| 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 |
$8$ |
$66$ |
\(\Q(\sqrt{3}, \sqrt{11})\) |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$11.79539$ |
$\textsf{none}$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-132$ |
$N(\mathrm{U}(1))$ |
✓ |
|
✓ |
✓ |
|
|
$9$ |
\( 1 \) |
$1$ |
$56.05000782$ |
0.955397860 |
\( -520380952416000 a^{3} - 412291047168000 a^{2} + 3316013824032000 a + 2627234539704000 \) |
\( \bigl[\frac{1}{2} a^{3} - \frac{5}{2} a + 1\) , \( \frac{1}{2} a^{3} + a^{2} - \frac{5}{2} a - 3\) , \( a^{2} + a - 3\) , \( -\frac{7}{2} a^{3} + 5 a^{2} + \frac{47}{2} a - 29\) , \( -\frac{31}{2} a^{3} + 14 a^{2} + \frac{201}{2} a - 85\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-\frac{5}{2}a+1\right){x}{y}+\left(a^{2}+a-3\right){y}={x}^{3}+\left(\frac{1}{2}a^{3}+a^{2}-\frac{5}{2}a-3\right){x}^{2}+\left(-\frac{7}{2}a^{3}+5a^{2}+\frac{47}{2}a-29\right){x}-\frac{31}{2}a^{3}+14a^{2}+\frac{201}{2}a-85$ |
| 1.1-a2 |
1.1-a |
$8$ |
$66$ |
\(\Q(\sqrt{3}, \sqrt{11})\) |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$11.79539$ |
$\textsf{none}$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-132$ |
$N(\mathrm{U}(1))$ |
✓ |
|
✓ |
✓ |
|
|
$1$ |
\( 1 \) |
$1$ |
$504.4500704$ |
0.955397860 |
\( -520380952416000 a^{3} - 412291047168000 a^{2} + 3316013824032000 a + 2627234539704000 \) |
\( \bigl[\frac{1}{2} a^{3} - \frac{5}{2} a + 1\) , \( \frac{1}{2} a^{3} - a^{2} - \frac{5}{2} a + 4\) , \( \frac{1}{2} a^{3} + a^{2} - \frac{3}{2} a - 4\) , \( -2 a^{3} + 3 a^{2} + 10 a - 23\) , \( \frac{3}{2} a^{3} - 5 a^{2} - \frac{27}{2} a + 20\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-\frac{5}{2}a+1\right){x}{y}+\left(\frac{1}{2}a^{3}+a^{2}-\frac{3}{2}a-4\right){y}={x}^{3}+\left(\frac{1}{2}a^{3}-a^{2}-\frac{5}{2}a+4\right){x}^{2}+\left(-2a^{3}+3a^{2}+10a-23\right){x}+\frac{3}{2}a^{3}-5a^{2}-\frac{27}{2}a+20$ |
| 1.1-a3 |
1.1-a |
$8$ |
$66$ |
\(\Q(\sqrt{3}, \sqrt{11})\) |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$11.79539$ |
$\textsf{none}$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-132$ |
$N(\mathrm{U}(1))$ |
✓ |
|
✓ |
✓ |
|
|
$1$ |
\( 1 \) |
$1$ |
$504.4500704$ |
0.955397860 |
\( -163326421440000 a^{3} + 412291047168000 a^{2} + 102523045248000 a - 258802790472000 \) |
\( \bigl[\frac{1}{2} a^{3} - \frac{5}{2} a + 1\) , \( \frac{1}{2} a^{3} + a^{2} - \frac{5}{2} a - 3\) , \( a^{2} + a - 3\) , \( -a^{3} - 5 a^{2} + a + 6\) , \( -a^{3} + 4 a^{2} + 8 a - 10\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-\frac{5}{2}a+1\right){x}{y}+\left(a^{2}+a-3\right){y}={x}^{3}+\left(\frac{1}{2}a^{3}+a^{2}-\frac{5}{2}a-3\right){x}^{2}+\left(-a^{3}-5a^{2}+a+6\right){x}-a^{3}+4a^{2}+8a-10$ |
| 1.1-a4 |
1.1-a |
$8$ |
$66$ |
\(\Q(\sqrt{3}, \sqrt{11})\) |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$11.79539$ |
$\textsf{none}$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-132$ |
$N(\mathrm{U}(1))$ |
✓ |
|
✓ |
✓ |
|
|
$9$ |
\( 1 \) |
$1$ |
$56.05000782$ |
0.955397860 |
\( -163326421440000 a^{3} + 412291047168000 a^{2} + 102523045248000 a - 258802790472000 \) |
\( \bigl[\frac{1}{2} a^{3} - \frac{5}{2} a + 1\) , \( \frac{1}{2} a^{3} - a^{2} - \frac{5}{2} a + 4\) , \( \frac{1}{2} a^{3} + a^{2} - \frac{3}{2} a - 4\) , \( \frac{1}{2} a^{3} - 7 a^{2} - \frac{25}{2} a + 12\) , \( -3 a^{3} - 15 a^{2} - 11 a + 15\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-\frac{5}{2}a+1\right){x}{y}+\left(\frac{1}{2}a^{3}+a^{2}-\frac{3}{2}a-4\right){y}={x}^{3}+\left(\frac{1}{2}a^{3}-a^{2}-\frac{5}{2}a+4\right){x}^{2}+\left(\frac{1}{2}a^{3}-7a^{2}-\frac{25}{2}a+12\right){x}-3a^{3}-15a^{2}-11a+15$ |
| 1.1-a5 |
1.1-a |
$8$ |
$66$ |
\(\Q(\sqrt{3}, \sqrt{11})\) |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$11.79539$ |
$\textsf{none}$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-132$ |
$N(\mathrm{U}(1))$ |
✓ |
|
✓ |
✓ |
|
|
$9$ |
\( 1 \) |
$1$ |
$56.05000782$ |
0.955397860 |
\( 520380952416000 a^{3} - 412291047168000 a^{2} - 3316013824032000 a + 2627234539704000 \) |
\( \bigl[\frac{1}{2} a^{3} - \frac{5}{2} a + 1\) , \( \frac{1}{2} a^{3} + a^{2} - \frac{5}{2} a - 3\) , \( \frac{1}{2} a^{3} + a^{2} - \frac{3}{2} a - 4\) , \( 4 a^{3} + 5 a^{2} - 24 a - 30\) , \( \frac{9}{2} a^{3} + 9 a^{2} - \frac{61}{2} a - 54\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-\frac{5}{2}a+1\right){x}{y}+\left(\frac{1}{2}a^{3}+a^{2}-\frac{3}{2}a-4\right){y}={x}^{3}+\left(\frac{1}{2}a^{3}+a^{2}-\frac{5}{2}a-3\right){x}^{2}+\left(4a^{3}+5a^{2}-24a-30\right){x}+\frac{9}{2}a^{3}+9a^{2}-\frac{61}{2}a-54$ |
