| 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 |
$4$ |
$10$ |
\(\Q(\sqrt{5}, \sqrt{6})\) |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$10.72309$ |
$\textsf{none}$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-40$ |
$N(\mathrm{U}(1))$ |
✓ |
|
✓ |
✓ |
|
|
$1$ |
\( 1 \) |
$1$ |
$867.8742824$ |
1.808071421 |
\( \frac{380712960}{19} a^{3} - \frac{571069440}{19} a^{2} - \frac{3426416640}{19} a + 308024640 \) |
\( \bigl[-\frac{2}{19} a^{3} + \frac{3}{19} a^{2} + \frac{37}{19} a - 1\) , \( 0\) , \( -\frac{2}{19} a^{3} + \frac{3}{19} a^{2} + \frac{37}{19} a\) , \( -\frac{34}{19} a^{3} + \frac{89}{19} a^{2} + \frac{401}{19} a - 47\) , \( -\frac{136}{19} a^{3} + \frac{394}{19} a^{2} + \frac{1395}{19} a - 163\bigr] \) |
${y}^2+\left(-\frac{2}{19}a^{3}+\frac{3}{19}a^{2}+\frac{37}{19}a-1\right){x}{y}+\left(-\frac{2}{19}a^{3}+\frac{3}{19}a^{2}+\frac{37}{19}a\right){y}={x}^{3}+\left(-\frac{34}{19}a^{3}+\frac{89}{19}a^{2}+\frac{401}{19}a-47\right){x}-\frac{136}{19}a^{3}+\frac{394}{19}a^{2}+\frac{1395}{19}a-163$ |
| 1.1-a2 |
1.1-a |
$4$ |
$10$ |
\(\Q(\sqrt{5}, \sqrt{6})\) |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$10.72309$ |
$\textsf{none}$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-40$ |
$N(\mathrm{U}(1))$ |
✓ |
|
✓ |
✓ |
|
|
$1$ |
\( 1 \) |
$1$ |
$867.8742824$ |
1.808071421 |
\( -\frac{380712960}{19} a^{3} + \frac{571069440}{19} a^{2} + \frac{3426416640}{19} a + 117668160 \) |
\( \bigl[-\frac{2}{19} a^{3} + \frac{3}{19} a^{2} + \frac{37}{19} a - 1\) , \( 0\) , \( -\frac{2}{19} a^{3} + \frac{3}{19} a^{2} + \frac{37}{19} a\) , \( \frac{36}{19} a^{3} - \frac{16}{19} a^{2} - \frac{514}{19} a - 22\) , \( \frac{138}{19} a^{3} - \frac{17}{19} a^{2} - \frac{1812}{19} a - 75\bigr] \) |
${y}^2+\left(-\frac{2}{19}a^{3}+\frac{3}{19}a^{2}+\frac{37}{19}a-1\right){x}{y}+\left(-\frac{2}{19}a^{3}+\frac{3}{19}a^{2}+\frac{37}{19}a\right){y}={x}^{3}+\left(\frac{36}{19}a^{3}-\frac{16}{19}a^{2}-\frac{514}{19}a-22\right){x}+\frac{138}{19}a^{3}-\frac{17}{19}a^{2}-\frac{1812}{19}a-75$ |
| 1.1-a3 |
1.1-a |
$4$ |
$10$ |
\(\Q(\sqrt{5}, \sqrt{6})\) |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$10.72309$ |
$\textsf{none}$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-40$ |
$N(\mathrm{U}(1))$ |
✓ |
|
✓ |
✓ |
|
|
$1$ |
\( 1 \) |
$1$ |
$867.8742824$ |
1.808071421 |
\( -\frac{380712960}{19} a^{3} + \frac{571069440}{19} a^{2} + \frac{3426416640}{19} a + 117668160 \) |
\( \bigl[-\frac{2}{19} a^{3} + \frac{3}{19} a^{2} + \frac{37}{19} a - 1\) , \( 0\) , \( -\frac{2}{19} a^{3} + \frac{3}{19} a^{2} + \frac{37}{19} a\) , \( \frac{6}{19} a^{3} - \frac{47}{19} a^{2} + \frac{117}{19} a - 9\) , \( \frac{60}{19} a^{3} - \frac{280}{19} a^{2} + \frac{11}{19} a + 26\bigr] \) |
${y}^2+\left(-\frac{2}{19}a^{3}+\frac{3}{19}a^{2}+\frac{37}{19}a-1\right){x}{y}+\left(-\frac{2}{19}a^{3}+\frac{3}{19}a^{2}+\frac{37}{19}a\right){y}={x}^{3}+\left(\frac{6}{19}a^{3}-\frac{47}{19}a^{2}+\frac{117}{19}a-9\right){x}+\frac{60}{19}a^{3}-\frac{280}{19}a^{2}+\frac{11}{19}a+26$ |
| 1.1-a4 |
1.1-a |
$4$ |
$10$ |
\(\Q(\sqrt{5}, \sqrt{6})\) |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$10.72309$ |
$\textsf{none}$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-40$ |
$N(\mathrm{U}(1))$ |
✓ |
|
✓ |
✓ |
|
|
$1$ |
\( 1 \) |
$1$ |
$867.8742824$ |
1.808071421 |
\( \frac{380712960}{19} a^{3} - \frac{571069440}{19} a^{2} - \frac{3426416640}{19} a + 308024640 \) |
\( \bigl[-\frac{2}{19} a^{3} + \frac{3}{19} a^{2} + \frac{37}{19} a - 1\) , \( 0\) , \( -\frac{2}{19} a^{3} + \frac{3}{19} a^{2} + \frac{37}{19} a\) , \( -\frac{4}{19} a^{3} - \frac{32}{19} a^{2} - \frac{78}{19} a - 4\) , \( -\frac{58}{19} a^{3} - \frac{103}{19} a^{2} + \frac{332}{19} a + 16\bigr] \) |
${y}^2+\left(-\frac{2}{19}a^{3}+\frac{3}{19}a^{2}+\frac{37}{19}a-1\right){x}{y}+\left(-\frac{2}{19}a^{3}+\frac{3}{19}a^{2}+\frac{37}{19}a\right){y}={x}^{3}+\left(-\frac{4}{19}a^{3}-\frac{32}{19}a^{2}-\frac{78}{19}a-4\right){x}-\frac{58}{19}a^{3}-\frac{103}{19}a^{2}+\frac{332}{19}a+16$ |
| 1.1-b1 |
1.1-b |
$8$ |
$30$ |
\(\Q(\sqrt{5}, \sqrt{6})\) |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$10.72309$ |
$\textsf{none}$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-60$ |
$N(\mathrm{U}(1))$ |
✓ |
|
✓ |
✓ |
|
|
$1$ |
\( 1 \) |
$1$ |
$558.1508429$ |
1.162814256 |
\( -\frac{33109966890}{19} a^{3} + \frac{49664950335}{19} a^{2} + \frac{297989702010}{19} a + 10231546590 \) |
\( \bigl[-\frac{1}{19} a^{3} + \frac{11}{19} a^{2} - \frac{10}{19} a - 4\) , \( -\frac{3}{19} a^{3} + \frac{14}{19} a^{2} + \frac{27}{19} a - 6\) , \( -\frac{3}{19} a^{3} + \frac{14}{19} a^{2} + \frac{27}{19} a - 5\) , \( 5 a^{3} - 28 a^{2} + 18 a + 29\) , \( -\frac{643}{19} a^{3} + \frac{3292}{19} a^{2} - \frac{1623}{19} a - 217\bigr] \) |
${y}^2+\left(-\frac{1}{19}a^{3}+\frac{11}{19}a^{2}-\frac{10}{19}a-4\right){x}{y}+\left(-\frac{3}{19}a^{3}+\frac{14}{19}a^{2}+\frac{27}{19}a-5\right){y}={x}^{3}+\left(-\frac{3}{19}a^{3}+\frac{14}{19}a^{2}+\frac{27}{19}a-6\right){x}^{2}+\left(5a^{3}-28a^{2}+18a+29\right){x}-\frac{643}{19}a^{3}+\frac{3292}{19}a^{2}-\frac{1623}{19}a-217$ |
| 1.1-b2 |
1.1-b |
$8$ |
$30$ |
\(\Q(\sqrt{5}, \sqrt{6})\) |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$10.72309$ |
$\textsf{none}$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-60$ |
$N(\mathrm{U}(1))$ |
✓ |
|
✓ |
✓ |
|
|
$1$ |
\( 1 \) |
$1$ |
$558.1508429$ |
1.162814256 |
\( -\frac{33109966890}{19} a^{3} + \frac{49664950335}{19} a^{2} + \frac{297989702010}{19} a + 10231546590 \) |
\( \bigl[-\frac{1}{19} a^{3} + \frac{11}{19} a^{2} - \frac{10}{19} a - 4\) , \( -\frac{3}{19} a^{3} - \frac{5}{19} a^{2} + \frac{46}{19} a + 1\) , \( -\frac{3}{19} a^{3} + \frac{14}{19} a^{2} + \frac{27}{19} a - 5\) , \( \frac{260}{19} a^{3} + \frac{9}{19} a^{2} - \frac{3499}{19} a - 179\) , \( -\frac{1716}{19} a^{3} + \frac{256}{19} a^{2} + \frac{22873}{19} a + 958\bigr] \) |
${y}^2+\left(-\frac{1}{19}a^{3}+\frac{11}{19}a^{2}-\frac{10}{19}a-4\right){x}{y}+\left(-\frac{3}{19}a^{3}+\frac{14}{19}a^{2}+\frac{27}{19}a-5\right){y}={x}^{3}+\left(-\frac{3}{19}a^{3}-\frac{5}{19}a^{2}+\frac{46}{19}a+1\right){x}^{2}+\left(\frac{260}{19}a^{3}+\frac{9}{19}a^{2}-\frac{3499}{19}a-179\right){x}-\frac{1716}{19}a^{3}+\frac{256}{19}a^{2}+\frac{22873}{19}a+958$ |
| 1.1-b3 |
1.1-b |
$8$ |
$30$ |
\(\Q(\sqrt{5}, \sqrt{6})\) |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$10.72309$ |
$\textsf{none}$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-15$ |
$N(\mathrm{U}(1))$ |
✓ |
|
✓ |
✓ |
|
|
$1$ |
\( 1 \) |
$1$ |
$558.1508429$ |
1.162814256 |
\( \frac{171990}{19} a^{3} - \frac{257985}{19} a^{2} - \frac{1547910}{19} a - 52515 \) |
