| 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 |
$16$ |
$112$ |
\(\Q(\sqrt{2}, \sqrt{7})\) |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$10.00821$ |
$\textsf{none}$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-448$ |
$N(\mathrm{U}(1))$ |
✓ |
|
✓ |
✓ |
|
|
$16$ |
\( 1 \) |
$1$ |
$42.78422004$ |
1.528007858 |
\( -6136856843335637994418047750 a^{3} - 7141594780626801397104384000 a^{2} + 40784024412413521021760079375 a + 47461262876442602610547041000 \) |
\( \bigl[\frac{1}{3} a^{3} + a^{2} - \frac{5}{3} a - 4\) , \( -\frac{1}{3} a^{3} + \frac{2}{3} a\) , \( \frac{1}{3} a^{3} - \frac{2}{3} a + 1\) , \( -\frac{520}{3} a^{3} + 164 a^{2} + \frac{3938}{3} a - 1514\) , \( -\frac{12935}{3} a^{3} + 5403 a^{2} + \frac{81508}{3} a - 32085\bigr] \) |
${y}^2+\left(\frac{1}{3}a^{3}+a^{2}-\frac{5}{3}a-4\right){x}{y}+\left(\frac{1}{3}a^{3}-\frac{2}{3}a+1\right){y}={x}^{3}+\left(-\frac{1}{3}a^{3}+\frac{2}{3}a\right){x}^{2}+\left(-\frac{520}{3}a^{3}+164a^{2}+\frac{3938}{3}a-1514\right){x}-\frac{12935}{3}a^{3}+5403a^{2}+\frac{81508}{3}a-32085$ |
| 1.1-a2 |
1.1-a |
$16$ |
$112$ |
\(\Q(\sqrt{2}, \sqrt{7})\) |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$10.00821$ |
$\textsf{none}$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-448$ |
$N(\mathrm{U}(1))$ |
✓ |
|
✓ |
✓ |
|
|
$16$ |
\( 1 \) |
$1$ |
$42.78422004$ |
1.528007858 |
\( 2770276778090527644528100875 a^{3} + 7141594780626801397104384000 a^{2} - 3751643694717307172970663750 a - 9671495368571808566288031000 \) |
\( \bigl[\frac{1}{3} a^{3} + a^{2} - \frac{5}{3} a - 4\) , \( -\frac{1}{3} a^{3} + \frac{2}{3} a\) , \( \frac{1}{3} a^{3} - \frac{2}{3} a + 1\) , \( \frac{65}{3} a^{3} - 166 a^{2} + \frac{1013}{3} a - 194\) , \( \frac{8015}{3} a^{3} - 5852 a^{2} - \frac{22252}{3} a + 12350\bigr] \) |
${y}^2+\left(\frac{1}{3}a^{3}+a^{2}-\frac{5}{3}a-4\right){x}{y}+\left(\frac{1}{3}a^{3}-\frac{2}{3}a+1\right){y}={x}^{3}+\left(-\frac{1}{3}a^{3}+\frac{2}{3}a\right){x}^{2}+\left(\frac{65}{3}a^{3}-166a^{2}+\frac{1013}{3}a-194\right){x}+\frac{8015}{3}a^{3}-5852a^{2}-\frac{22252}{3}a+12350$ |
| 1.1-a3 |
1.1-a |
$16$ |
$112$ |
\(\Q(\sqrt{2}, \sqrt{7})\) |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$10.00821$ |
$\textsf{none}$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{potential}$ |
$-28$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
✓ |
✓ |
$2$ |
2Cs |
$4$ |
\( 1 \) |
$1$ |
$684.5475207$ |
1.528007858 |
\( 16581375 \) |
\( \bigl[\frac{1}{3} a^{3} - \frac{5}{3} a + 1\) , \( \frac{1}{3} a^{3} - \frac{5}{3} a\) , \( a^{2} + a - 3\) , \( \frac{22}{3} a^{3} - a^{2} - \frac{242}{3} a - 75\) , \( -\frac{139}{3} a^{3} - 22 a^{2} + \frac{1280}{3} a + 452\bigr] \) |
${y}^2+\left(\frac{1}{3}a^{3}-\frac{5}{3}a+1\right){x}{y}+\left(a^{2}+a-3\right){y}={x}^{3}+\left(\frac{1}{3}a^{3}-\frac{5}{3}a\right){x}^{2}+\left(\frac{22}{3}a^{3}-a^{2}-\frac{242}{3}a-75\right){x}-\frac{139}{3}a^{3}-22a^{2}+\frac{1280}{3}a+452$ |
| 1.1-a4 |
1.1-a |
$16$ |
$112$ |
\(\Q(\sqrt{2}, \sqrt{7})\) |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$10.00821$ |
$\textsf{none}$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{potential}$ |
$-112$ |
$N(\mathrm{U}(1))$ |
✓ |
|
✓ |
✓ |
$2$ |
2Cs |
$16$ |
\( 1 \) |
$1$ |
$171.1368801$ |
1.528007858 |
\( 51954490735875 a^{2} - 70359300958500 \) |
\( \bigl[\frac{1}{3} a^{3} - \frac{5}{3} a + 1\) , \( \frac{1}{3} a^{3} - \frac{5}{3} a\) , \( a^{2} + a - 3\) , \( -\frac{238}{3} a^{3} - 226 a^{2} + \frac{98}{3} a + 225\) , \( \frac{4988}{3} a^{3} + 4373 a^{2} - \frac{5782}{3} a - 5546\bigr] \) |
${y}^2+\left(\frac{1}{3}a^{3}-\frac{5}{3}a+1\right){x}{y}+\left(a^{2}+a-3\right){y}={x}^{3}+\left(\frac{1}{3}a^{3}-\frac{5}{3}a\right){x}^{2}+\left(-\frac{238}{3}a^{3}-226a^{2}+\frac{98}{3}a+225\right){x}+\frac{4988}{3}a^{3}+4373a^{2}-\frac{5782}{3}a-5546$ |
| 1.1-a5 |
1.1-a |
$16$ |
$112$ |
\(\Q(\sqrt{2}, \sqrt{7})\) |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$10.00821$ |
$\textsf{none}$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{potential}$ |
$-112$ |
$N(\mathrm{U}(1))$ |
✓ |
|
✓ |
✓ |
$2$ |
2Cs |
$16$ |
\( 1 \) |
$1$ |
$171.1368801$ |
1.528007858 |
\( -51954490735875 a^{2} + 345276624928500 \) |
\( \bigl[\frac{1}{3} a^{3} - \frac{5}{3} a + 1\) , \( \frac{1}{3} a^{3} - \frac{5}{3} a\) , \( \frac{1}{3} a^{3} + a^{2} - \frac{2}{3} a - 3\) , \( -\frac{601}{3} a^{3} + 224 a^{2} + \frac{4088}{3} a - 1576\) , \( \frac{11375}{3} a^{3} - 4375 a^{2} - \frac{76042}{3} a + 29445\bigr] \) |
${y}^2+\left(\frac{1}{3}a^{3}-\frac{5}{3}a+1\right){x}{y}+\left(\frac{1}{3}a^{3}+a^{2}-\frac{2}{3}a-3\right){y}={x}^{3}+\left(\frac{1}{3}a^{3}-\frac{5}{3}a\right){x}^{2}+\left(-\frac{601}{3}a^{3}+224a^{2}+\frac{4088}{3}a-1576\right){x}+\frac{11375}{3}a^{3}-4375a^{2}-\frac{76042}{3}a+29445$ |
| 1.1-a6 |
1.1-a |
$16$ |
$112$ |
\(\Q(\sqrt{2}, \sqrt{7})\) |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$10.00821$ |
$\textsf{none}$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-448$ |
$N(\mathrm{U}(1))$ |
✓ |
|
✓ |
✓ |
|
|
$16$ |
\( 1 \) |
$1$ |
$42.78422004$ |
1.528007858 |