| 1.1-a6 |
1.1-a |
$8$ |
$66$ |
\(\Q(\sqrt{3}, \sqrt{11})\) |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$11.79539$ |
$\textsf{none}$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-132$ |
$N(\mathrm{U}(1))$ |
✓ |
|
✓ |
✓ |
|
|
$1$ |
\( 1 \) |
$1$ |
$504.4500704$ |
0.955397860 |
\( 520380952416000 a^{3} - 412291047168000 a^{2} - 3316013824032000 a + 2627234539704000 \) |
\( \bigl[\frac{1}{2} a^{3} - \frac{5}{2} a + 1\) , \( \frac{1}{2} a^{3} - a^{2} - \frac{5}{2} a + 4\) , \( a^{2} + a - 3\) , \( \frac{11}{2} a^{3} + 3 a^{2} - \frac{75}{2} a - 22\) , \( -11 a^{3} - 10 a^{2} + 70 a + 54\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-\frac{5}{2}a+1\right){x}{y}+\left(a^{2}+a-3\right){y}={x}^{3}+\left(\frac{1}{2}a^{3}-a^{2}-\frac{5}{2}a+4\right){x}^{2}+\left(\frac{11}{2}a^{3}+3a^{2}-\frac{75}{2}a-22\right){x}-11a^{3}-10a^{2}+70a+54$ |
| 1.1-a7 |
1.1-a |
$8$ |
$66$ |
\(\Q(\sqrt{3}, \sqrt{11})\) |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$11.79539$ |
$\textsf{none}$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-132$ |
$N(\mathrm{U}(1))$ |
✓ |
|
✓ |
✓ |
|
|
$1$ |
\( 1 \) |
$1$ |
$504.4500704$ |
0.955397860 |
\( 163326421440000 a^{3} + 412291047168000 a^{2} - 102523045248000 a - 258802790472000 \) |
\( \bigl[\frac{1}{2} a^{3} - \frac{5}{2} a + 1\) , \( \frac{1}{2} a^{3} + a^{2} - \frac{5}{2} a - 3\) , \( \frac{1}{2} a^{3} + a^{2} - \frac{3}{2} a - 4\) , \( \frac{3}{2} a^{3} - 5 a^{2} - \frac{3}{2} a + 5\) , \( -\frac{5}{2} a^{3} + 9 a^{2} - \frac{11}{2} a - 14\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-\frac{5}{2}a+1\right){x}{y}+\left(\frac{1}{2}a^{3}+a^{2}-\frac{3}{2}a-4\right){y}={x}^{3}+\left(\frac{1}{2}a^{3}+a^{2}-\frac{5}{2}a-3\right){x}^{2}+\left(\frac{3}{2}a^{3}-5a^{2}-\frac{3}{2}a+5\right){x}-\frac{5}{2}a^{3}+9a^{2}-\frac{11}{2}a-14$ |
| 1.1-a8 |
1.1-a |
$8$ |
$66$ |
\(\Q(\sqrt{3}, \sqrt{11})\) |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$11.79539$ |
$\textsf{none}$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-132$ |
$N(\mathrm{U}(1))$ |
✓ |
|
✓ |
✓ |
|
|
$9$ |
\( 1 \) |
$1$ |
$56.05000782$ |
0.955397860 |
\( 163326421440000 a^{3} + 412291047168000 a^{2} - 102523045248000 a - 258802790472000 \) |
\( \bigl[\frac{1}{2} a^{3} - \frac{5}{2} a + 1\) , \( \frac{1}{2} a^{3} - a^{2} - \frac{5}{2} a + 4\) , \( a^{2} + a - 3\) , \( 3 a^{3} - 7 a^{2} - 15 a + 13\) , \( a^{3} - 10 a^{2} + 14\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-\frac{5}{2}a+1\right){x}{y}+\left(a^{2}+a-3\right){y}={x}^{3}+\left(\frac{1}{2}a^{3}-a^{2}-\frac{5}{2}a+4\right){x}^{2}+\left(3a^{3}-7a^{2}-15a+13\right){x}+a^{3}-10a^{2}+14$ |
| 1.1-b1 |
1.1-b |
$6$ |
$99$ |
\(\Q(\sqrt{3}, \sqrt{11})\) |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$11.79539$ |
$\textsf{none}$ |
0 |
$\Z/3\Z$ |
$\textsf{potential}$ |
$-99$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
✓ |
✓ |
$3$ |
3B.1.1 |
$1$ |
\( 1 \) |
$1$ |
$531.9135261$ |
0.447738658 |
\( 6548115718144 a^{2} - 41726435491840 \) |
\( \bigl[0\) , \( -a^{2} + 3\) , \( 1\) , \( 25 a^{2} - 15\) , \( -72 a^{2} + 45\bigr] \) |
${y}^2+{y}={x}^{3}+\left(-a^{2}+3\right){x}^{2}+\left(25a^{2}-15\right){x}-72a^{2}+45$ |
| 1.1-b2 |
1.1-b |
$6$ |
$99$ |
\(\Q(\sqrt{3}, \sqrt{11})\) |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$11.79539$ |
$\textsf{none}$ |
0 |
$\Z/3\Z$ |
$\textsf{potential}$ |
$-11$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
✓ |
✓ |
$3$ |
3Cs.1.1 |
$1$ |
\( 1 \) |
$1$ |
$531.9135261$ |
0.447738658 |
\( -32768 \) |
\( \bigl[0\) , \( a^{2} - 3\) , \( \frac{1}{2} a^{3} - \frac{5}{2} a\) , \( -5 a^{2} + 5\) , \( 6 a^{2} - 5\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-\frac{5}{2}a\right){y}={x}^{3}+\left(a^{2}-3\right){x}^{2}+\left(-5a^{2}+5\right){x}+6a^{2}-5$ |
| 1.1-b3 |
1.1-b |
$6$ |
$99$ |
\(\Q(\sqrt{3}, \sqrt{11})\) |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$11.79539$ |
$\textsf{none}$ |
0 |
$\Z/3\Z$ |
$\textsf{potential}$ |
$-11$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
✓ |
✓ |
$3$ |
3Cs.1.1 |
$1$ |
\( 1 \) |
$1$ |
$531.9135261$ |
0.447738658 |
\( -32768 \) |
\( \bigl[0\) , \( -a^{2} + 4\) , \( \frac{1}{2} a^{3} - \frac{5}{2} a\) , \( 5 a^{2} - 30\) , \( -6 a^{2} + 37\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-\frac{5}{2}a\right){y}={x}^{3}+\left(-a^{2}+4\right){x}^{2}+\left(5a^{2}-30\right){x}-6a^{2}+37$ |
| 1.1-b4 |
