| 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 |
$4$ |
$4$ |
4.4.19225.1 |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( -1 \) |
$12.39001$ |
$\textsf{none}$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
✓ |
$2, 3$ |
2B, 3Ns |
$1$ |
\( 1 \) |
$1$ |
$1245.993776$ |
2.246584237 |
\( -109908 a^{3} - 70942 a^{2} + 1417356 a + 2298769 \) |
\( \bigl[-\frac{1}{2} a^{3} + \frac{5}{2} a^{2} + \frac{5}{2} a - 15\) , \( -\frac{1}{2} a^{3} + \frac{5}{2} a^{2} + \frac{7}{2} a - 15\) , \( -a^{3} + 4 a^{2} + 7 a - 22\) , \( a^{3} - 2 a^{2} - 6 a + 11\) , \( -\frac{1}{2} a^{3} + \frac{5}{2} a^{2} + \frac{9}{2} a - 14\bigr] \) |
${y}^2+\left(-\frac{1}{2}a^{3}+\frac{5}{2}a^{2}+\frac{5}{2}a-15\right){x}{y}+\left(-a^{3}+4a^{2}+7a-22\right){y}={x}^{3}+\left(-\frac{1}{2}a^{3}+\frac{5}{2}a^{2}+\frac{7}{2}a-15\right){x}^{2}+\left(a^{3}-2a^{2}-6a+11\right){x}-\frac{1}{2}a^{3}+\frac{5}{2}a^{2}+\frac{9}{2}a-14$ |
| 1.1-a2 |
1.1-a |
$4$ |
$4$ |
4.4.19225.1 |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$12.39001$ |
$\textsf{none}$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
✓ |
$2, 3$ |
2B, 3Ns |
$16$ |
\( 1 \) |
$1$ |
$77.87461102$ |
2.246584237 |
\( 21679505425 a^{3} - 65038516275 a^{2} - 151756537975 a + 373669430233 \) |
\( \bigl[a + 1\) , \( -\frac{1}{2} a^{3} + \frac{5}{2} a^{2} + \frac{3}{2} a - 14\) , \( -a^{3} + 4 a^{2} + 6 a - 22\) , \( -\frac{563}{2} a^{3} - \frac{453}{2} a^{2} + \frac{7411}{2} a + 6292\) , \( -\frac{17779}{2} a^{3} - \frac{15851}{2} a^{2} + \frac{236409}{2} a + 206024\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(-a^{3}+4a^{2}+6a-22\right){y}={x}^{3}+\left(-\frac{1}{2}a^{3}+\frac{5}{2}a^{2}+\frac{3}{2}a-14\right){x}^{2}+\left(-\frac{563}{2}a^{3}-\frac{453}{2}a^{2}+\frac{7411}{2}a+6292\right){x}-\frac{17779}{2}a^{3}-\frac{15851}{2}a^{2}+\frac{236409}{2}a+206024$ |
| 1.1-a3 |
1.1-a |
$4$ |
$4$ |
4.4.19225.1 |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( -1 \) |
$12.39001$ |
$\textsf{none}$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
✓ |
$2, 3$ |
2B, 3Ns |
$1$ |
\( 1 \) |
$1$ |
$1245.993776$ |
2.246584237 |
\( -787573 a^{3} + 2763385 a^{2} + 4865011 a - 13752529 \) |
\( \bigl[-\frac{1}{2} a^{3} + \frac{5}{2} a^{2} + \frac{5}{2} a - 14\) , \( \frac{1}{2} a^{3} - \frac{5}{2} a^{2} - \frac{3}{2} a + 14\) , \( 0\) , \( -a^{3} + a^{2} + 11 a + 8\) , \( -a^{3} + a^{2} + 11 a + 5\bigr] \) |
${y}^2+\left(-\frac{1}{2}a^{3}+\frac{5}{2}a^{2}+\frac{5}{2}a-14\right){x}{y}={x}^{3}+\left(\frac{1}{2}a^{3}-\frac{5}{2}a^{2}-\frac{3}{2}a+14\right){x}^{2}+\left(-a^{3}+a^{2}+11a+8\right){x}-a^{3}+a^{2}+11a+5$ |
| 1.1-a4 |
1.1-a |
$4$ |
$4$ |
4.4.19225.1 |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$12.39001$ |
$\textsf{none}$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
✓ |
$2, 3$ |
2Cs, 3Ns |
$4$ |
\( 1 \) |
$1$ |
$1245.993776$ |
2.246584237 |
\( 69156 a^{3} - 207468 a^{2} - 484092 a + 1194821 \) |
\( \bigl[\frac{1}{2} a^{3} - \frac{3}{2} a^{2} - \frac{5}{2} a + 9\) , \( -a^{3} + 4 a^{2} + 5 a - 24\) , \( \frac{1}{2} a^{3} - \frac{3}{2} a^{2} - \frac{5}{2} a + 8\) , \( 695 a^{3} - 2443 a^{2} - 4286 a + 12177\) , \( -\frac{17295}{2} a^{3} + \frac{60767}{2} a^{2} + \frac{106695}{2} a - 151392\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-\frac{3}{2}a^{2}-\frac{5}{2}a+9\right){x}{y}+\left(\frac{1}{2}a^{3}-\frac{3}{2}a^{2}-\frac{5}{2}a+8\right){y}={x}^{3}+\left(-a^{3}+4a^{2}+5a-24\right){x}^{2}+\left(695a^{3}-2443a^{2}-4286a+12177\right){x}-\frac{17295}{2}a^{3}+\frac{60767}{2}a^{2}+\frac{106695}{2}a-151392$ |
| 4.1-a1 |
4.1-a |
$2$ |
$2$ |
4.4.19225.1 |
$4$ |
$[4, 0]$ |
4.1 |
\( 2^{2} \) |
\( - 2^{8} \) |
$14.73429$ |
$(a^2-6)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$689.8164380$ |
