.1-a2 |
16.1-a |
$8$ |
$12$ |
\(\Q(\sqrt{3}, \sqrt{5})\) |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{16} \) |
$7.58237$ |
$(-2/7a^3+3/7a^2+19/7a-3/7)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-48$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 1 \) |
$1$ |
$313.1141542$ |
1.304642309 |
\( -\frac{1637253000}{7} a^{3} + \frac{2455879500}{7} a^{2} + \frac{15553903500}{7} a + \frac{1739070000}{7} \) |
\( \bigl[-\frac{3}{7} a^{3} + \frac{8}{7} a^{2} + \frac{18}{7} a - \frac{29}{7}\) , \( -\frac{4}{7} a^{3} + \frac{6}{7} a^{2} + \frac{31}{7} a - \frac{27}{7}\) , \( -\frac{2}{7} a^{3} + \frac{3}{7} a^{2} + \frac{19}{7} a - \frac{3}{7}\) , \( 5 a^{3} - 5 a^{2} - 40 a - 7\) , \( \frac{127}{7} a^{3} - \frac{110}{7} a^{2} - \frac{1007}{7} a - \frac{114}{7}\bigr] \) |
${y}^2+\left(-\frac{3}{7}a^{3}+\frac{8}{7}a^{2}+\frac{18}{7}a-\frac{29}{7}\right){x}{y}+\left(-\frac{2}{7}a^{3}+\frac{3}{7}a^{2}+\frac{19}{7}a-\frac{3}{7}\right){y}={x}^{3}+\left(-\frac{4}{7}a^{3}+\frac{6}{7}a^{2}+\frac{31}{7}a-\frac{27}{7}\right){x}^{2}+\left(5a^{3}-5a^{2}-40a-7\right){x}+\frac{127}{7}a^{3}-\frac{110}{7}a^{2}-\frac{1007}{7}a-\frac{114}{7}$ |
| 16.1-a3 |
16.1-a |
$8$ |
$12$ |
\(\Q(\sqrt{3}, \sqrt{5})\) |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{16} \) |
$7.58237$ |
$(-2/7a^3+3/7a^2+19/7a-3/7)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-48$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 1 \) |
$1$ |
$313.1141542$ |
1.304642309 |
\( \frac{1637253000}{7} a^{3} - \frac{2455879500}{7} a^{2} - \frac{15553903500}{7} a + \frac{18111600000}{7} \) |
\( \bigl[-\frac{1}{7} a^{3} + \frac{5}{7} a^{2} - \frac{1}{7} a - \frac{12}{7}\) , \( a + 1\) , \( -\frac{3}{7} a^{3} + \frac{8}{7} a^{2} + \frac{18}{7} a - \frac{29}{7}\) , \( -\frac{40}{7} a^{3} + \frac{81}{7} a^{2} + \frac{282}{7} a - \frac{354}{7}\) , \( \frac{85}{7} a^{3} - \frac{187}{7} a^{2} - \frac{552}{7} a + \frac{726}{7}\bigr] \) |
${y}^2+\left(-\frac{1}{7}a^{3}+\frac{5}{7}a^{2}-\frac{1}{7}a-\frac{12}{7}\right){x}{y}+\left(-\frac{3}{7}a^{3}+\frac{8}{7}a^{2}+\frac{18}{7}a-\frac{29}{7}\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-\frac{40}{7}a^{3}+\frac{81}{7}a^{2}+\frac{282}{7}a-\frac{354}{7}\right){x}+\frac{85}{7}a^{3}-\frac{187}{7}a^{2}-\frac{552}{7}a+\frac{726}{7}$ |
| 16.1-a4 |
16.1-a |
$8$ |
$12$ |
\(\Q(\sqrt{3}, \sqrt{5})\) |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{16} \) |
$7.58237$ |
$(-2/7a^3+3/7a^2+19/7a-3/7)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-48$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 1 \) |
$1$ |
$313.1141542$ |
1.304642309 |
\( -\frac{1637253000}{7} a^{3} + \frac{2455879500}{7} a^{2} + \frac{15553903500}{7} a + \frac{1739070000}{7} \) |
\( \bigl[-\frac{3}{7} a^{3} + \frac{8}{7} a^{2} + \frac{18}{7} a - \frac{29}{7}\) , \( -\frac{3}{7} a^{3} + \frac{8}{7} a^{2} + \frac{18}{7} a - \frac{36}{7}\) , \( -\frac{2}{7} a^{3} + \frac{3}{7} a^{2} + \frac{19}{7} a - \frac{3}{7}\) , \( 5 a^{3} - 5 a^{2} - 40 a - 7\) , \( -\frac{125}{7} a^{3} + \frac{107}{7} a^{2} + \frac{988}{7} a + \frac{110}{7}\bigr] \) |