\( \bigl[-\frac{1}{19} a^{3} + \frac{11}{19} a^{2} + \frac{9}{19} a - 3\) , \( \frac{1}{19} a^{3} + \frac{8}{19} a^{2} - \frac{28}{19} a - 4\) , \( -\frac{4}{19} a^{3} + \frac{6}{19} a^{2} + \frac{55}{19} a - 2\) , \( \frac{115}{19} a^{3} + \frac{8}{19} a^{2} - \frac{1548}{19} a - 70\) , \( -\frac{854}{19} a^{3} + \frac{160}{19} a^{2} + \frac{11372}{19} a + 462\bigr] \) |
${y}^2+\left(-\frac{1}{19}a^{3}+\frac{11}{19}a^{2}+\frac{9}{19}a-3\right){x}{y}+\left(-\frac{4}{19}a^{3}+\frac{6}{19}a^{2}+\frac{55}{19}a-2\right){y}={x}^{3}+\left(\frac{1}{19}a^{3}+\frac{8}{19}a^{2}-\frac{28}{19}a-4\right){x}^{2}+\left(\frac{115}{19}a^{3}+\frac{8}{19}a^{2}-\frac{1548}{19}a-70\right){x}-\frac{854}{19}a^{3}+\frac{160}{19}a^{2}+\frac{11372}{19}a+462$ |
| 1.1-b4 |
1.1-b |
$8$ |
$30$ |
\(\Q(\sqrt{5}, \sqrt{6})\) |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$10.72309$ |
$\textsf{none}$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-15$ |
$N(\mathrm{U}(1))$ |
✓ |
|
✓ |
✓ |
|
|
$1$ |
\( 1 \) |
$1$ |
$558.1508429$ |
1.162814256 |
\( -\frac{171990}{19} a^{3} + \frac{257985}{19} a^{2} + \frac{1547910}{19} a - 138510 \) |
\( \bigl[\frac{1}{19} a^{3} + \frac{8}{19} a^{2} - \frac{28}{19} a - 2\) , \( -\frac{1}{19} a^{3} + \frac{11}{19} a^{2} + \frac{9}{19} a - 5\) , \( -\frac{4}{19} a^{3} + \frac{6}{19} a^{2} + \frac{55}{19} a - 1\) , \( -\frac{126}{19} a^{3} + \frac{360}{19} a^{2} + \frac{1305}{19} a - 142\) , \( \frac{854}{19} a^{3} - \frac{2402}{19} a^{2} - \frac{9130}{19} a + 1024\bigr] \) |
${y}^2+\left(\frac{1}{19}a^{3}+\frac{8}{19}a^{2}-\frac{28}{19}a-2\right){x}{y}+\left(-\frac{4}{19}a^{3}+\frac{6}{19}a^{2}+\frac{55}{19}a-1\right){y}={x}^{3}+\left(-\frac{1}{19}a^{3}+\frac{11}{19}a^{2}+\frac{9}{19}a-5\right){x}^{2}+\left(-\frac{126}{19}a^{3}+\frac{360}{19}a^{2}+\frac{1305}{19}a-142\right){x}+\frac{854}{19}a^{3}-\frac{2402}{19}a^{2}-\frac{9130}{19}a+1024$ |
| 1.1-b5 |
1.1-b |
$8$ |
$30$ |
\(\Q(\sqrt{5}, \sqrt{6})\) |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$10.72309$ |
$\textsf{none}$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-15$ |
$N(\mathrm{U}(1))$ |
✓ |
|
✓ |
✓ |
|
|
$1$ |
\( 1 \) |
$1$ |
$558.1508429$ |
1.162814256 |
\( -\frac{171990}{19} a^{3} + \frac{257985}{19} a^{2} + \frac{1547910}{19} a - 138510 \) |
\( \bigl[\frac{1}{19} a^{3} + \frac{8}{19} a^{2} - \frac{28}{19} a - 2\) , \( \frac{3}{19} a^{3} + \frac{5}{19} a^{2} - \frac{65}{19} a - 3\) , \( -\frac{3}{19} a^{3} + \frac{14}{19} a^{2} + \frac{27}{19} a - 4\) , \( -\frac{63}{19} a^{3} - \frac{48}{19} a^{2} + \frac{282}{19} a + 11\) , \( \frac{236}{19} a^{3} + \frac{596}{19} a^{2} - \frac{1193}{19} a - 72\bigr] \) |
${y}^2+\left(\frac{1}{19}a^{3}+\frac{8}{19}a^{2}-\frac{28}{19}a-2\right){x}{y}+\left(-\frac{3}{19}a^{3}+\frac{14}{19}a^{2}+\frac{27}{19}a-4\right){y}={x}^{3}+\left(\frac{3}{19}a^{3}+\frac{5}{19}a^{2}-\frac{65}{19}a-3\right){x}^{2}+\left(-\frac{63}{19}a^{3}-\frac{48}{19}a^{2}+\frac{282}{19}a+11\right){x}+\frac{236}{19}a^{3}+\frac{596}{19}a^{2}-\frac{1193}{19}a-72$ |
| 1.1-b6 |
1.1-b |
$8$ |
$30$ |
\(\Q(\sqrt{5}, \sqrt{6})\) |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$10.72309$ |
$\textsf{none}$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-15$ |
$N(\mathrm{U}(1))$ |
✓ |
|
✓ |
✓ |
|
|
$1$ |
\( 1 \) |
$1$ |
$558.1508429$ |
1.162814256 |
\( \frac{171990}{19} a^{3} - \frac{257985}{19} a^{2} - \frac{1547910}{19} a - 52515 \) |
\( \bigl[\frac{1}{19} a^{3} + \frac{8}{19} a^{2} - \frac{28}{19} a - 2\) , \( \frac{3}{19} a^{3} + \frac{5}{19} a^{2} - \frac{65}{19} a - 3\) , \( -\frac{3}{19} a^{3} + \frac{14}{19} a^{2} + \frac{27}{19} a - 5\) , \( \frac{20}{19} a^{3} - \frac{49}{19} a^{2} - \frac{332}{19} a + 40\) , \( -\frac{146}{19} a^{3} + \frac{447}{19} a^{2} + \frac{1371}{19} a - 167\bigr] \) |
${y}^2+\left(\frac{1}{19}a^{3}+\frac{8}{19}a^{2}-\frac{28}{19}a-2\right){x}{y}+\left(-\frac{3}{19}a^{3}+\frac{14}{19}a^{2}+\frac{27}{19}a-5\right){y}={x}^{3}+\left(\frac{3}{19}a^{3}+\frac{5}{19}a^{2}-\frac{65}{19}a-3\right){x}^{2}+\left(\frac{20}{19}a^{3}-\frac{49}{19}a^{2}-\frac{332}{19}a+40\right){x}-\frac{146}{19}a^{3}+\frac{447}{19}a^{2}+\frac{1371}{19}a-167$ |
| 1.1-b7 |
1.1-b |
$8$ |
$30$ |
\(\Q(\sqrt{5}, \sqrt{6})\) |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$10.72309$ |
$\textsf{none}$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-60$ |
$N(\mathrm{U}(1))$ |
✓ |
|
✓ |
✓ |
|
|
$1$ |
\( 1 \) |
$1$ |
$558.1508429$ |
1.162814256 |
\( \frac{33109966890}{19} a^{3} - \frac{49664950335}{19} a^{2} - \frac{297989702010}{19} a + 26786530035 \) |
\( \bigl[-\frac{3}{19} a^{3} + \frac{14}{19} a^{2} + \frac{27}{19} a - 4\) , \( \frac{1}{19} a^{3} + \frac{8}{19} a^{2} - \frac{9}{19} a - 2\) , \( -\frac{2}{19} a^{3} + \frac{3}{19} a^{2} + \frac{37}{19} a - 1\) , \( -5 a^{3} - 12 a^{2} + 23 a + 24\) , \( \frac{544}{19} a^{3} + \frac{1122}{19} a^{2} - \frac{2521}{19} a - 134\bigr] \) |
${y}^2+\left(-\frac{3}{19}a^{3}+\frac{14}{19}a^{2}+\frac{27}{19}a-4\right){x}{y}+\left(-\frac{2}{19}a^{3}+\frac{3}{19}a^{2}+\frac{37}{19}a-1\right){y}={x}^{3}+\left(\frac{1}{19}a^{3}+\frac{8}{19}a^{2}-\frac{9}{19}a-2\right){x}^{2}+\left(-5a^{3}-12a^{2}+23a+24\right){x}+\frac{544}{19}a^{3}+\frac{1122}{19}a^{2}-\frac{2521}{19}a-134$ |
| 1.1-b8 |
1.1-b |
$8$ |
$30$ |
\(\Q(\sqrt{5}, \sqrt{6})\) |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$10.72309$ |
$\textsf{none}$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-60$ |
$N(\mathrm{U}(1))$ |
✓ |
|
✓ |
✓ |
|
|
$1$ |
\( 1 \) |
$1$ |
$558.1508429$ |
1.162814256 |
\( \frac{33109966890}{19} a^{3} - \frac{49664950335}{19} a^{2} - \frac{297989702010}{19} a + 26786530035 \) |
\( \bigl[-\frac{3}{19} a^{3} + \frac{14}{19} a^{2} + \frac{27}{19} a - 4\) , \( \frac{1}{19} a^{3} - \frac{11}{19} a^{2} + \frac{10}{19} a + 5\) , \( -\frac{2}{19} a^{3} + \frac{3}{19} a^{2} + \frac{37}{19} a - 1\) , \( -\frac{260}{19} a^{3} + \frac{770}{19} a^{2} + \frac{2739}{19} a - 335\) , \( \frac{1452}{19} a^{3} - \frac{4116}{19} a^{2} - \frac{15443}{19} a + 1748\bigr] \) |
${y}^2+\left(-\frac{3}{19}a^{3}+\frac{14}{19}a^{2}+\frac{27}{19}a-4\right){x}{y}+\left(-\frac{2}{19}a^{3}+\frac{3}{19}a^{2}+\frac{37}{19}a-1\right){y}={x}^{3}+\left(\frac{1}{19}a^{3}-\frac{11}{19}a^{2}+\frac{10}{19}a+5\right){x}^{2}+\left(-\frac{260}{19}a^{3}+\frac{770}{19}a^{2}+\frac{2739}{19}a-335\right){x}+\frac{1452}{19}a^{3}-\frac{4116}{19}a^{2}-\frac{15443}{19}a+1748$ |
| 1.1-c1 |
1.1-c |
$6$ |
$18$ |
\(\Q(\sqrt{5}, \sqrt{6})\) |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$10.72309$ |
$\textsf{none}$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-72$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
✓ |
✓ |
$3$ |
3B.1.2 |
$9$ |
\( 1 \) |
$1$ |
$31.80953449$ |
0.596428771 |