2.487541697 |
\( -\frac{54275165}{8} a^{3} + \frac{381292711}{16} a^{2} + \frac{669823423}{16} a - \frac{1899417277}{16} \) |
\( \bigl[-\frac{1}{2} a^{3} + \frac{5}{2} a^{2} + \frac{5}{2} a - 15\) , \( \frac{1}{2} a^{3} - \frac{5}{2} a^{2} - \frac{3}{2} a + 15\) , \( -a^{3} + 4 a^{2} + 7 a - 23\) , \( 22 a^{3} + 21 a^{2} - 296 a - 524\) , \( -\frac{351}{2} a^{3} - \frac{307}{2} a^{2} + \frac{4657}{2} a + 4034\bigr] \) |
${y}^2+\left(-\frac{1}{2}a^{3}+\frac{5}{2}a^{2}+\frac{5}{2}a-15\right){x}{y}+\left(-a^{3}+4a^{2}+7a-23\right){y}={x}^{3}+\left(\frac{1}{2}a^{3}-\frac{5}{2}a^{2}-\frac{3}{2}a+15\right){x}^{2}+\left(22a^{3}+21a^{2}-296a-524\right){x}-\frac{351}{2}a^{3}-\frac{307}{2}a^{2}+\frac{4657}{2}a+4034$ |
| 4.1-a2 |
4.1-a |
$2$ |
$2$ |
4.4.19225.1 |
$4$ |
$[4, 0]$ |
4.1 |
\( 2^{2} \) |
\( - 2^{16} \) |
$14.73429$ |
$(a^2-6)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$689.8164380$ |
2.487541697 |
\( -\frac{215153}{256} a^{3} + \frac{372017}{128} a^{2} + \frac{164813}{32} a - \frac{3103299}{256} \) |
\( \bigl[a + 1\) , \( a^{3} - 4 a^{2} - 5 a + 22\) , \( \frac{1}{2} a^{3} - \frac{3}{2} a^{2} - \frac{5}{2} a + 8\) , \( -\frac{3}{2} a^{3} + \frac{9}{2} a^{2} + \frac{25}{2} a - 15\) , \( a^{3} - 3 a^{2} - 3 a + 22\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(\frac{1}{2}a^{3}-\frac{3}{2}a^{2}-\frac{5}{2}a+8\right){y}={x}^{3}+\left(a^{3}-4a^{2}-5a+22\right){x}^{2}+\left(-\frac{3}{2}a^{3}+\frac{9}{2}a^{2}+\frac{25}{2}a-15\right){x}+a^{3}-3a^{2}-3a+22$ |
| 4.2-a1 |
4.2-a |
$2$ |
$2$ |
4.4.19225.1 |
$4$ |
$[4, 0]$ |
4.2 |
\( 2^{2} \) |
\( - 2^{8} \) |
$14.73429$ |
$(-2a^3+7a^2+13a-37)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$689.8164380$ |
2.487541697 |
\( -\frac{14460471}{16} a^{3} - \frac{3065077}{4} a^{2} + \frac{23906523}{2} a + \frac{41170355}{2} \) |
\( \bigl[-a^{3} + 4 a^{2} + 7 a - 23\) , \( -a^{3} + 4 a^{2} + 6 a - 24\) , \( \frac{1}{2} a^{3} - \frac{3}{2} a^{2} - \frac{5}{2} a + 8\) , \( \frac{2445}{2} a^{3} - \frac{8591}{2} a^{2} - \frac{15081}{2} a + 21406\) , \( -\frac{71071}{2} a^{3} + \frac{249705}{2} a^{2} + \frac{438455}{2} a - 622090\bigr] \) |
${y}^2+\left(-a^{3}+4a^{2}+7a-23\right){x}{y}+\left(\frac{1}{2}a^{3}-\frac{3}{2}a^{2}-\frac{5}{2}a+8\right){y}={x}^{3}+\left(-a^{3}+4a^{2}+6a-24\right){x}^{2}+\left(\frac{2445}{2}a^{3}-\frac{8591}{2}a^{2}-\frac{15081}{2}a+21406\right){x}-\frac{71071}{2}a^{3}+\frac{249705}{2}a^{2}+\frac{438455}{2}a-622090$ |
| 4.2-a2 |
4.2-a |
$2$ |
$2$ |
4.4.19225.1 |
$4$ |
$[4, 0]$ |
4.2 |
\( 2^{2} \) |
\( - 2^{16} \) |
$14.73429$ |
$(-2a^3+7a^2+13a-37)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$689.8164380$ |
2.487541697 |
\( -\frac{62499}{256} a^{3} + \frac{44461}{128} a^{2} + \frac{156265}{64} a + \frac{19395}{8} \) |
\( \bigl[\frac{1}{2} a^{3} - \frac{3}{2} a^{2} - \frac{5}{2} a + 9\) , \( \frac{1}{2} a^{3} - \frac{3}{2} a^{2} - \frac{7}{2} a + 7\) , \( 0\) , \( 2 a^{3} - 3 a^{2} - 13 a + 18\) , \( a^{3} + a^{2} - 5 a - 3\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-\frac{3}{2}a^{2}-\frac{5}{2}a+9\right){x}{y}={x}^{3}+\left(\frac{1}{2}a^{3}-\frac{3}{2}a^{2}-\frac{7}{2}a+7\right){x}^{2}+\left(2a^{3}-3a^{2}-13a+18\right){x}+a^{3}+a^{2}-5a-3$ |
| 9.1-a1 |
9.1-a |
$2$ |
$2$ |
4.4.19225.1 |
$4$ |
$[4, 0]$ |
9.1 |
\( 3^{2} \) |
\( - 3^{8} \) |
$16.30617$ |
$(1/2a^3-1/2a^2-5/2a+4)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1.034191567$ |
$128.2657412$ |
3.826823960 |
\( -\frac{3438185}{162} a^{3} - \frac{51316529}{162} a^{2} + \frac{36295711}{54} a + \frac{271782965}{81} \) |