\( 6136856843335637994418047750 a^{3} - 7141594780626801397104384000 a^{2} - 40784024412413521021760079375 a + 47461262876442602610547041000 \) |
\( \bigl[\frac{1}{3} a^{3} + a^{2} - \frac{5}{3} a - 4\) , \( -\frac{1}{3} a^{3} + \frac{2}{3} a\) , \( a + 1\) , \( \frac{512}{3} a^{3} + 164 a^{2} - \frac{3904}{3} a - 1513\) , \( \frac{13957}{3} a^{3} + 5851 a^{2} - \frac{87611}{3} a - 34461\bigr] \) |
${y}^2+\left(\frac{1}{3}a^{3}+a^{2}-\frac{5}{3}a-4\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-\frac{1}{3}a^{3}+\frac{2}{3}a\right){x}^{2}+\left(\frac{512}{3}a^{3}+164a^{2}-\frac{3904}{3}a-1513\right){x}+\frac{13957}{3}a^{3}+5851a^{2}-\frac{87611}{3}a-34461$ |
| 1.1-a7 |
1.1-a |
$16$ |
$112$ |
\(\Q(\sqrt{2}, \sqrt{7})\) |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$10.00821$ |
$\textsf{none}$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-448$ |
$N(\mathrm{U}(1))$ |
✓ |
|
✓ |
✓ |
|
|
$16$ |
\( 1 \) |
$1$ |
$42.78422004$ |
1.528007858 |
\( -2770276778090527644528100875 a^{3} + 7141594780626801397104384000 a^{2} + 3751643694717307172970663750 a - 9671495368571808566288031000 \) |
\( \bigl[\frac{1}{3} a^{3} + a^{2} - \frac{5}{3} a - 4\) , \( -\frac{1}{3} a^{3} + \frac{2}{3} a\) , \( a + 1\) , \( -\frac{73}{3} a^{3} - 166 a^{2} - \frac{979}{3} a - 193\) , \( -2441 a^{3} - 5404 a^{2} + 6593 a + 11144\bigr] \) |
${y}^2+\left(\frac{1}{3}a^{3}+a^{2}-\frac{5}{3}a-4\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-\frac{1}{3}a^{3}+\frac{2}{3}a\right){x}^{2}+\left(-\frac{73}{3}a^{3}-166a^{2}-\frac{979}{3}a-193\right){x}-2441a^{3}-5404a^{2}+6593a+11144$ |
| 1.1-a8 |
1.1-a |
$16$ |
$112$ |
\(\Q(\sqrt{2}, \sqrt{7})\) |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$10.00821$ |
$\textsf{none}$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-7$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
✓ |
✓ |
|
|
$1$ |
\( 1 \) |
$1$ |
$684.5475207$ |
1.528007858 |
\( -3375 \) |
\( \bigl[\frac{1}{3} a^{3} - \frac{5}{3} a + 1\) , \( \frac{1}{3} a^{3} - \frac{5}{3} a\) , \( \frac{1}{3} a^{3} + a^{2} - \frac{2}{3} a - 3\) , \( -\frac{1}{3} a^{3} - a^{2} + \frac{8}{3} a - 1\) , \( -\frac{2}{3} a^{3} - \frac{5}{3} a + 2\bigr] \) |
${y}^2+\left(\frac{1}{3}a^{3}-\frac{5}{3}a+1\right){x}{y}+\left(\frac{1}{3}a^{3}+a^{2}-\frac{2}{3}a-3\right){y}={x}^{3}+\left(\frac{1}{3}a^{3}-\frac{5}{3}a\right){x}^{2}+\left(-\frac{1}{3}a^{3}-a^{2}+\frac{8}{3}a-1\right){x}-\frac{2}{3}a^{3}-\frac{5}{3}a+2$ |
| 1.1-a9 |
1.1-a |
$16$ |
$112$ |
\(\Q(\sqrt{2}, \sqrt{7})\) |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$10.00821$ |
$\textsf{none}$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{potential}$ |
$-112$ |
$N(\mathrm{U}(1))$ |
✓ |
|
✓ |
✓ |
$2$ |
2Cs |
$16$ |
\( 1 \) |
$1$ |
$171.1368801$ |
1.528007858 |
\( 51954490735875 a^{2} - 70359300958500 \) |
\( \bigl[\frac{1}{3} a^{3} - \frac{5}{3} a + 1\) , \( \frac{1}{3} a^{3} - \frac{5}{3} a\) , \( \frac{1}{3} a^{3} + a^{2} - \frac{2}{3} a - 3\) , \( \frac{239}{3} a^{3} - 226 a^{2} - \frac{112}{3} a + 224\) , \( -1815 a^{3} + 4735 a^{2} + 2236 a - 6155\bigr] \) |
${y}^2+\left(\frac{1}{3}a^{3}-\frac{5}{3}a+1\right){x}{y}+\left(\frac{1}{3}a^{3}+a^{2}-\frac{2}{3}a-3\right){y}={x}^{3}+\left(\frac{1}{3}a^{3}-\frac{5}{3}a\right){x}^{2}+\left(\frac{239}{3}a^{3}-226a^{2}-\frac{112}{3}a+224\right){x}-1815a^{3}+4735a^{2}+2236a-6155$ |
| 1.1-a10 |
1.1-a |
$16$ |
$112$ |
\(\Q(\sqrt{2}, \sqrt{7})\) |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$10.00821$ |
$\textsf{none}$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-448$ |
$N(\mathrm{U}(1))$ |
✓ |
|
✓ |
✓ |
|
|
$64$ |
\( 1 \) |
$1$ |
$10.69605501$ |
1.528007858 |
\( -6136856843335637994418047750 a^{3} - 7141594780626801397104384000 a^{2} + 40784024412413521021760079375 a + 47461262876442602610547041000 \) |
\( \bigl[\frac{1}{3} a^{3} - \frac{5}{3} a + 1\) , \( \frac{1}{3} a^{3} - \frac{5}{3} a\) , \( \frac{1}{3} a^{3} + a^{2} - \frac{2}{3} a - 3\) , \( -172 a^{3} + 164 a^{2} + 1306 a - 1516\) , \( \frac{12416}{3} a^{3} - 5240 a^{2} - \frac{77578}{3} a + 30569\bigr] \) |
${y}^2+\left(\frac{1}{3}a^{3}-\frac{5}{3}a+1\right){x}{y}+\left(\frac{1}{3}a^{3}+a^{2}-\frac{2}{3}a-3\right){y}={x}^{3}+\left(\frac{1}{3}a^{3}-\frac{5}{3}a\right){x}^{2}+\left(-172a^{3}+164a^{2}+1306a-1516\right){x}+\frac{12416}{3}a^{3}-5240a^{2}-\frac{77578}{3}a+30569$ |
| 1.1-a11 |
1.1-a |
$16$ |
$112$ |
\(\Q(\sqrt{2}, \sqrt{7})\) |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$10.00821$ |
$\textsf{none}$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-448$ |
$N(\mathrm{U}(1))$ |
✓ |
|
✓ |
✓ |
|
|
$64$ |
\( 1 \) |
$1$ |
$10.69605501$ |
1.528007858 |
\( 2770276778090527644528100875 a^{3} + 7141594780626801397104384000 a^{2} - 3751643694717307172970663750 a - 9671495368571808566288031000 \) |
\( \bigl[\frac{1}{3} a^{3} - \frac{5}{3} a + 1\) , \( \frac{1}{3} a^{3} - \frac{5}{3} a\) , \( \frac{1}{3} a^{3} + a^{2} - \frac{2}{3} a - 3\) , \( 23 a^{3} - 166 a^{2} + 331 a - 196\) , \( -\frac{7949}{3} a^{3} + 5685 a^{2} + \frac{23257}{3} a - 12546\bigr] \) |