\( \frac{154184576000}{19} a^{3} - \frac{231276864000}{19} a^{2} - \frac{2852414656000}{19} a + 265929672000 \) |
\( \bigl[-\frac{2}{19} a^{3} + \frac{3}{19} a^{2} + \frac{37}{19} a - 1\) , \( -\frac{2}{19} a^{3} + \frac{3}{19} a^{2} + \frac{37}{19} a\) , \( -\frac{2}{19} a^{3} + \frac{3}{19} a^{2} + \frac{37}{19} a\) , \( -\frac{134}{19} a^{3} + \frac{201}{19} a^{2} + \frac{2479}{19} a - 228\) , \( -\frac{916}{19} a^{3} + \frac{1374}{19} a^{2} + \frac{16946}{19} a - 1580\bigr] \) |
${y}^2+\left(-\frac{2}{19}a^{3}+\frac{3}{19}a^{2}+\frac{37}{19}a-1\right){x}{y}+\left(-\frac{2}{19}a^{3}+\frac{3}{19}a^{2}+\frac{37}{19}a\right){y}={x}^{3}+\left(-\frac{2}{19}a^{3}+\frac{3}{19}a^{2}+\frac{37}{19}a\right){x}^{2}+\left(-\frac{134}{19}a^{3}+\frac{201}{19}a^{2}+\frac{2479}{19}a-228\right){x}-\frac{916}{19}a^{3}+\frac{1374}{19}a^{2}+\frac{16946}{19}a-1580$ |
| 1.1-c2 |
1.1-c |
$6$ |
$18$ |
\(\Q(\sqrt{5}, \sqrt{6})\) |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$10.72309$ |
$\textsf{none}$ |
0 |
$\Z/6\Z$ |
$\textsf{potential}$ |
$-72$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
✓ |
✓ |
$3$ |
3B.1.1 |
$1$ |
\( 1 \) |
$1$ |
$2576.572294$ |
0.596428771 |
\( -\frac{154184576000}{19} a^{3} + \frac{231276864000}{19} a^{2} + \frac{2852414656000}{19} a + 111745096000 \) |
\( \bigl[-\frac{2}{19} a^{3} + \frac{3}{19} a^{2} + \frac{37}{19} a - 1\) , \( -\frac{2}{19} a^{3} + \frac{3}{19} a^{2} + \frac{37}{19} a\) , \( -\frac{2}{19} a^{3} + \frac{3}{19} a^{2} + \frac{37}{19} a\) , \( -\frac{34}{19} a^{3} + \frac{51}{19} a^{2} + \frac{629}{19} a - 58\) , \( 6 a^{3} - 9 a^{2} - 111 a + 195\bigr] \) |
${y}^2+\left(-\frac{2}{19}a^{3}+\frac{3}{19}a^{2}+\frac{37}{19}a-1\right){x}{y}+\left(-\frac{2}{19}a^{3}+\frac{3}{19}a^{2}+\frac{37}{19}a\right){y}={x}^{3}+\left(-\frac{2}{19}a^{3}+\frac{3}{19}a^{2}+\frac{37}{19}a\right){x}^{2}+\left(-\frac{34}{19}a^{3}+\frac{51}{19}a^{2}+\frac{629}{19}a-58\right){x}+6a^{3}-9a^{2}-111a+195$ |
| 1.1-c3 |
1.1-c |
$6$ |
$18$ |
\(\Q(\sqrt{5}, \sqrt{6})\) |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$10.72309$ |
$\textsf{none}$ |
0 |
$\Z/6\Z$ |
$\textsf{potential}$ |
$-8$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
✓ |
✓ |
$3$ |
3Cs.1.1 |
$1$ |
\( 1 \) |
$1$ |
$2576.572294$ |
0.596428771 |
\( 8000 \) |
\( \bigl[-\frac{2}{19} a^{3} + \frac{3}{19} a^{2} + \frac{37}{19} a - 1\) , \( -\frac{2}{19} a^{3} + \frac{3}{19} a^{2} + \frac{37}{19} a\) , \( -\frac{2}{19} a^{3} + \frac{3}{19} a^{2} + \frac{37}{19} a\) , \( -\frac{4}{19} a^{3} + \frac{6}{19} a^{2} + \frac{74}{19} a - 3\) , \( -\frac{2}{19} a^{3} + \frac{3}{19} a^{2} + \frac{37}{19} a - 2\bigr] \) |
${y}^2+\left(-\frac{2}{19}a^{3}+\frac{3}{19}a^{2}+\frac{37}{19}a-1\right){x}{y}+\left(-\frac{2}{19}a^{3}+\frac{3}{19}a^{2}+\frac{37}{19}a\right){y}={x}^{3}+\left(-\frac{2}{19}a^{3}+\frac{3}{19}a^{2}+\frac{37}{19}a\right){x}^{2}+\left(-\frac{4}{19}a^{3}+\frac{6}{19}a^{2}+\frac{74}{19}a-3\right){x}-\frac{2}{19}a^{3}+\frac{3}{19}a^{2}+\frac{37}{19}a-2$ |
| 1.1-c4 |
1.1-c |
$6$ |
$18$ |
\(\Q(\sqrt{5}, \sqrt{6})\) |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$10.72309$ |
$\textsf{none}$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-72$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
✓ |
✓ |
$3$ |
3B.1.2 |
$9$ |
\( 1 \) |
$1$ |
$31.80953449$ |
0.596428771 |
\( -\frac{154184576000}{19} a^{3} + \frac{231276864000}{19} a^{2} + \frac{2852414656000}{19} a + 111745096000 \) |
\( \bigl[-\frac{2}{19} a^{3} + \frac{3}{19} a^{2} + \frac{37}{19} a - 1\) , \( \frac{2}{19} a^{3} - \frac{3}{19} a^{2} - \frac{37}{19} a + 2\) , \( -\frac{2}{19} a^{3} + \frac{3}{19} a^{2} + \frac{37}{19} a\) , \( \frac{136}{19} a^{3} - \frac{204}{19} a^{2} - \frac{2516}{19} a - 93\) , \( \frac{918}{19} a^{3} - \frac{1377}{19} a^{2} - \frac{16983}{19} a - 663\bigr] \) |
${y}^2+\left(-\frac{2}{19}a^{3}+\frac{3}{19}a^{2}+\frac{37}{19}a-1\right){x}{y}+\left(-\frac{2}{19}a^{3}+\frac{3}{19}a^{2}+\frac{37}{19}a\right){y}={x}^{3}+\left(\frac{2}{19}a^{3}-\frac{3}{19}a^{2}-\frac{37}{19}a+2\right){x}^{2}+\left(\frac{136}{19}a^{3}-\frac{204}{19}a^{2}-\frac{2516}{19}a-93\right){x}+\frac{918}{19}a^{3}-\frac{1377}{19}a^{2}-\frac{16983}{19}a-663$ |
| 1.1-c5 |
1.1-c |
$6$ |
$18$ |
\(\Q(\sqrt{5}, \sqrt{6})\) |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$10.72309$ |
$\textsf{none}$ |
0 |
$\Z/6\Z$ |
$\textsf{potential}$ |
$-72$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
✓ |
✓ |
$3$ |
3B.1.1 |
$1$ |
\( 1 \) |
$1$ |
$2576.572294$ |
0.596428771 |
\( \frac{154184576000}{19} a^{3} - \frac{231276864000}{19} a^{2} - \frac{2852414656000}{19} a + 265929672000 \) |
\( \bigl[-\frac{2}{19} a^{3} + \frac{3}{19} a^{2} + \frac{37}{19} a - 1\) , \( \frac{2}{19} a^{3} - \frac{3}{19} a^{2} - \frac{37}{19} a + 2\) , \( -\frac{2}{19} a^{3} + \frac{3}{19} a^{2} + \frac{37}{19} a\) , \( \frac{36}{19} a^{3} - \frac{54}{19} a^{2} - \frac{666}{19} a - 23\) , \( -\frac{112}{19} a^{3} + \frac{168}{19} a^{2} + \frac{2072}{19} a + 82\bigr] \) |
${y}^2+\left(-\frac{2}{19}a^{3}+\frac{3}{19}a^{2}+\frac{37}{19}a-1\right){x}{y}+\left(-\frac{2}{19}a^{3}+\frac{3}{19}a^{2}+\frac{37}{19}a\right){y}={x}^{3}+\left(\frac{2}{19}a^{3}-\frac{3}{19}a^{2}-\frac{37}{19}a+2\right){x}^{2}+\left(\frac{36}{19}a^{3}-\frac{54}{19}a^{2}-\frac{666}{19}a-23\right){x}-\frac{112}{19}a^{3}+\frac{168}{19}a^{2}+\frac{2072}{19}a+82$ |
| 1.1-c6 |
1.1-c |
$6$ |
$18$ |
\(\Q(\sqrt{5}, \sqrt{6})\) |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$10.72309$ |
$\textsf{none}$ |
0 |
$\Z/6\Z$ |
$\textsf{potential}$ |
$-8$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
✓ |
✓ |
$3$ |
3Cs.1.1 |
$1$ |
\( 1 \) |
$1$ |
$2576.572294$ |
0.596428771 |
\( 8000 \) |
\( \bigl[-\frac{2}{19} a^{3} + \frac{3}{19} a^{2} + \frac{37}{19} a - 1\) , \( \frac{2}{19} a^{3} - \frac{3}{19} a^{2} - \frac{37}{19} a + 2\) , \( -\frac{2}{19} a^{3} + \frac{3}{19} a^{2} + \frac{37}{19} a\) , \( \frac{6}{19} a^{3} - \frac{9}{19} a^{2} - \frac{111}{19} a + 2\) , \( \frac{4}{19} a^{3} - \frac{6}{19} a^{2} - \frac{74}{19} a + 1\bigr] \) |
${y}^2+\left(-\frac{2}{19}a^{3}+\frac{3}{19}a^{2}+\frac{37}{19}a-1\right){x}{y}+\left(-\frac{2}{19}a^{3}+\frac{3}{19}a^{2}+\frac{37}{19}a\right){y}={x}^{3}+\left(\frac{2}{19}a^{3}-\frac{3}{19}a^{2}-\frac{37}{19}a+2\right){x}^{2}+\left(\frac{6}{19}a^{3}-\frac{9}{19}a^{2}-\frac{111}{19}a+2\right){x}+\frac{4}{19}a^{3}-\frac{6}{19}a^{2}-\frac{74}{19}a+1$ |
| 5.1-a1 |
5.1-a |
$2$ |
$2$ |
\(\Q(\sqrt{5}, \sqrt{6})\) |
$4$ |
$[4, 0]$ |
5.1 |
\( 5 \) |
\( 5^{4} \) |
$13.11267$ |
$(3/19a^3+5/19a^2-8/19a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$372.0983287$ |
1.550409703 |
\( -\frac{17408512}{475} a^{3} + \frac{26112768}{475} a^{2} + \frac{322057472}{475} a + \frac{2538048}{5} \) |