\( \bigl[-\frac{1}{2} a^{3} + \frac{5}{2} a^{2} + \frac{5}{2} a - 14\) , \( -\frac{1}{2} a^{3} + \frac{3}{2} a^{2} + \frac{5}{2} a - 7\) , \( -\frac{1}{2} a^{3} + \frac{5}{2} a^{2} + \frac{7}{2} a - 15\) , \( -\frac{5}{2} a^{3} + \frac{21}{2} a^{2} + \frac{19}{2} a - 66\) , \( -a^{3} + 11 a^{2} - 8 a - 94\bigr] \) |
${y}^2+\left(-\frac{1}{2}a^{3}+\frac{5}{2}a^{2}+\frac{5}{2}a-14\right){x}{y}+\left(-\frac{1}{2}a^{3}+\frac{5}{2}a^{2}+\frac{7}{2}a-15\right){y}={x}^{3}+\left(-\frac{1}{2}a^{3}+\frac{3}{2}a^{2}+\frac{5}{2}a-7\right){x}^{2}+\left(-\frac{5}{2}a^{3}+\frac{21}{2}a^{2}+\frac{19}{2}a-66\right){x}-a^{3}+11a^{2}-8a-94$ |
| 9.1-a2 |
9.1-a |
$2$ |
$2$ |
4.4.19225.1 |
$4$ |
$[4, 0]$ |
9.1 |
\( 3^{2} \) |
\( - 3^{4} \) |
$16.30617$ |
$(1/2a^3-1/2a^2-5/2a+4)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$2.068383134$ |
$128.2657412$ |
3.826823960 |
\( \frac{1516181947}{2} a^{3} + \frac{40311628361}{18} a^{2} - \frac{45305651213}{18} a - \frac{75932151100}{9} \) |
\( \bigl[\frac{1}{2} a^{3} - \frac{3}{2} a^{2} - \frac{7}{2} a + 8\) , \( a^{3} - 4 a^{2} - 5 a + 23\) , \( 0\) , \( \frac{3649}{2} a^{3} - \frac{12823}{2} a^{2} - \frac{22507}{2} a + 31952\) , \( \frac{127687}{2} a^{3} - \frac{448621}{2} a^{2} - \frac{787731}{2} a + 1117652\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-\frac{3}{2}a^{2}-\frac{7}{2}a+8\right){x}{y}={x}^{3}+\left(a^{3}-4a^{2}-5a+23\right){x}^{2}+\left(\frac{3649}{2}a^{3}-\frac{12823}{2}a^{2}-\frac{22507}{2}a+31952\right){x}+\frac{127687}{2}a^{3}-\frac{448621}{2}a^{2}-\frac{787731}{2}a+1117652$ |
| 9.1-b1 |
9.1-b |
$8$ |
$12$ |
4.4.19225.1 |
$4$ |
$[4, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{12} \) |
$16.30617$ |
$(1/2a^3-1/2a^2-5/2a+4)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2Cs, 3B |
$1$ |
\( 2 \cdot 3 \) |
$0.397386121$ |
$921.7020045$ |
3.962427342 |
\( \frac{17670731}{1458} a^{3} - \frac{59030497}{1458} a^{2} - \frac{42229463}{486} a + \frac{169601050}{729} \) |
\( \bigl[-a^{3} + 4 a^{2} + 7 a - 23\) , \( \frac{3}{2} a^{3} - \frac{11}{2} a^{2} - \frac{21}{2} a + 32\) , \( -\frac{1}{2} a^{3} + \frac{5}{2} a^{2} + \frac{5}{2} a - 14\) , \( \frac{17}{2} a^{3} - \frac{57}{2} a^{2} - \frac{123}{2} a + 159\) , \( \frac{15}{2} a^{3} - \frac{49}{2} a^{2} - \frac{109}{2} a + 134\bigr] \) |
${y}^2+\left(-a^{3}+4a^{2}+7a-23\right){x}{y}+\left(-\frac{1}{2}a^{3}+\frac{5}{2}a^{2}+\frac{5}{2}a-14\right){y}={x}^{3}+\left(\frac{3}{2}a^{3}-\frac{11}{2}a^{2}-\frac{21}{2}a+32\right){x}^{2}+\left(\frac{17}{2}a^{3}-\frac{57}{2}a^{2}-\frac{123}{2}a+159\right){x}+\frac{15}{2}a^{3}-\frac{49}{2}a^{2}-\frac{109}{2}a+134$ |
| 9.1-b2 |
9.1-b |
$8$ |
$12$ |
4.4.19225.1 |
$4$ |
$[4, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{2} \) |
$16.30617$ |
$(1/2a^3-1/2a^2-5/2a+4)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 1 \) |
$2.384316726$ |
$921.7020045$ |
3.962427342 |
\( \frac{40099084753}{2} a^{3} + \frac{355351522255}{6} a^{2} - \frac{399418083865}{6} a - \frac{669341338094}{3} \) |
\( \bigl[-\frac{1}{2} a^{3} + \frac{5}{2} a^{2} + \frac{5}{2} a - 15\) , \( -a^{3} + 4 a^{2} + 5 a - 22\) , \( 1\) , \( -\frac{59}{2} a^{3} + \frac{197}{2} a^{2} + \frac{421}{2} a - 550\) , \( \frac{115}{2} a^{3} - \frac{385}{2} a^{2} - \frac{821}{2} a + 1078\bigr] \) |
${y}^2+\left(-\frac{1}{2}a^{3}+\frac{5}{2}a^{2}+\frac{5}{2}a-15\right){x}{y}+{y}={x}^{3}+\left(-a^{3}+4a^{2}+5a-22\right){x}^{2}+\left(-\frac{59}{2}a^{3}+\frac{197}{2}a^{2}+\frac{421}{2}a-550\right){x}+\frac{115}{2}a^{3}-\frac{385}{2}a^{2}-\frac{821}{2}a+1078$ |
| 9.1-b3 |
9.1-b |
$8$ |
$12$ |
4.4.19225.1 |
$4$ |
$[4, 0]$ |
9.1 |
\( 3^{2} \) |
\( - 3^{24} \) |
$16.30617$ |
$(1/2a^3-1/2a^2-5/2a+4)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \cdot 3 \) |
$0.794772242$ |
$57.60637528$ |
3.962427342 |