${y}^2+\left(-\frac{3}{7}a^{3}+\frac{8}{7}a^{2}+\frac{18}{7}a-\frac{29}{7}\right){x}{y}+\left(-\frac{2}{7}a^{3}+\frac{3}{7}a^{2}+\frac{19}{7}a-\frac{3}{7}\right){y}={x}^{3}+\left(-\frac{3}{7}a^{3}+\frac{8}{7}a^{2}+\frac{18}{7}a-\frac{36}{7}\right){x}^{2}+\left(5a^{3}-5a^{2}-40a-7\right){x}-\frac{125}{7}a^{3}+\frac{107}{7}a^{2}+\frac{988}{7}a+\frac{110}{7}$ |
| 16.1-a5 |
16.1-a |
$8$ |
$12$ |
\(\Q(\sqrt{3}, \sqrt{5})\) |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{16} \) |
$7.58237$ |
$(-2/7a^3+3/7a^2+19/7a-3/7)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-48$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 1 \) |
$1$ |
$313.1141542$ |
1.304642309 |
\( \frac{1637253000}{7} a^{3} - \frac{2455879500}{7} a^{2} - \frac{15553903500}{7} a + \frac{18111600000}{7} \) |
\( \bigl[-\frac{1}{7} a^{3} + \frac{5}{7} a^{2} - \frac{1}{7} a - \frac{12}{7}\) , \( \frac{1}{7} a^{3} - \frac{5}{7} a^{2} + \frac{1}{7} a + \frac{26}{7}\) , \( -\frac{3}{7} a^{3} + \frac{8}{7} a^{2} + \frac{18}{7} a - \frac{29}{7}\) , \( -\frac{38}{7} a^{3} + \frac{71}{7} a^{2} + \frac{270}{7} a - \frac{316}{7}\) , \( -\frac{166}{7} a^{3} + \frac{347}{7} a^{2} + \frac{1115}{7} a - \frac{1439}{7}\bigr] \) |
${y}^2+\left(-\frac{1}{7}a^{3}+\frac{5}{7}a^{2}-\frac{1}{7}a-\frac{12}{7}\right){x}{y}+\left(-\frac{3}{7}a^{3}+\frac{8}{7}a^{2}+\frac{18}{7}a-\frac{29}{7}\right){y}={x}^{3}+\left(\frac{1}{7}a^{3}-\frac{5}{7}a^{2}+\frac{1}{7}a+\frac{26}{7}\right){x}^{2}+\left(-\frac{38}{7}a^{3}+\frac{71}{7}a^{2}+\frac{270}{7}a-\frac{316}{7}\right){x}-\frac{166}{7}a^{3}+\frac{347}{7}a^{2}+\frac{1115}{7}a-\frac{1439}{7}$ |
| 16.1-a6 |
16.1-a |
$8$ |
$12$ |
\(\Q(\sqrt{3}, \sqrt{5})\) |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{8} \) |
$7.58237$ |
$(-2/7a^3+3/7a^2+19/7a-3/7)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{potential}$ |
$-12$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$2$ |
2Cs |
$1$ |
\( 1 \) |
$1$ |
$1252.456616$ |
1.304642309 |
\( 54000 \) |
\( \bigl[-\frac{3}{7} a^{3} + \frac{8}{7} a^{2} + \frac{18}{7} a - \frac{29}{7}\) , \( -\frac{4}{7} a^{3} + \frac{6}{7} a^{2} + \frac{31}{7} a - \frac{27}{7}\) , \( -\frac{2}{7} a^{3} + \frac{3}{7} a^{2} + \frac{19}{7} a - \frac{3}{7}\) , \( -2\) , \( \frac{3}{7} a^{3} - \frac{1}{7} a^{2} - \frac{32}{7} a - \frac{6}{7}\bigr] \) |
${y}^2+\left(-\frac{3}{7}a^{3}+\frac{8}{7}a^{2}+\frac{18}{7}a-\frac{29}{7}\right){x}{y}+\left(-\frac{2}{7}a^{3}+\frac{3}{7}a^{2}+\frac{19}{7}a-\frac{3}{7}\right){y}={x}^{3}+\left(-\frac{4}{7}a^{3}+\frac{6}{7}a^{2}+\frac{31}{7}a-\frac{27}{7}\right){x}^{2}-2{x}+\frac{3}{7}a^{3}-\frac{1}{7}a^{2}-\frac{32}{7}a-\frac{6}{7}$ |
| 16.1-a7 |
16.1-a |
$8$ |
$12$ |
\(\Q(\sqrt{3}, \sqrt{5})\) |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{16} \) |
$7.58237$ |
$(-2/7a^3+3/7a^2+19/7a-3/7)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-3$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$313.1141542$ |
1.304642309 |
\( 0 \) |