\( \bigl[-\frac{2}{19} a^{3} + \frac{3}{19} a^{2} + \frac{37}{19} a - 1\) , \( -\frac{3}{19} a^{3} - \frac{5}{19} a^{2} + \frac{46}{19} a + 1\) , \( -\frac{1}{19} a^{3} + \frac{11}{19} a^{2} + \frac{9}{19} a - 3\) , \( -\frac{454}{19} a^{3} + \frac{1270}{19} a^{2} + \frac{4827}{19} a - 535\) , \( -\frac{2934}{19} a^{3} + \frac{8296}{19} a^{2} + \frac{31232}{19} a - 3525\bigr] \) |
${y}^2+\left(-\frac{2}{19}a^{3}+\frac{3}{19}a^{2}+\frac{37}{19}a-1\right){x}{y}+\left(-\frac{1}{19}a^{3}+\frac{11}{19}a^{2}+\frac{9}{19}a-3\right){y}={x}^{3}+\left(-\frac{3}{19}a^{3}-\frac{5}{19}a^{2}+\frac{46}{19}a+1\right){x}^{2}+\left(-\frac{454}{19}a^{3}+\frac{1270}{19}a^{2}+\frac{4827}{19}a-535\right){x}-\frac{2934}{19}a^{3}+\frac{8296}{19}a^{2}+\frac{31232}{19}a-3525$ |
| 5.1-a2 |
5.1-a |
$2$ |
$2$ |
\(\Q(\sqrt{5}, \sqrt{6})\) |
$4$ |
$[4, 0]$ |
5.1 |
\( 5 \) |
\( 5^{8} \) |
$13.11267$ |
$(3/19a^3+5/19a^2-8/19a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
✓ |
|
$2$ |
2B |
$4$ |
\( 2 \) |
$1$ |
$93.02458218$ |
1.550409703 |
\( \frac{426496}{11875} a^{3} - \frac{639744}{11875} a^{2} - \frac{7890176}{11875} a + \frac{59456}{125} \) |
\( \bigl[-\frac{2}{19} a^{3} + \frac{3}{19} a^{2} + \frac{37}{19} a - 1\) , \( \frac{1}{19} a^{3} - \frac{11}{19} a^{2} + \frac{10}{19} a + 5\) , \( \frac{1}{19} a^{3} + \frac{8}{19} a^{2} - \frac{28}{19} a - 2\) , \( -\frac{14}{19} a^{3} - \frac{17}{19} a^{2} + \frac{88}{19} a + 14\) , \( -\frac{32}{19} a^{3} - \frac{104}{19} a^{2} + \frac{174}{19} a + 17\bigr] \) |
${y}^2+\left(-\frac{2}{19}a^{3}+\frac{3}{19}a^{2}+\frac{37}{19}a-1\right){x}{y}+\left(\frac{1}{19}a^{3}+\frac{8}{19}a^{2}-\frac{28}{19}a-2\right){y}={x}^{3}+\left(\frac{1}{19}a^{3}-\frac{11}{19}a^{2}+\frac{10}{19}a+5\right){x}^{2}+\left(-\frac{14}{19}a^{3}-\frac{17}{19}a^{2}+\frac{88}{19}a+14\right){x}-\frac{32}{19}a^{3}-\frac{104}{19}a^{2}+\frac{174}{19}a+17$ |
| 5.1-b1 |
5.1-b |
$2$ |
$2$ |
\(\Q(\sqrt{5}, \sqrt{6})\) |
$4$ |
$[4, 0]$ |
5.1 |
\( 5 \) |
\( 5^{4} \) |
$13.11267$ |
$(3/19a^3+5/19a^2-8/19a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.023808089$ |
$2876.367198$ |
2.282693617 |
\( -\frac{17408512}{475} a^{3} + \frac{26112768}{475} a^{2} + \frac{322057472}{475} a + \frac{2538048}{5} \) |
\( \bigl[-\frac{2}{19} a^{3} + \frac{3}{19} a^{2} + \frac{37}{19} a - 1\) , \( \frac{1}{19} a^{3} - \frac{11}{19} a^{2} + \frac{10}{19} a + 5\) , \( -\frac{1}{19} a^{3} + \frac{11}{19} a^{2} + \frac{9}{19} a - 3\) , \( -\frac{40}{19} a^{3} - \frac{92}{19} a^{2} + \frac{227}{19} a + 19\) , \( \frac{136}{19} a^{3} + \frac{290}{19} a^{2} - \frac{616}{19} a - 29\bigr] \) |
${y}^2+\left(-\frac{2}{19}a^{3}+\frac{3}{19}a^{2}+\frac{37}{19}a-1\right){x}{y}+\left(-\frac{1}{19}a^{3}+\frac{11}{19}a^{2}+\frac{9}{19}a-3\right){y}={x}^{3}+\left(\frac{1}{19}a^{3}-\frac{11}{19}a^{2}+\frac{10}{19}a+5\right){x}^{2}+\left(-\frac{40}{19}a^{3}-\frac{92}{19}a^{2}+\frac{227}{19}a+19\right){x}+\frac{136}{19}a^{3}+\frac{290}{19}a^{2}-\frac{616}{19}a-29$ |
| 5.1-b2 |
5.1-b |
$2$ |
$2$ |
\(\Q(\sqrt{5}, \sqrt{6})\) |
$4$ |
$[4, 0]$ |
5.1 |
\( 5 \) |
\( 5^{8} \) |
$13.11267$ |
$(3/19a^3+5/19a^2-8/19a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.047616179$ |
$719.0917996$ |
2.282693617 |
\( \frac{426496}{11875} a^{3} - \frac{639744}{11875} a^{2} - \frac{7890176}{11875} a + \frac{59456}{125} \) |
\( \bigl[-\frac{2}{19} a^{3} + \frac{3}{19} a^{2} + \frac{37}{19} a - 1\) , \( \frac{1}{19} a^{3} + \frac{8}{19} a^{2} - \frac{9}{19} a - 2\) , \( \frac{1}{19} a^{3} + \frac{8}{19} a^{2} - \frac{28}{19} a - 2\) , \( -\frac{122}{19} a^{3} + \frac{639}{19} a^{2} - \frac{308}{19} a - 40\) , \( -\frac{1060}{19} a^{3} + \frac{5409}{19} a^{2} - \frac{2753}{19} a - 349\bigr] \) |
${y}^2+\left(-\frac{2}{19}a^{3}+\frac{3}{19}a^{2}+\frac{37}{19}a-1\right){x}{y}+\left(\frac{1}{19}a^{3}+\frac{8}{19}a^{2}-\frac{28}{19}a-2\right){y}={x}^{3}+\left(\frac{1}{19}a^{3}+\frac{8}{19}a^{2}-\frac{9}{19}a-2\right){x}^{2}+\left(-\frac{122}{19}a^{3}+\frac{639}{19}a^{2}-\frac{308}{19}a-40\right){x}-\frac{1060}{19}a^{3}+\frac{5409}{19}a^{2}-\frac{2753}{19}a-349$ |
| 5.2-a1 |
5.2-a |
$2$ |
$2$ |
\(\Q(\sqrt{5}, \sqrt{6})\) |
$4$ |
$[4, 0]$ |
5.2 |
\( 5 \) |
\( 5^{8} \) |
$13.11267$ |
$(4/19a^3-6/19a^2-55/19a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
✓ |
|
$2$ |
2B |
$4$ |
\( 2 \) |
$1$ |
$93.02458218$ |
1.550409703 |
\( -\frac{426496}{11875} a^{3} + \frac{639744}{11875} a^{2} + \frac{7890176}{11875} a - \frac{129216}{625} \) |
\( \bigl[-\frac{2}{19} a^{3} + \frac{3}{19} a^{2} + \frac{37}{19} a - 1\) , \( \frac{3}{19} a^{3} + \frac{5}{19} a^{2} - \frac{46}{19} a - 1\) , \( \frac{1}{19} a^{3} + \frac{8}{19} a^{2} - \frac{28}{19} a - 2\) , \( -\frac{28}{19} a^{3} + \frac{80}{19} a^{2} + \frac{271}{19} a - 21\) , \( -\frac{89}{19} a^{3} + \frac{276}{19} a^{2} + \frac{934}{19} a - 120\bigr] \) |
${y}^2+\left(-\frac{2}{19}a^{3}+\frac{3}{19}a^{2}+\frac{37}{19}a-1\right){x}{y}+\left(\frac{1}{19}a^{3}+\frac{8}{19}a^{2}-\frac{28}{19}a-2\right){y}={x}^{3}+\left(\frac{3}{19}a^{3}+\frac{5}{19}a^{2}-\frac{46}{19}a-1\right){x}^{2}+\left(-\frac{28}{19}a^{3}+\frac{80}{19}a^{2}+\frac{271}{19}a-21\right){x}-\frac{89}{19}a^{3}+\frac{276}{19}a^{2}+\frac{934}{19}a-120$ |
| 5.2-a2 |
5.2-a |
$2$ |
$2$ |
\(\Q(\sqrt{5}, \sqrt{6})\) |
$4$ |
$[4, 0]$ |
5.2 |
\( 5 \) |
\( 5^{4} \) |
$13.11267$ |
$(4/19a^3-6/19a^2-55/19a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$372.0983287$ |
1.550409703 |
\( \frac{17408512}{475} a^{3} - \frac{26112768}{475} a^{2} - \frac{322057472}{475} a + \frac{30098752}{25} \) |
\( \bigl[-\frac{2}{19} a^{3} + \frac{3}{19} a^{2} + \frac{37}{19} a - 1\) , \( \frac{3}{19} a^{3} - \frac{14}{19} a^{2} - \frac{27}{19} a + 6\) , \( -\frac{1}{19} a^{3} + \frac{11}{19} a^{2} + \frac{9}{19} a - 3\) , \( \frac{450}{19} a^{3} - \frac{105}{19} a^{2} - \frac{5988}{19} a - 228\) , \( \frac{3381}{19} a^{3} - \frac{597}{19} a^{2} - \frac{44983}{19} a - 1832\bigr] \) |
${y}^2+\left(-\frac{2}{19}a^{3}+\frac{3}{19}a^{2}+\frac{37}{19}a-1\right){x}{y}+\left(-\frac{1}{19}a^{3}+\frac{11}{19}a^{2}+\frac{9}{19}a-3\right){y}={x}^{3}+\left(\frac{3}{19}a^{3}-\frac{14}{19}a^{2}-\frac{27}{19}a+6\right){x}^{2}+\left(\frac{450}{19}a^{3}-\frac{105}{19}a^{2}-\frac{5988}{19}a-228\right){x}+\frac{3381}{19}a^{3}-\frac{597}{19}a^{2}-\frac{44983}{19}a-1832$ |
| 5.2-b1 |
5.2-b |
$2$ |
$2$ |
\(\Q(\sqrt{5}, \sqrt{6})\) |
$4$ |
$[4, 0]$ |
5.2 |
\( 5 \) |
\( 5^{8} \) |
$13.11267$ |
$(4/19a^3-6/19a^2-55/19a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.047616179$ |
$719.0917996$ |
2.282693617 |
\( -\frac{426496}{11875} a^{3} + \frac{639744}{11875} a^{2} + \frac{7890176}{11875} a - \frac{129216}{625} \) |