\( -\frac{503770130623}{1062882} a^{3} - \frac{140707755641}{354294} a^{2} + \frac{6654452510549}{1062882} a + \frac{5714449379285}{531441} \) |
\( \bigl[-\frac{1}{2} a^{3} + \frac{5}{2} a^{2} + \frac{5}{2} a - 14\) , \( -a^{3} + 4 a^{2} + 6 a - 23\) , \( -\frac{1}{2} a^{3} + \frac{5}{2} a^{2} + \frac{7}{2} a - 14\) , \( -\frac{113}{2} a^{3} + \frac{379}{2} a^{2} + \frac{807}{2} a - 1070\) , \( -\frac{237}{2} a^{3} + \frac{791}{2} a^{2} + \frac{1703}{2} a - 2233\bigr] \) |
${y}^2+\left(-\frac{1}{2}a^{3}+\frac{5}{2}a^{2}+\frac{5}{2}a-14\right){x}{y}+\left(-\frac{1}{2}a^{3}+\frac{5}{2}a^{2}+\frac{7}{2}a-14\right){y}={x}^{3}+\left(-a^{3}+4a^{2}+6a-23\right){x}^{2}+\left(-\frac{113}{2}a^{3}+\frac{379}{2}a^{2}+\frac{807}{2}a-1070\right){x}-\frac{237}{2}a^{3}+\frac{791}{2}a^{2}+\frac{1703}{2}a-2233$ |
| 9.1-b4 |
9.1-b |
$8$ |
$12$ |
4.4.19225.1 |
$4$ |
$[4, 0]$ |
9.1 |
\( 3^{2} \) |
\( - 3^{6} \) |
$16.30617$ |
$(1/2a^3-1/2a^2-5/2a+4)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 3 \) |
$0.198693060$ |
$921.7020045$ |
3.962427342 |
\( -\frac{28939141}{54} a^{3} + \frac{186555307}{54} a^{2} + \frac{216096607}{54} a - \frac{147001283}{9} \) |
\( \bigl[-\frac{1}{2} a^{3} + \frac{5}{2} a^{2} + \frac{7}{2} a - 14\) , \( -\frac{3}{2} a^{3} + \frac{11}{2} a^{2} + \frac{17}{2} a - 31\) , \( -a^{3} + 4 a^{2} + 6 a - 22\) , \( a^{3} - 4 a^{2} + 13 a - 13\) , \( 12903 a^{3} - 43032 a^{2} - 93033 a + 243062\bigr] \) |
${y}^2+\left(-\frac{1}{2}a^{3}+\frac{5}{2}a^{2}+\frac{7}{2}a-14\right){x}{y}+\left(-a^{3}+4a^{2}+6a-22\right){y}={x}^{3}+\left(-\frac{3}{2}a^{3}+\frac{11}{2}a^{2}+\frac{17}{2}a-31\right){x}^{2}+\left(a^{3}-4a^{2}+13a-13\right){x}+12903a^{3}-43032a^{2}-93033a+243062$ |
| 9.1-b5 |
9.1-b |
$8$ |
$12$ |
4.4.19225.1 |
$4$ |
$[4, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{4} \) |
$16.30617$ |
$(1/2a^3-1/2a^2-5/2a+4)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2Cs, 3B |
$1$ |
\( 2 \) |
$1.192158363$ |
$921.7020045$ |
3.962427342 |
\( -\frac{21331331}{18} a^{3} + \frac{73802737}{18} a^{2} + \frac{45673303}{6} a - \frac{176825299}{9} \) |
\( \bigl[a + 1\) , \( \frac{3}{2} a^{3} - \frac{11}{2} a^{2} - \frac{19}{2} a + 31\) , \( -\frac{1}{2} a^{3} + \frac{5}{2} a^{2} + \frac{7}{2} a - 15\) , \( -\frac{9}{2} a^{3} - \frac{31}{2} a^{2} + \frac{31}{2} a + 68\) , \( \frac{51}{2} a^{3} + \frac{147}{2} a^{2} - \frac{171}{2} a - 275\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(-\frac{1}{2}a^{3}+\frac{5}{2}a^{2}+\frac{7}{2}a-15\right){y}={x}^{3}+\left(\frac{3}{2}a^{3}-\frac{11}{2}a^{2}-\frac{19}{2}a+31\right){x}^{2}+\left(-\frac{9}{2}a^{3}-\frac{31}{2}a^{2}+\frac{31}{2}a+68\right){x}+\frac{51}{2}a^{3}+\frac{147}{2}a^{2}-\frac{171}{2}a-275$ |
| 9.1-b6 |
9.1-b |
$8$ |
$12$ |
4.4.19225.1 |
$4$ |
$[4, 0]$ |
9.1 |
\( 3^{2} \) |
\( - 3^{8} \) |
$16.30617$ |
$(1/2a^3-1/2a^2-5/2a+4)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \) |
$2.384316726$ |
$57.60637528$ |
3.962427342 |
\( -\frac{1128418234932265}{162} a^{3} + \frac{1321542991802765}{54} a^{2} + \frac{6961421702143739}{162} a - \frac{9876980886338302}{81} \) |
\( \bigl[a + 1\) , \( \frac{3}{2} a^{3} - \frac{11}{2} a^{2} - \frac{19}{2} a + 31\) , \( -\frac{1}{2} a^{3} + \frac{5}{2} a^{2} + \frac{7}{2} a - 15\) , \( -2 a^{3} - 18 a^{2} + 3 a + 83\) , \( \frac{85}{2} a^{3} + \frac{249}{2} a^{2} - \frac{283}{2} a - 470\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(-\frac{1}{2}a^{3}+\frac{5}{2}a^{2}+\frac{7}{2}a-15\right){y}={x}^{3}+\left(\frac{3}{2}a^{3}-\frac{11}{2}a^{2}-\frac{19}{2}a+31\right){x}^{2}+\left(-2a^{3}-18a^{2}+3a+83\right){x}+\frac{85}{2}a^{3}+\frac{249}{2}a^{2}-\frac{283}{2}a-470$ |
| 9.1-b7 |
9.1-b |
$8$ |
$12$ |
4.4.19225.1 |
$4$ |
$[4, 0]$ |
9.1 |
\( 3^{2} \) |
\( - 3^{2} \) |
$16.30617$ |