${y}^2+\left(\frac{1}{3}a^{3}-\frac{5}{3}a+1\right){x}{y}+\left(\frac{1}{3}a^{3}+a^{2}-\frac{2}{3}a-3\right){y}={x}^{3}+\left(\frac{1}{3}a^{3}-\frac{5}{3}a\right){x}^{2}+\left(23a^{3}-166a^{2}+331a-196\right){x}-\frac{7949}{3}a^{3}+5685a^{2}+\frac{23257}{3}a-12546$ |
| 1.1-a12 |
1.1-a |
$16$ |
$112$ |
\(\Q(\sqrt{2}, \sqrt{7})\) |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$10.00821$ |
$\textsf{none}$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{potential}$ |
$-28$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
✓ |
✓ |
$2$ |
2Cs |
$4$ |
\( 1 \) |
$1$ |
$684.5475207$ |
1.528007858 |
\( 16581375 \) |
\( \bigl[\frac{1}{3} a^{3} + a^{2} - \frac{5}{3} a - 4\) , \( -\frac{1}{3} a^{3} + \frac{2}{3} a\) , \( a + 1\) , \( \frac{17}{3} a^{3} - a^{2} - \frac{214}{3} a - 73\) , \( \frac{158}{3} a^{3} + 21 a^{2} - \frac{1507}{3} a - 530\bigr] \) |
${y}^2+\left(\frac{1}{3}a^{3}+a^{2}-\frac{5}{3}a-4\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-\frac{1}{3}a^{3}+\frac{2}{3}a\right){x}^{2}+\left(\frac{17}{3}a^{3}-a^{2}-\frac{214}{3}a-73\right){x}+\frac{158}{3}a^{3}+21a^{2}-\frac{1507}{3}a-530$ |
| 1.1-a13 |
1.1-a |
$16$ |
$112$ |
\(\Q(\sqrt{2}, \sqrt{7})\) |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$10.00821$ |
$\textsf{none}$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{potential}$ |
$-112$ |
$N(\mathrm{U}(1))$ |
✓ |
|
✓ |
✓ |
$2$ |
2Cs |
$16$ |
\( 1 \) |
$1$ |
$171.1368801$ |
1.528007858 |
\( -51954490735875 a^{2} + 345276624928500 \) |
\( \bigl[\frac{1}{3} a^{3} + a^{2} - \frac{5}{3} a - 4\) , \( -\frac{1}{3} a^{3} + \frac{2}{3} a\) , \( \frac{1}{3} a^{3} - \frac{2}{3} a + 1\) , \( -\frac{605}{3} a^{3} + 224 a^{2} + \frac{4108}{3} a - 1574\) , \( -3993 a^{3} + 4598 a^{2} + 26714 a - 31021\bigr] \) |
${y}^2+\left(\frac{1}{3}a^{3}+a^{2}-\frac{5}{3}a-4\right){x}{y}+\left(\frac{1}{3}a^{3}-\frac{2}{3}a+1\right){y}={x}^{3}+\left(-\frac{1}{3}a^{3}+\frac{2}{3}a\right){x}^{2}+\left(-\frac{605}{3}a^{3}+224a^{2}+\frac{4108}{3}a-1574\right){x}-3993a^{3}+4598a^{2}+26714a-31021$ |
| 1.1-a14 |
1.1-a |
$16$ |
$112$ |
\(\Q(\sqrt{2}, \sqrt{7})\) |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$10.00821$ |
$\textsf{none}$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-448$ |
$N(\mathrm{U}(1))$ |
✓ |
|
✓ |
✓ |
|
|
$64$ |
\( 1 \) |
$1$ |
$10.69605501$ |
1.528007858 |
\( 6136856843335637994418047750 a^{3} - 7141594780626801397104384000 a^{2} - 40784024412413521021760079375 a + 47461262876442602610547041000 \) |
\( \bigl[\frac{1}{3} a^{3} - \frac{5}{3} a + 1\) , \( \frac{1}{3} a^{3} - \frac{5}{3} a\) , \( a^{2} + a - 3\) , \( \frac{517}{3} a^{3} + 164 a^{2} - \frac{3932}{3} a - 1515\) , \( -4481 a^{3} - 5687 a^{2} + 27898 a + 32943\bigr] \) |
${y}^2+\left(\frac{1}{3}a^{3}-\frac{5}{3}a+1\right){x}{y}+\left(a^{2}+a-3\right){y}={x}^{3}+\left(\frac{1}{3}a^{3}-\frac{5}{3}a\right){x}^{2}+\left(\frac{517}{3}a^{3}+164a^{2}-\frac{3932}{3}a-1515\right){x}-4481a^{3}-5687a^{2}+27898a+32943$ |
| 1.1-a15 |
1.1-a |
$16$ |
$112$ |
\(\Q(\sqrt{2}, \sqrt{7})\) |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$10.00821$ |
$\textsf{none}$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-448$ |
$N(\mathrm{U}(1))$ |
✓ |
|
✓ |
✓ |
|
|
$64$ |
\( 1 \) |
$1$ |
$10.69605501$ |
1.528007858 |
\( -2770276778090527644528100875 a^{3} + 7141594780626801397104384000 a^{2} + 3751643694717307172970663750 a - 9671495368571808566288031000 \) |
\( \bigl[\frac{1}{3} a^{3} - \frac{5}{3} a + 1\) , \( \frac{1}{3} a^{3} - \frac{5}{3} a\) , \( a^{2} + a - 3\) , \( -\frac{68}{3} a^{3} - 166 a^{2} - \frac{1007}{3} a - 195\) , \( \frac{7252}{3} a^{3} + 5238 a^{2} - \frac{20771}{3} a - 11342\bigr] \) |
${y}^2+\left(\frac{1}{3}a^{3}-\frac{5}{3}a+1\right){x}{y}+\left(a^{2}+a-3\right){y}={x}^{3}+\left(\frac{1}{3}a^{3}-\frac{5}{3}a\right){x}^{2}+\left(-\frac{68}{3}a^{3}-166a^{2}-\frac{1007}{3}a-195\right){x}+\frac{7252}{3}a^{3}+5238a^{2}-\frac{20771}{3}a-11342$ |
| 1.1-a16 |
1.1-a |
$16$ |
$112$ |
\(\Q(\sqrt{2}, \sqrt{7})\) |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$10.00821$ |
$\textsf{none}$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-7$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
✓ |
✓ |
|
|
$1$ |
\( 1 \) |
$1$ |
$684.5475207$ |
1.528007858 |
\( -3375 \) |
\( \bigl[\frac{1}{3} a^{3} + a^{2} - \frac{5}{3} a - 4\) , \( -\frac{1}{3} a^{3} + \frac{2}{3} a\) , \( \frac{1}{3} a^{3} - \frac{2}{3} a + 1\) , \( -\frac{5}{3} a^{3} - a^{2} + \frac{28}{3} a + 1\) , \( -\frac{2}{3} a^{3} - 2 a^{2} + \frac{25}{3} a - 3\bigr] \) |
${y}^2+\left(\frac{1}{3}a^{3}+a^{2}-\frac{5}{3}a-4\right){x}{y}+\left(\frac{1}{3}a^{3}-\frac{2}{3}a+1\right){y}={x}^{3}+\left(-\frac{1}{3}a^{3}+\frac{2}{3}a\right){x}^{2}+\left(-\frac{5}{3}a^{3}-a^{2}+\frac{28}{3}a+1\right){x}-\frac{2}{3}a^{3}-2a^{2}+\frac{25}{3}a-3$ |
| 1.1-b1 |
1.1-b |
$16$ |
$112$ |
\(\Q(\sqrt{2}, \sqrt{7})\) |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$10.00821$ |
$\textsf{none}$ |
0 |
$\Z/4\Z$ |
$\textsf{potential}$ |
$-448$ |
$N(\mathrm{U}(1))$ |
✓ |
|
✓ |
✓ |
|
|
$4$ |
\( 1 \) |
$1$ |
$171.1368801$ |
0.382001964 |
\( -6136856843335637994418047750 a^{3} - 7141594780626801397104384000 a^{2} + 40784024412413521021760079375 a + 47461262876442602610547041000 \) |