\( \bigl[-\frac{2}{19} a^{3} + \frac{3}{19} a^{2} + \frac{37}{19} a - 1\) , \( \frac{3}{19} a^{3} - \frac{14}{19} a^{2} - \frac{27}{19} a + 6\) , \( \frac{1}{19} a^{3} + \frac{8}{19} a^{2} - \frac{28}{19} a - 2\) , \( -\frac{320}{19} a^{3} + \frac{24}{19} a^{2} + \frac{4267}{19} a + 197\) , \( -\frac{2845}{19} a^{3} + \frac{439}{19} a^{2} + \frac{37917}{19} a + 1576\bigr] \) |
${y}^2+\left(-\frac{2}{19}a^{3}+\frac{3}{19}a^{2}+\frac{37}{19}a-1\right){x}{y}+\left(\frac{1}{19}a^{3}+\frac{8}{19}a^{2}-\frac{28}{19}a-2\right){y}={x}^{3}+\left(\frac{3}{19}a^{3}-\frac{14}{19}a^{2}-\frac{27}{19}a+6\right){x}^{2}+\left(-\frac{320}{19}a^{3}+\frac{24}{19}a^{2}+\frac{4267}{19}a+197\right){x}-\frac{2845}{19}a^{3}+\frac{439}{19}a^{2}+\frac{37917}{19}a+1576$ |
| 5.2-b2 |
5.2-b |
$2$ |
$2$ |
\(\Q(\sqrt{5}, \sqrt{6})\) |
$4$ |
$[4, 0]$ |
5.2 |
\( 5 \) |
\( 5^{4} \) |
$13.11267$ |
$(4/19a^3-6/19a^2-55/19a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.023808089$ |
$2876.367198$ |
2.282693617 |
\( \frac{17408512}{475} a^{3} - \frac{26112768}{475} a^{2} - \frac{322057472}{475} a + \frac{30098752}{25} \) |
\( \bigl[-\frac{2}{19} a^{3} + \frac{3}{19} a^{2} + \frac{37}{19} a - 1\) , \( -\frac{1}{19} a^{3} - \frac{8}{19} a^{2} + \frac{9}{19} a + 2\) , \( -\frac{1}{19} a^{3} + \frac{11}{19} a^{2} + \frac{9}{19} a - 3\) , \( \frac{32}{19} a^{3} - \frac{181}{19} a^{2} + \frac{130}{19} a + 12\) , \( -\frac{177}{19} a^{3} + \frac{902}{19} a^{2} - \frac{440}{19} a - 59\bigr] \) |
${y}^2+\left(-\frac{2}{19}a^{3}+\frac{3}{19}a^{2}+\frac{37}{19}a-1\right){x}{y}+\left(-\frac{1}{19}a^{3}+\frac{11}{19}a^{2}+\frac{9}{19}a-3\right){y}={x}^{3}+\left(-\frac{1}{19}a^{3}-\frac{8}{19}a^{2}+\frac{9}{19}a+2\right){x}^{2}+\left(\frac{32}{19}a^{3}-\frac{181}{19}a^{2}+\frac{130}{19}a+12\right){x}-\frac{177}{19}a^{3}+\frac{902}{19}a^{2}-\frac{440}{19}a-59$ |
| 9.1-a1 |
9.1-a |
$2$ |
$2$ |
\(\Q(\sqrt{5}, \sqrt{6})\) |
$4$ |
$[4, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{8} \) |
$14.11238$ |
$(5/19a^3+2/19a^2-45/19a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$698.8887966$ |
2.912036652 |
\( \frac{3241792}{9} \) |
\( \bigl[-\frac{1}{19} a^{3} + \frac{11}{19} a^{2} + \frac{9}{19} a - 4\) , \( -\frac{3}{19} a^{3} + \frac{14}{19} a^{2} + \frac{27}{19} a - 5\) , \( -\frac{1}{19} a^{3} + \frac{11}{19} a^{2} + \frac{9}{19} a - 3\) , \( \frac{47}{19} a^{3} - \frac{4}{19} a^{2} - \frac{651}{19} a - 32\) , \( \frac{163}{19} a^{3} - \frac{45}{19} a^{2} - \frac{2246}{19} a - 94\bigr] \) |
${y}^2+\left(-\frac{1}{19}a^{3}+\frac{11}{19}a^{2}+\frac{9}{19}a-4\right){x}{y}+\left(-\frac{1}{19}a^{3}+\frac{11}{19}a^{2}+\frac{9}{19}a-3\right){y}={x}^{3}+\left(-\frac{3}{19}a^{3}+\frac{14}{19}a^{2}+\frac{27}{19}a-5\right){x}^{2}+\left(\frac{47}{19}a^{3}-\frac{4}{19}a^{2}-\frac{651}{19}a-32\right){x}+\frac{163}{19}a^{3}-\frac{45}{19}a^{2}-\frac{2246}{19}a-94$ |
| 9.1-a2 |
9.1-a |
$2$ |
$2$ |
\(\Q(\sqrt{5}, \sqrt{6})\) |
$4$ |
$[4, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{16} \) |
$14.11238$ |
$(5/19a^3+2/19a^2-45/19a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$698.8887966$ |
2.912036652 |
\( \frac{140608}{81} \) |
\( \bigl[\frac{1}{19} a^{3} + \frac{8}{19} a^{2} - \frac{28}{19} a - 3\) , \( \frac{3}{19} a^{3} + \frac{5}{19} a^{2} - \frac{46}{19} a - 3\) , \( \frac{1}{19} a^{3} + \frac{8}{19} a^{2} - \frac{28}{19} a - 2\) , \( -\frac{15}{19} a^{3} + \frac{51}{19} a^{2} + \frac{154}{19} a - 24\) , \( \frac{7}{19} a^{3} - \frac{20}{19} a^{2} - \frac{63}{19} a + 5\bigr] \) |
${y}^2+\left(\frac{1}{19}a^{3}+\frac{8}{19}a^{2}-\frac{28}{19}a-3\right){x}{y}+\left(\frac{1}{19}a^{3}+\frac{8}{19}a^{2}-\frac{28}{19}a-2\right){y}={x}^{3}+\left(\frac{3}{19}a^{3}+\frac{5}{19}a^{2}-\frac{46}{19}a-3\right){x}^{2}+\left(-\frac{15}{19}a^{3}+\frac{51}{19}a^{2}+\frac{154}{19}a-24\right){x}+\frac{7}{19}a^{3}-\frac{20}{19}a^{2}-\frac{63}{19}a+5$ |
| 9.1-b1 |
9.1-b |
$2$ |
$2$ |
\(\Q(\sqrt{5}, \sqrt{6})\) |
$4$ |
$[4, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{8} \) |
$14.11238$ |
$(5/19a^3+2/19a^2-45/19a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$698.8887966$ |
2.912036652 |
\( \frac{3241792}{9} \) |
\( \bigl[-\frac{1}{19} a^{3} + \frac{11}{19} a^{2} + \frac{9}{19} a - 4\) , \( -\frac{1}{19} a^{3} - \frac{8}{19} a^{2} + \frac{9}{19} a + 3\) , \( -\frac{1}{19} a^{3} + \frac{11}{19} a^{2} + \frac{9}{19} a - 3\) , \( \frac{14}{19} a^{3} - \frac{97}{19} a^{2} + \frac{102}{19} a + 4\) , \( \frac{42}{19} a^{3} - \frac{272}{19} a^{2} + \frac{401}{19} a - 4\bigr] \) |
${y}^2+\left(-\frac{1}{19}a^{3}+\frac{11}{19}a^{2}+\frac{9}{19}a-4\right){x}{y}+\left(-\frac{1}{19}a^{3}+\frac{11}{19}a^{2}+\frac{9}{19}a-3\right){y}={x}^{3}+\left(-\frac{1}{19}a^{3}-\frac{8}{19}a^{2}+\frac{9}{19}a+3\right){x}^{2}+\left(\frac{14}{19}a^{3}-\frac{97}{19}a^{2}+\frac{102}{19}a+4\right){x}+\frac{42}{19}a^{3}-\frac{272}{19}a^{2}+\frac{401}{19}a-4$ |
| 9.1-b2 |
9.1-b |
$2$ |
$2$ |
\(\Q(\sqrt{5}, \sqrt{6})\) |
$4$ |
$[4, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{16} \) |
$14.11238$ |
$(5/19a^3+2/19a^2-45/19a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$698.8887966$ |
2.912036652 |
\( \frac{140608}{81} \) |
\( \bigl[\frac{1}{19} a^{3} + \frac{8}{19} a^{2} - \frac{28}{19} a - 3\) , \( \frac{1}{19} a^{3} - \frac{11}{19} a^{2} + \frac{10}{19} a + 3\) , \( \frac{1}{19} a^{3} + \frac{8}{19} a^{2} - \frac{28}{19} a - 2\) , \( -\frac{6}{19} a^{3} - \frac{29}{19} a^{2} + \frac{54}{19} a + 5\) , \( \frac{4}{19} a^{3} - \frac{6}{19} a^{2} - \frac{17}{19} a\bigr] \) |
${y}^2+\left(\frac{1}{19}a^{3}+\frac{8}{19}a^{2}-\frac{28}{19}a-3\right){x}{y}+\left(\frac{1}{19}a^{3}+\frac{8}{19}a^{2}-\frac{28}{19}a-2\right){y}={x}^{3}+\left(\frac{1}{19}a^{3}-\frac{11}{19}a^{2}+\frac{10}{19}a+3\right){x}^{2}+\left(-\frac{6}{19}a^{3}-\frac{29}{19}a^{2}+\frac{54}{19}a+5\right){x}+\frac{4}{19}a^{3}-\frac{6}{19}a^{2}-\frac{17}{19}a$ |
| 16.1-a1 |
16.1-a |
$4$ |
$6$ |
\(\Q(\sqrt{5}, \sqrt{6})\) |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{8} \) |
$15.16473$ |
$(-3/19a^3-5/19a^2+27/19a+2)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-12$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
|
|
$1$ |
\( 3 \) |
$0.033930534$ |
$1252.456616$ |
4.249652223 |
\( 54000 \) |
\( \bigl[-\frac{2}{19} a^{3} + \frac{3}{19} a^{2} + \frac{37}{19} a - 1\) , \( \frac{3}{19} a^{3} + \frac{5}{19} a^{2} - \frac{65}{19} a - 2\) , \( \frac{1}{19} a^{3} + \frac{8}{19} a^{2} - \frac{28}{19} a - 3\) , \( -\frac{80}{19} a^{3} - \frac{108}{19} a^{2} + \frac{397}{19} a + 19\) , \( -\frac{422}{19} a^{3} - \frac{868}{19} a^{2} + \frac{1879}{19} a + 101\bigr] \) |