1.1-b |
$6$ |
$99$ |
\(\Q(\sqrt{3}, \sqrt{11})\) |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$11.79539$ |
$\textsf{none}$ |
0 |
$\Z/3\Z$ |
$\textsf{potential}$ |
$-99$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
✓ |
✓ |
$3$ |
3B.1.1 |
$1$ |
\( 1 \) |
$1$ |
$531.9135261$ |
0.447738658 |
\( -6548115718144 a^{2} + 4110374535168 \) |
\( \bigl[0\) , \( a^{2} - 4\) , \( 1\) , \( -25 a^{2} + 160\) , \( 72 a^{2} - 459\bigr] \) |
${y}^2+{y}={x}^{3}+\left(a^{2}-4\right){x}^{2}+\left(-25a^{2}+160\right){x}+72a^{2}-459$ |
| 1.1-b5 |
1.1-b |
$6$ |
$99$ |
\(\Q(\sqrt{3}, \sqrt{11})\) |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$11.79539$ |
$\textsf{none}$ |
0 |
$\mathsf{trivial}$ |
$\textsf{potential}$ |
$-99$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
✓ |
✓ |
$3$ |
3B.1.2 |
$9$ |
\( 1 \) |
$1$ |
$6.566833655$ |
0.447738658 |
\( 6548115718144 a^{2} - 41726435491840 \) |
\( \bigl[0\) , \( a^{2} - 3\) , \( \frac{1}{2} a^{3} - \frac{5}{2} a\) , \( 25 a^{2} - 15\) , \( 72 a^{2} - 46\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-\frac{5}{2}a\right){y}={x}^{3}+\left(a^{2}-3\right){x}^{2}+\left(25a^{2}-15\right){x}+72a^{2}-46$ |
| 1.1-b6 |
1.1-b |
$6$ |
$99$ |
\(\Q(\sqrt{3}, \sqrt{11})\) |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$11.79539$ |
$\textsf{none}$ |
0 |
$\mathsf{trivial}$ |
$\textsf{potential}$ |
$-99$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
✓ |
✓ |
$3$ |
3B.1.2 |
$9$ |
\( 1 \) |
$1$ |
$6.566833655$ |
0.447738658 |
\( -6548115718144 a^{2} + 4110374535168 \) |
\( \bigl[0\) , \( -a^{2} + 4\) , \( \frac{1}{2} a^{3} - \frac{5}{2} a\) , \( -25 a^{2} + 160\) , \( -72 a^{2} + 458\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-\frac{5}{2}a\right){y}={x}^{3}+\left(-a^{2}+4\right){x}^{2}+\left(-25a^{2}+160\right){x}-72a^{2}+458$ |
| 4.1-a1 |
4.1-a |
$2$ |
$3$ |
\(\Q(\sqrt{3}, \sqrt{11})\) |
$4$ |
$[4, 0]$ |
4.1 |
\( 2^{2} \) |
\( 2^{4} \) |
$14.02717$ |
$(1/2a^3-7/2a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{potential}$ |
$-3$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
|
|
$1$ |
\( 1 \) |
$0.040727548$ |
$1878.684925$ |
2.318613059 |
\( 0 \) |
\( \bigl[0\) , \( \frac{1}{2} a^{3} - \frac{5}{2} a\) , \( \frac{1}{2} a^{3} + a^{2} - \frac{5}{2} a - 3\) , \( 1\) , \( -2 a^{3} - 2 a^{2} + 12 a + 10\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}+a^{2}-\frac{5}{2}a-3\right){y}={x}^{3}+\left(\frac{1}{2}a^{3}-\frac{5}{2}a\right){x}^{2}+{x}-2a^{3}-2a^{2}+12a+10$ |
| 4.1-a2 |
4.1-a |
$2$ |
$3$ |
\(\Q(\sqrt{3}, \sqrt{11})\) |
$4$ |
$[4, 0]$ |
4.1 |
\( 2^{2} \) |
\( 2^{4} \) |
$14.02717$ |
$(1/2a^3-7/2a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{potential}$ |
$-3$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
|
|
$1$ |
\( 3 \) |
$0.122182644$ |
$208.7427694$ |
2.318613059 |
\( 0 \) |
\( \bigl[0\) , \( -\frac{1}{2} a^{3} + \frac{5}{2} a\) , \( \frac{1}{2} a^{3} + a^{2} - \frac{5}{2} a - 3\) , \( 1\) , \( 6430 a^{3} + 5094 a^{2} - 40975 a - 32464\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}+a^{2}-\frac{5}{2}a-3\right){y}={x}^{3}+\left(-\frac{1}{2}a^{3}+\frac{5}{2}a\right){x}^{2}+{x}+6430a^{3}+5094a^{2}-40975a-32464$ |
| 4.2-a1 |
4.2-a |
$6$ |
$18$ |
\(\Q(\sqrt{3}, \sqrt{11})\) |
$4$ |
$[4, 0]$ |
4.2 |
\( 2^{2} \) |
\( 2^{18} \) |
$14.02717$ |
$(1/2a^3-7/2a+1), (-1/2a^3-a^2+1/2a)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3Cs.1.1 |
$1$ |
\( 2^{3} \cdot 3^{2} \) |
$1$ |
$179.7659609$ |
2.723726681 |
\( \frac{286425}{64} a^{2} - \frac{179083}{64} \) |
\( \bigl[1\) , \( a^{2} - 5\) , \( a^{2} - 3\) , \( -5 a^{2} + 10\) , \( -8 a^{2} + 1\bigr] \) |
${y}^2+{x}{y}+\left(a^{2}-3\right){y}={x}^{3}+\left(a^{2}-5\right){x}^{2}+\left(-5a^{2}+10\right){x}-8a^{2}+1$ |
| 4.2-a2 |
4.2-a |
$6$ |
$18$ |
\(\Q(\sqrt{3}, \sqrt{11})\) |
$4$ |
$[4, 0]$ |
4.2 |
\( 2^{2} \) |
\( 2^{54} \) |
$14.02717$ |
$(1/2a^3-7/2a+1), (-1/2a^3-a^2+1/2a)$ |
0 |
$\Z/18\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{3} \cdot 3^{4} \) |
$1$ |
$179.7659609$ |
2.723726681 |
\( \frac{5519537297}{262144} a^{2} - \frac{3467643755}{262144} \) |
\( \bigl[1\) , \( a^{2} - 5\) , \( a^{2} - 3\) , \( -45 a^{2} + 35\) , \( 241 a^{2} - 155\bigr] \) |
${y}^2+{x}{y}+\left(a^{2}-3\right){y}={x}^{3}+\left(a^{2}-5\right){x}^{2}+\left(-45a^{2}+35\right){x}+241a^{2}-155$ |
| 4.2-a3 |
4.2-a |
$6$ |
$18$ |
\(\Q(\sqrt{3}, \sqrt{11})\) |
$4$ |
$[4, 0]$ |
4.2 |
\( 2^{2} \) |
\( 2^{6} \) |
$14.02717$ |