\( \bigl[\frac{1}{3} a^{3} - \frac{2}{3} a\) , \( 1\) , \( \frac{1}{3} a^{3} - \frac{2}{3} a\) , \( 105 a^{3} + 135 a^{2} - 690 a - 905\) , \( -\frac{4525}{3} a^{3} - 1806 a^{2} + \frac{30065}{3} a + 12004\bigr] \) |
${y}^2+\left(\frac{1}{3}a^{3}-\frac{2}{3}a\right){x}{y}+\left(\frac{1}{3}a^{3}-\frac{2}{3}a\right){y}={x}^{3}+{x}^{2}+\left(105a^{3}+135a^{2}-690a-905\right){x}-\frac{4525}{3}a^{3}-1806a^{2}+\frac{30065}{3}a+12004$ |
| 1.1-b2 |
1.1-b |
$16$ |
$112$ |
\(\Q(\sqrt{2}, \sqrt{7})\) |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$10.00821$ |
$\textsf{none}$ |
0 |
$\Z/4\Z$ |
$\textsf{potential}$ |
$-448$ |
$N(\mathrm{U}(1))$ |
✓ |
|
✓ |
✓ |
|
|
$4$ |
\( 1 \) |
$1$ |
$171.1368801$ |
0.382001964 |
\( 6136856843335637994418047750 a^{3} - 7141594780626801397104384000 a^{2} - 40784024412413521021760079375 a + 47461262876442602610547041000 \) |
\( \bigl[\frac{1}{3} a^{3} - \frac{2}{3} a\) , \( 1\) , \( \frac{1}{3} a^{3} - \frac{2}{3} a\) , \( -105 a^{3} + 135 a^{2} + 690 a - 905\) , \( \frac{4525}{3} a^{3} - 1806 a^{2} - \frac{30065}{3} a + 12004\bigr] \) |
${y}^2+\left(\frac{1}{3}a^{3}-\frac{2}{3}a\right){x}{y}+\left(\frac{1}{3}a^{3}-\frac{2}{3}a\right){y}={x}^{3}+{x}^{2}+\left(-105a^{3}+135a^{2}+690a-905\right){x}+\frac{4525}{3}a^{3}-1806a^{2}-\frac{30065}{3}a+12004$ |
| 1.1-b3 |
1.1-b |
$16$ |
$112$ |
\(\Q(\sqrt{2}, \sqrt{7})\) |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$10.00821$ |
$\textsf{none}$ |
0 |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{potential}$ |
$-112$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
✓ |
✓ |
$2$ |
2Cs |
$4$ |
\( 1 \) |
$1$ |
$684.5475207$ |
0.382001964 |
\( -51954490735875 a^{2} + 345276624928500 \) |
\( \bigl[\frac{1}{3} a^{3} - \frac{2}{3} a\) , \( 1\) , \( \frac{1}{3} a^{3} - \frac{2}{3} a\) , \( 15 a^{2} - 105\) , \( -54 a^{2} + 346\bigr] \) |
${y}^2+\left(\frac{1}{3}a^{3}-\frac{2}{3}a\right){x}{y}+\left(\frac{1}{3}a^{3}-\frac{2}{3}a\right){y}={x}^{3}+{x}^{2}+\left(15a^{2}-105\right){x}-54a^{2}+346$ |
| 1.1-b4 |
1.1-b |
$16$ |
$112$ |
\(\Q(\sqrt{2}, \sqrt{7})\) |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$10.00821$ |
$\textsf{none}$ |
0 |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{potential}$ |
$-28$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
✓ |
✓ |
$2$ |
2Cs |
$4$ |
\( 1 \) |
$1$ |
$684.5475207$ |
0.382001964 |
\( 16581375 \) |
\( \bigl[\frac{1}{3} a^{3} - \frac{2}{3} a\) , \( 1\) , \( \frac{1}{3} a^{3} - \frac{2}{3} a\) , \( -5\) , \( -3 a^{2} + 7\bigr] \) |
${y}^2+\left(\frac{1}{3}a^{3}-\frac{2}{3}a\right){x}{y}+\left(\frac{1}{3}a^{3}-\frac{2}{3}a\right){y}={x}^{3}+{x}^{2}-5{x}-3a^{2}+7$ |
| 1.1-b5 |
1.1-b |
$16$ |
$112$ |
\(\Q(\sqrt{2}, \sqrt{7})\) |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$10.00821$ |
$\textsf{none}$ |
0 |
$\Z/4\Z$ |
$\textsf{potential}$ |
$-7$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
✓ |
✓ |
|
|
$1$ |
\( 1 \) |
$1$ |
$684.5475207$ |
0.382001964 |
\( -3375 \) |
\( \bigl[\frac{1}{3} a^{3} - \frac{2}{3} a\) , \( 1\) , \( \frac{1}{3} a^{3} - \frac{2}{3} a\) , \( 0\) , \( 0\bigr] \) |
${y}^2+\left(\frac{1}{3}a^{3}-\frac{2}{3}a\right){x}{y}+\left(\frac{1}{3}a^{3}-\frac{2}{3}a\right){y}={x}^{3}+{x}^{2}$ |
| 1.1-b6 |
1.1-b |
$16$ |
$112$ |
\(\Q(\sqrt{2}, \sqrt{7})\) |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$10.00821$ |
$\textsf{none}$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{potential}$ |
$-112$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
✓ |
✓ |
$2$ |
2Cs |
$16$ |
\( 1 \) |
$1$ |
$42.78422004$ |
0.382001964 |
\( 51954490735875 a^{2} - 70359300958500 \) |
\( \bigl[\frac{1}{3} a^{3} - \frac{2}{3} a\) , \( 1\) , \( \frac{1}{3} a^{3} - \frac{2}{3} a\) , \( -15 a^{2} + 15\) , \( -84 a^{2} + 116\bigr] \) |
${y}^2+\left(\frac{1}{3}a^{3}-\frac{2}{3}a\right){x}{y}+\left(\frac{1}{3}a^{3}-\frac{2}{3}a\right){y}={x}^{3}+{x}^{2}+\left(-15a^{2}+15\right){x}-84a^{2}+116$ |
| 1.1-b7 |
1.1-b |
$16$ |
$112$ |
\(\Q(\sqrt{2}, \sqrt{7})\) |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$10.00821$ |
$\textsf{none}$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-448$ |
$N(\mathrm{U}(1))$ |
✓ |
|
✓ |
✓ |
|
|
$64$ |
\( 1 \) |
$1$ |
$2.674013753$ |
0.382001964 |
\( -2770276778090527644528100875 a^{3} + 7141594780626801397104384000 a^{2} + 3751643694717307172970663750 a - 9671495368571808566288031000 \) |
\( \bigl[\frac{1}{3} a^{3} - \frac{2}{3} a\) , \( 1\) , \( \frac{1}{3} a^{3} - \frac{2}{3} a\) , \( 50 a^{3} - 135 a^{2} - 85 a + 175\) , \( \frac{2345}{3} a^{3} - 2076 a^{2} - \frac{3295}{3} a + 2794\bigr] \) |
${y}^2+\left(\frac{1}{3}a^{3}-\frac{2}{3}a\right){x}{y}+\left(\frac{1}{3}a^{3}-\frac{2}{3}a\right){y}={x}^{3}+{x}^{2}+\left(50a^{3}-135a^{2}-85a+175\right){x}+\frac{2345}{3}a^{3}-2076a^{2}-\frac{3295}{3}a+2794$ |
| 1.1-b8 |
1.1-b |
$16$ |
$112$ |
\(\Q(\sqrt{2}, \sqrt{7})\) |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$10.00821$ |
$\textsf{none}$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-448$ |
$N(\mathrm{U}(1))$ |
✓ |
|
✓ |
✓ |
|
|
$64$ |
\( 1 \) |
$1$ |
$2.674013753$ |
0.382001964 |