${y}^2+\left(-\frac{2}{19}a^{3}+\frac{3}{19}a^{2}+\frac{37}{19}a-1\right){x}{y}+\left(\frac{1}{19}a^{3}+\frac{8}{19}a^{2}-\frac{28}{19}a-3\right){y}={x}^{3}+\left(\frac{3}{19}a^{3}+\frac{5}{19}a^{2}-\frac{65}{19}a-2\right){x}^{2}+\left(-\frac{80}{19}a^{3}-\frac{108}{19}a^{2}+\frac{397}{19}a+19\right){x}-\frac{422}{19}a^{3}-\frac{868}{19}a^{2}+\frac{1879}{19}a+101$ |
| 16.1-a2 |
16.1-a |
$4$ |
$6$ |
\(\Q(\sqrt{5}, \sqrt{6})\) |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{8} \) |
$15.16473$ |
$(-3/19a^3-5/19a^2+27/19a+2)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-12$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
|
|
$1$ |
\( 3 \) |
$0.033930534$ |
$1252.456616$ |
4.249652223 |
\( 54000 \) |
\( \bigl[-\frac{2}{19} a^{3} + \frac{3}{19} a^{2} + \frac{37}{19} a - 1\) , \( -\frac{3}{19} a^{3} - \frac{5}{19} a^{2} + \frac{65}{19} a + 2\) , \( \frac{1}{19} a^{3} + \frac{8}{19} a^{2} - \frac{28}{19} a - 3\) , \( -\frac{196}{19} a^{3} + \frac{522}{19} a^{2} + \frac{2087}{19} a - 207\) , \( -\frac{1142}{19} a^{3} + \frac{3214}{19} a^{2} + \frac{12197}{19} a - 1365\bigr] \) |
${y}^2+\left(-\frac{2}{19}a^{3}+\frac{3}{19}a^{2}+\frac{37}{19}a-1\right){x}{y}+\left(\frac{1}{19}a^{3}+\frac{8}{19}a^{2}-\frac{28}{19}a-3\right){y}={x}^{3}+\left(-\frac{3}{19}a^{3}-\frac{5}{19}a^{2}+\frac{65}{19}a+2\right){x}^{2}+\left(-\frac{196}{19}a^{3}+\frac{522}{19}a^{2}+\frac{2087}{19}a-207\right){x}-\frac{1142}{19}a^{3}+\frac{3214}{19}a^{2}+\frac{12197}{19}a-1365$ |
| 16.1-a3 |
16.1-a |
$4$ |
$6$ |
\(\Q(\sqrt{5}, \sqrt{6})\) |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{16} \) |
$15.16473$ |
$(-3/19a^3-5/19a^2+27/19a+2)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-3$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$2$ |
2B |
$1$ |
\( 3 \) |
$0.135722137$ |
$313.1141542$ |
4.249652223 |
\( 0 \) |
\( \bigl[0\) , \( \frac{3}{19} a^{3} + \frac{5}{19} a^{2} - \frac{65}{19} a - 2\) , \( 0\) , \( -\frac{12}{19} a^{3} + \frac{18}{19} a^{2} + \frac{108}{19} a + 4\) , \( -\frac{146}{19} a^{3} + \frac{770}{19} a^{2} - \frac{472}{19} a - 53\bigr] \) |
${y}^2={x}^{3}+\left(\frac{3}{19}a^{3}+\frac{5}{19}a^{2}-\frac{65}{19}a-2\right){x}^{2}+\left(-\frac{12}{19}a^{3}+\frac{18}{19}a^{2}+\frac{108}{19}a+4\right){x}-\frac{146}{19}a^{3}+\frac{770}{19}a^{2}-\frac{472}{19}a-53$ |
| 16.1-a4 |
16.1-a |
$4$ |
$6$ |
\(\Q(\sqrt{5}, \sqrt{6})\) |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{16} \) |
$15.16473$ |
$(-3/19a^3-5/19a^2+27/19a+2)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-3$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$2$ |
2B |
$1$ |
\( 3 \) |
$0.135722137$ |
$313.1141542$ |
4.249652223 |
\( 0 \) |
\( \bigl[0\) , \( \frac{3}{19} a^{3} + \frac{5}{19} a^{2} - \frac{65}{19} a - 2\) , \( 0\) , \( -\frac{12}{19} a^{3} + \frac{18}{19} a^{2} + \frac{108}{19} a + 4\) , \( \frac{154}{19} a^{3} + \frac{320}{19} a^{2} - \frac{778}{19} a - 41\bigr] \) |
${y}^2={x}^{3}+\left(\frac{3}{19}a^{3}+\frac{5}{19}a^{2}-\frac{65}{19}a-2\right){x}^{2}+\left(-\frac{12}{19}a^{3}+\frac{18}{19}a^{2}+\frac{108}{19}a+4\right){x}+\frac{154}{19}a^{3}+\frac{320}{19}a^{2}-\frac{778}{19}a-41$ |
| 20.1-a1 |
20.1-a |
$1$ |
$1$ |
\(\Q(\sqrt{5}, \sqrt{6})\) |
$4$ |
$[4, 0]$ |
20.1 |
\( 2^{2} \cdot 5 \) |
\( - 2^{6} \cdot 5^{3} \) |
$15.59368$ |
$(3/19a^3+5/19a^2-8/19a), (-3/19a^3-5/19a^2+27/19a+2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3Ns |
$1$ |
\( 3 \) |
$0.021023224$ |
$1531.868036$ |
3.220480513 |
\( -\frac{14486688}{475} a^{3} - \frac{118587159}{1900} a^{2} + \frac{53185653}{380} a + \frac{14145543}{100} \) |
\( \bigl[\frac{1}{19} a^{3} + \frac{8}{19} a^{2} - \frac{28}{19} a - 2\) , \( \frac{1}{19} a^{3} + \frac{8}{19} a^{2} - \frac{28}{19} a - 4\) , \( -\frac{3}{19} a^{3} + \frac{14}{19} a^{2} + \frac{27}{19} a - 5\) , \( \frac{91}{19} a^{3} - \frac{469}{19} a^{2} + \frac{245}{19} a + 31\) , \( -\frac{328}{19} a^{3} + \frac{1651}{19} a^{2} - \frac{772}{19} a - 112\bigr] \) |
${y}^2+\left(\frac{1}{19}a^{3}+\frac{8}{19}a^{2}-\frac{28}{19}a-2\right){x}{y}+\left(-\frac{3}{19}a^{3}+\frac{14}{19}a^{2}+\frac{27}{19}a-5\right){y}={x}^{3}+\left(\frac{1}{19}a^{3}+\frac{8}{19}a^{2}-\frac{28}{19}a-4\right){x}^{2}+\left(\frac{91}{19}a^{3}-\frac{469}{19}a^{2}+\frac{245}{19}a+31\right){x}-\frac{328}{19}a^{3}+\frac{1651}{19}a^{2}-\frac{772}{19}a-112$ |
| 20.1-b1 |
20.1-b |
$2$ |
$3$ |
\(\Q(\sqrt{5}, \sqrt{6})\) |
$4$ |
$[4, 0]$ |
20.1 |
\( 2^{2} \cdot 5 \) |
\( 2^{10} \cdot 5^{6} \) |
$15.59368$ |
$(3/19a^3+5/19a^2-8/19a), (-3/19a^3-5/19a^2+27/19a+2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
✓ |
|
$3$ |
3B |
$1$ |
\( 2 \cdot 5 \) |
$0.017063725$ |
$538.3716486$ |
3.062208605 |
\( \frac{6648609843}{9500} a^{3} - \frac{19945829529}{19000} a^{2} - \frac{245998564191}{19000} a - \frac{1927168929}{200} \) |
\( \bigl[-\frac{1}{19} a^{3} + \frac{11}{19} a^{2} + \frac{9}{19} a - 3\) , \( -\frac{1}{19} a^{3} - \frac{8}{19} a^{2} + \frac{28}{19} a + 2\) , \( 0\) , \( -\frac{231}{19} a^{3} + \frac{1154}{19} a^{2} - \frac{581}{19} a - 70\) , \( -\frac{1420}{19} a^{3} + \frac{7203}{19} a^{2} - \frac{3636}{19} a - 461\bigr] \) |
${y}^2+\left(-\frac{1}{19}a^{3}+\frac{11}{19}a^{2}+\frac{9}{19}a-3\right){x}{y}={x}^{3}+\left(-\frac{1}{19}a^{3}-\frac{8}{19}a^{2}+\frac{28}{19}a+2\right){x}^{2}+\left(-\frac{231}{19}a^{3}+\frac{1154}{19}a^{2}-\frac{581}{19}a-70\right){x}-\frac{1420}{19}a^{3}+\frac{7203}{19}a^{2}-\frac{3636}{19}a-461$ |
| 20.1-b2 |
20.1-b |
$2$ |
$3$ |
\(\Q(\sqrt{5}, \sqrt{6})\) |
$4$ |
$[4, 0]$ |
20.1 |
\( 2^{2} \cdot 5 \) |
\( 2^{30} \cdot 5^{2} \) |
$15.59368$ |
$(3/19a^3+5/19a^2-8/19a), (-3/19a^3-5/19a^2+27/19a+2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
✓ |
|
$3$ |
3B |
$1$ |
\( 2 \cdot 3 \cdot 5 \) |
$0.005687908$ |
$538.3716486$ |
3.062208605 |
\( -\frac{14537151}{12160} a^{3} + \frac{43611453}{24320} a^{2} + \frac{537874587}{24320} a - \frac{10030635}{256} \) |
\( \bigl[\frac{1}{19} a^{3} + \frac{8}{19} a^{2} - \frac{28}{19} a - 2\) , \( \frac{1}{19} a^{3} - \frac{11}{19} a^{2} - \frac{9}{19} a + 3\) , \( \frac{1}{19} a^{3} + \frac{8}{19} a^{2} - \frac{28}{19} a - 2\) , \( \frac{2}{19} a^{3} - \frac{60}{19} a^{2} + \frac{20}{19} a + 6\) , \( \frac{351}{19} a^{3} + \frac{737}{19} a^{2} - \frac{1639}{19} a - 87\bigr] \) |
${y}^2+\left(\frac{1}{19}a^{3}+\frac{8}{19}a^{2}-\frac{28}{19}a-2\right){x}{y}+\left(\frac{1}{19}a^{3}+\frac{8}{19}a^{2}-\frac{28}{19}a-2\right){y}={x}^{3}+\left(\frac{1}{19}a^{3}-\frac{11}{19}a^{2}-\frac{9}{19}a+3\right){x}^{2}+\left(\frac{2}{19}a^{3}-\frac{60}{19}a^{2}+\frac{20}{19}a+6\right){x}+\frac{351}{19}a^{3}+\frac{737}{19}a^{2}-\frac{1639}{19}a-87$ |
| 20.1-c1 |
20.1-c |
$1$ |
$1$ |
\(\Q(\sqrt{5}, \sqrt{6})\) |
$4$ |
$[4, 0]$ |
20.1 |
\( 2^{2} \cdot 5 \) |
\( - 2^{6} \cdot 5^{3} \) |
