| 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 |
$4$ |
$35$ |
\(\Q(\sqrt{5}, \sqrt{7})\) |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$12.51027$ |
$\textsf{none}$ |
0 |
$\mathsf{trivial}$ |
$\textsf{potential}$ |
$-35$ |
$N(\mathrm{U}(1))$ |
✓ |
|
✓ |
✓ |
|
|
$1$ |
\( 1 \) |
$1$ |
$291.1899442$ |
2.079928173 |
\( 4587520 a^{3} - 6881280 a^{2} - 45875200 a - 34897920 \) |
\( \bigl[0\) , \( -\frac{2}{23} a^{3} + \frac{3}{23} a^{2} + \frac{20}{23} a - \frac{45}{23}\) , \( -\frac{3}{23} a^{3} + \frac{16}{23} a^{2} + \frac{30}{23} a - \frac{102}{23}\) , \( \frac{166}{23} a^{3} + \frac{211}{23} a^{2} - \frac{740}{23} a - \frac{750}{23}\) , \( 38 a^{3} + 64 a^{2} - 179 a - 217\bigr] \) |
${y}^2+\left(-\frac{3}{23}a^{3}+\frac{16}{23}a^{2}+\frac{30}{23}a-\frac{102}{23}\right){y}={x}^{3}+\left(-\frac{2}{23}a^{3}+\frac{3}{23}a^{2}+\frac{20}{23}a-\frac{45}{23}\right){x}^{2}+\left(\frac{166}{23}a^{3}+\frac{211}{23}a^{2}-\frac{740}{23}a-\frac{750}{23}\right){x}+38a^{3}+64a^{2}-179a-217$ |
| 1.1-a2 |
1.1-a |
$4$ |
$35$ |
\(\Q(\sqrt{5}, \sqrt{7})\) |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$12.51027$ |
$\textsf{none}$ |
0 |
$\mathsf{trivial}$ |
$\textsf{potential}$ |
$-35$ |
$N(\mathrm{U}(1))$ |
✓ |
|
✓ |
✓ |
|
|
$1$ |
\( 1 \) |
$1$ |
$291.1899442$ |
2.079928173 |
\( -4587520 a^{3} + 6881280 a^{2} + 45875200 a - 83066880 \) |
\( \bigl[0\) , \( -\frac{2}{23} a^{3} + \frac{3}{23} a^{2} + \frac{43}{23} a - \frac{22}{23}\) , \( 1\) , \( -\frac{348}{23} a^{3} + \frac{1626}{23} a^{2} + \frac{536}{23} a - \frac{4817}{23}\) , \( -\frac{1502}{23} a^{3} + \frac{9038}{23} a^{2} - \frac{10395}{23} a - \frac{3550}{23}\bigr] \) |
${y}^2+{y}={x}^{3}+\left(-\frac{2}{23}a^{3}+\frac{3}{23}a^{2}+\frac{43}{23}a-\frac{22}{23}\right){x}^{2}+\left(-\frac{348}{23}a^{3}+\frac{1626}{23}a^{2}+\frac{536}{23}a-\frac{4817}{23}\right){x}-\frac{1502}{23}a^{3}+\frac{9038}{23}a^{2}-\frac{10395}{23}a-\frac{3550}{23}$ |
| 1.1-a3 |
1.1-a |
$4$ |
$35$ |
\(\Q(\sqrt{5}, \sqrt{7})\) |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$12.51027$ |
$\textsf{none}$ |
0 |
$\mathsf{trivial}$ |
$\textsf{potential}$ |
$-35$ |
$N(\mathrm{U}(1))$ |
✓ |
|
✓ |
✓ |
|
|
$1$ |
\( 1 \) |
$1$ |
$291.1899442$ |
2.079928173 |
\( 4587520 a^{3} - 6881280 a^{2} - 45875200 a - 34897920 \) |
\( \bigl[0\) , \( \frac{2}{23} a^{3} - \frac{3}{23} a^{2} - \frac{20}{23} a + \frac{45}{23}\) , \( -\frac{1}{23} a^{3} + \frac{13}{23} a^{2} - \frac{13}{23} a - \frac{103}{23}\) , \( \frac{166}{23} a^{3} + \frac{211}{23} a^{2} - \frac{740}{23} a - \frac{750}{23}\) , \( -\frac{876}{23} a^{3} - \frac{1469}{23} a^{2} + \frac{4160}{23} a + \frac{4831}{23}\bigr] \) |
${y}^2+\left(-\frac{1}{23}a^{3}+\frac{13}{23}a^{2}-\frac{13}{23}a-\frac{103}{23}\right){y}={x}^{3}+\left(\frac{2}{23}a^{3}-\frac{3}{23}a^{2}-\frac{20}{23}a+\frac{45}{23}\right){x}^{2}+\left(\frac{166}{23}a^{3}+\frac{211}{23}a^{2}-\frac{740}{23}a-\frac{750}{23}\right){x}-\frac{876}{23}a^{3}-\frac{1469}{23}a^{2}+\frac{4160}{23}a+\frac{4831}{23}$ |
| 1.1-a4 |
1.1-a |
$4$ |
$35$ |
\(\Q(\sqrt{5}, \sqrt{7})\) |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$12.51027$ |
$\textsf{none}$ |
0 |
$\mathsf{trivial}$ |
$\textsf{potential}$ |
$-35$ |
$N(\mathrm{U}(1))$ |
✓ |
|
✓ |
✓ |
|
|
$1$ |
\( 1 \) |
$1$ |
$291.1899442$ |
2.079928173 |
\( -4587520 a^{3} + 6881280 a^{2} + 45875200 a - 83066880 \) |
\( \bigl[0\) , \( -\frac{2}{23} a^{3} + \frac{3}{23} a^{2} + \frac{20}{23} a - \frac{45}{23}\) , \( -\frac{3}{23} a^{3} + \frac{16}{23} a^{2} + \frac{30}{23} a - \frac{102}{23}\) , \( -\frac{162}{23} a^{3} + \frac{703}{23} a^{2} - \frac{220}{23} a - \frac{1092}{23}\) , \( \frac{1038}{23} a^{3} - \frac{4800}{23} a^{2} + \frac{1649}{23} a + \frac{7738}{23}\bigr] \) |
${y}^2+\left(-\frac{3}{23}a^{3}+\frac{16}{23}a^{2}+\frac{30}{23}a-\frac{102}{23}\right){y}={x}^{3}+\left(-\frac{2}{23}a^{3}+\frac{3}{23}a^{2}+\frac{20}{23}a-\frac{45}{23}\right){x}^{2}+\left(-\frac{162}{23}a^{3}+\frac{703}{23}a^{2}-\frac{220}{23}a-\frac{1092}{23}\right){x}+\frac{1038}{23}a^{3}-\frac{4800}{23}a^{2}+\frac{1649}{23}a+\frac{7738}{23}$ |
| 1.1-b1 |
1.1-b |
$4$ |
$10$ |
\(\Q(\sqrt{5}, \sqrt{7})\) |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$12.51027$ |
$\textsf{none}$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-20$ |
$N(\mathrm{U}(1))$ |
✓ |
|
✓ |
✓ |
$7$ |
7Ns.2.1 |
$1$ |
\( 1 \) |
$1$ |
$932.9796544$ |
1.666035097 |
\( -\frac{1131520}{23} a^{3} + \frac{1697280}{23} a^{2} + \frac{11315200}{23} a + \frac{8595520}{23} \) |
\( \bigl[-\frac{2}{23} a^{3} + \frac{3}{23} a^{2} + \frac{43}{23} a + \frac{1}{23}\) , \( \frac{1}{23} a^{3} + \frac{10}{23} a^{2} - \frac{33}{23} a - \frac{81}{23}\) , \( -\frac{1}{23} a^{3} + \frac{13}{23} a^{2} - \frac{13}{23} a - \frac{103}{23}\) , \( \frac{61}{23} a^{3} - \frac{333}{23} a^{2} + \frac{218}{23} a + \frac{579}{23}\) , \( \frac{542}{23} a^{3} - \frac{2837}{23} a^{2} + \frac{1158}{23} a + \frac{4720}{23}\bigr] \) |
${y}^2+\left(-\frac{2}{23}a^{3}+\frac{3}{23}a^{2}+\frac{43}{23}a+\frac{1}{23}\right){x}{y}+\left(-\frac{1}{23}a^{3}+\frac{13}{23}a^{2}-\frac{13}{23}a-\frac{103}{23}\right){y}={x}^{3}+\left(\frac{1}{23}a^{3}+\frac{10}{23}a^{2}-\frac{33}{23}a-\frac{81}{23}\right){x}^{2}+\left(\frac{61}{23}a^{3}-\frac{333}{23}a^{2}+\frac{218}{23}a+\frac{579}{23}\right){x}+\frac{542}{23}a^{3}-\frac{2837}{23}a^{2}+\frac{1158}{23}a+\frac{4720}{23}$ |
| 1.1-b2 |
1.1-b |
$4$ |
$10$ |
\(\Q(\sqrt{5}, \sqrt{7})\) |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$12.51027$ |
$\textsf{none}$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-20$ |
$N(\mathrm{U}(1))$ |
✓ |
|
✓ |
✓ |
$7$ |
7Ns.2.1 |
$1$ |
\( 1 \) |
$1$ |
$932.9796544$ |
1.666035097 |
\( \frac{1131520}{23} a^{3} - \frac{1697280}{23} a^{2} - \frac{11315200}{23} a + \frac{20476480}{23} \) |
\( \bigl[-\frac{2}{23} a^{3} + \frac{3}{23} a^{2} + \frac{43}{23} a + \frac{1}{23}\) , \( \frac{1}{23} a^{3} + \frac{10}{23} a^{2} - \frac{33}{23} a - \frac{81}{23}\) , \( -\frac{3}{23} a^{3} + \frac{16}{23} a^{2} + \frac{30}{23} a - \frac{102}{23}\) , \( -\frac{73}{23} a^{3} - \frac{132}{23} a^{2} + \frac{385}{23} a + \frac{370}{23}\) , \( -\frac{544}{23} a^{3} - \frac{1208}{23} a^{2} + \frac{2933}{23} a + \frac{3561}{23}\bigr] \) |
${y}^2+\left(-\frac{2}{23}a^{3}+\frac{3}{23}a^{2}+\frac{43}{23}a+\frac{1}{23}\right){x}{y}+\left(-\frac{3}{23}a^{3}+\frac{16}{23}a^{2}+\frac{30}{23}a-\frac{102}{23}\right){y}={x}^{3}+\left(\frac{1}{23}a^{3}+\frac{10}{23}a^{2}-\frac{33}{23}a-\frac{81}{23}\right){x}^{2}+\left(-\frac{73}{23}a^{3}-\frac{132}{23}a^{2}+\frac{385}{23}a+\frac{370}{23}\right){x}-\frac{544}{23}a^{3}-\frac{1208}{23}a^{2}+\frac{2933}{23}a+\frac{3561}{23}$ |
| 1.1-b3 |
1.1-b |
$4$ |
$10$ |
\(\Q(\sqrt{5}, \sqrt{7})\) |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$12.51027$ |
$\textsf{none}$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-20$ |
$N(\mathrm{U}(1))$ |
✓ |
|
✓ |
✓ |
$7$ |
7Ns.2.1 |
$1$ |
\( 1 \) |
$1$ |
$932.9796544$ |
1.666035097 |
\( -\frac{1131520}{23} a^{3} + \frac{1697280}{23} a^{2} + \frac{11315200}{23} a + \frac{8595520}{23} \) |