\( 2770276778090527644528100875 a^{3} + 7141594780626801397104384000 a^{2} - 3751643694717307172970663750 a - 9671495368571808566288031000 \) |
\( \bigl[\frac{1}{3} a^{3} - \frac{2}{3} a\) , \( 1\) , \( \frac{1}{3} a^{3} - \frac{2}{3} a\) , \( -50 a^{3} - 135 a^{2} + 85 a + 175\) , \( -\frac{2345}{3} a^{3} - 2076 a^{2} + \frac{3295}{3} a + 2794\bigr] \) |
${y}^2+\left(\frac{1}{3}a^{3}-\frac{2}{3}a\right){x}{y}+\left(\frac{1}{3}a^{3}-\frac{2}{3}a\right){y}={x}^{3}+{x}^{2}+\left(-50a^{3}-135a^{2}+85a+175\right){x}-\frac{2345}{3}a^{3}-2076a^{2}+\frac{3295}{3}a+2794$ |
| 1.1-b9 |
1.1-b |
$16$ |
$112$ |
\(\Q(\sqrt{2}, \sqrt{7})\) |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$10.00821$ |
$\textsf{none}$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-448$ |
$N(\mathrm{U}(1))$ |
✓ |
|
✓ |
✓ |
|
|
$64$ |
\( 1 \) |
$1$ |
$2.674013753$ |
0.382001964 |
\( -6136856843335637994418047750 a^{3} - 7141594780626801397104384000 a^{2} + 40784024412413521021760079375 a + 47461262876442602610547041000 \) |
\( \bigl[a\) , \( -a^{2} + 3\) , \( 0\) , \( 105 a^{3} + 135 a^{2} - 690 a - 904\) , \( \frac{4840}{3} a^{3} + 1941 a^{2} - \frac{32135}{3} a - 12909\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-a^{2}+3\right){x}^{2}+\left(105a^{3}+135a^{2}-690a-904\right){x}+\frac{4840}{3}a^{3}+1941a^{2}-\frac{32135}{3}a-12909$ |
| 1.1-b10 |
1.1-b |
$16$ |
$112$ |
\(\Q(\sqrt{2}, \sqrt{7})\) |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$10.00821$ |
$\textsf{none}$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-448$ |
$N(\mathrm{U}(1))$ |
✓ |
|
✓ |
✓ |
|
|
$64$ |
\( 1 \) |
$1$ |
$2.674013753$ |
0.382001964 |
\( 6136856843335637994418047750 a^{3} - 7141594780626801397104384000 a^{2} - 40784024412413521021760079375 a + 47461262876442602610547041000 \) |
\( \bigl[a\) , \( -a^{2} + 3\) , \( 0\) , \( -105 a^{3} + 135 a^{2} + 690 a - 904\) , \( -\frac{4840}{3} a^{3} + 1941 a^{2} + \frac{32135}{3} a - 12909\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-a^{2}+3\right){x}^{2}+\left(-105a^{3}+135a^{2}+690a-904\right){x}-\frac{4840}{3}a^{3}+1941a^{2}+\frac{32135}{3}a-12909$ |
| 1.1-b11 |
1.1-b |
$16$ |
$112$ |
\(\Q(\sqrt{2}, \sqrt{7})\) |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$10.00821$ |
$\textsf{none}$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{potential}$ |
$-112$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
✓ |
✓ |
$2$ |
2Cs |
$16$ |
\( 1 \) |
$1$ |
$42.78422004$ |
0.382001964 |
\( -51954490735875 a^{2} + 345276624928500 \) |
\( \bigl[a\) , \( -a^{2} + 3\) , \( 0\) , \( 15 a^{2} - 104\) , \( 69 a^{2} - 451\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-a^{2}+3\right){x}^{2}+\left(15a^{2}-104\right){x}+69a^{2}-451$ |
| 1.1-b12 |
1.1-b |
$16$ |
$112$ |
\(\Q(\sqrt{2}, \sqrt{7})\) |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$10.00821$ |
$\textsf{none}$ |
0 |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{potential}$ |
$-28$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
✓ |
✓ |
$2$ |
2Cs |
$4$ |
\( 1 \) |
$1$ |
$684.5475207$ |
0.382001964 |
\( 16581375 \) |
\( \bigl[a\) , \( -a^{2} + 3\) , \( 0\) , \( -4\) , \( 3 a^{2} - 12\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-a^{2}+3\right){x}^{2}-4{x}+3a^{2}-12$ |
| 1.1-b13 |
1.1-b |
$16$ |
$112$ |
\(\Q(\sqrt{2}, \sqrt{7})\) |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$10.00821$ |
$\textsf{none}$ |
0 |
$\Z/4\Z$ |
$\textsf{potential}$ |
$-7$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
✓ |
✓ |
|
|
$1$ |
\( 1 \) |
$1$ |
$684.5475207$ |
0.382001964 |
\( -3375 \) |
\( \bigl[a\) , \( -a^{2} + 3\) , \( 0\) , \( 1\) , \( 0\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-a^{2}+3\right){x}^{2}+{x}$ |
| 1.1-b14 |
1.1-b |
$16$ |
$112$ |
\(\Q(\sqrt{2}, \sqrt{7})\) |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$10.00821$ |
$\textsf{none}$ |
0 |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{potential}$ |
$-112$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
✓ |
✓ |
$2$ |
2Cs |
$4$ |
\( 1 \) |
$1$ |
$684.5475207$ |
0.382001964 |
\( 51954490735875 a^{2} - 70359300958500 \) |
\( \bigl[a\) , \( -a^{2} + 3\) , \( 0\) , \( -15 a^{2} + 16\) , \( 69 a^{2} - 101\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-a^{2}+3\right){x}^{2}+\left(-15a^{2}+16\right){x}+69a^{2}-101$ |
| 1.1-b15 |
1.1-b |
$16$ |
$112$ |
\(\Q(\sqrt{2}, \sqrt{7})\) |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$10.00821$ |
$\textsf{none}$ |
0 |
$\Z/4\Z$ |
$\textsf{potential}$ |
$-448$ |
$N(\mathrm{U}(1))$ |
✓ |
|
✓ |
✓ |
|
|
$4$ |
\( 1 \) |
$1$ |
$171.1368801$ |
0.382001964 |
\( -2770276778090527644528100875 a^{3} + 7141594780626801397104384000 a^{2} + 3751643694717307172970663750 a - 9671495368571808566288031000 \) |
\( \bigl[a\) , \( -a^{2} + 3\) , \( 0\) , \( 50 a^{3} - 135 a^{2} - 85 a + 176\) , \( -\frac{2195}{3} a^{3} + 1941 a^{2} + \frac{3040}{3} a - 2619\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-a^{2}+3\right){x}^{2}+\left(50a^{3}-135a^{2}-85a+176\right){x}-\frac{2195}{3}a^{3}+1941a^{2}+\frac{3040}{3}a-2619$ |
| 1.1-b16 |
1.1-b |
$16$ |
$112$ |