\( \bigl[0\) , \( \frac{1}{7} a^{3} + \frac{2}{7} a^{2} - \frac{13}{7} a - \frac{9}{7}\) , \( 0\) , \( -\frac{2}{7} a^{3} + \frac{3}{7} a^{2} + \frac{12}{7} a + \frac{4}{7}\) , \( \frac{32}{7} a^{3} - \frac{27}{7} a^{2} - \frac{255}{7} a - \frac{29}{7}\bigr] \) |
${y}^2={x}^{3}+\left(\frac{1}{7}a^{3}+\frac{2}{7}a^{2}-\frac{13}{7}a-\frac{9}{7}\right){x}^{2}+\left(-\frac{2}{7}a^{3}+\frac{3}{7}a^{2}+\frac{12}{7}a+\frac{4}{7}\right){x}+\frac{32}{7}a^{3}-\frac{27}{7}a^{2}-\frac{255}{7}a-\frac{29}{7}$ |
| 16.1-a8 |
16.1-a |
$8$ |
$12$ |
\(\Q(\sqrt{3}, \sqrt{5})\) |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{16} \) |
$7.58237$ |
$(-2/7a^3+3/7a^2+19/7a-3/7)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-3$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$313.1141542$ |
1.304642309 |
\( 0 \) |
\( \bigl[0\) , \( \frac{1}{7} a^{3} - \frac{5}{7} a^{2} - \frac{6}{7} a + \frac{19}{7}\) , \( 0\) , \( \frac{2}{7} a^{3} - \frac{3}{7} a^{2} - \frac{12}{7} a + \frac{17}{7}\) , \( \frac{32}{7} a^{3} - \frac{69}{7} a^{2} - \frac{213}{7} a + \frac{279}{7}\bigr] \) |
${y}^2={x}^{3}+\left(\frac{1}{7}a^{3}-\frac{5}{7}a^{2}-\frac{6}{7}a+\frac{19}{7}\right){x}^{2}+\left(\frac{2}{7}a^{3}-\frac{3}{7}a^{2}-\frac{12}{7}a+\frac{17}{7}\right){x}+\frac{32}{7}a^{3}-\frac{69}{7}a^{2}-\frac{213}{7}a+\frac{279}{7}$ |
| 36.1-a1 |
36.1-a |
$4$ |
$10$ |
\(\Q(\sqrt{3}, \sqrt{5})\) |
$4$ |
$[4, 0]$ |
36.1 |
\( 2^{2} \cdot 3^{2} \) |
\( 2^{4} \cdot 3^{8} \) |
$8.39127$ |
$(-2/7a^3+3/7a^2+19/7a-3/7), (-2/7a^3+3/7a^2+19/7a-10/7)$ |
0 |
$\Z/10\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 5$ |
2B, 5B.1.1[2] |
$1$ |
\( 2^{2} \) |
$1$ |
$1962.456482$ |
1.308304321 |
\( \frac{131872229}{18} \) |
\( \bigl[-\frac{2}{7} a^{3} + \frac{3}{7} a^{2} + \frac{12}{7} a - \frac{10}{7}\) , \( \frac{2}{7} a^{3} - \frac{3}{7} a^{2} - \frac{12}{7} a + \frac{3}{7}\) , \( -\frac{2}{7} a^{3} + \frac{3}{7} a^{2} + \frac{12}{7} a - \frac{10}{7}\) , \( \frac{20}{7} a^{3} - \frac{30}{7} a^{2} - \frac{120}{7} a - \frac{47}{7}\) , \( -\frac{62}{7} a^{3} + \frac{93}{7} a^{2} + \frac{372}{7} a + \frac{47}{7}\bigr] \) |
${y}^2+\left(-\frac{2}{7}a^{3}+\frac{3}{7}a^{2}+\frac{12}{7}a-\frac{10}{7}\right){x}{y}+\left(-\frac{2}{7}a^{3}+\frac{3}{7}a^{2}+\frac{12}{7}a-\frac{10}{7}\right){y}={x}^{3}+\left(\frac{2}{7}a^{3}-\frac{3}{7}a^{2}-\frac{12}{7}a+\frac{3}{7}\right){x}^{2}+\left(\frac{20}{7}a^{3}-\frac{30}{7}a^{2}-\frac{120}{7}a-\frac{47}{7}\right){x}-\frac{62}{7}a^{3}+\frac{93}{7}a^{2}+\frac{372}{7}a+\frac{47}{7}$ |
| 36.1-a2 |
36.1-a |
$4$ |
$10$ |
\(\Q(\sqrt{3}, \sqrt{5})\) |
$4$ |
$[4, 0]$ |
36.1 |
\( 2^{2} \cdot 3^{2} \) |
\( 2^{40} \cdot 3^{20} \) |
$8.39127$ |
$(-2/7a^3+3/7a^2+19/7a-3/7), (-2/7a^3+3/7a^2+19/7a-10/7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 5$ |
2B, 5B.1.4[2] |
$25$ |
\( 2^{2} \) |
$1$ |
$3.139930371$ |
1.308304321 |
\( -\frac{19465109}{248832} \) |