\( \bigl[-\frac{2}{23} a^{3} + \frac{3}{23} a^{2} + \frac{43}{23} a + \frac{1}{23}\) , \( \frac{1}{23} a^{3} - \frac{13}{23} a^{2} - \frac{10}{23} a + \frac{80}{23}\) , \( -\frac{1}{23} a^{3} + \frac{13}{23} a^{2} - \frac{13}{23} a - \frac{103}{23}\) , \( \frac{61}{23} a^{3} - \frac{356}{23} a^{2} + \frac{241}{23} a + \frac{740}{23}\) , \( -\frac{470}{23} a^{3} + \frac{2476}{23} a^{2} - \frac{1027}{23} a - \frac{4204}{23}\bigr] \) |
${y}^2+\left(-\frac{2}{23}a^{3}+\frac{3}{23}a^{2}+\frac{43}{23}a+\frac{1}{23}\right){x}{y}+\left(-\frac{1}{23}a^{3}+\frac{13}{23}a^{2}-\frac{13}{23}a-\frac{103}{23}\right){y}={x}^{3}+\left(\frac{1}{23}a^{3}-\frac{13}{23}a^{2}-\frac{10}{23}a+\frac{80}{23}\right){x}^{2}+\left(\frac{61}{23}a^{3}-\frac{356}{23}a^{2}+\frac{241}{23}a+\frac{740}{23}\right){x}-\frac{470}{23}a^{3}+\frac{2476}{23}a^{2}-\frac{1027}{23}a-\frac{4204}{23}$ |
| 1.1-b4 |
1.1-b |
$4$ |
$10$ |
\(\Q(\sqrt{5}, \sqrt{7})\) |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$12.51027$ |
$\textsf{none}$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-20$ |
$N(\mathrm{U}(1))$ |
✓ |
|
✓ |
✓ |
$7$ |
7Ns.2.1 |
$1$ |
\( 1 \) |
$1$ |
$932.9796544$ |
1.666035097 |
\( \frac{1131520}{23} a^{3} - \frac{1697280}{23} a^{2} - \frac{11315200}{23} a + \frac{20476480}{23} \) |
\( \bigl[-\frac{2}{23} a^{3} + \frac{3}{23} a^{2} + \frac{43}{23} a + \frac{1}{23}\) , \( \frac{1}{23} a^{3} - \frac{13}{23} a^{2} - \frac{10}{23} a + \frac{80}{23}\) , \( -\frac{3}{23} a^{3} + \frac{16}{23} a^{2} + \frac{30}{23} a - \frac{102}{23}\) , \( -\frac{73}{23} a^{3} - \frac{155}{23} a^{2} + \frac{408}{23} a + \frac{531}{23}\) , \( \frac{468}{23} a^{3} + \frac{1069}{23} a^{2} - \frac{2472}{23} a - \frac{3247}{23}\bigr] \) |
${y}^2+\left(-\frac{2}{23}a^{3}+\frac{3}{23}a^{2}+\frac{43}{23}a+\frac{1}{23}\right){x}{y}+\left(-\frac{3}{23}a^{3}+\frac{16}{23}a^{2}+\frac{30}{23}a-\frac{102}{23}\right){y}={x}^{3}+\left(\frac{1}{23}a^{3}-\frac{13}{23}a^{2}-\frac{10}{23}a+\frac{80}{23}\right){x}^{2}+\left(-\frac{73}{23}a^{3}-\frac{155}{23}a^{2}+\frac{408}{23}a+\frac{531}{23}\right){x}+\frac{468}{23}a^{3}+\frac{1069}{23}a^{2}-\frac{2472}{23}a-\frac{3247}{23}$ |
| 1.1-c1 |
1.1-c |
$8$ |
$28$ |
\(\Q(\sqrt{5}, \sqrt{7})\) |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$12.51027$ |
$\textsf{none}$ |
0 |
$\Z/4\Z$ |
$\textsf{potential}$ |
$-7$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
✓ |
✓ |
|
|
$1$ |
\( 1 \) |
$1$ |
$684.5475207$ |
0.305601571 |
\( -3375 \) |
\( \bigl[-\frac{1}{23} a^{3} + \frac{13}{23} a^{2} - \frac{13}{23} a - \frac{103}{23}\) , \( \frac{2}{23} a^{3} - \frac{3}{23} a^{2} - \frac{43}{23} a + \frac{22}{23}\) , \( -\frac{1}{23} a^{3} + \frac{13}{23} a^{2} - \frac{13}{23} a - \frac{103}{23}\) , \( \frac{4}{23} a^{3} - \frac{75}{23} a^{2} - \frac{17}{23} a + \frac{159}{23}\) , \( -\frac{30}{23} a^{3} - \frac{24}{23} a^{2} + \frac{70}{23} a + \frac{130}{23}\bigr] \) |
${y}^2+\left(-\frac{1}{23}a^{3}+\frac{13}{23}a^{2}-\frac{13}{23}a-\frac{103}{23}\right){x}{y}+\left(-\frac{1}{23}a^{3}+\frac{13}{23}a^{2}-\frac{13}{23}a-\frac{103}{23}\right){y}={x}^{3}+\left(\frac{2}{23}a^{3}-\frac{3}{23}a^{2}-\frac{43}{23}a+\frac{22}{23}\right){x}^{2}+\left(\frac{4}{23}a^{3}-\frac{75}{23}a^{2}-\frac{17}{23}a+\frac{159}{23}\right){x}-\frac{30}{23}a^{3}-\frac{24}{23}a^{2}+\frac{70}{23}a+\frac{130}{23}$ |
| 1.1-c2 |
1.1-c |
$8$ |
$28$ |
\(\Q(\sqrt{5}, \sqrt{7})\) |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$12.51027$ |
$\textsf{none}$ |
0 |
$\Z/4\Z$ |
$\textsf{potential}$ |
$-112$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
✓ |
✓ |
|
|
$1$ |
\( 1 \) |
$1$ |
$684.5475207$ |
0.305601571 |
\( -\frac{103908981471750}{23} a^{3} + \frac{155863472207625}{23} a^{2} + \frac{2234043101642625}{23} a + \frac{2018550429465750}{23} \) |
\( \bigl[-\frac{2}{23} a^{3} + \frac{3}{23} a^{2} + \frac{43}{23} a - \frac{22}{23}\) , \( -1\) , \( -\frac{2}{23} a^{3} + \frac{3}{23} a^{2} + \frac{43}{23} a - \frac{22}{23}\) , \( -\frac{540}{23} a^{3} + \frac{810}{23} a^{2} + \frac{11610}{23} a - \frac{22454}{23}\) , \( -\frac{6446}{23} a^{3} + \frac{9669}{23} a^{2} + \frac{138589}{23} a - \frac{267073}{23}\bigr] \) |
${y}^2+\left(-\frac{2}{23}a^{3}+\frac{3}{23}a^{2}+\frac{43}{23}a-\frac{22}{23}\right){x}{y}+\left(-\frac{2}{23}a^{3}+\frac{3}{23}a^{2}+\frac{43}{23}a-\frac{22}{23}\right){y}={x}^{3}-{x}^{2}+\left(-\frac{540}{23}a^{3}+\frac{810}{23}a^{2}+\frac{11610}{23}a-\frac{22454}{23}\right){x}-\frac{6446}{23}a^{3}+\frac{9669}{23}a^{2}+\frac{138589}{23}a-\frac{267073}{23}$ |
| 1.1-c3 |
1.1-c |
$8$ |
$28$ |
\(\Q(\sqrt{5}, \sqrt{7})\) |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$12.51027$ |
$\textsf{none}$ |
0 |
$\Z/4\Z$ |
$\textsf{potential}$ |
$-112$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
✓ |
✓ |
|
|
$1$ |
\( 1 \) |
$1$ |
$684.5475207$ |
0.305601571 |
\( \frac{103908981471750}{23} a^{3} - \frac{155863472207625}{23} a^{2} - \frac{2234043101642625}{23} a + \frac{4304548021844250}{23} \) |
\( \bigl[-\frac{2}{23} a^{3} + \frac{3}{23} a^{2} + \frac{43}{23} a - \frac{22}{23}\) , \( -1\) , \( -\frac{2}{23} a^{3} + \frac{3}{23} a^{2} + \frac{43}{23} a - \frac{22}{23}\) , \( \frac{540}{23} a^{3} - \frac{810}{23} a^{2} - \frac{11610}{23} a - \frac{10574}{23}\) , \( \frac{6446}{23} a^{3} - \frac{9669}{23} a^{2} - \frac{138589}{23} a - \frac{125261}{23}\bigr] \) |
${y}^2+\left(-\frac{2}{23}a^{3}+\frac{3}{23}a^{2}+\frac{43}{23}a-\frac{22}{23}\right){x}{y}+\left(-\frac{2}{23}a^{3}+\frac{3}{23}a^{2}+\frac{43}{23}a-\frac{22}{23}\right){y}={x}^{3}-{x}^{2}+\left(\frac{540}{23}a^{3}-\frac{810}{23}a^{2}-\frac{11610}{23}a-\frac{10574}{23}\right){x}+\frac{6446}{23}a^{3}-\frac{9669}{23}a^{2}-\frac{138589}{23}a-\frac{125261}{23}$ |
| 1.1-c4 |
1.1-c |
$8$ |
$28$ |
\(\Q(\sqrt{5}, \sqrt{7})\) |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$12.51027$ |
$\textsf{none}$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{potential}$ |
$-28$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
✓ |
✓ |
$2$ |
2Cs |
$1$ |
\( 1 \) |
$1$ |
$684.5475207$ |
0.305601571 |
\( 16581375 \) |
\( \bigl[-\frac{2}{23} a^{3} + \frac{3}{23} a^{2} + \frac{43}{23} a - \frac{22}{23}\) , \( -1\) , \( -\frac{2}{23} a^{3} + \frac{3}{23} a^{2} + \frac{43}{23} a - \frac{22}{23}\) , \( \frac{510}{23} a^{3} - \frac{765}{23} a^{2} - \frac{10965}{23} a - \frac{9984}{23}\) , \( \frac{7338}{23} a^{3} - \frac{11007}{23} a^{2} - \frac{157767}{23} a - \frac{142589}{23}\bigr] \) |
${y}^2+\left(-\frac{2}{23}a^{3}+\frac{3}{23}a^{2}+\frac{43}{23}a-\frac{22}{23}\right){x}{y}+\left(-\frac{2}{23}a^{3}+\frac{3}{23}a^{2}+\frac{43}{23}a-\frac{22}{23}\right){y}={x}^{3}-{x}^{2}+\left(\frac{510}{23}a^{3}-\frac{765}{23}a^{2}-\frac{10965}{23}a-\frac{9984}{23}\right){x}+\frac{7338}{23}a^{3}-\frac{11007}{23}a^{2}-\frac{157767}{23}a-\frac{142589}{23}$ |
| 1.1-c5 |
1.1-c |
$8$ |
$28$ |
\(\Q(\sqrt{5}, \sqrt{7})\) |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$12.51027$ |
$\textsf{none}$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-112$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
✓ |
✓ |
|
|
$4$ |
\( 1 \) |
$1$ |
$42.78422004$ |
0.305601571 |