$(1/2a^3-7/2a+1), (-1/2a^3-a^2+1/2a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$81$ |
\( 2^{3} \) |
$1$ |
$2.219332851$ |
2.723726681 |
\( \frac{10838595115443}{4} a^{2} - \frac{6803604361891}{4} \) |
\( \bigl[1\) , \( a^{2} - 5\) , \( a^{2} - 3\) , \( -295 a^{2} + 190\) , \( -4810 a^{2} + 3017\bigr] \) |
${y}^2+{x}{y}+\left(a^{2}-3\right){y}={x}^{3}+\left(a^{2}-5\right){x}^{2}+\left(-295a^{2}+190\right){x}-4810a^{2}+3017$ |
| 4.2-a4 |
4.2-a |
$6$ |
$18$ |
\(\Q(\sqrt{3}, \sqrt{11})\) |
$4$ |
$[4, 0]$ |
4.2 |
\( 2^{2} \) |
\( 2^{6} \) |
$14.02717$ |
$(1/2a^3-7/2a+1), (-1/2a^3-a^2+1/2a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$81$ |
\( 2^{3} \) |
$1$ |
$2.219332851$ |
2.723726681 |
\( -\frac{10838595115443}{4} a^{2} + \frac{34533280723105}{2} \) |
\( \bigl[1\) , \( -a^{2} + 5\) , \( a^{2} - 3\) , \( 292 a^{2} - 1864\) , \( 5103 a^{2} - 32521\bigr] \) |
${y}^2+{x}{y}+\left(a^{2}-3\right){y}={x}^{3}+\left(-a^{2}+5\right){x}^{2}+\left(292a^{2}-1864\right){x}+5103a^{2}-32521$ |
| 4.2-a5 |
4.2-a |
$6$ |
$18$ |
\(\Q(\sqrt{3}, \sqrt{11})\) |
$4$ |
$[4, 0]$ |
4.2 |
\( 2^{2} \) |
\( 2^{54} \) |
$14.02717$ |
$(1/2a^3-7/2a+1), (-1/2a^3-a^2+1/2a)$ |
0 |
$\Z/18\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{3} \cdot 3^{4} \) |
$1$ |
$179.7659609$ |
2.723726681 |
\( -\frac{5519537297}{262144} a^{2} + \frac{8792279331}{65536} \) |
\( \bigl[1\) , \( -a^{2} + 5\) , \( a^{2} - 3\) , \( 42 a^{2} - 269\) , \( -198 a^{2} + 1259\bigr] \) |
${y}^2+{x}{y}+\left(a^{2}-3\right){y}={x}^{3}+\left(-a^{2}+5\right){x}^{2}+\left(42a^{2}-269\right){x}-198a^{2}+1259$ |
| 4.2-a6 |
4.2-a |
$6$ |
$18$ |
\(\Q(\sqrt{3}, \sqrt{11})\) |
$4$ |
$[4, 0]$ |
4.2 |
\( 2^{2} \) |
\( 2^{18} \) |
$14.02717$ |
$(1/2a^3-7/2a+1), (-1/2a^3-a^2+1/2a)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3Cs.1.1 |
$1$ |
\( 2^{3} \cdot 3^{2} \) |
$1$ |
$179.7659609$ |
2.723726681 |
\( -\frac{286425}{64} a^{2} + \frac{456473}{16} \) |
\( \bigl[1\) , \( -a^{2} + 5\) , \( a^{2} - 3\) , \( 2 a^{2} - 14\) , \( 11 a^{2} - 73\bigr] \) |
${y}^2+{x}{y}+\left(a^{2}-3\right){y}={x}^{3}+\left(-a^{2}+5\right){x}^{2}+\left(2a^{2}-14\right){x}+11a^{2}-73$ |
| 4.2-b1 |
4.2-b |
$8$ |
$12$ |
\(\Q(\sqrt{3}, \sqrt{11})\) |
$4$ |
$[4, 0]$ |
4.2 |
\( 2^{2} \) |
\( 2^{14} \) |
$14.02717$ |
$(1/2a^3-7/2a+1), (-1/2a^3-a^2+1/2a)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{4} \) |
$0.043390543$ |
$2005.666846$ |
2.637181033 |
\( -\frac{28006803}{16} a^{2} + \frac{89226225}{8} \) |
\( \bigl[\frac{1}{2} a^{3} + a^{2} - \frac{3}{2} a - 4\) , \( a\) , \( \frac{1}{2} a^{3} - \frac{5}{2} a\) , \( \frac{3}{2} a^{3} + 8 a^{2} + \frac{3}{2} a - 24\) , \( \frac{13}{2} a^{3} + 4 a^{2} - \frac{47}{2} a + 19\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}+a^{2}-\frac{3}{2}a-4\right){x}{y}+\left(\frac{1}{2}a^{3}-\frac{5}{2}a\right){y}={x}^{3}+a{x}^{2}+\left(\frac{3}{2}a^{3}+8a^{2}+\frac{3}{2}a-24\right){x}+\frac{13}{2}a^{3}+4a^{2}-\frac{47}{2}a+19$ |
| 4.2-b2 |
4.2-b |
$8$ |
$12$ |
\(\Q(\sqrt{3}, \sqrt{11})\) |
$4$ |
$[4, 0]$ |
4.2 |
\( 2^{2} \) |
\( 2^{14} \) |
$14.02717$ |
$(1/2a^3-7/2a+1), (-1/2a^3-a^2+1/2a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \cdot 3 \) |
$0.520686519$ |
$55.71296795$ |
2.637181033 |
\( \frac{28006803}{16} a^{2} - \frac{17595171}{16} \) |
\( \bigl[\frac{1}{2} a^{3} + a^{2} - \frac{3}{2} a - 4\) , \( a\) , \( \frac{1}{2} a^{3} - \frac{5}{2} a\) , \( \frac{3}{2} a^{3} + \frac{3}{2} a + 4\) , \( -\frac{3}{2} a^{3} - 8 a^{2} + \frac{9}{2} a + 7\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}+a^{2}-\frac{3}{2}a-4\right){x}{y}+\left(\frac{1}{2}a^{3}-\frac{5}{2}a\right){y}={x}^{3}+a{x}^{2}+\left(\frac{3}{2}a^{3}+\frac{3}{2}a+4\right){x}-\frac{3}{2}a^{3}-8a^{2}+\frac{9}{2}a+7$ |
| 4.2-b3 |
4.2-b |
$8$ |
$12$ |
\(\Q(\sqrt{3}, \sqrt{11})\) |
$4$ |
$[4, 0]$ |
4.2 |
\( 2^{2} \) |
\( 2^{8} \) |
$14.02717$ |
$(1/2a^3-7/2a+1), (-1/2a^3-a^2+1/2a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \) |
$0.173562173$ |
$501.4167115$ |
2.637181033 |
\( \frac{8022622470093}{8} a^{2} - \frac{5035949811387}{8} \) |
\( \bigl[a^{2} + a - 3\) , \( -\frac{1}{2} a^{3} - a^{2} + \frac{3}{2} a + 5\) , \( a^{2} - 3\) , \( -\frac{1}{2} a^{3} + 59 a^{2} + \frac{3}{2} a - 380\) , \( 541 a^{2} - 3450\bigr] \) |
${y}^2+\left(a^{2}+a-3\right){x}{y}+\left(a^{2}-3\right){y}={x}^{3}+\left(-\frac{1}{2}a^{3}-a^{2}+\frac{3}{2}a+5\right){x}^{2}+\left(-\frac{1}{2}a^{3}+59a^{2}+\frac{3}{2}a-380\right){x}+541a^{2}-3450$ |