\( \bigl[-\frac{2}{7} a^{3} + \frac{3}{7} a^{2} + \frac{12}{7} a - \frac{10}{7}\) , \( \frac{2}{7} a^{3} - \frac{3}{7} a^{2} - \frac{12}{7} a + \frac{3}{7}\) , \( -\frac{2}{7} a^{3} + \frac{3}{7} a^{2} + \frac{12}{7} a - \frac{10}{7}\) , \( \frac{10}{7} a^{3} - \frac{15}{7} a^{2} - \frac{60}{7} a - \frac{27}{7}\) , \( \frac{80}{7} a^{3} - \frac{120}{7} a^{2} - \frac{480}{7} a - \frac{104}{7}\bigr] \) |
${y}^2+\left(-\frac{2}{7}a^{3}+\frac{3}{7}a^{2}+\frac{12}{7}a-\frac{10}{7}\right){x}{y}+\left(-\frac{2}{7}a^{3}+\frac{3}{7}a^{2}+\frac{12}{7}a-\frac{10}{7}\right){y}={x}^{3}+\left(\frac{2}{7}a^{3}-\frac{3}{7}a^{2}-\frac{12}{7}a+\frac{3}{7}\right){x}^{2}+\left(\frac{10}{7}a^{3}-\frac{15}{7}a^{2}-\frac{60}{7}a-\frac{27}{7}\right){x}+\frac{80}{7}a^{3}-\frac{120}{7}a^{2}-\frac{480}{7}a-\frac{104}{7}$ |
| 36.1-a3 |
36.1-a |
$4$ |
$10$ |
\(\Q(\sqrt{3}, \sqrt{5})\) |
$4$ |
$[4, 0]$ |
36.1 |
\( 2^{2} \cdot 3^{2} \) |
\( 2^{8} \cdot 3^{4} \) |
$8.39127$ |
$(-2/7a^3+3/7a^2+19/7a-3/7), (-2/7a^3+3/7a^2+19/7a-10/7)$ |
0 |
$\Z/10\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 5$ |
2B, 5B.1.1[2] |
$1$ |
\( 2^{2} \) |
$1$ |
$1962.456482$ |
1.308304321 |
\( -\frac{24389}{12} \) |
\( \bigl[-\frac{2}{7} a^{3} + \frac{3}{7} a^{2} + \frac{12}{7} a - \frac{10}{7}\) , \( \frac{2}{7} a^{3} - \frac{3}{7} a^{2} - \frac{12}{7} a + \frac{3}{7}\) , \( -\frac{2}{7} a^{3} + \frac{3}{7} a^{2} + \frac{12}{7} a - \frac{10}{7}\) , \( -1\) , \( -\frac{2}{7} a^{3} + \frac{3}{7} a^{2} + \frac{12}{7} a - \frac{3}{7}\bigr] \) |
${y}^2+\left(-\frac{2}{7}a^{3}+\frac{3}{7}a^{2}+\frac{12}{7}a-\frac{10}{7}\right){x}{y}+\left(-\frac{2}{7}a^{3}+\frac{3}{7}a^{2}+\frac{12}{7}a-\frac{10}{7}\right){y}={x}^{3}+\left(\frac{2}{7}a^{3}-\frac{3}{7}a^{2}-\frac{12}{7}a+\frac{3}{7}\right){x}^{2}-{x}-\frac{2}{7}a^{3}+\frac{3}{7}a^{2}+\frac{12}{7}a-\frac{3}{7}$ |
| 36.1-a4 |
36.1-a |
$4$ |
$10$ |
\(\Q(\sqrt{3}, \sqrt{5})\) |
$4$ |
$[4, 0]$ |
36.1 |
\( 2^{2} \cdot 3^{2} \) |
\( 2^{20} \cdot 3^{40} \) |
$8.39127$ |
$(-2/7a^3+3/7a^2+19/7a-3/7), (-2/7a^3+3/7a^2+19/7a-10/7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 5$ |
2B, 5B.1.4[2] |
$25$ |
\( 2^{2} \) |
$1$ |
$3.139930371$ |
1.308304321 |
\( \frac{502270291349}{1889568} \) |
\( \bigl[-\frac{2}{7} a^{3} + \frac{3}{7} a^{2} + \frac{12}{7} a - \frac{10}{7}\) , \( \frac{2}{7} a^{3} - \frac{3}{7} a^{2} - \frac{12}{7} a + \frac{3}{7}\) , \( -\frac{2}{7} a^{3} + \frac{3}{7} a^{2} + \frac{12}{7} a - \frac{10}{7}\) , \( \frac{330}{7} a^{3} - \frac{495}{7} a^{2} - \frac{1980}{7} a - \frac{667}{7}\) , \( \frac{2704}{7} a^{3} - \frac{4056}{7} a^{2} - \frac{16224}{7} a - \frac{3336}{7}\bigr] \) |
${y}^2+\left(-\frac{2}{7}a^{3}+\frac{3}{7}a^{2}+\frac{12}{7}a-\frac{10}{7}\right){x}{y}+\left(-\frac{2}{7}a^{3}+\frac{3}{7}a^{2}+\frac{12}{7}a-\frac{10}{7}\right){y}={x}^{3}+\left(\frac{2}{7}a^{3}-\frac{3}{7}a^{2}-\frac{12}{7}a+\frac{3}{7}\right){x}^{2}+\left(\frac{330}{7}a^{3}-\frac{495}{7}a^{2}-\frac{1980}{7}a-\frac{667}{7}\right){x}+\frac{2704}{7}a^{3}-\frac{4056}{7}a^{2}-\frac{16224}{7}a-\frac{3336}{7}$ |
| 36.1-b1 |
36.1-b |
$4$ |
$10$ |
\(\Q(\sqrt{3}, \sqrt{5})\) |
$4$ |
$[4, 0]$ |
36.1 |
\( 2^{2} \cdot 3^{2} \) |
\( 2^{4} \cdot 3^{8} \) |
$8.39127$ |