\(\Q(\sqrt{2}, \sqrt{7})\) |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$10.00821$ |
$\textsf{none}$ |
0 |
$\Z/4\Z$ |
$\textsf{potential}$ |
$-448$ |
$N(\mathrm{U}(1))$ |
✓ |
|
✓ |
✓ |
|
|
$4$ |
\( 1 \) |
$1$ |
$171.1368801$ |
0.382001964 |
\( 2770276778090527644528100875 a^{3} + 7141594780626801397104384000 a^{2} - 3751643694717307172970663750 a - 9671495368571808566288031000 \) |
\( \bigl[a\) , \( -a^{2} + 3\) , \( 0\) , \( -50 a^{3} - 135 a^{2} + 85 a + 176\) , \( \frac{2195}{3} a^{3} + 1941 a^{2} - \frac{3040}{3} a - 2619\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-a^{2}+3\right){x}^{2}+\left(-50a^{3}-135a^{2}+85a+176\right){x}+\frac{2195}{3}a^{3}+1941a^{2}-\frac{3040}{3}a-2619$ |
| 16.1-a1 |
16.1-a |
$4$ |
$6$ |
\(\Q(\sqrt{2}, \sqrt{7})\) |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{12} \) |
$14.15375$ |
$(1/3a^3+a^2-2/3a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2, 3$ |
2B, 3B |
$9$ |
\( 1 \) |
$1$ |
$81.17829785$ |
1.630814019 |
\( \frac{466410496}{3} a^{3} + 400779264 a^{2} - \frac{631637504}{3} a - 542752960 \) |
\( \bigl[\frac{1}{3} a^{3} + a^{2} - \frac{5}{3} a - 3\) , \( \frac{1}{3} a^{3} + a^{2} - \frac{5}{3} a - 5\) , \( \frac{1}{3} a^{3} + a^{2} - \frac{5}{3} a - 3\) , \( \frac{1}{3} a^{3} - a^{2} - \frac{5}{3} a + 1\) , \( -\frac{7}{3} a^{3} - 8 a^{2} + \frac{5}{3} a + 9\bigr] \) |
${y}^2+\left(\frac{1}{3}a^{3}+a^{2}-\frac{5}{3}a-3\right){x}{y}+\left(\frac{1}{3}a^{3}+a^{2}-\frac{5}{3}a-3\right){y}={x}^{3}+\left(\frac{1}{3}a^{3}+a^{2}-\frac{5}{3}a-5\right){x}^{2}+\left(\frac{1}{3}a^{3}-a^{2}-\frac{5}{3}a+1\right){x}-\frac{7}{3}a^{3}-8a^{2}+\frac{5}{3}a+9$ |
| 16.1-a2 |
16.1-a |
$4$ |
$6$ |
\(\Q(\sqrt{2}, \sqrt{7})\) |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{12} \) |
$14.15375$ |
$(1/3a^3+a^2-2/3a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2, 3$ |
2B, 3B |
$9$ |
\( 1 \) |
$1$ |
$81.17829785$ |
1.630814019 |
\( -\frac{1033215488}{3} a^{3} - 400779264 a^{2} + \frac{6866492416}{3} a + 2663481152 \) |
\( \bigl[\frac{1}{3} a^{3} + a^{2} - \frac{5}{3} a - 3\) , \( \frac{1}{3} a^{3} + a^{2} - \frac{5}{3} a - 5\) , \( 0\) , \( \frac{7}{3} a^{3} + 5 a^{2} - \frac{29}{3} a - 18\) , \( \frac{8}{3} a^{3} + 5 a^{2} - \frac{34}{3} a - 17\bigr] \) |
${y}^2+\left(\frac{1}{3}a^{3}+a^{2}-\frac{5}{3}a-3\right){x}{y}={x}^{3}+\left(\frac{1}{3}a^{3}+a^{2}-\frac{5}{3}a-5\right){x}^{2}+\left(\frac{7}{3}a^{3}+5a^{2}-\frac{29}{3}a-18\right){x}+\frac{8}{3}a^{3}+5a^{2}-\frac{34}{3}a-17$ |
| 16.1-a3 |
16.1-a |
$4$ |
$6$ |
\(\Q(\sqrt{2}, \sqrt{7})\) |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{12} \) |
$14.15375$ |
$(1/3a^3+a^2-2/3a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2, 3$ |
2B, 3B |
$9$ |
\( 1 \) |
$1$ |
$81.17829785$ |
1.630814019 |
\( \frac{1033215488}{3} a^{3} - 400779264 a^{2} - \frac{6866492416}{3} a + 2663481152 \) |
\( \bigl[\frac{1}{3} a^{3} + a^{2} - \frac{5}{3} a - 3\) , \( -\frac{1}{3} a^{3} + a^{2} + \frac{8}{3} a - 5\) , \( \frac{1}{3} a^{3} + a^{2} - \frac{5}{3} a - 3\) , \( \frac{2}{3} a^{3} + 3 a^{2} - \frac{4}{3} a - 13\) , \( \frac{4}{3} a^{3} + 3 a^{2} - \frac{14}{3} a - 10\bigr] \) |
${y}^2+\left(\frac{1}{3}a^{3}+a^{2}-\frac{5}{3}a-3\right){x}{y}+\left(\frac{1}{3}a^{3}+a^{2}-\frac{5}{3}a-3\right){y}={x}^{3}+\left(-\frac{1}{3}a^{3}+a^{2}+\frac{8}{3}a-5\right){x}^{2}+\left(\frac{2}{3}a^{3}+3a^{2}-\frac{4}{3}a-13\right){x}+\frac{4}{3}a^{3}+3a^{2}-\frac{14}{3}a-10$ |
| 16.1-a4 |
16.1-a |
$4$ |
$6$ |
\(\Q(\sqrt{2}, \sqrt{7})\) |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{12} \) |
$14.15375$ |
$(1/3a^3+a^2-2/3a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2, 3$ |
2B, 3B |
$9$ |
\( 1 \) |
$1$ |
$81.17829785$ |
1.630814019 |
\( -\frac{466410496}{3} a^{3} + 400779264 a^{2} + \frac{631637504}{3} a - 542752960 \) |
\( \bigl[\frac{1}{3} a^{3} + a^{2} - \frac{5}{3} a - 3\) , \( -\frac{1}{3} a^{3} + a^{2} + \frac{8}{3} a - 5\) , \( 0\) , \( \frac{8}{3} a^{3} - a^{2} - \frac{28}{3} a + 8\) , \( \frac{4}{3} a^{3} - 3 a^{2} + \frac{7}{3} a - 1\bigr] \) |
${y}^2+\left(\frac{1}{3}a^{3}+a^{2}-\frac{5}{3}a-3\right){x}{y}={x}^{3}+\left(-\frac{1}{3}a^{3}+a^{2}+\frac{8}{3}a-5\right){x}^{2}+\left(\frac{8}{3}a^{3}-a^{2}-\frac{28}{3}a+8\right){x}+\frac{4}{3}a^{3}-3a^{2}+\frac{7}{3}a-1$ |
| 16.1-b1 |
16.1-b |
$8$ |
$12$ |
\(\Q(\sqrt{2}, \sqrt{7})\) |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{4} \) |
$14.15375$ |
$(1/3a^3+a^2-2/3a-2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2, 3$ |
2Cs, 3B |
$4$ |
\( 1 \) |
$1$ |
$838.9896983$ |
1.872744862 |
\( -50184204 a^{2} + 333513488 \) |
\( \bigl[\frac{1}{3} a^{3} + a^{2} - \frac{2}{3} a - 4\) , \( -a^{2} + a + 4\) , \( \frac{1}{3} a^{3} - \frac{5}{3} a\) , \( -a^{3} + 3 a^{2} + 10 a - 5\) , \( -\frac{10}{3} a^{3} + 3 a^{2} + \frac{71}{3} a - 20\bigr] \) |
${y}^2+\left(\frac{1}{3}a^{3}+a^{2}-\frac{2}{3}a-4\right){x}{y}+\left(\frac{1}{3}a^{3}-\frac{5}{3}a\right){y}={x}^{3}+\left(-a^{2}+a+4\right){x}^{2}+\left(-a^{3}+3a^{2}+10a-5\right){x}-\frac{10}{3}a^{3}+3a^{2}+\frac{71}{3}a-20$ |
| 16.1-b2 |
16.1-b |
$8$ |
$12$ |
\(\Q(\sqrt{2}, \sqrt{7})\) |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{8} \) |