\( -\frac{103908981471750}{23} a^{3} + \frac{155863472207625}{23} a^{2} + \frac{2234043101642625}{23} a + \frac{2018550429465750}{23} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -\frac{540}{23} a^{3} + \frac{810}{23} a^{2} + \frac{11610}{23} a - \frac{22385}{23}\) , \( \frac{6446}{23} a^{3} - \frac{9669}{23} a^{2} - \frac{138589}{23} a + \frac{267027}{23}\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}+\left(-\frac{540}{23}a^{3}+\frac{810}{23}a^{2}+\frac{11610}{23}a-\frac{22385}{23}\right){x}+\frac{6446}{23}a^{3}-\frac{9669}{23}a^{2}-\frac{138589}{23}a+\frac{267027}{23}$ |
| 1.1-c6 |
1.1-c |
$8$ |
$28$ |
\(\Q(\sqrt{5}, \sqrt{7})\) |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$12.51027$ |
$\textsf{none}$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-112$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
✓ |
✓ |
|
|
$4$ |
\( 1 \) |
$1$ |
$42.78422004$ |
0.305601571 |
\( \frac{103908981471750}{23} a^{3} - \frac{155863472207625}{23} a^{2} - \frac{2234043101642625}{23} a + \frac{4304548021844250}{23} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( \frac{540}{23} a^{3} - \frac{810}{23} a^{2} - \frac{11610}{23} a - \frac{10505}{23}\) , \( -\frac{6446}{23} a^{3} + \frac{9669}{23} a^{2} + \frac{138589}{23} a + \frac{125215}{23}\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}+\left(\frac{540}{23}a^{3}-\frac{810}{23}a^{2}-\frac{11610}{23}a-\frac{10505}{23}\right){x}-\frac{6446}{23}a^{3}+\frac{9669}{23}a^{2}+\frac{138589}{23}a+\frac{125215}{23}$ |
| 1.1-c7 |
1.1-c |
$8$ |
$28$ |
\(\Q(\sqrt{5}, \sqrt{7})\) |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$12.51027$ |
$\textsf{none}$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{potential}$ |
$-28$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
✓ |
✓ |
$2$ |
2Cs |
$1$ |
\( 1 \) |
$1$ |
$684.5475207$ |
0.305601571 |
\( 16581375 \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( \frac{510}{23} a^{3} - \frac{765}{23} a^{2} - \frac{10965}{23} a - \frac{9915}{23}\) , \( -\frac{7338}{23} a^{3} + \frac{11007}{23} a^{2} + \frac{157767}{23} a + \frac{142543}{23}\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}+\left(\frac{510}{23}a^{3}-\frac{765}{23}a^{2}-\frac{10965}{23}a-\frac{9915}{23}\right){x}-\frac{7338}{23}a^{3}+\frac{11007}{23}a^{2}+\frac{157767}{23}a+\frac{142543}{23}$ |
| 1.1-c8 |
1.1-c |
$8$ |
$28$ |
\(\Q(\sqrt{5}, \sqrt{7})\) |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$12.51027$ |
$\textsf{none}$ |
0 |
$\Z/4\Z$ |
$\textsf{potential}$ |
$-7$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
✓ |
✓ |
|
|
$1$ |
\( 1 \) |
$1$ |
$684.5475207$ |
0.305601571 |
\( -3375 \) |
\( \bigl[-\frac{3}{23} a^{3} + \frac{16}{23} a^{2} + \frac{30}{23} a - \frac{102}{23}\) , \( \frac{2}{23} a^{3} - \frac{3}{23} a^{2} - \frac{43}{23} a + \frac{22}{23}\) , \( -\frac{2}{23} a^{3} + \frac{3}{23} a^{2} + \frac{43}{23} a + \frac{1}{23}\) , \( \frac{7}{23} a^{3} - \frac{114}{23} a^{2} - \frac{47}{23} a + \frac{560}{23}\) , \( \frac{105}{23} a^{3} - \frac{261}{23} a^{2} - \frac{268}{23} a + \frac{649}{23}\bigr] \) |
${y}^2+\left(-\frac{3}{23}a^{3}+\frac{16}{23}a^{2}+\frac{30}{23}a-\frac{102}{23}\right){x}{y}+\left(-\frac{2}{23}a^{3}+\frac{3}{23}a^{2}+\frac{43}{23}a+\frac{1}{23}\right){y}={x}^{3}+\left(\frac{2}{23}a^{3}-\frac{3}{23}a^{2}-\frac{43}{23}a+\frac{22}{23}\right){x}^{2}+\left(\frac{7}{23}a^{3}-\frac{114}{23}a^{2}-\frac{47}{23}a+\frac{560}{23}\right){x}+\frac{105}{23}a^{3}-\frac{261}{23}a^{2}-\frac{268}{23}a+\frac{649}{23}$ |
| 16.1-a1 |
16.1-a |
$4$ |
$6$ |
\(\Q(\sqrt{5}, \sqrt{7})\) |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{16} \) |
$17.69219$ |
$(3/23a^3+7/23a^2-53/23a-128/23)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2, 3$ |
2B, 3B |
$1$ |
\( 3 \) |
$1$ |
$419.4948491$ |
2.247293834 |
\( -\frac{100368408}{23} a^{3} + \frac{150552612}{23} a^{2} + \frac{2157920772}{23} a + \frac{1949810968}{23} \) |
\( \bigl[-\frac{1}{23} a^{3} + \frac{13}{23} a^{2} - \frac{13}{23} a - \frac{80}{23}\) , \( \frac{5}{23} a^{3} + \frac{4}{23} a^{2} - \frac{96}{23} a - \frac{60}{23}\) , \( 0\) , \( -\frac{62}{23} a^{3} - \frac{45}{23} a^{2} + \frac{91}{23} a + \frac{123}{23}\) , \( \frac{312}{23} a^{3} + \frac{889}{23} a^{2} - \frac{1924}{23} a - \frac{2571}{23}\bigr] \) |
${y}^2+\left(-\frac{1}{23}a^{3}+\frac{13}{23}a^{2}-\frac{13}{23}a-\frac{80}{23}\right){x}{y}={x}^{3}+\left(\frac{5}{23}a^{3}+\frac{4}{23}a^{2}-\frac{96}{23}a-\frac{60}{23}\right){x}^{2}+\left(-\frac{62}{23}a^{3}-\frac{45}{23}a^{2}+\frac{91}{23}a+\frac{123}{23}\right){x}+\frac{312}{23}a^{3}+\frac{889}{23}a^{2}-\frac{1924}{23}a-\frac{2571}{23}$ |
| 16.1-a2 |
16.1-a |
$4$ |
$6$ |
\(\Q(\sqrt{5}, \sqrt{7})\) |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{8} \) |
$17.69219$ |
$(3/23a^3+7/23a^2-53/23a-128/23)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2, 3$ |
2B, 3B |
$1$ |
\( 3 \) |
$1$ |
$419.4948491$ |
2.247293834 |
\( \frac{6528}{23} a^{3} - \frac{9792}{23} a^{2} - \frac{140352}{23} a - \frac{87536}{23} \) |
\( \bigl[-\frac{3}{23} a^{3} + \frac{16}{23} a^{2} + \frac{30}{23} a - \frac{125}{23}\) , \( -\frac{3}{23} a^{3} - \frac{7}{23} a^{2} + \frac{76}{23} a + \frac{36}{23}\) , \( -\frac{3}{23} a^{3} + \frac{16}{23} a^{2} + \frac{30}{23} a - \frac{125}{23}\) , \( -\frac{5}{23} a^{3} + \frac{19}{23} a^{2} + \frac{4}{23} a - \frac{78}{23}\) , \( \frac{30}{23} a^{3} - \frac{22}{23} a^{2} - \frac{392}{23} a - \frac{291}{23}\bigr] \) |
${y}^2+\left(-\frac{3}{23}a^{3}+\frac{16}{23}a^{2}+\frac{30}{23}a-\frac{125}{23}\right){x}{y}+\left(-\frac{3}{23}a^{3}+\frac{16}{23}a^{2}+\frac{30}{23}a-\frac{125}{23}\right){y}={x}^{3}+\left(-\frac{3}{23}a^{3}-\frac{7}{23}a^{2}+\frac{76}{23}a+\frac{36}{23}\right){x}^{2}+\left(-\frac{5}{23}a^{3}+\frac{19}{23}a^{2}+\frac{4}{23}a-\frac{78}{23}\right){x}+\frac{30}{23}a^{3}-\frac{22}{23}a^{2}-\frac{392}{23}a-\frac{291}{23}$ |
| 16.1-a3 |
16.1-a |
$4$ |
$6$ |
\(\Q(\sqrt{5}, \sqrt{7})\) |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{16} \) |
$17.69219$ |
$(3/23a^3+7/23a^2-53/23a-128/23)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2, 3$ |
2B, 3B |
$1$ |
\( 3 \) |
$1$ |
$419.4948491$ |
2.247293834 |
\( \frac{100368408}{23} a^{3} - \frac{150552612}{23} a^{2} - \frac{2157920772}{23} a + \frac{4157915944}{23} \) |
\( \bigl[-\frac{1}{23} a^{3} + \frac{13}{23} a^{2} - \frac{13}{23} a - \frac{80}{23}\) , \( \frac{5}{23} a^{3} + \frac{4}{23} a^{2} - \frac{96}{23} a - \frac{60}{23}\) , \( -\frac{2}{23} a^{3} + \frac{3}{23} a^{2} + \frac{43}{23} a + \frac{1}{23}\) , \( -\frac{164}{23} a^{3} + \frac{476}{23} a^{2} + \frac{1847}{23} a - \frac{3874}{23}\) , \( \frac{715}{23} a^{3} - \frac{2211}{23} a^{2} - \frac{8093}{23} a + \frac{19204}{23}\bigr] \) |
${y}^2+\left(-\frac{1}{23}a^{3}+\frac{13}{23}a^{2}-\frac{13}{23}a-\frac{80}{23}\right){x}{y}+\left(-\frac{2}{23}a^{3}+\frac{3}{23}a^{2}+\frac{43}{23}a+\frac{1}{23}\right){y}={x}^{3}+\left(\frac{5}{23}a^{3}+\frac{4}{23}a^{2}-\frac{96}{23}a-\frac{60}{23}\right){x}^{2}+\left(-\frac{164}{23}a^{3}+\frac{476}{23}a^{2}+\frac{1847}{23}a-\frac{3874}{23}\right){x}+\frac{715}{23}a^{3}-\frac{2211}{23}a^{2}-\frac{8093}{23}a+\frac{19204}{23}$ |
| 16.1-a4 |
16.1-a |
$4$ |
$6$ |
\(\Q(\sqrt{5}, \sqrt{7})\) |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{8} \) |
$17.69219$ |