$(-2/7a^3+3/7a^2+19/7a-3/7), (-2/7a^3+3/7a^2+19/7a-10/7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 5$ |
2B, 5B.4.1[2] |
$1$ |
\( 2^{2} \) |
$1$ |
$48.99321078$ |
0.816553513 |
\( \frac{131872229}{18} \) |
\( \bigl[-\frac{1}{7} a^{3} + \frac{5}{7} a^{2} + \frac{6}{7} a - \frac{19}{7}\) , \( \frac{2}{7} a^{3} - \frac{3}{7} a^{2} - \frac{12}{7} a + \frac{10}{7}\) , \( -\frac{2}{7} a^{3} + \frac{3}{7} a^{2} + \frac{19}{7} a - \frac{10}{7}\) , \( \frac{22}{7} a^{3} - \frac{33}{7} a^{2} - \frac{132}{7} a - \frac{30}{7}\) , \( 6 a^{3} - 9 a^{2} - 36 a - 11\bigr] \) |
${y}^2+\left(-\frac{1}{7}a^{3}+\frac{5}{7}a^{2}+\frac{6}{7}a-\frac{19}{7}\right){x}{y}+\left(-\frac{2}{7}a^{3}+\frac{3}{7}a^{2}+\frac{19}{7}a-\frac{10}{7}\right){y}={x}^{3}+\left(\frac{2}{7}a^{3}-\frac{3}{7}a^{2}-\frac{12}{7}a+\frac{10}{7}\right){x}^{2}+\left(\frac{22}{7}a^{3}-\frac{33}{7}a^{2}-\frac{132}{7}a-\frac{30}{7}\right){x}+6a^{3}-9a^{2}-36a-11$ |
| 36.1-b2 |
36.1-b |
$4$ |
$10$ |
\(\Q(\sqrt{3}, \sqrt{5})\) |
$4$ |
$[4, 0]$ |
36.1 |
\( 2^{2} \cdot 3^{2} \) |
\( 2^{40} \cdot 3^{20} \) |
$8.39127$ |
$(-2/7a^3+3/7a^2+19/7a-3/7), (-2/7a^3+3/7a^2+19/7a-10/7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 5$ |
2B, 5B.4.1[2] |
$1$ |
\( 2^{2} \) |
$1$ |
$48.99321078$ |
0.816553513 |
\( -\frac{19465109}{248832} \) |
\( \bigl[-\frac{1}{7} a^{3} + \frac{5}{7} a^{2} + \frac{6}{7} a - \frac{19}{7}\) , \( \frac{2}{7} a^{3} - \frac{3}{7} a^{2} - \frac{12}{7} a + \frac{10}{7}\) , \( -\frac{2}{7} a^{3} + \frac{3}{7} a^{2} + \frac{19}{7} a - \frac{10}{7}\) , \( \frac{12}{7} a^{3} - \frac{18}{7} a^{2} - \frac{72}{7} a - \frac{10}{7}\) , \( -\frac{90}{7} a^{3} + \frac{135}{7} a^{2} + \frac{540}{7} a + \frac{89}{7}\bigr] \) |
${y}^2+\left(-\frac{1}{7}a^{3}+\frac{5}{7}a^{2}+\frac{6}{7}a-\frac{19}{7}\right){x}{y}+\left(-\frac{2}{7}a^{3}+\frac{3}{7}a^{2}+\frac{19}{7}a-\frac{10}{7}\right){y}={x}^{3}+\left(\frac{2}{7}a^{3}-\frac{3}{7}a^{2}-\frac{12}{7}a+\frac{10}{7}\right){x}^{2}+\left(\frac{12}{7}a^{3}-\frac{18}{7}a^{2}-\frac{72}{7}a-\frac{10}{7}\right){x}-\frac{90}{7}a^{3}+\frac{135}{7}a^{2}+\frac{540}{7}a+\frac{89}{7}$ |
| 36.1-b3 |
36.1-b |
$4$ |
$10$ |
\(\Q(\sqrt{3}, \sqrt{5})\) |
$4$ |
$[4, 0]$ |
36.1 |
\( 2^{2} \cdot 3^{2} \) |
\( 2^{8} \cdot 3^{4} \) |
$8.39127$ |
$(-2/7a^3+3/7a^2+19/7a-3/7), (-2/7a^3+3/7a^2+19/7a-10/7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 5$ |
2B, 5B.4.1[2] |
$1$ |
\( 2^{2} \) |
$1$ |
$48.99321078$ |
0.816553513 |
\( -\frac{24389}{12} \) |
\( \bigl[-\frac{1}{7} a^{3} + \frac{5}{7} a^{2} + \frac{6}{7} a - \frac{19}{7}\) , \( \frac{2}{7} a^{3} - \frac{3}{7} a^{2} - \frac{12}{7} a + \frac{10}{7}\) , \( -\frac{2}{7} a^{3} + \frac{3}{7} a^{2} + \frac{19}{7} a - \frac{10}{7}\) , \( \frac{2}{7} a^{3} - \frac{3}{7} a^{2} - \frac{12}{7} a + \frac{10}{7}\) , \( \frac{2}{7} a^{3} - \frac{3}{7} a^{2} - \frac{12}{7} a + \frac{3}{7}\bigr] \) |