$14.15375$ |
$(1/3a^3+a^2-2/3a-2)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2, 3$ |
2B, 3B |
$4$ |
\( 1 \) |
$1$ |
$838.9896983$ |
1.872744862 |
\( -\frac{17177439525499012}{3} a^{3} - 6663254257042944 a^{2} + \frac{114156991247194394}{3} a + 44282330715007720 \) |
\( \bigl[\frac{1}{3} a^{3} + a^{2} - \frac{2}{3} a - 4\) , \( -a^{2} + a + 4\) , \( \frac{1}{3} a^{3} - \frac{5}{3} a\) , \( -\frac{13}{3} a^{3} - 7 a^{2} + \frac{35}{3} a + 5\) , \( a^{3} + 15 a^{2} + 15 a - 39\bigr] \) |
${y}^2+\left(\frac{1}{3}a^{3}+a^{2}-\frac{2}{3}a-4\right){x}{y}+\left(\frac{1}{3}a^{3}-\frac{5}{3}a\right){y}={x}^{3}+\left(-a^{2}+a+4\right){x}^{2}+\left(-\frac{13}{3}a^{3}-7a^{2}+\frac{35}{3}a+5\right){x}+a^{3}+15a^{2}+15a-39$ |
| 16.1-b3 |
16.1-b |
$8$ |
$12$ |
\(\Q(\sqrt{2}, \sqrt{7})\) |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{8} \) |
$14.15375$ |
$(1/3a^3+a^2-2/3a-2)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2, 3$ |
2B, 3B |
$4$ |
\( 1 \) |
$1$ |
$838.9896983$ |
1.872744862 |
\( -\frac{7754174985599234}{3} a^{3} + 6663254257042944 a^{2} + \frac{10501081308296836}{3} a - 9023703341335832 \) |
\( \bigl[a^{2} + a - 4\) , \( -\frac{1}{3} a^{3} + \frac{5}{3} a + 1\) , \( \frac{1}{3} a^{3} - \frac{2}{3} a + 1\) , \( -\frac{29}{3} a^{3} + 9 a^{2} + \frac{187}{3} a - 70\) , \( 29 a^{3} - 41 a^{2} - 203 a + 246\bigr] \) |
${y}^2+\left(a^{2}+a-4\right){x}{y}+\left(\frac{1}{3}a^{3}-\frac{2}{3}a+1\right){y}={x}^{3}+\left(-\frac{1}{3}a^{3}+\frac{5}{3}a+1\right){x}^{2}+\left(-\frac{29}{3}a^{3}+9a^{2}+\frac{187}{3}a-70\right){x}+29a^{3}-41a^{2}-203a+246$ |
| 16.1-b4 |
16.1-b |
$8$ |
$12$ |
\(\Q(\sqrt{2}, \sqrt{7})\) |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{8} \) |
$14.15375$ |
$(1/3a^3+a^2-2/3a-2)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2, 3$ |
2B, 3B |
$4$ |
\( 2 \) |
$1$ |
$419.4948491$ |
1.872744862 |
\( -3264 a^{2} + 6128 \) |
\( \bigl[\frac{1}{3} a^{3} - \frac{5}{3} a\) , \( -\frac{1}{3} a^{3} + a^{2} + \frac{5}{3} a - 3\) , \( 0\) , \( -6 a^{3} - 14 a^{2} + 8 a + 21\) , \( -\frac{104}{3} a^{3} - 88 a^{2} + \frac{142}{3} a + 119\bigr] \) |
${y}^2+\left(\frac{1}{3}a^{3}-\frac{5}{3}a\right){x}{y}={x}^{3}+\left(-\frac{1}{3}a^{3}+a^{2}+\frac{5}{3}a-3\right){x}^{2}+\left(-6a^{3}-14a^{2}+8a+21\right){x}-\frac{104}{3}a^{3}-88a^{2}+\frac{142}{3}a+119$ |
| 16.1-b5 |
16.1-b |
$8$ |
$12$ |
\(\Q(\sqrt{2}, \sqrt{7})\) |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{8} \) |
$14.15375$ |
$(1/3a^3+a^2-2/3a-2)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2, 3$ |
2B, 3B |
$4$ |
\( 2 \) |
$1$ |
$419.4948491$ |
1.872744862 |
\( 3264 a^{2} - 19984 \) |
\( \bigl[\frac{1}{3} a^{3} - \frac{5}{3} a\) , \( -\frac{1}{3} a^{3} - a^{2} + \frac{5}{3} a + 5\) , \( 0\) , \( -\frac{40}{3} a^{3} + 14 a^{2} + \frac{266}{3} a - 91\) , \( -\frac{230}{3} a^{3} + 88 a^{2} + \frac{1528}{3} a - 585\bigr] \) |
${y}^2+\left(\frac{1}{3}a^{3}-\frac{5}{3}a\right){x}{y}={x}^{3}+\left(-\frac{1}{3}a^{3}-a^{2}+\frac{5}{3}a+5\right){x}^{2}+\left(-\frac{40}{3}a^{3}+14a^{2}+\frac{266}{3}a-91\right){x}-\frac{230}{3}a^{3}+88a^{2}+\frac{1528}{3}a-585$ |
| 16.1-b6 |
16.1-b |
$8$ |
$12$ |
\(\Q(\sqrt{2}, \sqrt{7})\) |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{8} \) |
$14.15375$ |
$(1/3a^3+a^2-2/3a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2, 3$ |
2B, 3B |
$16$ |
\( 1 \) |
$1$ |
$52.43685614$ |
1.872744862 |
\( \frac{7754174985599234}{3} a^{3} + 6663254257042944 a^{2} - \frac{10501081308296836}{3} a - 9023703341335832 \) |
\( \bigl[\frac{1}{3} a^{3} - \frac{2}{3} a + 1\) , \( -a^{2} + 4\) , \( a^{2} + a - 4\) , \( \frac{29}{3} a^{3} + 8 a^{2} - \frac{193}{3} a - 69\) , \( 48 a^{3} + 60 a^{2} - 328 a - 397\bigr] \) |
${y}^2+\left(\frac{1}{3}a^{3}-\frac{2}{3}a+1\right){x}{y}+\left(a^{2}+a-4\right){y}={x}^{3}+\left(-a^{2}+4\right){x}^{2}+\left(\frac{29}{3}a^{3}+8a^{2}-\frac{193}{3}a-69\right){x}+48a^{3}+60a^{2}-328a-397$ |
| 16.1-b7 |
16.1-b |
$8$ |
$12$ |
\(\Q(\sqrt{2}, \sqrt{7})\) |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{4} \) |
$14.15375$ |
$(1/3a^3+a^2-2/3a-2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2, 3$ |
2Cs, 3B |
$4$ |
\( 1 \) |
$1$ |
$838.9896983$ |
1.872744862 |
\( 50184204 a^{2} - 67960144 \) |
\( \bigl[\frac{1}{3} a^{3} - \frac{2}{3} a + 1\) , \( -a^{2} + 4\) , \( a^{2} + a - 4\) , \( \frac{4}{3} a^{3} - 2 a^{2} - \frac{23}{3} a + 1\) , \( -\frac{2}{3} a^{3} + 3 a^{2} - \frac{5}{3} a - 10\bigr] \) |
${y}^2+\left(\frac{1}{3}a^{3}-\frac{2}{3}a+1\right){x}{y}+\left(a^{2}+a-4\right){y}={x}^{3}+\left(-a^{2}+4\right){x}^{2}+\left(\frac{4}{3}a^{3}-2a^{2}-\frac{23}{3}a+1\right){x}-\frac{2}{3}a^{3}+3a^{2}-\frac{5}{3}a-10$ |
| 16.1-b8 |
16.1-b |
$8$ |
$12$ |
\(\Q(\sqrt{2}, \sqrt{7})\) |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{8} \) |
$14.15375$ |
$(1/3a^3+a^2-2/3a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2, 3$ |
2B, 3B |
$16$ |
\( 1 \) |
$1$ |
$52.43685614$ |
1.872744862 |
\( \frac{17177439525499012}{3} a^{3} - 6663254257042944 a^{2} - \frac{114156991247194394}{3} a + 44282330715007720 \) |