$(1/2a^3-1/2a^2-5/2a+4)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 1 \) |
$0.596079181$ |
$921.7020045$ |
3.962427342 |
\( -\frac{108077555357}{2} a^{3} - \frac{290315649703}{6} a^{2} + \frac{4313227675057}{6} a + \frac{3763398102038}{3} \) |
\( \bigl[\frac{1}{2} a^{3} - \frac{3}{2} a^{2} - \frac{7}{2} a + 8\) , \( -\frac{1}{2} a^{3} + \frac{5}{2} a^{2} + \frac{3}{2} a - 14\) , \( \frac{1}{2} a^{3} - \frac{3}{2} a^{2} - \frac{7}{2} a + 9\) , \( -\frac{1}{2} a^{3} + \frac{1}{2} a^{2} + \frac{9}{2} a + 3\) , \( -\frac{1}{2} a^{3} + \frac{3}{2} a^{2} + \frac{13}{2} a - 20\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-\frac{3}{2}a^{2}-\frac{7}{2}a+8\right){x}{y}+\left(\frac{1}{2}a^{3}-\frac{3}{2}a^{2}-\frac{7}{2}a+9\right){y}={x}^{3}+\left(-\frac{1}{2}a^{3}+\frac{5}{2}a^{2}+\frac{3}{2}a-14\right){x}^{2}+\left(-\frac{1}{2}a^{3}+\frac{1}{2}a^{2}+\frac{9}{2}a+3\right){x}-\frac{1}{2}a^{3}+\frac{3}{2}a^{2}+\frac{13}{2}a-20$ |
| 9.1-b8 |
9.1-b |
$8$ |
$12$ |
4.4.19225.1 |
$4$ |
$[4, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{6} \) |
$16.30617$ |
$(1/2a^3-1/2a^2-5/2a+4)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 3 \) |
$0.794772242$ |
$921.7020045$ |
3.962427342 |
\( \frac{40433729905}{54} a^{3} - \frac{134883302215}{54} a^{2} - \frac{291430322983}{54} a + \frac{126937136051}{9} \) |
\( \bigl[\frac{1}{2} a^{3} - \frac{3}{2} a^{2} - \frac{7}{2} a + 9\) , \( -\frac{3}{2} a^{3} + \frac{11}{2} a^{2} + \frac{19}{2} a - 31\) , \( -\frac{1}{2} a^{3} + \frac{5}{2} a^{2} + \frac{7}{2} a - 15\) , \( -\frac{5}{2} a^{3} - \frac{9}{2} a^{2} + \frac{57}{2} a + 65\) , \( 14 a^{3} + 18 a^{2} - 186 a - 357\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-\frac{3}{2}a^{2}-\frac{7}{2}a+9\right){x}{y}+\left(-\frac{1}{2}a^{3}+\frac{5}{2}a^{2}+\frac{7}{2}a-15\right){y}={x}^{3}+\left(-\frac{3}{2}a^{3}+\frac{11}{2}a^{2}+\frac{19}{2}a-31\right){x}^{2}+\left(-\frac{5}{2}a^{3}-\frac{9}{2}a^{2}+\frac{57}{2}a+65\right){x}+14a^{3}+18a^{2}-186a-357$ |
| 9.2-a1 |
9.2-a |
$2$ |
$2$ |
4.4.19225.1 |
$4$ |
$[4, 0]$ |
9.2 |
\( 3^{2} \) |
\( - 3^{8} \) |
$16.30617$ |
$(3/2a^3-11/2a^2-19/2a+31)$ |
$0 \le r \le 1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
|
\( 2^{2} \) |
$1$ |
$128.2657412$ |
3.826823960 |
\( -\frac{57552988}{81} a^{3} + \frac{203474506}{81} a^{2} + \frac{360460997}{81} a - \frac{1022161409}{81} \) |
\( \bigl[-\frac{1}{2} a^{3} + \frac{5}{2} a^{2} + \frac{5}{2} a - 15\) , \( -\frac{1}{2} a^{3} + \frac{3}{2} a^{2} + \frac{7}{2} a - 7\) , \( -a^{3} + 4 a^{2} + 7 a - 22\) , \( 3 a^{3} - 13 a^{2} - 15 a + 68\) , \( 13 a^{3} - 48 a^{2} - 77 a + 241\bigr] \) |
${y}^2+\left(-\frac{1}{2}a^{3}+\frac{5}{2}a^{2}+\frac{5}{2}a-15\right){x}{y}+\left(-a^{3}+4a^{2}+7a-22\right){y}={x}^{3}+\left(-\frac{1}{2}a^{3}+\frac{3}{2}a^{2}+\frac{7}{2}a-7\right){x}^{2}+\left(3a^{3}-13a^{2}-15a+68\right){x}+13a^{3}-48a^{2}-77a+241$ |
| 9.2-a2 |
9.2-a |
$2$ |
$2$ |
4.4.19225.1 |
$4$ |
$[4, 0]$ |
9.2 |
\( 3^{2} \) |
\( - 3^{4} \) |
$16.30617$ |
$(3/2a^3-11/2a^2-19/2a+31)$ |
$0 \le r \le 1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
|
\( 2 \) |
$1$ |
$128.2657412$ |
3.826823960 |
\( \frac{120936947786}{9} a^{3} - \frac{403435113823}{9} a^{2} - \frac{871665540226}{9} a + \frac{2278009429337}{9} \) |
\( \bigl[\frac{1}{2} a^{3} - \frac{3}{2} a^{2} - \frac{7}{2} a + 9\) , \( -\frac{1}{2} a^{3} + \frac{3}{2} a^{2} + \frac{5}{2} a - 7\) , \( 1\) , \( \frac{65}{2} a^{3} + \frac{81}{2} a^{2} - \frac{899}{2} a - 864\) , \( \frac{971}{2} a^{3} + \frac{913}{2} a^{2} - \frac{12981}{2} a - 11486\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-\frac{3}{2}a^{2}-\frac{7}{2}a+9\right){x}{y}+{y}={x}^{3}+\left(-\frac{1}{2}a^{3}+\frac{3}{2}a^{2}+\frac{5}{2}a-7\right){x}^{2}+\left(\frac{65}{2}a^{3}+\frac{81}{2}a^{2}-\frac{899}{2}a-864\right){x}+\frac{971}{2}a^{3}+\frac{913}{2}a^{2}-\frac{12981}{2}a-11486$ |