${y}^2+\left(-\frac{1}{7}a^{3}+\frac{5}{7}a^{2}+\frac{6}{7}a-\frac{19}{7}\right){x}{y}+\left(-\frac{2}{7}a^{3}+\frac{3}{7}a^{2}+\frac{19}{7}a-\frac{10}{7}\right){y}={x}^{3}+\left(\frac{2}{7}a^{3}-\frac{3}{7}a^{2}-\frac{12}{7}a+\frac{10}{7}\right){x}^{2}+\left(\frac{2}{7}a^{3}-\frac{3}{7}a^{2}-\frac{12}{7}a+\frac{10}{7}\right){x}+\frac{2}{7}a^{3}-\frac{3}{7}a^{2}-\frac{12}{7}a+\frac{3}{7}$ |
| 36.1-b4 |
36.1-b |
$4$ |
$10$ |
\(\Q(\sqrt{3}, \sqrt{5})\) |
$4$ |
$[4, 0]$ |
36.1 |
\( 2^{2} \cdot 3^{2} \) |
\( 2^{20} \cdot 3^{40} \) |
$8.39127$ |
$(-2/7a^3+3/7a^2+19/7a-3/7), (-2/7a^3+3/7a^2+19/7a-10/7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 5$ |
2B, 5B.4.1[2] |
$1$ |
\( 2^{2} \) |
$1$ |
$48.99321078$ |
0.816553513 |
\( \frac{502270291349}{1889568} \) |
\( \bigl[-\frac{1}{7} a^{3} + \frac{5}{7} a^{2} + \frac{6}{7} a - \frac{19}{7}\) , \( \frac{2}{7} a^{3} - \frac{3}{7} a^{2} - \frac{12}{7} a + \frac{10}{7}\) , \( -\frac{2}{7} a^{3} + \frac{3}{7} a^{2} + \frac{19}{7} a - \frac{10}{7}\) , \( \frac{332}{7} a^{3} - \frac{498}{7} a^{2} - \frac{1992}{7} a - \frac{650}{7}\) , \( -\frac{3034}{7} a^{3} + \frac{4551}{7} a^{2} + \frac{18204}{7} a + \frac{2841}{7}\bigr] \) |
${y}^2+\left(-\frac{1}{7}a^{3}+\frac{5}{7}a^{2}+\frac{6}{7}a-\frac{19}{7}\right){x}{y}+\left(-\frac{2}{7}a^{3}+\frac{3}{7}a^{2}+\frac{19}{7}a-\frac{10}{7}\right){y}={x}^{3}+\left(\frac{2}{7}a^{3}-\frac{3}{7}a^{2}-\frac{12}{7}a+\frac{10}{7}\right){x}^{2}+\left(\frac{332}{7}a^{3}-\frac{498}{7}a^{2}-\frac{1992}{7}a-\frac{650}{7}\right){x}-\frac{3034}{7}a^{3}+\frac{4551}{7}a^{2}+\frac{18204}{7}a+\frac{2841}{7}$ |
| 44.1-a1 |
44.1-a |
$4$ |
$15$ |
\(\Q(\sqrt{3}, \sqrt{5})\) |
$4$ |
$[4, 0]$ |
44.1 |
\( 2^{2} \cdot 11 \) |
\( - 2^{10} \cdot 11^{15} \) |
$8.60442$ |
$(-a-1), (-2/7a^3+3/7a^2+19/7a-3/7)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3, 5$ |
3B, 5B.4.1[2] |
$1$ |
\( 1 \) |
$1$ |
$81.47538819$ |
1.357923136 |
\( \frac{285812804825123208537052917}{233925897487276456} a^{3} - \frac{63306062689216323449408751}{58481474371819114} a^{2} - \frac{1141392143254916514939191883}{116962948743638228} a - \frac{256560366081684650116632975}{233925897487276456} \) |
\( \bigl[-\frac{3}{7} a^{3} + \frac{8}{7} a^{2} + \frac{18}{7} a - \frac{22}{7}\) , \( \frac{3}{7} a^{3} - \frac{8}{7} a^{2} - \frac{18}{7} a + \frac{36}{7}\) , \( -\frac{2}{7} a^{3} + \frac{3}{7} a^{2} + \frac{12}{7} a - \frac{10}{7}\) , \( -10 a^{3} + 37 a^{2} + 50 a - 212\) , \( \frac{1899}{7} a^{3} - \frac{4434}{7} a^{2} - \frac{12430}{7} a + \frac{20037}{7}\bigr] \) |
${y}^2+\left(-\frac{3}{7}a^{3}+\frac{8}{7}a^{2}+\frac{18}{7}a-\frac{22}{7}\right){x}{y}+\left(-\frac{2}{7}a^{3}+\frac{3}{7}a^{2}+\frac{12}{7}a-\frac{10}{7}\right){y}={x}^{3}+\left(\frac{3}{7}a^{3}-\frac{8}{7}a^{2}-\frac{18}{7}a+\frac{36}{7}\right){x}^{2}+\left(-10a^{3}+37a^{2}+50a-212\right){x}+\frac{1899}{7}a^{3}-\frac{4434}{7}a^{2}-\frac{12430}{7}a+\frac{20037}{7}$ |
| 44.1-a2 |
44.1-a |
$4$ |
$15$ |
\(\Q(\sqrt{3}, \sqrt{5})\) |
$4$ |
$[4, 0]$ |
44.1 |
\( 2^{2} \cdot 11 \) |
\( - 2^{2} \cdot 11^{3} \) |
$8.60442$ |
$(-a-1), (-2/7a^3+3/7a^2+19/7a-3/7)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3, 5$ |
3B, 5B.4.1[2] |
$1$ |
\( 1 \) |
$1$ |
$81.47538819$ |
1.357923136 |