\( \bigl[a + 1\) , \( \frac{1}{3} a^{3} - \frac{8}{3} a + 1\) , \( \frac{1}{3} a^{3} + a^{2} - \frac{2}{3} a - 4\) , \( \frac{14}{3} a^{3} - 11 a^{2} - \frac{31}{3} a + 7\) , \( 19 a^{3} - 61 a^{2} - 9 a + 86\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(\frac{1}{3}a^{3}+a^{2}-\frac{2}{3}a-4\right){y}={x}^{3}+\left(\frac{1}{3}a^{3}-\frac{8}{3}a+1\right){x}^{2}+\left(\frac{14}{3}a^{3}-11a^{2}-\frac{31}{3}a+7\right){x}+19a^{3}-61a^{2}-9a+86$ |
| 16.1-c1 |
16.1-c |
$8$ |
$12$ |
\(\Q(\sqrt{2}, \sqrt{7})\) |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{4} \) |
$14.15375$ |
$(1/3a^3+a^2-2/3a-2)$ |
$2$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
✓ |
$2, 3$ |
2Cs, 3B |
$1$ |
\( 1 \) |
$0.145223206$ |
$2665.378925$ |
3.456025666 |
\( -50184204 a^{2} + 333513488 \) |
\( \bigl[a^{2} + a - 4\) , \( \frac{1}{3} a^{3} - \frac{5}{3} a - 1\) , \( a^{2} + a - 4\) , \( \frac{35}{3} a^{3} - 31 a^{2} - \frac{28}{3} a + 34\) , \( -20 a^{3} + 53 a^{2} + 27 a - 72\bigr] \) |
${y}^2+\left(a^{2}+a-4\right){x}{y}+\left(a^{2}+a-4\right){y}={x}^{3}+\left(\frac{1}{3}a^{3}-\frac{5}{3}a-1\right){x}^{2}+\left(\frac{35}{3}a^{3}-31a^{2}-\frac{28}{3}a+34\right){x}-20a^{3}+53a^{2}+27a-72$ |
| 16.1-c2 |
16.1-c |
$8$ |
$12$ |
\(\Q(\sqrt{2}, \sqrt{7})\) |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{8} \) |
$14.15375$ |
$(1/3a^3+a^2-2/3a-2)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
✓ |
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$0.036305801$ |
$1332.689462$ |
3.456025666 |
\( -3264 a^{2} + 6128 \) |
\( \bigl[a^{2} - 3\) , \( a^{2} - 4\) , \( a^{2} - 3\) , \( 0\) , \( -1\bigr] \) |
${y}^2+\left(a^{2}-3\right){x}{y}+\left(a^{2}-3\right){y}={x}^{3}+\left(a^{2}-4\right){x}^{2}-1$ |
| 16.1-c3 |
16.1-c |
$8$ |
$12$ |
\(\Q(\sqrt{2}, \sqrt{7})\) |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{8} \) |
$14.15375$ |
$(1/3a^3+a^2-2/3a-2)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
✓ |
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$0.036305801$ |
$1332.689462$ |
3.456025666 |
\( 3264 a^{2} - 19984 \) |
\( \bigl[a^{2} - 3\) , \( a^{2} - 4\) , \( 0\) , \( 3 a^{2} - 8\) , \( 8\bigr] \) |
${y}^2+\left(a^{2}-3\right){x}{y}={x}^{3}+\left(a^{2}-4\right){x}^{2}+\left(3a^{2}-8\right){x}+8$ |
| 16.1-c4 |
16.1-c |
$8$ |
$12$ |
\(\Q(\sqrt{2}, \sqrt{7})\) |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{8} \) |
$14.15375$ |
$(1/3a^3+a^2-2/3a-2)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2, 3$ |
2B, 3B |
$1$ |
\( 1 \) |
$0.145223206$ |
$666.3447312$ |
3.456025666 |
\( -\frac{17177439525499012}{3} a^{3} - 6663254257042944 a^{2} + \frac{114156991247194394}{3} a + 44282330715007720 \) |
\( \bigl[\frac{1}{3} a^{3} - \frac{2}{3} a + 1\) , \( \frac{1}{3} a^{3} + a^{2} - \frac{8}{3} a - 5\) , \( \frac{1}{3} a^{3} + a^{2} - \frac{2}{3} a - 4\) , \( -\frac{106}{3} a^{3} + 32 a^{2} + \frac{767}{3} a - 272\) , \( \frac{905}{3} a^{3} - 335 a^{2} - \frac{6199}{3} a + 2373\bigr] \) |
${y}^2+\left(\frac{1}{3}a^{3}-\frac{2}{3}a+1\right){x}{y}+\left(\frac{1}{3}a^{3}+a^{2}-\frac{2}{3}a-4\right){y}={x}^{3}+\left(\frac{1}{3}a^{3}+a^{2}-\frac{8}{3}a-5\right){x}^{2}+\left(-\frac{106}{3}a^{3}+32a^{2}+\frac{767}{3}a-272\right){x}+\frac{905}{3}a^{3}-335a^{2}-\frac{6199}{3}a+2373$ |
| 16.1-c5 |
16.1-c |
$8$ |
$12$ |
\(\Q(\sqrt{2}, \sqrt{7})\) |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{8} \) |
$14.15375$ |
$(1/3a^3+a^2-2/3a-2)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2, 3$ |
2B, 3B |
$1$ |
\( 1 \) |
$0.145223206$ |
$666.3447312$ |
3.456025666 |
\( \frac{17177439525499012}{3} a^{3} - 6663254257042944 a^{2} - \frac{114156991247194394}{3} a + 44282330715007720 \) |
\( \bigl[\frac{1}{3} a^{3} - \frac{2}{3} a + 1\) , \( \frac{1}{3} a^{3} + a^{2} - \frac{5}{3} a - 5\) , \( a + 1\) , \( \frac{103}{3} a^{3} + 34 a^{2} - \frac{740}{3} a - 278\) , \( -\frac{1081}{3} a^{3} - 412 a^{2} + \frac{7280}{3} a + 2814\bigr] \) |
${y}^2+\left(\frac{1}{3}a^{3}-\frac{2}{3}a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(\frac{1}{3}a^{3}+a^{2}-\frac{5}{3}a-5\right){x}^{2}+\left(\frac{103}{3}a^{3}+34a^{2}-\frac{740}{3}a-278\right){x}-\frac{1081}{3}a^{3}-412a^{2}+\frac{7280}{3}a+2814$ |
| 16.1-c6 |
16.1-c |
$8$ |
$12$ |
\(\Q(\sqrt{2}, \sqrt{7})\) |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{8} \) |
$14.15375$ |
$(1/3a^3+a^2-2/3a-2)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2, 3$ |
2B, 3B |
$1$ |
\( 1 \) |
$0.145223206$ |
$666.3447312$ |
3.456025666 |
\( -\frac{7754174985599234}{3} a^{3} + 6663254257042944 a^{2} + \frac{10501081308296836}{3} a - 9023703341335832 \) |
\( \bigl[a + 1\) , \( \frac{1}{3} a^{3} + a^{2} - \frac{5}{3} a - 4\) , \( \frac{1}{3} a^{3} - \frac{5}{3} a\) , \( -\frac{23}{3} a^{3} - 32 a^{2} - \frac{113}{3} a - 16\) , \( \frac{137}{3} a^{3} + 189 a^{2} + \frac{611}{3} a + 51\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(\frac{1}{3}a^{3}-\frac{5}{3}a\right){y}={x}^{3}+\left(\frac{1}{3}a^{3}+a^{2}-\frac{5}{3}a-4\right){x}^{2}+\left(-\frac{23}{3}a^{3}-32a^{2}-\frac{113}{3}a-16\right){x}+\frac{137}{3}a^{3}+189a^{2}+\frac{611}{3}a+51$ |
*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.