$(3/23a^3+7/23a^2-53/23a-128/23)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2, 3$ |
2B, 3B |
$1$ |
\( 3 \) |
$1$ |
$419.4948491$ |
2.247293834 |
\( -\frac{6528}{23} a^{3} + \frac{9792}{23} a^{2} + \frac{140352}{23} a - \frac{231152}{23} \) |
\( \bigl[-\frac{1}{23} a^{3} + \frac{13}{23} a^{2} - \frac{13}{23} a - \frac{80}{23}\) , \( \frac{5}{23} a^{3} + \frac{4}{23} a^{2} - \frac{96}{23} a - \frac{60}{23}\) , \( -\frac{2}{23} a^{3} + \frac{3}{23} a^{2} + \frac{43}{23} a + \frac{1}{23}\) , \( -\frac{39}{23} a^{3} + \frac{116}{23} a^{2} + \frac{252}{23} a - \frac{199}{23}\) , \( -\frac{10}{23} a^{3} + \frac{107}{23} a^{2} - \frac{245}{23} a - \frac{202}{23}\bigr] \) |
${y}^2+\left(-\frac{1}{23}a^{3}+\frac{13}{23}a^{2}-\frac{13}{23}a-\frac{80}{23}\right){x}{y}+\left(-\frac{2}{23}a^{3}+\frac{3}{23}a^{2}+\frac{43}{23}a+\frac{1}{23}\right){y}={x}^{3}+\left(\frac{5}{23}a^{3}+\frac{4}{23}a^{2}-\frac{96}{23}a-\frac{60}{23}\right){x}^{2}+\left(-\frac{39}{23}a^{3}+\frac{116}{23}a^{2}+\frac{252}{23}a-\frac{199}{23}\right){x}-\frac{10}{23}a^{3}+\frac{107}{23}a^{2}-\frac{245}{23}a-\frac{202}{23}$ |
| 16.1-b1 |
16.1-b |
$4$ |
$6$ |
\(\Q(\sqrt{5}, \sqrt{7})\) |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{16} \) |
$17.69219$ |
$(3/23a^3+7/23a^2-53/23a-128/23)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2, 3$ |
2B, 3B |
$1$ |
\( 3 \) |
$1$ |
$419.4948491$ |
2.247293834 |
\( \frac{100368408}{23} a^{3} - \frac{150552612}{23} a^{2} - \frac{2157920772}{23} a + \frac{4157915944}{23} \) |
\( \bigl[-\frac{3}{23} a^{3} + \frac{16}{23} a^{2} + \frac{30}{23} a - \frac{125}{23}\) , \( -\frac{5}{23} a^{3} - \frac{4}{23} a^{2} + \frac{96}{23} a + \frac{37}{23}\) , \( -\frac{1}{23} a^{3} + \frac{13}{23} a^{2} - \frac{13}{23} a - \frac{80}{23}\) , \( \frac{28}{23} a^{3} - \frac{249}{23} a^{2} + \frac{502}{23} a + \frac{193}{23}\) , \( -\frac{514}{23} a^{3} + \frac{2473}{23} a^{2} + \frac{195}{23} a - \frac{5953}{23}\bigr] \) |
${y}^2+\left(-\frac{3}{23}a^{3}+\frac{16}{23}a^{2}+\frac{30}{23}a-\frac{125}{23}\right){x}{y}+\left(-\frac{1}{23}a^{3}+\frac{13}{23}a^{2}-\frac{13}{23}a-\frac{80}{23}\right){y}={x}^{3}+\left(-\frac{5}{23}a^{3}-\frac{4}{23}a^{2}+\frac{96}{23}a+\frac{37}{23}\right){x}^{2}+\left(\frac{28}{23}a^{3}-\frac{249}{23}a^{2}+\frac{502}{23}a+\frac{193}{23}\right){x}-\frac{514}{23}a^{3}+\frac{2473}{23}a^{2}+\frac{195}{23}a-\frac{5953}{23}$ |
| 16.1-b2 |
16.1-b |
$4$ |
$6$ |
\(\Q(\sqrt{5}, \sqrt{7})\) |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{8} \) |
$17.69219$ |
$(3/23a^3+7/23a^2-53/23a-128/23)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2, 3$ |
2B, 3B |
$1$ |
\( 3 \) |
$1$ |
$419.4948491$ |
2.247293834 |
\( -\frac{6528}{23} a^{3} + \frac{9792}{23} a^{2} + \frac{140352}{23} a - \frac{231152}{23} \) |
\( \bigl[-\frac{3}{23} a^{3} + \frac{16}{23} a^{2} + \frac{30}{23} a - \frac{125}{23}\) , \( -\frac{5}{23} a^{3} - \frac{4}{23} a^{2} + \frac{96}{23} a + \frac{37}{23}\) , \( -\frac{1}{23} a^{3} + \frac{13}{23} a^{2} - \frac{13}{23} a - \frac{80}{23}\) , \( -\frac{7}{23} a^{3} - \frac{24}{23} a^{2} + \frac{162}{23} a + \frac{268}{23}\) , \( -\frac{17}{23} a^{3} + \frac{37}{23} a^{2} + \frac{124}{23} a + \frac{112}{23}\bigr] \) |
${y}^2+\left(-\frac{3}{23}a^{3}+\frac{16}{23}a^{2}+\frac{30}{23}a-\frac{125}{23}\right){x}{y}+\left(-\frac{1}{23}a^{3}+\frac{13}{23}a^{2}-\frac{13}{23}a-\frac{80}{23}\right){y}={x}^{3}+\left(-\frac{5}{23}a^{3}-\frac{4}{23}a^{2}+\frac{96}{23}a+\frac{37}{23}\right){x}^{2}+\left(-\frac{7}{23}a^{3}-\frac{24}{23}a^{2}+\frac{162}{23}a+\frac{268}{23}\right){x}-\frac{17}{23}a^{3}+\frac{37}{23}a^{2}+\frac{124}{23}a+\frac{112}{23}$ |
| 16.1-b3 |
16.1-b |
$4$ |
$6$ |
\(\Q(\sqrt{5}, \sqrt{7})\) |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{8} \) |
$17.69219$ |
$(3/23a^3+7/23a^2-53/23a-128/23)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2, 3$ |
2B, 3B |
$1$ |
\( 3 \) |
$1$ |
$419.4948491$ |
2.247293834 |
\( \frac{6528}{23} a^{3} - \frac{9792}{23} a^{2} - \frac{140352}{23} a - \frac{87536}{23} \) |
\( \bigl[-\frac{3}{23} a^{3} + \frac{16}{23} a^{2} + \frac{30}{23} a - \frac{125}{23}\) , \( -\frac{5}{23} a^{3} - \frac{4}{23} a^{2} + \frac{96}{23} a + \frac{37}{23}\) , \( -\frac{3}{23} a^{3} + \frac{16}{23} a^{2} + \frac{30}{23} a - \frac{125}{23}\) , \( -\frac{10}{23} a^{3} + \frac{15}{23} a^{2} + \frac{100}{23} a - \frac{41}{23}\) , \( -\frac{1}{23} a^{3} - \frac{10}{23} a^{2} + \frac{33}{23} a + \frac{35}{23}\bigr] \) |
${y}^2+\left(-\frac{3}{23}a^{3}+\frac{16}{23}a^{2}+\frac{30}{23}a-\frac{125}{23}\right){x}{y}+\left(-\frac{3}{23}a^{3}+\frac{16}{23}a^{2}+\frac{30}{23}a-\frac{125}{23}\right){y}={x}^{3}+\left(-\frac{5}{23}a^{3}-\frac{4}{23}a^{2}+\frac{96}{23}a+\frac{37}{23}\right){x}^{2}+\left(-\frac{10}{23}a^{3}+\frac{15}{23}a^{2}+\frac{100}{23}a-\frac{41}{23}\right){x}-\frac{1}{23}a^{3}-\frac{10}{23}a^{2}+\frac{33}{23}a+\frac{35}{23}$ |
| 16.1-b4 |
16.1-b |
$4$ |
$6$ |
\(\Q(\sqrt{5}, \sqrt{7})\) |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{16} \) |
$17.69219$ |
$(3/23a^3+7/23a^2-53/23a-128/23)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2, 3$ |
2B, 3B |
$1$ |
\( 3 \) |
$1$ |
$419.4948491$ |
2.247293834 |
\( -\frac{100368408}{23} a^{3} + \frac{150552612}{23} a^{2} + \frac{2157920772}{23} a + \frac{1949810968}{23} \) |
\( \bigl[-\frac{3}{23} a^{3} + \frac{16}{23} a^{2} + \frac{30}{23} a - \frac{125}{23}\) , \( -\frac{5}{23} a^{3} - \frac{4}{23} a^{2} + \frac{96}{23} a + \frac{37}{23}\) , \( -\frac{3}{23} a^{3} + \frac{16}{23} a^{2} + \frac{30}{23} a - \frac{125}{23}\) , \( 5 a^{3} - 80 a - 82\) , \( -\frac{476}{23} a^{3} - \frac{68}{23} a^{2} + \frac{6922}{23} a + \frac{6655}{23}\bigr] \) |
${y}^2+\left(-\frac{3}{23}a^{3}+\frac{16}{23}a^{2}+\frac{30}{23}a-\frac{125}{23}\right){x}{y}+\left(-\frac{3}{23}a^{3}+\frac{16}{23}a^{2}+\frac{30}{23}a-\frac{125}{23}\right){y}={x}^{3}+\left(-\frac{5}{23}a^{3}-\frac{4}{23}a^{2}+\frac{96}{23}a+\frac{37}{23}\right){x}^{2}+\left(5a^{3}-80a-82\right){x}-\frac{476}{23}a^{3}-\frac{68}{23}a^{2}+\frac{6922}{23}a+\frac{6655}{23}$ |
| 25.1-a1 |
25.1-a |
$1$ |
$1$ |
\(\Q(\sqrt{5}, \sqrt{7})\) |
$4$ |
$[4, 0]$ |
25.1 |
\( 5^{2} \) |
\( 5^{8} \) |
$18.70721$ |
$(4/23a^3-6/23a^2-40/23a+21/23)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2^{2} \) |
$0.147496153$ |
$255.8522261$ |
4.312825049 |
\( \frac{4096}{25} a^{2} - \frac{4096}{25} a - \frac{57344}{25} \) |
\( \bigl[0\) , \( -\frac{3}{23} a^{3} + \frac{16}{23} a^{2} + \frac{30}{23} a - \frac{102}{23}\) , \( -\frac{1}{23} a^{3} + \frac{13}{23} a^{2} - \frac{13}{23} a - \frac{103}{23}\) , \( \frac{11}{23} a^{3} - \frac{5}{23} a^{2} - \frac{156}{23} a + \frac{6}{23}\) , \( -\frac{11}{23} a^{3} + \frac{5}{23} a^{2} + \frac{179}{23} a + \frac{40}{23}\bigr] \) |
${y}^2+\left(-\frac{1}{23}a^{3}+\frac{13}{23}a^{2}-\frac{13}{23}a-\frac{103}{23}\right){y}={x}^{3}+\left(-\frac{3}{23}a^{3}+\frac{16}{23}a^{2}+\frac{30}{23}a-\frac{102}{23}\right){x}^{2}+\left(\frac{11}{23}a^{3}-\frac{5}{23}a^{2}-\frac{156}{23}a+\frac{6}{23}\right){x}-\frac{11}{23}a^{3}+\frac{5}{23}a^{2}+\frac{179}{23}a+\frac{40}{23}$ |
| 25.1-b1 |
25.1-b |
$1$ |
$1$ |
\(\Q(\sqrt{5}, \sqrt{7})\) |
$4$ |
$[4, 0]$ |
25.1 |
\( 5^{2} \) |
\( 5^{12} \) |