| 4.2-b4 |
4.2-b |
$8$ |
$12$ |
\(\Q(\sqrt{3}, \sqrt{11})\) |
$4$ |
$[4, 0]$ |
4.2 |
\( 2^{2} \) |
\( 2^{16} \) |
$14.02717$ |
$(1/2a^3-7/2a+1), (-1/2a^3-a^2+1/2a)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2Cs, 3B |
$1$ |
\( 2^{3} \) |
$0.086781086$ |
$2005.666846$ |
2.637181033 |
\( \frac{26704161}{64} a^{2} - \frac{16508043}{64} \) |
\( \bigl[a^{2} + a - 3\) , \( -\frac{1}{2} a^{3} - a^{2} + \frac{3}{2} a + 5\) , \( a^{2} - 3\) , \( -\frac{1}{2} a^{3} + 9 a^{2} + \frac{3}{2} a - 60\) , \( -5 a^{2} + 30\bigr] \) |
${y}^2+\left(a^{2}+a-3\right){x}{y}+\left(a^{2}-3\right){y}={x}^{3}+\left(-\frac{1}{2}a^{3}-a^{2}+\frac{3}{2}a+5\right){x}^{2}+\left(-\frac{1}{2}a^{3}+9a^{2}+\frac{3}{2}a-60\right){x}-5a^{2}+30$ |
| 4.2-b5 |
4.2-b |
$8$ |
$12$ |
\(\Q(\sqrt{3}, \sqrt{11})\) |
$4$ |
$[4, 0]$ |
4.2 |
\( 2^{2} \) |
\( 2^{26} \) |
$14.02717$ |
$(1/2a^3-7/2a+1), (-1/2a^3-a^2+1/2a)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{4} \cdot 3 \) |
$0.130171629$ |
$222.8518718$ |
2.637181033 |
\( -\frac{1257201}{4096} a^{2} + \frac{2685123}{1024} \) |
\( \bigl[a^{2} + a - 3\) , \( -\frac{1}{2} a^{3} - a^{2} + \frac{3}{2} a + 5\) , \( a^{2} - 3\) , \( -\frac{1}{2} a^{3} - a^{2} + \frac{3}{2} a + 4\) , \( a^{2} - 8\bigr] \) |
${y}^2+\left(a^{2}+a-3\right){x}{y}+\left(a^{2}-3\right){y}={x}^{3}+\left(-\frac{1}{2}a^{3}-a^{2}+\frac{3}{2}a+5\right){x}^{2}+\left(-\frac{1}{2}a^{3}-a^{2}+\frac{3}{2}a+4\right){x}+a^{2}-8$ |
| 4.2-b6 |
4.2-b |
$8$ |
$12$ |
\(\Q(\sqrt{3}, \sqrt{11})\) |
$4$ |
$[4, 0]$ |
4.2 |
\( 2^{2} \) |
\( 2^{26} \) |
$14.02717$ |
$(1/2a^3-7/2a+1), (-1/2a^3-a^2+1/2a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \) |
$0.173562173$ |
$501.4167115$ |
2.637181033 |
\( \frac{1257201}{4096} a^{2} + \frac{1940085}{4096} \) |
\( \bigl[a^{2} + a - 3\) , \( -\frac{1}{2} a^{3} - a^{2} + \frac{3}{2} a + 5\) , \( a^{2} - 3\) , \( -\frac{1}{2} a^{3} - 3 a^{2} + \frac{3}{2} a + 11\) , \( -2 a^{2} + 8\bigr] \) |
${y}^2+\left(a^{2}+a-3\right){x}{y}+\left(a^{2}-3\right){y}={x}^{3}+\left(-\frac{1}{2}a^{3}-a^{2}+\frac{3}{2}a+5\right){x}^{2}+\left(-\frac{1}{2}a^{3}-3a^{2}+\frac{3}{2}a+11\right){x}-2a^{2}+8$ |
| 4.2-b7 |
4.2-b |
$8$ |
$12$ |
\(\Q(\sqrt{3}, \sqrt{11})\) |
$4$ |
$[4, 0]$ |
4.2 |
\( 2^{2} \) |
\( 2^{16} \) |
$14.02717$ |
$(1/2a^3-7/2a+1), (-1/2a^3-a^2+1/2a)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2Cs, 3B |
$1$ |
\( 2^{3} \cdot 3 \) |
$0.260343259$ |
$222.8518718$ |
2.637181033 |
\( -\frac{26704161}{64} a^{2} + \frac{42605271}{16} \) |
\( \bigl[a^{2} + a - 3\) , \( -\frac{1}{2} a^{3} - a^{2} + \frac{3}{2} a + 5\) , \( a^{2} - 3\) , \( -\frac{1}{2} a^{3} - 13 a^{2} + \frac{3}{2} a + 17\) , \( -38 a^{2} + 30\bigr] \) |
${y}^2+\left(a^{2}+a-3\right){x}{y}+\left(a^{2}-3\right){y}={x}^{3}+\left(-\frac{1}{2}a^{3}-a^{2}+\frac{3}{2}a+5\right){x}^{2}+\left(-\frac{1}{2}a^{3}-13a^{2}+\frac{3}{2}a+17\right){x}-38a^{2}+30$ |
| 4.2-b8 |
4.2-b |
$8$ |
$12$ |
\(\Q(\sqrt{3}, \sqrt{11})\) |
$4$ |
$[4, 0]$ |
4.2 |
\( 2^{2} \) |
\( 2^{8} \) |
$14.02717$ |
$(1/2a^3-7/2a+1), (-1/2a^3-a^2+1/2a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \cdot 3 \) |
$0.520686519$ |
$55.71296795$ |
2.637181033 |
\( -\frac{8022622470093}{8} a^{2} + 6390300934908 \) |
\( \bigl[a^{2} + a - 3\) , \( -\frac{1}{2} a^{3} - a^{2} + \frac{3}{2} a + 5\) , \( a^{2} - 3\) , \( -\frac{1}{2} a^{3} - 63 a^{2} + \frac{3}{2} a + 47\) , \( 358 a^{2} - 222\bigr] \) |
${y}^2+\left(a^{2}+a-3\right){x}{y}+\left(a^{2}-3\right){y}={x}^{3}+\left(-\frac{1}{2}a^{3}-a^{2}+\frac{3}{2}a+5\right){x}^{2}+\left(-\frac{1}{2}a^{3}-63a^{2}+\frac{3}{2}a+47\right){x}+358a^{2}-222$ |
| 4.2-c1 |
4.2-c |
$6$ |
$18$ |
\(\Q(\sqrt{3}, \sqrt{11})\) |
$4$ |
$[4, 0]$ |
4.2 |
\( 2^{2} \) |
\( 2^{6} \) |
$14.02717$ |
$(1/2a^3-7/2a+1), (-1/2a^3-a^2+1/2a)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{2} \) |
$1$ |
$1212.357383$ |
1.020502847 |
\( -\frac{10838595115443}{4} a^{2} + \frac{34533280723105}{2} \) |
\( \bigl[\frac{1}{2} a^{3} - \frac{5}{2} a\) , \( a^{2} - 3\) , \( a\) , \( 294 a^{2} - 1872\) , \( -4810 a^{2} + 30650\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-\frac{5}{2}a\right){x}{y}+a{y}={x}^{3}+\left(a^{2}-3\right){x}^{2}+\left(294a^{2}-1872\right){x}-4810a^{2}+30650$ |
| 4.2-c2 |
4.2-c |
$6$ |
$18$ |
\(\Q(\sqrt{3}, \sqrt{11})\) |
$4$ |
$[4, 0]$ |
4.2 |
\( 2^{2} \) |
\( 2^{54} \) |
$14.02717$ |
$(1/2a^3-7/2a+1), (-1/2a^3-a^2+1/2a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$9$ |