$15.59368$ |
$(3/19a^3+5/19a^2-8/19a), (-3/19a^3-5/19a^2+27/19a+2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3Ns |
$1$ |
\( 1 \) |
$1$ |
$92.13318633$ |
0.767776552 |
\( -\frac{14486688}{475} a^{3} - \frac{118587159}{1900} a^{2} + \frac{53185653}{380} a + \frac{14145543}{100} \) |
\( \bigl[-\frac{1}{19} a^{3} + \frac{11}{19} a^{2} + \frac{9}{19} a - 3\) , \( -\frac{1}{19} a^{3} + \frac{11}{19} a^{2} + \frac{9}{19} a - 5\) , \( -\frac{4}{19} a^{3} + \frac{6}{19} a^{2} + \frac{55}{19} a - 2\) , \( -\frac{26}{19} a^{3} - \frac{37}{19} a^{2} + \frac{158}{19} a + 4\) , \( -\frac{186}{19} a^{3} - \frac{386}{19} a^{2} + \frac{857}{19} a + 41\bigr] \) |
${y}^2+\left(-\frac{1}{19}a^{3}+\frac{11}{19}a^{2}+\frac{9}{19}a-3\right){x}{y}+\left(-\frac{4}{19}a^{3}+\frac{6}{19}a^{2}+\frac{55}{19}a-2\right){y}={x}^{3}+\left(-\frac{1}{19}a^{3}+\frac{11}{19}a^{2}+\frac{9}{19}a-5\right){x}^{2}+\left(-\frac{26}{19}a^{3}-\frac{37}{19}a^{2}+\frac{158}{19}a+4\right){x}-\frac{186}{19}a^{3}-\frac{386}{19}a^{2}+\frac{857}{19}a+41$ |
| 20.1-d1 |
20.1-d |
$2$ |
$3$ |
\(\Q(\sqrt{5}, \sqrt{6})\) |
$4$ |
$[4, 0]$ |
20.1 |
\( 2^{2} \cdot 5 \) |
\( 2^{30} \cdot 5^{2} \) |
$15.59368$ |
$(3/19a^3+5/19a^2-8/19a), (-3/19a^3-5/19a^2+27/19a+2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
✓ |
|
$3$ |
3B |
$1$ |
\( 2 \cdot 3 \cdot 5 \) |
$1$ |
$13.17815798$ |
3.294539496 |
\( -\frac{14537151}{12160} a^{3} + \frac{43611453}{24320} a^{2} + \frac{537874587}{24320} a - \frac{10030635}{256} \) |
\( \bigl[\frac{1}{19} a^{3} + \frac{8}{19} a^{2} - \frac{28}{19} a - 2\) , \( -\frac{2}{19} a^{3} + \frac{3}{19} a^{2} + \frac{37}{19} a - 2\) , \( \frac{1}{19} a^{3} + \frac{8}{19} a^{2} - \frac{28}{19} a - 2\) , \( -\frac{1404}{19} a^{3} + \frac{3968}{19} a^{2} + \frac{14992}{19} a - 1692\) , \( -\frac{24048}{19} a^{3} + \frac{68087}{19} a^{2} + \frac{256047}{19} a - 28928\bigr] \) |
${y}^2+\left(\frac{1}{19}a^{3}+\frac{8}{19}a^{2}-\frac{28}{19}a-2\right){x}{y}+\left(\frac{1}{19}a^{3}+\frac{8}{19}a^{2}-\frac{28}{19}a-2\right){y}={x}^{3}+\left(-\frac{2}{19}a^{3}+\frac{3}{19}a^{2}+\frac{37}{19}a-2\right){x}^{2}+\left(-\frac{1404}{19}a^{3}+\frac{3968}{19}a^{2}+\frac{14992}{19}a-1692\right){x}-\frac{24048}{19}a^{3}+\frac{68087}{19}a^{2}+\frac{256047}{19}a-28928$ |
| 20.1-d2 |
20.1-d |
$2$ |
$3$ |
\(\Q(\sqrt{5}, \sqrt{6})\) |
$4$ |
$[4, 0]$ |
20.1 |
\( 2^{2} \cdot 5 \) |
\( 2^{10} \cdot 5^{6} \) |
$15.59368$ |
$(3/19a^3+5/19a^2-8/19a), (-3/19a^3-5/19a^2+27/19a+2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
✓ |
|
$3$ |
3B |
$1$ |
\( 2 \cdot 3 \cdot 5 \) |
$1$ |
$13.17815798$ |
3.294539496 |
\( \frac{6648609843}{9500} a^{3} - \frac{19945829529}{19000} a^{2} - \frac{245998564191}{19000} a - \frac{1927168929}{200} \) |
\( \bigl[\frac{1}{19} a^{3} + \frac{8}{19} a^{2} - \frac{28}{19} a - 2\) , \( \frac{1}{19} a^{3} - \frac{11}{19} a^{2} - \frac{9}{19} a + 3\) , \( 0\) , \( -\frac{289}{19} a^{3} - \frac{583}{19} a^{2} + \frac{1290}{19} a + 72\) , \( -\frac{3500}{19} a^{3} - \frac{7233}{19} a^{2} + \frac{16034}{19} a + 860\bigr] \) |
${y}^2+\left(\frac{1}{19}a^{3}+\frac{8}{19}a^{2}-\frac{28}{19}a-2\right){x}{y}={x}^{3}+\left(\frac{1}{19}a^{3}-\frac{11}{19}a^{2}-\frac{9}{19}a+3\right){x}^{2}+\left(-\frac{289}{19}a^{3}-\frac{583}{19}a^{2}+\frac{1290}{19}a+72\right){x}-\frac{3500}{19}a^{3}-\frac{7233}{19}a^{2}+\frac{16034}{19}a+860$ |
| 20.1-e1 |
20.1-e |
$3$ |
$9$ |
\(\Q(\sqrt{5}, \sqrt{6})\) |
$4$ |
$[4, 0]$ |
20.1 |
\( 2^{2} \cdot 5 \) |
\( 2^{2} \cdot 5^{2} \) |
$15.59368$ |
$(3/19a^3+5/19a^2-8/19a), (-3/19a^3-5/19a^2+27/19a+2)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
✓ |
|
$3$ |
3B.1.1 |
$1$ |
\( 2 \) |
$0.421324291$ |
$1270.594306$ |
3.965424047 |
\( -\frac{2849985813237}{95} a^{3} + \frac{8549957439711}{190} a^{2} + \frac{105449475089769}{190} a - \frac{1966397675905}{2} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( \frac{332}{19} a^{3} - \frac{498}{19} a^{2} - \frac{6142}{19} a - 247\) , \( -\frac{3654}{19} a^{3} + \frac{5481}{19} a^{2} + \frac{67599}{19} a + 2653\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(\frac{332}{19}a^{3}-\frac{498}{19}a^{2}-\frac{6142}{19}a-247\right){x}-\frac{3654}{19}a^{3}+\frac{5481}{19}a^{2}+\frac{67599}{19}a+2653$ |
| 20.1-e2 |
20.1-e |
$3$ |
$9$ |
\(\Q(\sqrt{5}, \sqrt{6})\) |
$4$ |
$[4, 0]$ |
20.1 |
\( 2^{2} \cdot 5 \) |
\( 2^{6} \cdot 5^{6} \) |
$15.59368$ |
$(3/19a^3+5/19a^2-8/19a), (-3/19a^3-5/19a^2+27/19a+2)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
✓ |
|
$3$ |
3Cs.1.1 |
$1$ |
\( 2 \cdot 3 \) |
$0.140441430$ |
$1270.594306$ |
3.965424047 |
\( -\frac{1061271}{4750} a^{3} + \frac{3183813}{9500} a^{2} + \frac{39267027}{9500} a - \frac{737387}{100} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( \frac{2}{19} a^{3} - \frac{3}{19} a^{2} - \frac{37}{19} a - 2\) , \( -\frac{10}{19} a^{3} + \frac{15}{19} a^{2} + \frac{185}{19} a + 7\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(\frac{2}{19}a^{3}-\frac{3}{19}a^{2}-\frac{37}{19}a-2\right){x}-\frac{10}{19}a^{3}+\frac{15}{19}a^{2}+\frac{185}{19}a+7$ |
| 20.1-e3 |
20.1-e |
$3$ |
$9$ |
\(\Q(\sqrt{5}, \sqrt{6})\) |
$4$ |
$[4, 0]$ |
20.1 |
\( 2^{2} \cdot 5 \) |
\( 2^{18} \cdot 5^{18} \) |
$15.59368$ |
$(3/19a^3+5/19a^2-8/19a), (-3/19a^3-5/19a^2+27/19a+2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
✓ |
|
$3$ |
3B.1.2 |
$1$ |
\( 2 \cdot 3^{2} \) |
$0.421324291$ |
$15.68634946$ |
3.965424047 |
\( \frac{21355471243}{593750000} a^{3} - \frac{64066413729}{1187500000} a^{2} - \frac{790152435991}{1187500000} a + \frac{15371527471}{12500000} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -\frac{18}{19} a^{3} + \frac{27}{19} a^{2} + \frac{333}{19} a + 13\) , \( 14 a^{3} - 21 a^{2} - 259 a - 193\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(-\frac{18}{19}a^{3}+\frac{27}{19}a^{2}+\frac{333}{19}a+13\right){x}+14a^{3}-21a^{2}-259a-193$ |
| 20.1-f1 |
20.1-f |
$1$ |
$1$ |
\(\Q(\sqrt{5}, \sqrt{6})\) |
$4$ |
$[4, 0]$ |
20.1 |
\( 2^{2} \cdot 5 \) |
\( - 2^{6} \cdot 5^{3} \) |
$15.59368$ |
$(3/19a^3+5/19a^2-8/19a), (-3/19a^3-5/19a^2+27/19a+2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3Ns |
$1$ |
\( 3 \) |
$0.021023224$ |
$1531.868036$ |
3.220480513 |
\( \frac{2039742}{25} a^{3} - \frac{1422279}{100} a^{2} - \frac{21703059}{20} a - \frac{84039093}{100} \) |
\( \bigl[-\frac{1}{19} a^{3} + \frac{11}{19} a^{2} + \frac{9}{19} a - 3\) , \( -\frac{1}{19} a^{3} + \frac{11}{19} a^{2} + \frac{9}{19} a - 5\) , \( -\frac{4}{19} a^{3} + \frac{6}{19} a^{2} + \frac{55}{19} a - 1\) , \( -\frac{259}{19} a^{3} + \frac{759}{19} a^{2} + \frac{2787}{19} a - 317\) , \( \frac{1891}{19} a^{3} - \frac{5316}{19} a^{2} - \frac{20097}{19} a + 2261\bigr] \) |