$18.70721$ |
$(4/23a^3-6/23a^2-40/23a+21/23)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3$ |
3Nn |
$1$ |
\( 2 \) |
$1$ |
$148.3015636$ |
2.118593766 |
\( -\frac{110592}{125} \) |
\( \bigl[0\) , \( 0\) , \( -\frac{3}{23} a^{3} + \frac{16}{23} a^{2} + \frac{30}{23} a - \frac{102}{23}\) , \( -12 a^{2} + 12 a + 25\) , \( -\frac{582}{23} a^{3} + \frac{873}{23} a^{2} + \frac{967}{23} a - \frac{698}{23}\bigr] \) |
${y}^2+\left(-\frac{3}{23}a^{3}+\frac{16}{23}a^{2}+\frac{30}{23}a-\frac{102}{23}\right){y}={x}^{3}+\left(-12a^{2}+12a+25\right){x}-\frac{582}{23}a^{3}+\frac{873}{23}a^{2}+\frac{967}{23}a-\frac{698}{23}$ |
| 25.1-c1 |
25.1-c |
$1$ |
$1$ |
\(\Q(\sqrt{5}, \sqrt{7})\) |
$4$ |
$[4, 0]$ |
25.1 |
\( 5^{2} \) |
\( 5^{8} \) |
$18.70721$ |
$(4/23a^3-6/23a^2-40/23a+21/23)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2^{2} \) |
$0.147496153$ |
$255.8522261$ |
4.312825049 |
\( -\frac{4096}{25} a^{2} + \frac{4096}{25} a + \frac{8192}{25} \) |
\( \bigl[0\) , \( -\frac{1}{23} a^{3} + \frac{13}{23} a^{2} - \frac{13}{23} a - \frac{103}{23}\) , \( -\frac{1}{23} a^{3} + \frac{13}{23} a^{2} - \frac{13}{23} a - \frac{103}{23}\) , \( -\frac{5}{23} a^{3} - \frac{4}{23} a^{2} + \frac{27}{23} a + \frac{106}{23}\) , \( -\frac{3}{23} a^{3} - \frac{7}{23} a^{2} + \frac{7}{23} a - \frac{79}{23}\bigr] \) |
${y}^2+\left(-\frac{1}{23}a^{3}+\frac{13}{23}a^{2}-\frac{13}{23}a-\frac{103}{23}\right){y}={x}^{3}+\left(-\frac{1}{23}a^{3}+\frac{13}{23}a^{2}-\frac{13}{23}a-\frac{103}{23}\right){x}^{2}+\left(-\frac{5}{23}a^{3}-\frac{4}{23}a^{2}+\frac{27}{23}a+\frac{106}{23}\right){x}-\frac{3}{23}a^{3}-\frac{7}{23}a^{2}+\frac{7}{23}a-\frac{79}{23}$ |
| 25.1-d1 |
25.1-d |
$1$ |
$1$ |
\(\Q(\sqrt{5}, \sqrt{7})\) |
$4$ |
$[4, 0]$ |
25.1 |
\( 5^{2} \) |
\( 5^{12} \) |
$18.70721$ |
$(4/23a^3-6/23a^2-40/23a+21/23)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3$ |
3Nn |
$1$ |
\( 2 \) |
$1$ |
$148.3015636$ |
2.118593766 |
\( -\frac{110592}{125} \) |
\( \bigl[0\) , \( 0\) , \( -\frac{2}{23} a^{3} + \frac{3}{23} a^{2} + \frac{43}{23} a - \frac{22}{23}\) , \( \frac{96}{23} a^{3} - \frac{144}{23} a^{2} - \frac{2064}{23} a - \frac{1865}{23}\) , \( -44 a^{3} + 66 a^{2} + 946 a + 853\bigr] \) |
${y}^2+\left(-\frac{2}{23}a^{3}+\frac{3}{23}a^{2}+\frac{43}{23}a-\frac{22}{23}\right){y}={x}^{3}+\left(\frac{96}{23}a^{3}-\frac{144}{23}a^{2}-\frac{2064}{23}a-\frac{1865}{23}\right){x}-44a^{3}+66a^{2}+946a+853$ |
| 25.1-e1 |
25.1-e |
$1$ |
$1$ |
\(\Q(\sqrt{5}, \sqrt{7})\) |
$4$ |
$[4, 0]$ |
25.1 |
\( 5^{2} \) |
\( 5^{8} \) |
$18.70721$ |
$(4/23a^3-6/23a^2-40/23a+21/23)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2^{2} \) |
$0.147496153$ |
$255.8522261$ |
4.312825049 |
\( \frac{4096}{25} a^{2} - \frac{4096}{25} a - \frac{57344}{25} \) |
\( \bigl[0\) , \( \frac{3}{23} a^{3} - \frac{16}{23} a^{2} - \frac{30}{23} a + \frac{102}{23}\) , \( -\frac{3}{23} a^{3} + \frac{16}{23} a^{2} + \frac{30}{23} a - \frac{102}{23}\) , \( \frac{11}{23} a^{3} - \frac{5}{23} a^{2} - \frac{156}{23} a + \frac{6}{23}\) , \( \frac{9}{23} a^{3} - \frac{2}{23} a^{2} - \frac{136}{23} a - \frac{200}{23}\bigr] \) |
${y}^2+\left(-\frac{3}{23}a^{3}+\frac{16}{23}a^{2}+\frac{30}{23}a-\frac{102}{23}\right){y}={x}^{3}+\left(\frac{3}{23}a^{3}-\frac{16}{23}a^{2}-\frac{30}{23}a+\frac{102}{23}\right){x}^{2}+\left(\frac{11}{23}a^{3}-\frac{5}{23}a^{2}-\frac{156}{23}a+\frac{6}{23}\right){x}+\frac{9}{23}a^{3}-\frac{2}{23}a^{2}-\frac{136}{23}a-\frac{200}{23}$ |
| 25.1-f1 |
25.1-f |
$1$ |
$1$ |
\(\Q(\sqrt{5}, \sqrt{7})\) |
$4$ |
$[4, 0]$ |
25.1 |
\( 5^{2} \) |
\( 5^{8} \) |
$18.70721$ |
$(4/23a^3-6/23a^2-40/23a+21/23)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2^{2} \) |
$0.147496153$ |
$255.8522261$ |
4.312825049 |
\( -\frac{4096}{25} a^{2} + \frac{4096}{25} a + \frac{8192}{25} \) |
\( \bigl[0\) , \( \frac{1}{23} a^{3} - \frac{13}{23} a^{2} + \frac{13}{23} a + \frac{103}{23}\) , \( -\frac{3}{23} a^{3} + \frac{16}{23} a^{2} + \frac{30}{23} a - \frac{102}{23}\) , \( -\frac{5}{23} a^{3} - \frac{4}{23} a^{2} + \frac{27}{23} a + \frac{106}{23}\) , \( \frac{1}{23} a^{3} + \frac{10}{23} a^{2} + \frac{36}{23} a - \frac{81}{23}\bigr] \) |
${y}^2+\left(-\frac{3}{23}a^{3}+\frac{16}{23}a^{2}+\frac{30}{23}a-\frac{102}{23}\right){y}={x}^{3}+\left(\frac{1}{23}a^{3}-\frac{13}{23}a^{2}+\frac{13}{23}a+\frac{103}{23}\right){x}^{2}+\left(-\frac{5}{23}a^{3}-\frac{4}{23}a^{2}+\frac{27}{23}a+\frac{106}{23}\right){x}+\frac{1}{23}a^{3}+\frac{10}{23}a^{2}+\frac{36}{23}a-\frac{81}{23}$ |
| 29.1-a1 |
29.1-a |
$2$ |
$3$ |
\(\Q(\sqrt{5}, \sqrt{7})\) |
$4$ |
$[4, 0]$ |
29.1 |
\( 29 \) |
\( 29 \) |
$19.05752$ |
$(1/23a^3+10/23a^2-10/23a-58/23)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 1 \) |
$0.183254829$ |
$501.7034145$ |
2.626844961 |
\( -\frac{5568759973}{667} a^{3} + \frac{16860467555}{667} a^{2} + \frac{66203237496}{667} a - \frac{157137341477}{667} \) |
\( \bigl[-\frac{4}{23} a^{3} + \frac{6}{23} a^{2} + \frac{63}{23} a - \frac{44}{23}\) , \( \frac{1}{23} a^{3} - \frac{13}{23} a^{2} - \frac{10}{23} a + \frac{126}{23}\) , \( -\frac{3}{23} a^{3} + \frac{16}{23} a^{2} + \frac{30}{23} a - \frac{102}{23}\) , \( -\frac{8}{23} a^{3} + \frac{35}{23} a^{2} - \frac{58}{23} a + \frac{257}{23}\) , \( \frac{81}{23} a^{3} - \frac{432}{23} a^{2} + \frac{110}{23} a + \frac{1006}{23}\bigr] \) |
${y}^2+\left(-\frac{4}{23}a^{3}+\frac{6}{23}a^{2}+\frac{63}{23}a-\frac{44}{23}\right){x}{y}+\left(-\frac{3}{23}a^{3}+\frac{16}{23}a^{2}+\frac{30}{23}a-\frac{102}{23}\right){y}={x}^{3}+\left(\frac{1}{23}a^{3}-\frac{13}{23}a^{2}-\frac{10}{23}a+\frac{126}{23}\right){x}^{2}+\left(-\frac{8}{23}a^{3}+\frac{35}{23}a^{2}-\frac{58}{23}a+\frac{257}{23}\right){x}+\frac{81}{23}a^{3}-\frac{432}{23}a^{2}+\frac{110}{23}a+\frac{1006}{23}$ |
| 29.1-a2 |
29.1-a |
$2$ |
$3$ |
\(\Q(\sqrt{5}, \sqrt{7})\) |
$4$ |
$[4, 0]$ |
29.1 |
\( 29 \) |
\( 29^{3} \) |
$19.05752$ |
$(1/23a^3+10/23a^2-10/23a-58/23)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 3 \) |
$0.061084943$ |
$501.7034145$ |
2.626844961 |
\( \frac{12031685}{560947} a^{3} + \frac{20868070}{560947} a^{2} - \frac{74839295}{560947} a - \frac{184229169}{560947} \) |
\( \bigl[-\frac{3}{23} a^{3} + \frac{16}{23} a^{2} + \frac{30}{23} a - \frac{102}{23}\) , \( -a + 1\) , \( -\frac{2}{23} a^{3} + \frac{3}{23} a^{2} + \frac{43}{23} a - \frac{22}{23}\) , \( \frac{54}{23} a^{3} + \frac{103}{23} a^{2} - \frac{425}{23} a - \frac{142}{23}\) , \( \frac{129}{23} a^{3} + \frac{232}{23} a^{2} - \frac{876}{23} a - \frac{605}{23}\bigr] \) |
${y}^2+\left(-\frac{3}{23}a^{3}+\frac{16}{23}a^{2}+\frac{30}{23}a-\frac{102}{23}\right){x}{y}+\left(-\frac{2}{23}a^{3}+\frac{3}{23}a^{2}+\frac{43}{23}a-\frac{22}{23}\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(\frac{54}{23}a^{3}+\frac{103}{23}a^{2}-\frac{425}{23}a-\frac{142}{23}\right){x}+\frac{129}{23}a^{3}+\frac{232}{23}a^{2}-\frac{876}{23}a-\frac{605}{23}$ |
| 29.1-b1 |
29.1-b |
$2$ |
$3$ |
\(\Q(\sqrt{5}, \sqrt{7})\) |
$4$ |
$[4, 0]$ |
29.1 |
\( 29 \) |
\( 29 \) |
$19.05752$ |
$(1/23a^3+10/23a^2-10/23a-58/23)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 1 \) |
$0.527378321$ |
$217.9490740$ |
3.284046195 |