\( \frac{13816789785}{18634} a^{3} + \frac{18545971005}{18634} a^{2} - \frac{34102016955}{18634} a - \frac{2062947636}{9317} \) |
\( \bigl[-\frac{3}{7} a^{3} + \frac{8}{7} a^{2} + \frac{18}{7} a - \frac{22}{7}\) , \( \frac{3}{7} a^{3} - \frac{8}{7} a^{2} - \frac{18}{7} a + \frac{36}{7}\) , \( -\frac{2}{7} a^{3} + \frac{3}{7} a^{2} + \frac{12}{7} a - \frac{10}{7}\) , \( \frac{5}{7} a^{3} - \frac{11}{7} a^{2} - \frac{30}{7} a + \frac{46}{7}\) , \( -\frac{36}{7} a^{3} + \frac{75}{7} a^{2} + \frac{244}{7} a - \frac{313}{7}\bigr] \) |
${y}^2+\left(-\frac{3}{7}a^{3}+\frac{8}{7}a^{2}+\frac{18}{7}a-\frac{22}{7}\right){x}{y}+\left(-\frac{2}{7}a^{3}+\frac{3}{7}a^{2}+\frac{12}{7}a-\frac{10}{7}\right){y}={x}^{3}+\left(\frac{3}{7}a^{3}-\frac{8}{7}a^{2}-\frac{18}{7}a+\frac{36}{7}\right){x}^{2}+\left(\frac{5}{7}a^{3}-\frac{11}{7}a^{2}-\frac{30}{7}a+\frac{46}{7}\right){x}-\frac{36}{7}a^{3}+\frac{75}{7}a^{2}+\frac{244}{7}a-\frac{313}{7}$ |
| 44.1-a3 |
44.1-a |
$4$ |
$15$ |
\(\Q(\sqrt{3}, \sqrt{5})\) |
$4$ |
$[4, 0]$ |
44.1 |
\( 2^{2} \cdot 11 \) |
\( - 2^{30} \cdot 11^{5} \) |
$8.60442$ |
$(-a-1), (-2/7a^3+3/7a^2+19/7a-3/7)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3, 5$ |
3B, 5B.4.1[2] |
$1$ |
\( 1 \) |
$1$ |
$81.47538819$ |
1.357923136 |
\( \frac{85236268337281074069}{5153632} a^{3} + \frac{920609514941745194883}{41229056} a^{2} - \frac{1689111066390391215351}{41229056} a - \frac{203544144721592306217}{41229056} \) |
\( \bigl[-\frac{1}{7} a^{3} + \frac{5}{7} a^{2} - \frac{1}{7} a - \frac{19}{7}\) , \( -\frac{5}{7} a^{3} + \frac{4}{7} a^{2} + \frac{44}{7} a - \frac{18}{7}\) , \( -\frac{2}{7} a^{3} + \frac{3}{7} a^{2} + \frac{12}{7} a - \frac{3}{7}\) , \( \frac{167}{7} a^{3} - \frac{401}{7} a^{2} - \frac{1114}{7} a + \frac{1500}{7}\) , \( -\frac{2430}{7} a^{3} + \frac{5304}{7} a^{2} + \frac{16428}{7} a - \frac{21474}{7}\bigr] \) |
${y}^2+\left(-\frac{1}{7}a^{3}+\frac{5}{7}a^{2}-\frac{1}{7}a-\frac{19}{7}\right){x}{y}+\left(-\frac{2}{7}a^{3}+\frac{3}{7}a^{2}+\frac{12}{7}a-\frac{3}{7}\right){y}={x}^{3}+\left(-\frac{5}{7}a^{3}+\frac{4}{7}a^{2}+\frac{44}{7}a-\frac{18}{7}\right){x}^{2}+\left(\frac{167}{7}a^{3}-\frac{401}{7}a^{2}-\frac{1114}{7}a+\frac{1500}{7}\right){x}-\frac{2430}{7}a^{3}+\frac{5304}{7}a^{2}+\frac{16428}{7}a-\frac{21474}{7}$ |
| 44.1-a4 |
44.1-a |
$4$ |
$15$ |
\(\Q(\sqrt{3}, \sqrt{5})\) |
$4$ |
$[4, 0]$ |
44.1 |
\( 2^{2} \cdot 11 \) |
\( - 2^{6} \cdot 11 \) |
$8.60442$ |
$(-a-1), (-2/7a^3+3/7a^2+19/7a-3/7)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3, 5$ |
3B, 5B.4.1[2] |
$1$ |
\( 1 \) |
$1$ |
$81.47538819$ |
1.357923136 |
\( -\frac{4235861358}{11} a^{3} + \frac{35818738893}{44} a^{2} + \frac{114520174839}{44} a - \frac{148604802039}{44} \) |
\( \bigl[\frac{1}{7} a^{3} + \frac{2}{7} a^{2} - \frac{13}{7} a - \frac{9}{7}\) , \( \frac{1}{7} a^{3} + \frac{2}{7} a^{2} - \frac{13}{7} a - \frac{9}{7}\) , \( 1\) , \( -\frac{6}{7} a^{3} + \frac{9}{7} a^{2} + \frac{1}{7} a + \frac{5}{7}\) , \( -\frac{2}{7} a^{3} + \frac{10}{7} a^{2} - \frac{9}{7} a - \frac{3}{7}\bigr] \) |