| 9.2-b1 |
9.2-b |
$8$ |
$12$ |
4.4.19225.1 |
$4$ |
$[4, 0]$ |
9.2 |
\( 3^{2} \) |
\( - 3^{6} \) |
$16.30617$ |
$(3/2a^3-11/2a^2-19/2a+31)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 3 \) |
$0.198693060$ |
$921.7020045$ |
3.962427342 |
\( \frac{75722293}{18} a^{3} - \frac{781238521}{54} a^{2} - \frac{534563591}{18} a + \frac{2256140557}{27} \) |
\( \bigl[-a^{3} + 4 a^{2} + 7 a - 23\) , \( -a^{3} + 4 a^{2} + 5 a - 24\) , \( 0\) , \( \frac{3}{2} a^{3} - \frac{1}{2} a^{2} - \frac{59}{2} a - 40\) , \( 714 a^{3} + 2139 a^{2} - 2226 a - 7767\bigr] \) |
${y}^2+\left(-a^{3}+4a^{2}+7a-23\right){x}{y}={x}^{3}+\left(-a^{3}+4a^{2}+5a-24\right){x}^{2}+\left(\frac{3}{2}a^{3}-\frac{1}{2}a^{2}-\frac{59}{2}a-40\right){x}+714a^{3}+2139a^{2}-2226a-7767$ |
| 9.2-b2 |
9.2-b |
$8$ |
$12$ |
4.4.19225.1 |
$4$ |
$[4, 0]$ |
9.2 |
\( 3^{2} \) |
\( 3^{2} \) |
$16.30617$ |
$(3/2a^3-11/2a^2-19/2a+31)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 1 \) |
$2.384316726$ |
$921.7020045$ |
3.962427342 |
\( \frac{2132236814813}{6} a^{3} - \frac{7112953729471}{6} a^{2} - \frac{15368320399639}{6} a + \frac{20081756499046}{3} \) |
\( \bigl[-\frac{1}{2} a^{3} + \frac{5}{2} a^{2} + \frac{5}{2} a - 14\) , \( \frac{1}{2} a^{3} - \frac{5}{2} a^{2} - \frac{5}{2} a + 15\) , \( 1\) , \( -\frac{3}{2} a^{3} - \frac{13}{2} a^{2} + \frac{15}{2} a + 34\) , \( \frac{7}{2} a^{3} + \frac{19}{2} a^{2} - \frac{33}{2} a - 46\bigr] \) |
${y}^2+\left(-\frac{1}{2}a^{3}+\frac{5}{2}a^{2}+\frac{5}{2}a-14\right){x}{y}+{y}={x}^{3}+\left(\frac{1}{2}a^{3}-\frac{5}{2}a^{2}-\frac{5}{2}a+15\right){x}^{2}+\left(-\frac{3}{2}a^{3}-\frac{13}{2}a^{2}+\frac{15}{2}a+34\right){x}+\frac{7}{2}a^{3}+\frac{19}{2}a^{2}-\frac{33}{2}a-46$ |
| 9.2-b3 |
9.2-b |
$8$ |
$12$ |
4.4.19225.1 |
$4$ |
$[4, 0]$ |
9.2 |
\( 3^{2} \) |
\( 3^{12} \) |
$16.30617$ |
$(3/2a^3-11/2a^2-19/2a+31)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2Cs, 3B |
$1$ |
\( 2 \cdot 3 \) |
$0.397386121$ |
$921.7020045$ |
3.962427342 |
\( \frac{1128335}{1458} a^{3} + \frac{2633299}{1458} a^{2} - \frac{4905073}{1458} a - \frac{1857094}{729} \) |
\( \bigl[-\frac{1}{2} a^{3} + \frac{5}{2} a^{2} + \frac{7}{2} a - 14\) , \( -a + 1\) , \( -\frac{1}{2} a^{3} + \frac{5}{2} a^{2} + \frac{5}{2} a - 15\) , \( \frac{3}{2} a^{3} - \frac{5}{2} a^{2} - \frac{21}{2} a + 14\) , \( 2 a^{3} - 4 a^{2} - 13 a + 20\bigr] \) |
${y}^2+\left(-\frac{1}{2}a^{3}+\frac{5}{2}a^{2}+\frac{7}{2}a-14\right){x}{y}+\left(-\frac{1}{2}a^{3}+\frac{5}{2}a^{2}+\frac{5}{2}a-15\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(\frac{3}{2}a^{3}-\frac{5}{2}a^{2}-\frac{21}{2}a+14\right){x}+2a^{3}-4a^{2}-13a+20$ |
| 9.2-b4 |
9.2-b |
$8$ |
$12$ |
4.4.19225.1 |
$4$ |
$[4, 0]$ |
9.2 |
\( 3^{2} \) |
\( - 3^{24} \) |
$16.30617$ |
$(3/2a^3-11/2a^2-19/2a+31)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \cdot 3 \) |
$0.794772242$ |
$57.60637528$ |
3.962427342 |
\( -\frac{3773323479509}{1062882} a^{3} + \frac{4417801365773}{354294} a^{2} + \frac{23285202760375}{1062882} a - \frac{11003098731317}{177147} \) |
\( \bigl[-\frac{1}{2} a^{3} + \frac{5}{2} a^{2} + \frac{7}{2} a - 14\) , \( -a + 1\) , \( -\frac{1}{2} a^{3} + \frac{5}{2} a^{2} + \frac{5}{2} a - 15\) , \( 9 a^{3} - 30 a^{2} - 58 a + 149\) , \( \frac{59}{2} a^{3} - \frac{225}{2} a^{2} - \frac{377}{2} a + 553\bigr] \) |
${y}^2+\left(-\frac{1}{2}a^{3}+\frac{5}{2}a^{2}+\frac{7}{2}a-14\right){x}{y}+\left(-\frac{1}{2}a^{3}+\frac{5}{2}a^{2}+\frac{5}{2}a-15\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(9a^{3}-30a^{2}-58a+149\right){x}+\frac{59}{2}a^{3}-\frac{225}{2}a^{2}-\frac{377}{2}a+553$ |