\( -\frac{5568759973}{667} a^{3} + \frac{16860467555}{667} a^{2} + \frac{66203237496}{667} a - \frac{157137341477}{667} \) |
\( \bigl[-\frac{1}{23} a^{3} + \frac{13}{23} a^{2} + \frac{10}{23} a - \frac{80}{23}\) , \( \frac{1}{23} a^{3} + \frac{10}{23} a^{2} - \frac{10}{23} a - \frac{58}{23}\) , \( 0\) , \( 5 a^{2} - 3 a - 14\) , \( -\frac{71}{23} a^{3} + \frac{555}{23} a^{2} - \frac{279}{23} a - \frac{1126}{23}\bigr] \) |
${y}^2+\left(-\frac{1}{23}a^{3}+\frac{13}{23}a^{2}+\frac{10}{23}a-\frac{80}{23}\right){x}{y}={x}^{3}+\left(\frac{1}{23}a^{3}+\frac{10}{23}a^{2}-\frac{10}{23}a-\frac{58}{23}\right){x}^{2}+\left(5a^{2}-3a-14\right){x}-\frac{71}{23}a^{3}+\frac{555}{23}a^{2}-\frac{279}{23}a-\frac{1126}{23}$ |
| 29.1-b2 |
29.1-b |
$2$ |
$3$ |
\(\Q(\sqrt{5}, \sqrt{7})\) |
$4$ |
$[4, 0]$ |
29.1 |
\( 29 \) |
\( 29^{3} \) |
$19.05752$ |
$(1/23a^3+10/23a^2-10/23a-58/23)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 3 \) |
$0.175792773$ |
$217.9490740$ |
3.284046195 |
\( \frac{12031685}{560947} a^{3} + \frac{20868070}{560947} a^{2} - \frac{74839295}{560947} a - \frac{184229169}{560947} \) |
\( \bigl[-\frac{1}{23} a^{3} + \frac{13}{23} a^{2} - \frac{13}{23} a - \frac{103}{23}\) , \( \frac{4}{23} a^{3} - \frac{6}{23} a^{2} - \frac{63}{23} a + \frac{21}{23}\) , \( -\frac{3}{23} a^{3} + \frac{16}{23} a^{2} + \frac{30}{23} a - \frac{125}{23}\) , \( \frac{51}{23} a^{3} + \frac{119}{23} a^{2} - \frac{349}{23} a - \frac{382}{23}\) , \( -\frac{157}{23} a^{3} - \frac{305}{23} a^{2} + \frac{926}{23} a + \frac{1079}{23}\bigr] \) |
${y}^2+\left(-\frac{1}{23}a^{3}+\frac{13}{23}a^{2}-\frac{13}{23}a-\frac{103}{23}\right){x}{y}+\left(-\frac{3}{23}a^{3}+\frac{16}{23}a^{2}+\frac{30}{23}a-\frac{125}{23}\right){y}={x}^{3}+\left(\frac{4}{23}a^{3}-\frac{6}{23}a^{2}-\frac{63}{23}a+\frac{21}{23}\right){x}^{2}+\left(\frac{51}{23}a^{3}+\frac{119}{23}a^{2}-\frac{349}{23}a-\frac{382}{23}\right){x}-\frac{157}{23}a^{3}-\frac{305}{23}a^{2}+\frac{926}{23}a+\frac{1079}{23}$ |
| 29.2-a1 |
29.2-a |
$2$ |
$3$ |
\(\Q(\sqrt{5}, \sqrt{7})\) |
$4$ |
$[4, 0]$ |
29.2 |
\( 29 \) |
\( 29^{3} \) |
$19.05752$ |
$(-4/23a^3+6/23a^2+63/23a-21/23)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 3 \) |
$0.061084943$ |
$501.7034145$ |
2.626844961 |
\( -\frac{26708755}{560947} a^{3} + \frac{1147535}{560947} a^{2} + \frac{390396300}{560947} a + \frac{8104589}{19343} \) |
\( \bigl[-\frac{1}{23} a^{3} + \frac{13}{23} a^{2} - \frac{13}{23} a - \frac{103}{23}\) , \( \frac{4}{23} a^{3} - \frac{6}{23} a^{2} - \frac{63}{23} a + \frac{44}{23}\) , \( -\frac{2}{23} a^{3} + \frac{3}{23} a^{2} + \frac{43}{23} a - \frac{22}{23}\) , \( -\frac{121}{23} a^{3} + \frac{9}{23} a^{2} + \frac{1693}{23} a + \frac{1866}{23}\) , \( -\frac{275}{23} a^{3} - \frac{13}{23} a^{2} + \frac{4015}{23} a + \frac{4082}{23}\bigr] \) |
${y}^2+\left(-\frac{1}{23}a^{3}+\frac{13}{23}a^{2}-\frac{13}{23}a-\frac{103}{23}\right){x}{y}+\left(-\frac{2}{23}a^{3}+\frac{3}{23}a^{2}+\frac{43}{23}a-\frac{22}{23}\right){y}={x}^{3}+\left(\frac{4}{23}a^{3}-\frac{6}{23}a^{2}-\frac{63}{23}a+\frac{44}{23}\right){x}^{2}+\left(-\frac{121}{23}a^{3}+\frac{9}{23}a^{2}+\frac{1693}{23}a+\frac{1866}{23}\right){x}-\frac{275}{23}a^{3}-\frac{13}{23}a^{2}+\frac{4015}{23}a+\frac{4082}{23}$ |
| 29.2-a2 |
29.2-a |
$2$ |
$3$ |
\(\Q(\sqrt{5}, \sqrt{7})\) |
$4$ |
$[4, 0]$ |
29.2 |
\( 29 \) |
\( 29 \) |
$19.05752$ |
$(-4/23a^3+6/23a^2+63/23a-21/23)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 1 \) |
$0.183254829$ |
$501.7034145$ |
2.626844961 |
\( \frac{2260418171}{667} a^{3} - \frac{11897954852}{667} a^{2} + \frac{4926111247}{667} a + \frac{692520183}{23} \) |
\( \bigl[-\frac{4}{23} a^{3} + \frac{6}{23} a^{2} + \frac{63}{23} a - \frac{21}{23}\) , \( -\frac{1}{23} a^{3} - \frac{10}{23} a^{2} + \frac{33}{23} a + \frac{104}{23}\) , \( -\frac{2}{23} a^{3} + \frac{3}{23} a^{2} + \frac{43}{23} a + \frac{1}{23}\) , \( \frac{17}{23} a^{3} - \frac{106}{23} a^{2} - \frac{147}{23} a + \frac{1153}{23}\) , \( -\frac{160}{23} a^{3} + \frac{424}{23} a^{2} + \frac{1922}{23} a - \frac{3577}{23}\bigr] \) |
${y}^2+\left(-\frac{4}{23}a^{3}+\frac{6}{23}a^{2}+\frac{63}{23}a-\frac{21}{23}\right){x}{y}+\left(-\frac{2}{23}a^{3}+\frac{3}{23}a^{2}+\frac{43}{23}a+\frac{1}{23}\right){y}={x}^{3}+\left(-\frac{1}{23}a^{3}-\frac{10}{23}a^{2}+\frac{33}{23}a+\frac{104}{23}\right){x}^{2}+\left(\frac{17}{23}a^{3}-\frac{106}{23}a^{2}-\frac{147}{23}a+\frac{1153}{23}\right){x}-\frac{160}{23}a^{3}+\frac{424}{23}a^{2}+\frac{1922}{23}a-\frac{3577}{23}$ |
| 29.2-b1 |
29.2-b |
$2$ |
$3$ |
\(\Q(\sqrt{5}, \sqrt{7})\) |
$4$ |
$[4, 0]$ |
29.2 |
\( 29 \) |
\( 29^{3} \) |
$19.05752$ |
$(-4/23a^3+6/23a^2+63/23a-21/23)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 3 \) |
$0.175792773$ |
$217.9490740$ |
3.284046195 |
\( -\frac{26708755}{560947} a^{3} + \frac{1147535}{560947} a^{2} + \frac{390396300}{560947} a + \frac{8104589}{19343} \) |
\( \bigl[-\frac{3}{23} a^{3} + \frac{16}{23} a^{2} + \frac{30}{23} a - \frac{102}{23}\) , \( -a\) , \( -\frac{1}{23} a^{3} + \frac{13}{23} a^{2} - \frac{13}{23} a - \frac{80}{23}\) , \( -\frac{113}{23} a^{3} - \frac{26}{23} a^{2} + \frac{1682}{23} a + \frac{1885}{23}\) , \( \frac{363}{23} a^{3} - \frac{4}{23} a^{2} - \frac{5355}{23} a - \frac{4839}{23}\bigr] \) |
${y}^2+\left(-\frac{3}{23}a^{3}+\frac{16}{23}a^{2}+\frac{30}{23}a-\frac{102}{23}\right){x}{y}+\left(-\frac{1}{23}a^{3}+\frac{13}{23}a^{2}-\frac{13}{23}a-\frac{80}{23}\right){y}={x}^{3}-a{x}^{2}+\left(-\frac{113}{23}a^{3}-\frac{26}{23}a^{2}+\frac{1682}{23}a+\frac{1885}{23}\right){x}+\frac{363}{23}a^{3}-\frac{4}{23}a^{2}-\frac{5355}{23}a-\frac{4839}{23}$ |
| 29.2-b2 |
29.2-b |
$2$ |
$3$ |
\(\Q(\sqrt{5}, \sqrt{7})\) |
$4$ |
$[4, 0]$ |
29.2 |
\( 29 \) |
\( 29 \) |
$19.05752$ |
$(-4/23a^3+6/23a^2+63/23a-21/23)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 1 \) |
$0.527378321$ |
$217.9490740$ |
3.284046195 |
\( \frac{2260418171}{667} a^{3} - \frac{11897954852}{667} a^{2} + \frac{4926111247}{667} a + \frac{692520183}{23} \) |
\( \bigl[\frac{1}{23} a^{3} + \frac{10}{23} a^{2} - \frac{33}{23} a - \frac{58}{23}\) , \( -\frac{1}{23} a^{3} + \frac{13}{23} a^{2} - \frac{13}{23} a - \frac{126}{23}\) , \( -\frac{2}{23} a^{3} + \frac{3}{23} a^{2} + \frac{20}{23} a + \frac{1}{23}\) , \( \frac{22}{23} a^{3} - \frac{56}{23} a^{2} - \frac{358}{23} a + \frac{863}{23}\) , \( \frac{144}{23} a^{3} - \frac{423}{23} a^{2} - \frac{1785}{23} a + \frac{4137}{23}\bigr] \) |
${y}^2+\left(\frac{1}{23}a^{3}+\frac{10}{23}a^{2}-\frac{33}{23}a-\frac{58}{23}\right){x}{y}+\left(-\frac{2}{23}a^{3}+\frac{3}{23}a^{2}+\frac{20}{23}a+\frac{1}{23}\right){y}={x}^{3}+\left(-\frac{1}{23}a^{3}+\frac{13}{23}a^{2}-\frac{13}{23}a-\frac{126}{23}\right){x}^{2}+\left(\frac{22}{23}a^{3}-\frac{56}{23}a^{2}-\frac{358}{23}a+\frac{863}{23}\right){x}+\frac{144}{23}a^{3}-\frac{423}{23}a^{2}-\frac{1785}{23}a+\frac{4137}{23}$ |
| 29.3-a1 |
29.3-a |
$2$ |
$3$ |
\(\Q(\sqrt{5}, \sqrt{7})\) |
$4$ |
$[4, 0]$ |
29.3 |
\( 29 \) |
\( 29^{3} \) |
$19.05752$ |
$(-4/23a^3+6/23a^2+63/23a-44/23)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 3 \) |
$0.061084943$ |
$501.7034145$ |
2.626844961 |
\( \frac{26708755}{560947} a^{3} - \frac{78978730}{560947} a^{2} - \frac{312565105}{560947} a + \frac{20685109}{19343} \) |