${y}^2+\left(\frac{1}{7}a^{3}+\frac{2}{7}a^{2}-\frac{13}{7}a-\frac{9}{7}\right){x}{y}+{y}={x}^{3}+\left(\frac{1}{7}a^{3}+\frac{2}{7}a^{2}-\frac{13}{7}a-\frac{9}{7}\right){x}^{2}+\left(-\frac{6}{7}a^{3}+\frac{9}{7}a^{2}+\frac{1}{7}a+\frac{5}{7}\right){x}-\frac{2}{7}a^{3}+\frac{10}{7}a^{2}-\frac{9}{7}a-\frac{3}{7}$ |
| 44.1-b1 |
44.1-b |
$3$ |
$9$ |
\(\Q(\sqrt{3}, \sqrt{5})\) |
$4$ |
$[4, 0]$ |
44.1 |
\( 2^{2} \cdot 11 \) |
\( - 2^{6} \cdot 11^{3} \) |
$8.60442$ |
$(-a-1), (-2/7a^3+3/7a^2+19/7a-3/7)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3Cs.1.1 |
$1$ |
\( 3^{2} \) |
$1$ |
$102.2824192$ |
1.704706988 |
\( \frac{383931751}{2662} a^{3} - \frac{680040831}{5324} a^{2} - \frac{6131513109}{5324} a - \frac{687465461}{5324} \) |
\( \bigl[-\frac{2}{7} a^{3} + \frac{3}{7} a^{2} + \frac{12}{7} a - \frac{10}{7}\) , \( -\frac{1}{7} a^{3} - \frac{2}{7} a^{2} + \frac{20}{7} a + \frac{16}{7}\) , \( -\frac{1}{7} a^{3} + \frac{5}{7} a^{2} + \frac{6}{7} a - \frac{19}{7}\) , \( -\frac{6}{7} a^{3} + \frac{9}{7} a^{2} + \frac{43}{7} a + \frac{5}{7}\) , \( -\frac{1}{7} a^{3} - \frac{9}{7} a^{2} + \frac{34}{7} a - \frac{5}{7}\bigr] \) |
${y}^2+\left(-\frac{2}{7}a^{3}+\frac{3}{7}a^{2}+\frac{12}{7}a-\frac{10}{7}\right){x}{y}+\left(-\frac{1}{7}a^{3}+\frac{5}{7}a^{2}+\frac{6}{7}a-\frac{19}{7}\right){y}={x}^{3}+\left(-\frac{1}{7}a^{3}-\frac{2}{7}a^{2}+\frac{20}{7}a+\frac{16}{7}\right){x}^{2}+\left(-\frac{6}{7}a^{3}+\frac{9}{7}a^{2}+\frac{43}{7}a+\frac{5}{7}\right){x}-\frac{1}{7}a^{3}-\frac{9}{7}a^{2}+\frac{34}{7}a-\frac{5}{7}$ |
| 44.1-b2 |
44.1-b |
$3$ |
$9$ |
\(\Q(\sqrt{3}, \sqrt{5})\) |
$4$ |
$[4, 0]$ |
44.1 |
\( 2^{2} \cdot 11 \) |
\( - 2^{18} \cdot 11^{9} \) |
$8.60442$ |
$(-a-1), (-2/7a^3+3/7a^2+19/7a-3/7)$ |
0 |
$\Z/9\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1 |
$1$ |
\( 3^{4} \) |
$1$ |
$102.2824192$ |
1.704706988 |
\( \frac{2675528084795508647}{264090141392} a^{3} + \frac{7224458926822120703}{528180282784} a^{2} - \frac{13254997689846187503}{528180282784} a - \frac{1597466261765268145}{528180282784} \) |
\( \bigl[-\frac{2}{7} a^{3} + \frac{3}{7} a^{2} + \frac{12}{7} a - \frac{10}{7}\) , \( -\frac{1}{7} a^{3} - \frac{2}{7} a^{2} + \frac{20}{7} a + \frac{16}{7}\) , \( -\frac{1}{7} a^{3} + \frac{5}{7} a^{2} + \frac{6}{7} a - \frac{19}{7}\) , \( -\frac{46}{7} a^{3} - \frac{36}{7} a^{2} + \frac{143}{7} a + \frac{15}{7}\) , \( \frac{110}{7} a^{3} + \frac{528}{7} a^{2} - \frac{618}{7} a - \frac{87}{7}\bigr] \) |
${y}^2+\left(-\frac{2}{7}a^{3}+\frac{3}{7}a^{2}+\frac{12}{7}a-\frac{10}{7}\right){x}{y}+\left(-\frac{1}{7}a^{3}+\frac{5}{7}a^{2}+\frac{6}{7}a-\frac{19}{7}\right){y}={x}^{3}+\left(-\frac{1}{7}a^{3}-\frac{2}{7}a^{2}+\frac{20}{7}a+\frac{16}{7}\right){x}^{2}+\left(-\frac{46}{7}a^{3}-\frac{36}{7}a^{2}+\frac{143}{7}a+\frac{15}{7}\right){x}+\frac{110}{7}a^{3}+\frac{528}{7}a^{2}-\frac{618}{7}a-\frac{87}{7}$ |
*The rank, regulator and analytic order of Ш are
not known for all curves in the database; curves for which these are
unknown will not appear in searches specifying one of these
quantities.