| 9.2-b5 |
9.2-b |
$8$ |
$12$ |
4.4.19225.1 |
$4$ |
$[4, 0]$ |
9.2 |
\( 3^{2} \) |
\( 3^{6} \) |
$16.30617$ |
$(3/2a^3-11/2a^2-19/2a+31)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 3 \) |
$0.794772242$ |
$921.7020045$ |
3.962427342 |
\( \frac{760447277}{18} a^{3} + \frac{6738087007}{54} a^{2} - \frac{2525059723}{18} a - \frac{12691427689}{27} \) |
\( \bigl[\frac{1}{2} a^{3} - \frac{3}{2} a^{2} - \frac{7}{2} a + 8\) , \( -\frac{3}{2} a^{3} + \frac{11}{2} a^{2} + \frac{21}{2} a - 32\) , \( -\frac{1}{2} a^{3} + \frac{5}{2} a^{2} + \frac{5}{2} a - 14\) , \( -\frac{217}{2} a^{3} + \frac{763}{2} a^{2} + \frac{1335}{2} a - 1896\) , \( 1600 a^{3} - 5621 a^{2} - 9873 a + 28008\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-\frac{3}{2}a^{2}-\frac{7}{2}a+8\right){x}{y}+\left(-\frac{1}{2}a^{3}+\frac{5}{2}a^{2}+\frac{5}{2}a-14\right){y}={x}^{3}+\left(-\frac{3}{2}a^{3}+\frac{11}{2}a^{2}+\frac{21}{2}a-32\right){x}^{2}+\left(-\frac{217}{2}a^{3}+\frac{763}{2}a^{2}+\frac{1335}{2}a-1896\right){x}+1600a^{3}-5621a^{2}-9873a+28008$ |
| 9.2-b6 |
9.2-b |
$8$ |
$12$ |
4.4.19225.1 |
$4$ |
$[4, 0]$ |
9.2 |
\( 3^{2} \) |
\( - 3^{2} \) |
$16.30617$ |
$(3/2a^3-11/2a^2-19/2a+31)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 1 \) |
$0.596079181$ |
$921.7020045$ |
3.962427342 |
\( -\frac{2459967279581}{6} a^{3} + \frac{8642915486659}{6} a^{2} + \frac{15176171944507}{6} a - \frac{21532067517496}{3} \) |
\( \bigl[\frac{1}{2} a^{3} - \frac{3}{2} a^{2} - \frac{7}{2} a + 8\) , \( a^{3} - 4 a^{2} - 5 a + 23\) , \( \frac{1}{2} a^{3} - \frac{3}{2} a^{2} - \frac{7}{2} a + 9\) , \( -\frac{5}{2} a^{3} + \frac{17}{2} a^{2} + \frac{33}{2} a - 42\) , \( a^{3} - 3 a^{2} - 10 a + 4\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-\frac{3}{2}a^{2}-\frac{7}{2}a+8\right){x}{y}+\left(\frac{1}{2}a^{3}-\frac{3}{2}a^{2}-\frac{7}{2}a+9\right){y}={x}^{3}+\left(a^{3}-4a^{2}-5a+23\right){x}^{2}+\left(-\frac{5}{2}a^{3}+\frac{17}{2}a^{2}+\frac{33}{2}a-42\right){x}+a^{3}-3a^{2}-10a+4$ |
| 9.2-b7 |
9.2-b |
$8$ |
$12$ |
4.4.19225.1 |
$4$ |
$[4, 0]$ |
9.2 |
\( 3^{2} \) |
\( 3^{4} \) |
$16.30617$ |
$(3/2a^3-11/2a^2-19/2a+31)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2Cs, 3B |
$1$ |
\( 2 \) |
$1.192158363$ |
$921.7020045$ |
3.962427342 |
\( -\frac{2959175}{18} a^{3} - \frac{931219}{18} a^{2} + \frac{33013633}{18} a + \frac{33908785}{9} \) |
\( \bigl[\frac{1}{2} a^{3} - \frac{3}{2} a^{2} - \frac{5}{2} a + 9\) , \( \frac{1}{2} a^{3} - \frac{3}{2} a^{2} - \frac{5}{2} a + 8\) , \( -a^{3} + 4 a^{2} + 6 a - 22\) , \( -\frac{163}{2} a^{3} + \frac{555}{2} a^{2} + \frac{1183}{2} a - 1558\) , \( 641 a^{3} - 2126 a^{2} - 4613 a + 12014\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-\frac{3}{2}a^{2}-\frac{5}{2}a+9\right){x}{y}+\left(-a^{3}+4a^{2}+6a-22\right){y}={x}^{3}+\left(\frac{1}{2}a^{3}-\frac{3}{2}a^{2}-\frac{5}{2}a+8\right){x}^{2}+\left(-\frac{163}{2}a^{3}+\frac{555}{2}a^{2}+\frac{1183}{2}a-1558\right){x}+641a^{3}-2126a^{2}-4613a+12014$ |
| 9.2-b8 |
9.2-b |
$8$ |
$12$ |
4.4.19225.1 |
$4$ |
$[4, 0]$ |
9.2 |
\( 3^{2} \) |
\( - 3^{8} \) |
$16.30617$ |
$(3/2a^3-11/2a^2-19/2a+31)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \) |
$2.384316726$ |
$57.60637528$ |
3.962427342 |
\( -\frac{148735529594573}{162} a^{3} - \frac{44389227275927}{54} a^{2} + \frac{1978654649544127}{162} a + \frac{575471171779328}{27} \) |
\( \bigl[\frac{1}{2} a^{3} - \frac{3}{2} a^{2} - \frac{5}{2} a + 9\) , \( \frac{1}{2} a^{3} - \frac{3}{2} a^{2} - \frac{5}{2} a + 8\) , \( -a^{3} + 4 a^{2} + 6 a - 22\) , \( -64 a^{3} + 220 a^{2} + 464 a - 1238\) , \( \frac{1809}{2} a^{3} - \frac{6007}{2} a^{2} - \frac{13031}{2} a + 16959\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-\frac{3}{2}a^{2}-\frac{5}{2}a+9\right){x}{y}+\left(-a^{3}+4a^{2}+6a-22\right){y}={x}^{3}+\left(\frac{1}{2}a^{3}-\frac{3}{2}a^{2}-\frac{5}{2}a+8\right){x}^{2}+\left(-64a^{3}+220a^{2}+464a-1238\right){x}+\frac{1809}{2}a^{3}-\frac{6007}{2}a^{2}-\frac{13031}{2}a+16959$ |