\( \bigl[-\frac{3}{23} a^{3} + \frac{16}{23} a^{2} + \frac{30}{23} a - \frac{102}{23}\) , \( -a + 1\) , \( -\frac{3}{23} a^{3} + \frac{16}{23} a^{2} + \frac{30}{23} a - \frac{125}{23}\) , \( \frac{118}{23} a^{3} - \frac{361}{23} a^{2} - \frac{1433}{23} a + \frac{3414}{23}\) , \( \frac{594}{23} a^{3} - \frac{1811}{23} a^{2} - \frac{6998}{23} a + \frac{16677}{23}\bigr] \) |
${y}^2+\left(-\frac{3}{23}a^{3}+\frac{16}{23}a^{2}+\frac{30}{23}a-\frac{102}{23}\right){x}{y}+\left(-\frac{3}{23}a^{3}+\frac{16}{23}a^{2}+\frac{30}{23}a-\frac{125}{23}\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(\frac{118}{23}a^{3}-\frac{361}{23}a^{2}-\frac{1433}{23}a+\frac{3414}{23}\right){x}+\frac{594}{23}a^{3}-\frac{1811}{23}a^{2}-\frac{6998}{23}a+\frac{16677}{23}$ |
| 29.3-a2 |
29.3-a |
$2$ |
$3$ |
\(\Q(\sqrt{5}, \sqrt{7})\) |
$4$ |
$[4, 0]$ |
29.3 |
\( 29 \) |
\( 29 \) |
$19.05752$ |
$(-4/23a^3+6/23a^2+63/23a-44/23)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 1 \) |
$0.183254829$ |
$501.7034145$ |
2.626844961 |
\( -\frac{2260418171}{667} a^{3} - \frac{5116700339}{667} a^{2} + \frac{12088543944}{667} a + \frac{530057237}{23} \) |
\( \bigl[-\frac{4}{23} a^{3} + \frac{6}{23} a^{2} + \frac{63}{23} a - \frac{44}{23}\) , \( \frac{1}{23} a^{3} - \frac{13}{23} a^{2} - \frac{10}{23} a + \frac{126}{23}\) , \( -\frac{2}{23} a^{3} + \frac{3}{23} a^{2} + \frac{43}{23} a + \frac{1}{23}\) , \( -\frac{13}{23} a^{3} - \frac{61}{23} a^{2} + \frac{245}{23} a + \frac{961}{23}\) , \( \frac{162}{23} a^{3} - \frac{59}{23} a^{2} - \frac{2333}{23} a - \frac{1369}{23}\bigr] \) |
${y}^2+\left(-\frac{4}{23}a^{3}+\frac{6}{23}a^{2}+\frac{63}{23}a-\frac{44}{23}\right){x}{y}+\left(-\frac{2}{23}a^{3}+\frac{3}{23}a^{2}+\frac{43}{23}a+\frac{1}{23}\right){y}={x}^{3}+\left(\frac{1}{23}a^{3}-\frac{13}{23}a^{2}-\frac{10}{23}a+\frac{126}{23}\right){x}^{2}+\left(-\frac{13}{23}a^{3}-\frac{61}{23}a^{2}+\frac{245}{23}a+\frac{961}{23}\right){x}+\frac{162}{23}a^{3}-\frac{59}{23}a^{2}-\frac{2333}{23}a-\frac{1369}{23}$ |
| 29.3-b1 |
29.3-b |
$2$ |
$3$ |
\(\Q(\sqrt{5}, \sqrt{7})\) |
$4$ |
$[4, 0]$ |
29.3 |
\( 29 \) |
\( 29^{3} \) |
$19.05752$ |
$(-4/23a^3+6/23a^2+63/23a-44/23)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 3 \) |
$0.175792773$ |
$217.9490740$ |
3.284046195 |
\( \frac{26708755}{560947} a^{3} - \frac{78978730}{560947} a^{2} - \frac{312565105}{560947} a + \frac{20685109}{19343} \) |
\( \bigl[-\frac{1}{23} a^{3} + \frac{13}{23} a^{2} - \frac{13}{23} a - \frac{103}{23}\) , \( \frac{4}{23} a^{3} - \frac{6}{23} a^{2} - \frac{63}{23} a + \frac{21}{23}\) , \( 1\) , \( \frac{122}{23} a^{3} - \frac{367}{23} a^{2} - \frac{1473}{23} a + \frac{3527}{23}\) , \( -\frac{40}{23} a^{3} + \frac{129}{23} a^{2} + \frac{423}{23} a - \frac{1061}{23}\bigr] \) |
${y}^2+\left(-\frac{1}{23}a^{3}+\frac{13}{23}a^{2}-\frac{13}{23}a-\frac{103}{23}\right){x}{y}+{y}={x}^{3}+\left(\frac{4}{23}a^{3}-\frac{6}{23}a^{2}-\frac{63}{23}a+\frac{21}{23}\right){x}^{2}+\left(\frac{122}{23}a^{3}-\frac{367}{23}a^{2}-\frac{1473}{23}a+\frac{3527}{23}\right){x}-\frac{40}{23}a^{3}+\frac{129}{23}a^{2}+\frac{423}{23}a-\frac{1061}{23}$ |
| 29.3-b2 |
29.3-b |
$2$ |
$3$ |
\(\Q(\sqrt{5}, \sqrt{7})\) |
$4$ |
$[4, 0]$ |
29.3 |
\( 29 \) |
\( 29 \) |
$19.05752$ |
$(-4/23a^3+6/23a^2+63/23a-44/23)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 1 \) |
$0.527378321$ |
$217.9490740$ |
3.284046195 |
\( -\frac{2260418171}{667} a^{3} - \frac{5116700339}{667} a^{2} + \frac{12088543944}{667} a + \frac{530057237}{23} \) |
\( \bigl[-\frac{1}{23} a^{3} + \frac{13}{23} a^{2} + \frac{10}{23} a - \frac{80}{23}\) , \( \frac{1}{23} a^{3} + \frac{10}{23} a^{2} - \frac{10}{23} a - \frac{58}{23}\) , \( -\frac{3}{23} a^{3} + \frac{16}{23} a^{2} + \frac{30}{23} a - \frac{102}{23}\) , \( -\frac{21}{23} a^{3} + \frac{43}{23} a^{2} + \frac{417}{23} a + \frac{183}{23}\) , \( -\frac{166}{23} a^{3} + \frac{42}{23} a^{2} + \frac{2626}{23} a + \frac{2337}{23}\bigr] \) |
${y}^2+\left(-\frac{1}{23}a^{3}+\frac{13}{23}a^{2}+\frac{10}{23}a-\frac{80}{23}\right){x}{y}+\left(-\frac{3}{23}a^{3}+\frac{16}{23}a^{2}+\frac{30}{23}a-\frac{102}{23}\right){y}={x}^{3}+\left(\frac{1}{23}a^{3}+\frac{10}{23}a^{2}-\frac{10}{23}a-\frac{58}{23}\right){x}^{2}+\left(-\frac{21}{23}a^{3}+\frac{43}{23}a^{2}+\frac{417}{23}a+\frac{183}{23}\right){x}-\frac{166}{23}a^{3}+\frac{42}{23}a^{2}+\frac{2626}{23}a+\frac{2337}{23}$ |
| 29.4-a1 |
29.4-a |
$2$ |
$3$ |
\(\Q(\sqrt{5}, \sqrt{7})\) |
$4$ |
$[4, 0]$ |
29.4 |
\( 29 \) |
\( 29 \) |
$19.05752$ |
$(a-1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 1 \) |
$0.183254829$ |
$501.7034145$ |
2.626844961 |
\( \frac{5568759973}{667} a^{3} + \frac{154187636}{667} a^{2} - \frac{83217892687}{667} a - \frac{2746289531}{23} \) |
\( \bigl[-\frac{4}{23} a^{3} + \frac{6}{23} a^{2} + \frac{63}{23} a - \frac{21}{23}\) , \( -\frac{1}{23} a^{3} - \frac{10}{23} a^{2} + \frac{33}{23} a + \frac{104}{23}\) , \( -\frac{1}{23} a^{3} + \frac{13}{23} a^{2} - \frac{13}{23} a - \frac{103}{23}\) , \( -\frac{9}{23} a^{3} + \frac{25}{23} a^{2} + \frac{228}{23} a + \frac{292}{23}\) , \( -\frac{83}{23} a^{3} - \frac{186}{23} a^{2} + \frac{554}{23} a + \frac{743}{23}\bigr] \) |
${y}^2+\left(-\frac{4}{23}a^{3}+\frac{6}{23}a^{2}+\frac{63}{23}a-\frac{21}{23}\right){x}{y}+\left(-\frac{1}{23}a^{3}+\frac{13}{23}a^{2}-\frac{13}{23}a-\frac{103}{23}\right){y}={x}^{3}+\left(-\frac{1}{23}a^{3}-\frac{10}{23}a^{2}+\frac{33}{23}a+\frac{104}{23}\right){x}^{2}+\left(-\frac{9}{23}a^{3}+\frac{25}{23}a^{2}+\frac{228}{23}a+\frac{292}{23}\right){x}-\frac{83}{23}a^{3}-\frac{186}{23}a^{2}+\frac{554}{23}a+\frac{743}{23}$ |
| 29.4-a2 |
29.4-a |
$2$ |
$3$ |
\(\Q(\sqrt{5}, \sqrt{7})\) |
$4$ |
$[4, 0]$ |
29.4 |
\( 29 \) |
\( 29^{3} \) |
$19.05752$ |
$(a-1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 3 \) |
$0.061084943$ |
$501.7034145$ |
2.626844961 |
\( -\frac{12031685}{560947} a^{3} + \frac{56963125}{560947} a^{2} - \frac{2991900}{560947} a - \frac{7798921}{19343} \) |
\( \bigl[-\frac{1}{23} a^{3} + \frac{13}{23} a^{2} - \frac{13}{23} a - \frac{103}{23}\) , \( \frac{4}{23} a^{3} - \frac{6}{23} a^{2} - \frac{63}{23} a + \frac{44}{23}\) , \( -\frac{1}{23} a^{3} + \frac{13}{23} a^{2} - \frac{13}{23} a - \frac{80}{23}\) , \( -\frac{42}{23} a^{3} + \frac{247}{23} a^{2} - \frac{201}{23} a - \frac{370}{23}\) , \( -\frac{250}{23} a^{3} + \frac{1295}{23} a^{2} - \frac{398}{23} a - \frac{2474}{23}\bigr] \) |
${y}^2+\left(-\frac{1}{23}a^{3}+\frac{13}{23}a^{2}-\frac{13}{23}a-\frac{103}{23}\right){x}{y}+\left(-\frac{1}{23}a^{3}+\frac{13}{23}a^{2}-\frac{13}{23}a-\frac{80}{23}\right){y}={x}^{3}+\left(\frac{4}{23}a^{3}-\frac{6}{23}a^{2}-\frac{63}{23}a+\frac{44}{23}\right){x}^{2}+\left(-\frac{42}{23}a^{3}+\frac{247}{23}a^{2}-\frac{201}{23}a-\frac{370}{23}\right){x}-\frac{250}{23}a^{3}+\frac{1295}{23}a^{2}-\frac{398}{23}a-\frac{2474}{23}$ |
| 29.4-b1 |
29.4-b |
$2$ |
$3$ |
\(\Q(\sqrt{5}, \sqrt{7})\) |
$4$ |
$[4, 0]$ |
29.4 |
\( 29 \) |
\( 29 \) |
$19.05752$ |
$(a-1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 1 \) |
$0.527378321$ |
$217.9490740$ |
3.284046195 |
\( \frac{5568759973}{667} a^{3} + \frac{154187636}{667} a^{2} - \frac{83217892687}{667} a - \frac{2746289531}{23} \) |