${y}^2+\left(-\frac{1}{19}a^{3}+\frac{11}{19}a^{2}+\frac{9}{19}a-3\right){x}{y}+\left(-\frac{4}{19}a^{3}+\frac{6}{19}a^{2}+\frac{55}{19}a-1\right){y}={x}^{3}+\left(-\frac{1}{19}a^{3}+\frac{11}{19}a^{2}+\frac{9}{19}a-5\right){x}^{2}+\left(-\frac{259}{19}a^{3}+\frac{759}{19}a^{2}+\frac{2787}{19}a-317\right){x}+\frac{1891}{19}a^{3}-\frac{5316}{19}a^{2}-\frac{20097}{19}a+2261$ |
| 20.1-g1 |
20.1-g |
$1$ |
$1$ |
\(\Q(\sqrt{5}, \sqrt{6})\) |
$4$ |
$[4, 0]$ |
20.1 |
\( 2^{2} \cdot 5 \) |
\( - 2^{6} \cdot 5^{3} \) |
$15.59368$ |
$(3/19a^3+5/19a^2-8/19a), (-3/19a^3-5/19a^2+27/19a+2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3Ns |
$1$ |
\( 1 \) |
$1$ |
$92.13318633$ |
0.767776552 |
\( \frac{2039742}{25} a^{3} - \frac{1422279}{100} a^{2} - \frac{21703059}{20} a - \frac{84039093}{100} \) |
\( \bigl[\frac{1}{19} a^{3} + \frac{8}{19} a^{2} - \frac{28}{19} a - 2\) , \( \frac{1}{19} a^{3} + \frac{8}{19} a^{2} - \frac{28}{19} a - 4\) , \( -\frac{3}{19} a^{3} + \frac{14}{19} a^{2} + \frac{27}{19} a - 4\) , \( \frac{64}{19} a^{3} + \frac{18}{19} a^{2} - \frac{937}{19} a - 43\) , \( \frac{221}{19} a^{3} + \frac{1}{19} a^{2} - \frac{3053}{19} a - 132\bigr] \) |
${y}^2+\left(\frac{1}{19}a^{3}+\frac{8}{19}a^{2}-\frac{28}{19}a-2\right){x}{y}+\left(-\frac{3}{19}a^{3}+\frac{14}{19}a^{2}+\frac{27}{19}a-4\right){y}={x}^{3}+\left(\frac{1}{19}a^{3}+\frac{8}{19}a^{2}-\frac{28}{19}a-4\right){x}^{2}+\left(\frac{64}{19}a^{3}+\frac{18}{19}a^{2}-\frac{937}{19}a-43\right){x}+\frac{221}{19}a^{3}+\frac{1}{19}a^{2}-\frac{3053}{19}a-132$ |
| 20.1-h1 |
20.1-h |
$3$ |
$9$ |
\(\Q(\sqrt{5}, \sqrt{6})\) |
$4$ |
$[4, 0]$ |
20.1 |
\( 2^{2} \cdot 5 \) |
\( 2^{2} \cdot 5^{2} \) |
$15.59368$ |
$(3/19a^3+5/19a^2-8/19a), (-3/19a^3-5/19a^2+27/19a+2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
✓ |
|
$3$ |
3B.1.2 |
$81$ |
\( 2 \) |
$1$ |
$0.466842092$ |
0.630236825 |
\( -\frac{2849985813237}{95} a^{3} + \frac{8549957439711}{190} a^{2} + \frac{105449475089769}{190} a - \frac{1966397675905}{2} \) |
\( \bigl[-\frac{2}{19} a^{3} + \frac{3}{19} a^{2} + \frac{37}{19} a\) , \( 0\) , \( 0\) , \( -\frac{234}{19} a^{3} + \frac{351}{19} a^{2} + \frac{4329}{19} a - 409\) , \( -\frac{2222}{19} a^{3} + \frac{3333}{19} a^{2} + \frac{41107}{19} a - 3849\bigr] \) |
${y}^2+\left(-\frac{2}{19}a^{3}+\frac{3}{19}a^{2}+\frac{37}{19}a\right){x}{y}={x}^{3}+\left(-\frac{234}{19}a^{3}+\frac{351}{19}a^{2}+\frac{4329}{19}a-409\right){x}-\frac{2222}{19}a^{3}+\frac{3333}{19}a^{2}+\frac{41107}{19}a-3849$ |
| 20.1-h2 |
20.1-h |
$3$ |
$9$ |
\(\Q(\sqrt{5}, \sqrt{6})\) |
$4$ |
$[4, 0]$ |
20.1 |
\( 2^{2} \cdot 5 \) |
\( 2^{6} \cdot 5^{6} \) |
$15.59368$ |
$(3/19a^3+5/19a^2-8/19a), (-3/19a^3-5/19a^2+27/19a+2)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
✓ |
|
$3$ |
3Cs.1.1 |
$1$ |
\( 2 \cdot 3^{2} \) |
$1$ |
$37.81420953$ |
0.630236825 |
\( -\frac{1061271}{4750} a^{3} + \frac{3183813}{9500} a^{2} + \frac{39267027}{9500} a - \frac{737387}{100} \) |
\( \bigl[-\frac{2}{19} a^{3} + \frac{3}{19} a^{2} + \frac{37}{19} a\) , \( 0\) , \( 0\) , \( -\frac{4}{19} a^{3} + \frac{6}{19} a^{2} + \frac{74}{19} a - 4\) , \( -\frac{4}{19} a^{3} + \frac{6}{19} a^{2} + \frac{74}{19} a - 6\bigr] \) |
${y}^2+\left(-\frac{2}{19}a^{3}+\frac{3}{19}a^{2}+\frac{37}{19}a\right){x}{y}={x}^{3}+\left(-\frac{4}{19}a^{3}+\frac{6}{19}a^{2}+\frac{74}{19}a-4\right){x}-\frac{4}{19}a^{3}+\frac{6}{19}a^{2}+\frac{74}{19}a-6$ |
| 20.1-h3 |
20.1-h |
$3$ |
$9$ |
\(\Q(\sqrt{5}, \sqrt{6})\) |
$4$ |
$[4, 0]$ |
20.1 |
\( 2^{2} \cdot 5 \) |
\( 2^{18} \cdot 5^{18} \) |
$15.59368$ |
$(3/19a^3+5/19a^2-8/19a), (-3/19a^3-5/19a^2+27/19a+2)$ |
0 |
$\Z/9\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
✓ |
|
$3$ |
3B.1.1 |
$1$ |
\( 2 \cdot 3^{4} \) |
$1$ |
$37.81420953$ |
0.630236825 |
\( \frac{21355471243}{593750000} a^{3} - \frac{64066413729}{1187500000} a^{2} - \frac{790152435991}{1187500000} a + \frac{15371527471}{12500000} \) |
\( \bigl[-\frac{2}{19} a^{3} + \frac{3}{19} a^{2} + \frac{37}{19} a\) , \( 0\) , \( 0\) , \( \frac{16}{19} a^{3} - \frac{24}{19} a^{2} - \frac{296}{19} a + 31\) , \( \frac{4}{19} a^{3} - \frac{6}{19} a^{2} - \frac{74}{19} a + 9\bigr] \) |
${y}^2+\left(-\frac{2}{19}a^{3}+\frac{3}{19}a^{2}+\frac{37}{19}a\right){x}{y}={x}^{3}+\left(\frac{16}{19}a^{3}-\frac{24}{19}a^{2}-\frac{296}{19}a+31\right){x}+\frac{4}{19}a^{3}-\frac{6}{19}a^{2}-\frac{74}{19}a+9$ |
| 20.2-a1 |
20.2-a |
$1$ |
$1$ |
\(\Q(\sqrt{5}, \sqrt{6})\) |
$4$ |
$[4, 0]$ |
20.2 |
\( 2^{2} \cdot 5 \) |
\( - 2^{6} \cdot 5^{3} \) |
$15.59368$ |
$(4/19a^3-6/19a^2-55/19a+3), (-3/19a^3-5/19a^2+27/19a+2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3Ns |
$1$ |
\( 3 \) |
$0.021023224$ |
$1531.868036$ |
3.220480513 |
\( \frac{14486688}{475} a^{3} - \frac{58485483}{380} a^{2} + \frac{145086309}{1900} a + \frac{18850509}{100} \) |
\( \bigl[-\frac{1}{19} a^{3} + \frac{11}{19} a^{2} + \frac{9}{19} a - 3\) , \( -\frac{1}{19} a^{3} + \frac{11}{19} a^{2} + \frac{9}{19} a - 5\) , \( -\frac{1}{19} a^{3} + \frac{11}{19} a^{2} - \frac{10}{19} a - 3\) , \( -\frac{91}{19} a^{3} - \frac{196}{19} a^{2} + \frac{439}{19} a + 23\) , \( \frac{325}{19} a^{3} + \frac{662}{19} a^{2} - \frac{1481}{19} a - 81\bigr] \) |
${y}^2+\left(-\frac{1}{19}a^{3}+\frac{11}{19}a^{2}+\frac{9}{19}a-3\right){x}{y}+\left(-\frac{1}{19}a^{3}+\frac{11}{19}a^{2}-\frac{10}{19}a-3\right){y}={x}^{3}+\left(-\frac{1}{19}a^{3}+\frac{11}{19}a^{2}+\frac{9}{19}a-5\right){x}^{2}+\left(-\frac{91}{19}a^{3}-\frac{196}{19}a^{2}+\frac{439}{19}a+23\right){x}+\frac{325}{19}a^{3}+\frac{662}{19}a^{2}-\frac{1481}{19}a-81$ |
| 20.2-b1 |
20.2-b |
$2$ |
$3$ |
\(\Q(\sqrt{5}, \sqrt{6})\) |
$4$ |
$[4, 0]$ |
20.2 |
\( 2^{2} \cdot 5 \) |
\( 2^{10} \cdot 5^{6} \) |
$15.59368$ |
$(4/19a^3-6/19a^2-55/19a+3), (-3/19a^3-5/19a^2+27/19a+2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
✓ |
|
$3$ |
3B |
$1$ |
\( 2 \cdot 5 \) |
$0.017063725$ |
$538.3716486$ |
3.062208605 |
\( -\frac{6648609843}{9500} a^{3} + \frac{19945829529}{19000} a^{2} + \frac{245998564191}{19000} a - \frac{22933064331}{1000} \) |
\( \bigl[\frac{1}{19} a^{3} + \frac{8}{19} a^{2} - \frac{28}{19} a - 2\) , \( \frac{1}{19} a^{3} - \frac{11}{19} a^{2} - \frac{9}{19} a + 3\) , \( 0\) , \( \frac{231}{19} a^{3} + \frac{461}{19} a^{2} - \frac{1034}{19} a - 52\) , \( \frac{1420}{19} a^{3} + \frac{2943}{19} a^{2} - \frac{6510}{19} a - 348\bigr] \) |
${y}^2+\left(\frac{1}{19}a^{3}+\frac{8}{19}a^{2}-\frac{28}{19}a-2\right){x}{y}={x}^{3}+\left(\frac{1}{19}a^{3}-\frac{11}{19}a^{2}-\frac{9}{19}a+3\right){x}^{2}+\left(\frac{231}{19}a^{3}+\frac{461}{19}a^{2}-\frac{1034}{19}a-52\right){x}+\frac{1420}{19}a^{3}+\frac{2943}{19}a^{2}-\frac{6510}{19}a-348$ |
*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.