\( 2^{2} \) |
$1$ |
$14.96737510$ |
1.020502847 |
\( -\frac{5519537297}{262144} a^{2} + \frac{8792279331}{65536} \) |
\( \bigl[\frac{1}{2} a^{3} - \frac{5}{2} a\) , \( a^{2} - 3\) , \( a\) , \( 44 a^{2} - 277\) , \( 241 a^{2} - 1535\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-\frac{5}{2}a\right){x}{y}+a{y}={x}^{3}+\left(a^{2}-3\right){x}^{2}+\left(44a^{2}-277\right){x}+241a^{2}-1535$ |
| 4.2-c3 |
4.2-c |
$6$ |
$18$ |
\(\Q(\sqrt{3}, \sqrt{11})\) |
$4$ |
$[4, 0]$ |
4.2 |
\( 2^{2} \) |
\( 2^{18} \) |
$14.02717$ |
$(1/2a^3-7/2a+1), (-1/2a^3-a^2+1/2a)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3Cs.1.1 |
$1$ |
\( 2^{2} \) |
$1$ |
$1212.357383$ |
1.020502847 |
\( -\frac{286425}{64} a^{2} + \frac{456473}{16} \) |
\( \bigl[\frac{1}{2} a^{3} - \frac{5}{2} a\) , \( a^{2} - 3\) , \( a\) , \( 4 a^{2} - 22\) , \( -8 a^{2} + 52\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-\frac{5}{2}a\right){x}{y}+a{y}={x}^{3}+\left(a^{2}-3\right){x}^{2}+\left(4a^{2}-22\right){x}-8a^{2}+52$ |
| 4.2-c4 |
4.2-c |
$6$ |
$18$ |
\(\Q(\sqrt{3}, \sqrt{11})\) |
$4$ |
$[4, 0]$ |
4.2 |
\( 2^{2} \) |
\( 2^{18} \) |
$14.02717$ |
$(1/2a^3-7/2a+1), (-1/2a^3-a^2+1/2a)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3Cs.1.1 |
$1$ |
\( 2^{2} \) |
$1$ |
$1212.357383$ |
1.020502847 |
\( \frac{286425}{64} a^{2} - \frac{179083}{64} \) |
\( \bigl[\frac{1}{2} a^{3} - \frac{5}{2} a\) , \( -a^{2} + 4\) , \( \frac{1}{2} a^{3} - \frac{3}{2} a\) , \( -5 a^{2} + 8\) , \( 7 a^{2} - 2\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-\frac{5}{2}a\right){x}{y}+\left(\frac{1}{2}a^{3}-\frac{3}{2}a\right){y}={x}^{3}+\left(-a^{2}+4\right){x}^{2}+\left(-5a^{2}+8\right){x}+7a^{2}-2$ |
| 4.2-c5 |
4.2-c |
$6$ |
$18$ |
\(\Q(\sqrt{3}, \sqrt{11})\) |
$4$ |
$[4, 0]$ |
4.2 |
\( 2^{2} \) |
\( 2^{54} \) |
$14.02717$ |
$(1/2a^3-7/2a+1), (-1/2a^3-a^2+1/2a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$9$ |
\( 2^{2} \) |
$1$ |
$14.96737510$ |
1.020502847 |
\( \frac{5519537297}{262144} a^{2} - \frac{3467643755}{262144} \) |
\( \bigl[\frac{1}{2} a^{3} - \frac{5}{2} a\) , \( -a^{2} + 4\) , \( \frac{1}{2} a^{3} - \frac{3}{2} a\) , \( -45 a^{2} + 33\) , \( -242 a^{2} + 154\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-\frac{5}{2}a\right){x}{y}+\left(\frac{1}{2}a^{3}-\frac{3}{2}a\right){y}={x}^{3}+\left(-a^{2}+4\right){x}^{2}+\left(-45a^{2}+33\right){x}-242a^{2}+154$ |
| 4.2-c6 |
4.2-c |
$6$ |
$18$ |
\(\Q(\sqrt{3}, \sqrt{11})\) |
$4$ |
$[4, 0]$ |
4.2 |
\( 2^{2} \) |
\( 2^{6} \) |
$14.02717$ |
$(1/2a^3-7/2a+1), (-1/2a^3-a^2+1/2a)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{2} \) |
$1$ |
$1212.357383$ |
1.020502847 |
\( \frac{10838595115443}{4} a^{2} - \frac{6803604361891}{4} \) |
\( \bigl[\frac{1}{2} a^{3} - \frac{5}{2} a\) , \( -a^{2} + 4\) , \( \frac{1}{2} a^{3} - \frac{3}{2} a\) , \( -295 a^{2} + 188\) , \( 4809 a^{2} - 3018\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-\frac{5}{2}a\right){x}{y}+\left(\frac{1}{2}a^{3}-\frac{3}{2}a\right){y}={x}^{3}+\left(-a^{2}+4\right){x}^{2}+\left(-295a^{2}+188\right){x}+4809a^{2}-3018$ |
| 4.2-d1 |
4.2-d |
$8$ |
$12$ |
\(\Q(\sqrt{3}, \sqrt{11})\) |
$4$ |
$[4, 0]$ |
4.2 |
\( 2^{2} \) |
\( 2^{8} \) |
$14.02717$ |
$(1/2a^3-7/2a+1), (-1/2a^3-a^2+1/2a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \cdot 3 \) |
$0.520686519$ |
$55.71296795$ |
2.637181033 |
\( \frac{8022622470093}{8} a^{2} - \frac{5035949811387}{8} \) |
\( \bigl[\frac{1}{2} a^{3} + a^{2} - \frac{3}{2} a - 4\) , \( a\) , \( a^{2} + a - 4\) , \( \frac{1}{2} a^{3} + 65 a^{2} + \frac{11}{2} a - 393\) , \( 63 a^{3} - 352 a^{2} - 386 a + 2282\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}+a^{2}-\frac{3}{2}a-4\right){x}{y}+\left(a^{2}+a-4\right){y}={x}^{3}+a{x}^{2}+\left(\frac{1}{2}a^{3}+65a^{2}+\frac{11}{2}a-393\right){x}+63a^{3}-352a^{2}-386a+2282$ |
| 4.2-d2 |
4.2-d |
$8$ |
$12$ |
\(\Q(\sqrt{3}, \sqrt{11})\) |
$4$ |
$[4, 0]$ |
4.2 |
\( 2^{2} \) |
\( 2^{16} \) |
$14.02717$ |
$(1/2a^3-7/2a+1), (-1/2a^3-a^2+1/2a)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2Cs, 3B |
$1$ |
\( 2^{3} \cdot 3 \) |
$0.260343259$ |
$222.8518718$ |
2.637181033 |
\( \frac{26704161}{64} a^{2} - \frac{16508043}{64} \) |
\( \bigl[\frac{1}{2} a^{3} + a^{2} - \frac{3}{2} a - 4\) , \( a\) , \( a^{2} + a - 4\) , \( \frac{1}{2} a^{3} + 15 a^{2} + \frac{11}{2} a - 73\) , \( 13 a^{3} + 44 a^{2} - 66 a - 238\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}+a^{2}-\frac{3}{2}a-4\right){x}{y}+\left(a^{2}+a-4\right){y}={x}^{3}+a{x}^{2}+\left(\frac{1}{2}a^{3}+15a^{2}+\frac{11}{2}a-73\right){x}+13a^{3}+44a^{2}-66a-238$ |