\( \bigl[\frac{1}{23} a^{3} + \frac{10}{23} a^{2} - \frac{33}{23} a - \frac{58}{23}\) , \( -\frac{1}{23} a^{3} + \frac{13}{23} a^{2} - \frac{13}{23} a - \frac{126}{23}\) , \( \frac{1}{23} a^{3} + \frac{10}{23} a^{2} - \frac{33}{23} a - \frac{58}{23}\) , \( \frac{14}{23} a^{3} + \frac{48}{23} a^{2} - \frac{209}{23} a - \frac{122}{23}\) , \( \frac{70}{23} a^{3} + \frac{240}{23} a^{2} - \frac{470}{23} a - \frac{725}{23}\bigr] \) |
${y}^2+\left(\frac{1}{23}a^{3}+\frac{10}{23}a^{2}-\frac{33}{23}a-\frac{58}{23}\right){x}{y}+\left(\frac{1}{23}a^{3}+\frac{10}{23}a^{2}-\frac{33}{23}a-\frac{58}{23}\right){y}={x}^{3}+\left(-\frac{1}{23}a^{3}+\frac{13}{23}a^{2}-\frac{13}{23}a-\frac{126}{23}\right){x}^{2}+\left(\frac{14}{23}a^{3}+\frac{48}{23}a^{2}-\frac{209}{23}a-\frac{122}{23}\right){x}+\frac{70}{23}a^{3}+\frac{240}{23}a^{2}-\frac{470}{23}a-\frac{725}{23}$ |
| 29.4-b2 |
29.4-b |
$2$ |
$3$ |
\(\Q(\sqrt{5}, \sqrt{7})\) |
$4$ |
$[4, 0]$ |
29.4 |
\( 29 \) |
\( 29^{3} \) |
$19.05752$ |
$(a-1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 3 \) |
$0.175792773$ |
$217.9490740$ |
3.284046195 |
\( -\frac{12031685}{560947} a^{3} + \frac{56963125}{560947} a^{2} - \frac{2991900}{560947} a - \frac{7798921}{19343} \) |
\( \bigl[-\frac{3}{23} a^{3} + \frac{16}{23} a^{2} + \frac{30}{23} a - \frac{102}{23}\) , \( -a\) , \( 1\) , \( -\frac{43}{23} a^{3} + \frac{237}{23} a^{2} - \frac{191}{23} a - \frac{197}{23}\) , \( \frac{24}{23} a^{3} - \frac{105}{23} a^{2} - \frac{79}{23} a + \frac{379}{23}\bigr] \) |
${y}^2+\left(-\frac{3}{23}a^{3}+\frac{16}{23}a^{2}+\frac{30}{23}a-\frac{102}{23}\right){x}{y}+{y}={x}^{3}-a{x}^{2}+\left(-\frac{43}{23}a^{3}+\frac{237}{23}a^{2}-\frac{191}{23}a-\frac{197}{23}\right){x}+\frac{24}{23}a^{3}-\frac{105}{23}a^{2}-\frac{79}{23}a+\frac{379}{23}$ |
| 36.1-a1 |
36.1-a |
$4$ |
$6$ |
\(\Q(\sqrt{5}, \sqrt{7})\) |
$4$ |
$[4, 0]$ |
36.1 |
\( 2^{2} \cdot 3^{2} \) |
\( 2^{12} \cdot 3^{4} \) |
$19.57963$ |
$(3/23a^3+7/23a^2-53/23a-128/23), (3/23a^3+7/23a^2-30/23a-59/23)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \cdot 3 \) |
$0.285216073$ |
$204.1774933$ |
4.991545974 |
\( -\frac{65221}{36} a^{3} + \frac{65221}{24} a^{2} + \frac{2804503}{72} a - \frac{2698279}{36} \) |
\( \bigl[-\frac{4}{23} a^{3} + \frac{6}{23} a^{2} + \frac{63}{23} a - \frac{21}{23}\) , \( -\frac{1}{23} a^{3} - \frac{10}{23} a^{2} + \frac{33}{23} a + \frac{104}{23}\) , \( -\frac{1}{23} a^{3} + \frac{13}{23} a^{2} + \frac{10}{23} a - \frac{80}{23}\) , \( -\frac{20}{23} a^{3} - \frac{16}{23} a^{2} + \frac{315}{23} a + \frac{378}{23}\) , \( -\frac{30}{23} a^{3} + \frac{22}{23} a^{2} + \frac{346}{23} a + \frac{291}{23}\bigr] \) |
${y}^2+\left(-\frac{4}{23}a^{3}+\frac{6}{23}a^{2}+\frac{63}{23}a-\frac{21}{23}\right){x}{y}+\left(-\frac{1}{23}a^{3}+\frac{13}{23}a^{2}+\frac{10}{23}a-\frac{80}{23}\right){y}={x}^{3}+\left(-\frac{1}{23}a^{3}-\frac{10}{23}a^{2}+\frac{33}{23}a+\frac{104}{23}\right){x}^{2}+\left(-\frac{20}{23}a^{3}-\frac{16}{23}a^{2}+\frac{315}{23}a+\frac{378}{23}\right){x}-\frac{30}{23}a^{3}+\frac{22}{23}a^{2}+\frac{346}{23}a+\frac{291}{23}$ |
| 36.1-a2 |
36.1-a |
$4$ |
$6$ |
\(\Q(\sqrt{5}, \sqrt{7})\) |
$4$ |
$[4, 0]$ |
36.1 |
\( 2^{2} \cdot 3^{2} \) |
\( 2^{4} \cdot 3^{12} \) |
$19.57963$ |
$(3/23a^3+7/23a^2-53/23a-128/23), (3/23a^3+7/23a^2-30/23a-59/23)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \) |
$0.855648221$ |
$204.1774933$ |
4.991545974 |
\( \frac{275587}{16767} a^{3} - \frac{275587}{11178} a^{2} - \frac{11850241}{33534} a + \frac{9679561}{16767} \) |
\( \bigl[\frac{1}{23} a^{3} + \frac{10}{23} a^{2} - \frac{33}{23} a - \frac{58}{23}\) , \( \frac{1}{23} a^{3} + \frac{10}{23} a^{2} - \frac{33}{23} a - \frac{58}{23}\) , \( -\frac{2}{23} a^{3} + \frac{3}{23} a^{2} + \frac{20}{23} a + \frac{1}{23}\) , \( -\frac{41}{23} a^{3} + \frac{257}{23} a^{2} - \frac{303}{23} a - \frac{37}{23}\) , \( -\frac{461}{23} a^{3} + \frac{2359}{23} a^{2} - \frac{542}{23} a - \frac{4772}{23}\bigr] \) |
${y}^2+\left(\frac{1}{23}a^{3}+\frac{10}{23}a^{2}-\frac{33}{23}a-\frac{58}{23}\right){x}{y}+\left(-\frac{2}{23}a^{3}+\frac{3}{23}a^{2}+\frac{20}{23}a+\frac{1}{23}\right){y}={x}^{3}+\left(\frac{1}{23}a^{3}+\frac{10}{23}a^{2}-\frac{33}{23}a-\frac{58}{23}\right){x}^{2}+\left(-\frac{41}{23}a^{3}+\frac{257}{23}a^{2}-\frac{303}{23}a-\frac{37}{23}\right){x}-\frac{461}{23}a^{3}+\frac{2359}{23}a^{2}-\frac{542}{23}a-\frac{4772}{23}$ |
| 36.1-a3 |
36.1-a |
$4$ |
$6$ |
\(\Q(\sqrt{5}, \sqrt{7})\) |
$4$ |
$[4, 0]$ |
36.1 |
\( 2^{2} \cdot 3^{2} \) |
\( 2^{2} \cdot 3^{24} \) |
$19.57963$ |
$(3/23a^3+7/23a^2-53/23a-128/23), (3/23a^3+7/23a^2-30/23a-59/23)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$1.711296443$ |
$204.1774933$ |
4.991545974 |
\( -\frac{62446099201}{12223143} a^{3} + \frac{62446099201}{8148762} a^{2} + \frac{2685182265643}{24446286} a + \frac{2502971947885}{24446286} \) |
\( \bigl[-\frac{4}{23} a^{3} + \frac{6}{23} a^{2} + \frac{63}{23} a - \frac{44}{23}\) , \( \frac{3}{23} a^{3} - \frac{16}{23} a^{2} - \frac{30}{23} a + \frac{148}{23}\) , \( \frac{1}{23} a^{3} + \frac{10}{23} a^{2} - \frac{33}{23} a - \frac{58}{23}\) , \( -\frac{582}{23} a^{3} + \frac{1655}{23} a^{2} + \frac{7453}{23} a - \frac{16775}{23}\) , \( -\frac{7718}{23} a^{3} + \frac{23629}{23} a^{2} + \frac{90083}{23} a - \frac{215446}{23}\bigr] \) |
${y}^2+\left(-\frac{4}{23}a^{3}+\frac{6}{23}a^{2}+\frac{63}{23}a-\frac{44}{23}\right){x}{y}+\left(\frac{1}{23}a^{3}+\frac{10}{23}a^{2}-\frac{33}{23}a-\frac{58}{23}\right){y}={x}^{3}+\left(\frac{3}{23}a^{3}-\frac{16}{23}a^{2}-\frac{30}{23}a+\frac{148}{23}\right){x}^{2}+\left(-\frac{582}{23}a^{3}+\frac{1655}{23}a^{2}+\frac{7453}{23}a-\frac{16775}{23}\right){x}-\frac{7718}{23}a^{3}+\frac{23629}{23}a^{2}+\frac{90083}{23}a-\frac{215446}{23}$ |
| 36.1-a4 |
36.1-a |
$4$ |
$6$ |
\(\Q(\sqrt{5}, \sqrt{7})\) |
$4$ |
$[4, 0]$ |
36.1 |
\( 2^{2} \cdot 3^{2} \) |
\( 2^{6} \cdot 3^{8} \) |
$19.57963$ |
$(3/23a^3+7/23a^2-53/23a-128/23), (3/23a^3+7/23a^2-30/23a-59/23)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \cdot 3 \) |
$0.570432147$ |
$204.1774933$ |
4.991545974 |
\( \frac{32734969937}{162} a^{3} - \frac{32734969937}{108} a^{2} - \frac{1407603707291}{324} a + \frac{2712170905513}{324} \) |
\( \bigl[-\frac{4}{23} a^{3} + \frac{6}{23} a^{2} + \frac{63}{23} a - \frac{21}{23}\) , \( -\frac{1}{23} a^{3} - \frac{10}{23} a^{2} + \frac{33}{23} a + \frac{104}{23}\) , \( -\frac{1}{23} a^{3} + \frac{13}{23} a^{2} + \frac{10}{23} a - \frac{80}{23}\) , \( \frac{10}{23} a^{3} - \frac{176}{23} a^{2} + \frac{475}{23} a + \frac{248}{23}\) , \( -\frac{288}{23} a^{3} + \frac{1398}{23} a^{2} + \frac{74}{23} a - \frac{3559}{23}\bigr] \) |
${y}^2+\left(-\frac{4}{23}a^{3}+\frac{6}{23}a^{2}+\frac{63}{23}a-\frac{21}{23}\right){x}{y}+\left(-\frac{1}{23}a^{3}+\frac{13}{23}a^{2}+\frac{10}{23}a-\frac{80}{23}\right){y}={x}^{3}+\left(-\frac{1}{23}a^{3}-\frac{10}{23}a^{2}+\frac{33}{23}a+\frac{104}{23}\right){x}^{2}+\left(\frac{10}{23}a^{3}-\frac{176}{23}a^{2}+\frac{475}{23}a+\frac{248}{23}\right){x}-\frac{288}{23}a^{3}+\frac{1398}{23}a^{2}+\frac{74}{23}a-\frac{3559}{23}$ |
*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.