| 4.2-d3 |
4.2-d |
$8$ |
$12$ |
\(\Q(\sqrt{3}, \sqrt{11})\) |
$4$ |
$[4, 0]$ |
4.2 |
\( 2^{2} \) |
\( 2^{26} \) |
$14.02717$ |
$(1/2a^3-7/2a+1), (-1/2a^3-a^2+1/2a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \) |
$0.173562173$ |
$501.4167115$ |
2.637181033 |
\( -\frac{1257201}{4096} a^{2} + \frac{2685123}{1024} \) |
\( \bigl[\frac{1}{2} a^{3} + a^{2} - \frac{3}{2} a - 4\) , \( a\) , \( a^{2} + a - 4\) , \( \frac{1}{2} a^{3} + 5 a^{2} + \frac{11}{2} a - 9\) , \( 3 a^{3} + 8 a^{2} - 2 a - 8\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}+a^{2}-\frac{3}{2}a-4\right){x}{y}+\left(a^{2}+a-4\right){y}={x}^{3}+a{x}^{2}+\left(\frac{1}{2}a^{3}+5a^{2}+\frac{11}{2}a-9\right){x}+3a^{3}+8a^{2}-2a-8$ |
| 4.2-d4 |
4.2-d |
$8$ |
$12$ |
\(\Q(\sqrt{3}, \sqrt{11})\) |
$4$ |
$[4, 0]$ |
4.2 |
\( 2^{2} \) |
\( 2^{26} \) |
$14.02717$ |
$(1/2a^3-7/2a+1), (-1/2a^3-a^2+1/2a)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{4} \cdot 3 \) |
$0.130171629$ |
$222.8518718$ |
2.637181033 |
\( \frac{1257201}{4096} a^{2} + \frac{1940085}{4096} \) |
\( \bigl[\frac{1}{2} a^{3} + a^{2} - \frac{3}{2} a - 4\) , \( a\) , \( a^{2} + a - 4\) , \( \frac{1}{2} a^{3} + 3 a^{2} + \frac{11}{2} a - 2\) , \( a^{3} + 5 a^{2} + 5 a - 3\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}+a^{2}-\frac{3}{2}a-4\right){x}{y}+\left(a^{2}+a-4\right){y}={x}^{3}+a{x}^{2}+\left(\frac{1}{2}a^{3}+3a^{2}+\frac{11}{2}a-2\right){x}+a^{3}+5a^{2}+5a-3$ |
| 4.2-d5 |
4.2-d |
$8$ |
$12$ |
\(\Q(\sqrt{3}, \sqrt{11})\) |
$4$ |
$[4, 0]$ |
4.2 |
\( 2^{2} \) |
\( 2^{16} \) |
$14.02717$ |
$(1/2a^3-7/2a+1), (-1/2a^3-a^2+1/2a)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2Cs, 3B |
$1$ |
\( 2^{3} \) |
$0.086781086$ |
$2005.666846$ |
2.637181033 |
\( -\frac{26704161}{64} a^{2} + \frac{42605271}{16} \) |
\( \bigl[\frac{1}{2} a^{3} + a^{2} - \frac{3}{2} a - 4\) , \( a\) , \( a^{2} + a - 4\) , \( \frac{1}{2} a^{3} - 7 a^{2} + \frac{11}{2} a + 4\) , \( -9 a^{3} + 11 a^{2} + 11 a - 7\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}+a^{2}-\frac{3}{2}a-4\right){x}{y}+\left(a^{2}+a-4\right){y}={x}^{3}+a{x}^{2}+\left(\frac{1}{2}a^{3}-7a^{2}+\frac{11}{2}a+4\right){x}-9a^{3}+11a^{2}+11a-7$ |
| 4.2-d6 |
4.2-d |
$8$ |
$12$ |
\(\Q(\sqrt{3}, \sqrt{11})\) |
$4$ |
$[4, 0]$ |
4.2 |
\( 2^{2} \) |
\( 2^{8} \) |
$14.02717$ |
$(1/2a^3-7/2a+1), (-1/2a^3-a^2+1/2a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \) |
$0.173562173$ |
$501.4167115$ |
2.637181033 |
\( -\frac{8022622470093}{8} a^{2} + 6390300934908 \) |
\( \bigl[\frac{1}{2} a^{3} + a^{2} - \frac{3}{2} a - 4\) , \( a\) , \( a^{2} + a - 4\) , \( \frac{1}{2} a^{3} - 57 a^{2} + \frac{11}{2} a + 34\) , \( -59 a^{3} - 535 a^{2} + 41 a + 335\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}+a^{2}-\frac{3}{2}a-4\right){x}{y}+\left(a^{2}+a-4\right){y}={x}^{3}+a{x}^{2}+\left(\frac{1}{2}a^{3}-57a^{2}+\frac{11}{2}a+34\right){x}-59a^{3}-535a^{2}+41a+335$ |
| 4.2-d7 |
4.2-d |
$8$ |
$12$ |
\(\Q(\sqrt{3}, \sqrt{11})\) |
$4$ |
$[4, 0]$ |
4.2 |
\( 2^{2} \) |
\( 2^{14} \) |
$14.02717$ |
$(1/2a^3-7/2a+1), (-1/2a^3-a^2+1/2a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \cdot 3 \) |
$0.520686519$ |
$55.71296795$ |
2.637181033 |
\( -\frac{28006803}{16} a^{2} + \frac{89226225}{8} \) |
\( \bigl[a^{2} + a - 3\) , \( -\frac{1}{2} a^{3} - a^{2} + \frac{3}{2} a + 5\) , \( a\) , \( -\frac{1}{2} a^{3} + 2 a^{2} + \frac{3}{2} a - 13\) , \( 14 a^{2} - 90\bigr] \) |
${y}^2+\left(a^{2}+a-3\right){x}{y}+a{y}={x}^{3}+\left(-\frac{1}{2}a^{3}-a^{2}+\frac{3}{2}a+5\right){x}^{2}+\left(-\frac{1}{2}a^{3}+2a^{2}+\frac{3}{2}a-13\right){x}+14a^{2}-90$ |
| 4.2-d8 |
4.2-d |
$8$ |
$12$ |
\(\Q(\sqrt{3}, \sqrt{11})\) |
$4$ |
$[4, 0]$ |
4.2 |
\( 2^{2} \) |
\( 2^{14} \) |
$14.02717$ |
$(1/2a^3-7/2a+1), (-1/2a^3-a^2+1/2a)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{4} \) |
$0.043390543$ |
$2005.666846$ |
2.637181033 |
\( \frac{28006803}{16} a^{2} - \frac{17595171}{16} \) |
\( \bigl[a^{2} + a - 3\) , \( -\frac{1}{2} a^{3} - a^{2} + \frac{3}{2} a + 5\) , \( a\) , \( -\frac{1}{2} a^{3} - 6 a^{2} + \frac{3}{2} a + 15\) , \( 2 a^{2} + 6\bigr] \) |
${y}^2+\left(a^{2}+a-3\right){x}{y}+a{y}={x}^{3}+\left(-\frac{1}{2}a^{3}-a^{2}+\frac{3}{2}a+5\right){x}^{2}+\left(-\frac{1}{2}a^{3}-6a^{2}+\frac{3}{2}a+15\right){x}+2a^{2}+6$ |
| 4.3-a1 |
4.3-a |
$2$ |
$3$ |
\(\Q(\sqrt{3}, \sqrt{11})\) |
$4$ |
$[4, 0]$ |
4.3 |
\( 2^{2} \) |
\( 2^{4} \) |
$14.02717$ |
$(-1/2a^3-a^2+1/2a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{potential}$ |
$-3$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
|
|
$1$ |
\( 1 \) |
$0.040727548$ |
$1878.684925$ |
2.318613059 |
\( 0 \) |
\( \bigl[0\) , \( -\frac{1}{2} a^{3} + \frac{5}{2} a\) , \( \frac{1}{2} a^{3} + a^{2} - \frac{5}{2} a - 4\) , \( 1\) , \( a^{3} + 2 a^{2} - 3 a - 4\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}+a^{2}-\frac{5}{2}a-4\right){y}={x}^{3}+\left(-\frac{1}{2}a^{3}+\frac{5}{2}a\right){x}^{2}+{x}+a^{3}+2a^{2}-3a-4$ |
| 4.3-a2 |
4.3-a |
$2$ |
$3$ |
\(\Q(\sqrt{3}, \sqrt{11})\) |
$4$ |
$[4, 0]$ |
4.3 |
\( 2^{2} \) |
\( 2^{4} \) |
$14.02717$ |
$(-1/2a^3-a^2+1/2a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{potential}$ |
$-3$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
|
|
$1$ |
\( 3 \) |
$0.122182644$ |
$208.7427694$ |
2.318613059 |
\( 0 \) |
\( \bigl[0\) , \( \frac{1}{2} a^{3} - \frac{5}{2} a\) , \( a + 1\) , \( 1\) , \( -\frac{1}{2} a^{3} - 2 a^{2} - \frac{3}{2} a\bigr] \) |
${y}^2+\left(a+1\right){y}={x}^{3}+\left(\frac{1}{2}a^{3}-\frac{5}{2}a\right){x}^{2}+{x}-\frac{1}{2}a^{3}-2a^{2}-\frac{3}{2}a$ |
| 9.1-a1 |
9.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{3}, \sqrt{11})\) |
$4$ |
$[4, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{4} \) |
$15.52361$ |
$(1/2a^3-5/2a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1.391170063$ |
$109.0490262$ |
2.298571830 |
\( -\frac{1205808257396435}{6} a^{3} - \frac{477673098227809}{3} a^{2} + \frac{2561249812685883}{2} a + \frac{3043867362456206}{3} \) |
\( \bigl[\frac{1}{2} a^{3} + a^{2} - \frac{3}{2} a - 4\) , \( \frac{1}{2} a^{3} - \frac{5}{2} a\) , \( \frac{1}{2} a^{3} - \frac{3}{2} a\) , \( \frac{13}{2} a^{3} - 4 a^{2} - \frac{31}{2} a - 2\) , \( -\frac{15}{2} a^{3} + 42 a^{2} - \frac{35}{2} a - 43\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}+a^{2}-\frac{3}{2}a-4\right){x}{y}+\left(\frac{1}{2}a^{3}-\frac{3}{2}a\right){y}={x}^{3}+\left(\frac{1}{2}a^{3}-\frac{5}{2}a\right){x}^{2}+\left(\frac{13}{2}a^{3}-4a^{2}-\frac{31}{2}a-2\right){x}-\frac{15}{2}a^{3}+42a^{2}-\frac{35}{2}a-43$ |
| 9.1-a2 |
9.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{3}, \sqrt{11})\) |
$4$ |
$[4, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{16} \) |
$15.52361$ |
$(1/2a^3-5/2a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.347792515$ |
$109.0490262$ |
2.298571830 |
\( \frac{2539030883543}{162} a^{3} - \frac{12695154417715}{162} a + \frac{4397731084762}{81} \) |
\( \bigl[a^{2} + a - 3\) , \( -a^{2} + 5\) , \( 1\) , \( 4 a^{3} - a^{2} - 19 a - 15\) , \( \frac{19}{2} a^{3} + 14 a^{2} - \frac{185}{2} a - 77\bigr] \) |
${y}^2+\left(a^{2}+a-3\right){x}{y}+{y}={x}^{3}+\left(-a^{2}+5\right){x}^{2}+\left(4a^{3}-a^{2}-19a-15\right){x}+\frac{19}{2}a^{3}+14a^{2}-\frac{185}{2}a-77$ |
| 9.1-a3 |
9.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{3}, \sqrt{11})\) |
$4$ |
$[4, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{8} \) |
$15.52361$ |
$(1/2a^3-5/2a)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$0.695585031$ |
$436.1961049$ |
2.298571830 |
\( -\frac{55132946}{9} a^{3} + \frac{275664730}{9} a + \frac{193958543}{9} \) |
\( \bigl[a^{2} + a - 3\) , \( -a^{2} + 5\) , \( 1\) , \( \frac{13}{2} a^{3} - a^{2} - \frac{63}{2} a - 5\) , \( \frac{27}{2} a^{3} + 21 a^{2} - \frac{207}{2} a - 79\bigr] \) |
${y}^2+\left(a^{2}+a-3\right){x}{y}+{y}={x}^{3}+\left(-a^{2}+5\right){x}^{2}+\left(\frac{13}{2}a^{3}-a^{2}-\frac{63}{2}a-5\right){x}+\frac{27}{2}a^{3}+21a^{2}-\frac{207}{2}a-79$ |
| 9.1-a4 |
9.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{3}, \sqrt{11})\) |
$4$ |
$[4, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{4} \) |
$15.52361$ |
$(1/2a^3-5/2a)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1.391170063$ |
$436.1961049$ |
2.298571830 |
\( -\frac{189227090929349}{3} a^{3} + \frac{477673098227809}{3} a^{2} + 39593793036336 a - \frac{299844325138457}{3} \) |
\( \bigl[a^{2} + a - 3\) , \( -\frac{1}{2} a^{3} - a^{2} + \frac{7}{2} a + 5\) , \( a\) , \( -41 a^{3} + 30 a^{2} + 262 a - 187\) , \( 1113 a^{3} - 885 a^{2} - 7093 a + 5636\bigr] \) |
${y}^2+\left(a^{2}+a-3\right){x}{y}+a{y}={x}^{3}+\left(-\frac{1}{2}a^{3}-a^{2}+\frac{7}{2}a+5\right){x}^{2}+\left(-41a^{3}+30a^{2}+262a-187\right){x}+1113a^{3}-885a^{2}-7093a+5636$ |
*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.