| 16.1-a1 |
16.1-a |
$2$ |
$2$ |
4.4.19225.1 |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{10} \) |
$17.52212$ |
$(-2a^3+7a^2+13a-37), (a^2-6)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.109256890$ |
$868.9965230$ |
2.739010459 |
\( \frac{27137}{16} a^{3} - \frac{72249}{16} a^{2} - \frac{92063}{8} a + \frac{106131}{4} \) |
\( \bigl[a + 1\) , \( \frac{1}{2} a^{3} - \frac{5}{2} a^{2} - \frac{3}{2} a + 14\) , \( -a^{3} + 4 a^{2} + 7 a - 23\) , \( -\frac{11}{2} a^{3} + \frac{33}{2} a^{2} + \frac{77}{2} a - 72\) , \( -\frac{417}{2} a^{3} + \frac{1461}{2} a^{2} + \frac{2581}{2} a - 3635\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(-a^{3}+4a^{2}+7a-23\right){y}={x}^{3}+\left(\frac{1}{2}a^{3}-\frac{5}{2}a^{2}-\frac{3}{2}a+14\right){x}^{2}+\left(-\frac{11}{2}a^{3}+\frac{33}{2}a^{2}+\frac{77}{2}a-72\right){x}-\frac{417}{2}a^{3}+\frac{1461}{2}a^{2}+\frac{2581}{2}a-3635$ |
| 16.1-a2 |
16.1-a |
$2$ |
$2$ |
4.4.19225.1 |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( - 2^{8} \) |
$17.52212$ |
$(-2a^3+7a^2+13a-37), (a^2-6)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.054628445$ |
$1737.993046$ |
2.739010459 |
\( -\frac{53943}{8} a^{3} + \frac{176915}{8} a^{2} + \frac{341859}{8} a - \frac{195643}{2} \) |
\( \bigl[\frac{1}{2} a^{3} - \frac{3}{2} a^{2} - \frac{7}{2} a + 8\) , \( -\frac{3}{2} a^{3} + \frac{11}{2} a^{2} + \frac{17}{2} a - 32\) , \( a\) , \( -a^{3} + 4 a^{2} + 7 a - 15\) , \( -\frac{5}{2} a^{3} + \frac{1}{2} a^{2} + \frac{31}{2} a\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-\frac{3}{2}a^{2}-\frac{7}{2}a+8\right){x}{y}+a{y}={x}^{3}+\left(-\frac{3}{2}a^{3}+\frac{11}{2}a^{2}+\frac{17}{2}a-32\right){x}^{2}+\left(-a^{3}+4a^{2}+7a-15\right){x}-\frac{5}{2}a^{3}+\frac{1}{2}a^{2}+\frac{31}{2}a$ |
| 16.1-b1 |
16.1-b |
$8$ |
$12$ |
4.4.19225.1 |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( - 2^{28} \) |
$17.52212$ |
$(-2a^3+7a^2+13a-37), (a^2-6)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \) |
$1$ |
$51.04861173$ |
0.368172004 |
\( -\frac{234165500393559}{256} a^{3} + \frac{411361557295555}{128} a^{2} + \frac{22572310413547}{4} a - \frac{1024823361232605}{64} \) |
\( \bigl[-\frac{1}{2} a^{3} + \frac{5}{2} a^{2} + \frac{5}{2} a - 15\) , \( -\frac{3}{2} a^{3} + \frac{11}{2} a^{2} + \frac{21}{2} a - 32\) , \( -\frac{1}{2} a^{3} + \frac{5}{2} a^{2} + \frac{7}{2} a - 14\) , \( 262 a^{3} + 199 a^{2} - 3437 a - 5736\) , \( 9813 a^{3} + 9138 a^{2} - 131057 a - 231318\bigr] \) |
${y}^2+\left(-\frac{1}{2}a^{3}+\frac{5}{2}a^{2}+\frac{5}{2}a-15\right){x}{y}+\left(-\frac{1}{2}a^{3}+\frac{5}{2}a^{2}+\frac{7}{2}a-14\right){y}={x}^{3}+\left(-\frac{3}{2}a^{3}+\frac{11}{2}a^{2}+\frac{21}{2}a-32\right){x}^{2}+\left(262a^{3}+199a^{2}-3437a-5736\right){x}+9813a^{3}+9138a^{2}-131057a-231318$ |
| 16.1-b2 |
16.1-b |
$8$ |
$12$ |
4.4.19225.1 |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{16} \) |
$17.52212$ |
$(-2a^3+7a^2+13a-37), (a^2-6)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$16$ |
\( 2^{2} \) |
$1$ |
$3.190538233$ |
0.368172004 |
\( \frac{20787147431302811904648477}{32} a^{3} + \frac{122808208953132080189865401}{64} a^{2} - \frac{138037434957503352975511039}{64} a - \frac{462643930715730870800106435}{64} \) |
\( \bigl[-\frac{1}{2} a^{3} + \frac{5}{2} a^{2} + \frac{5}{2} a - 15\) , \( \frac{3}{2} a^{3} - \frac{11}{2} a^{2} - \frac{21}{2} a + 30\) , \( \frac{1}{2} a^{3} - \frac{3}{2} a^{2} - \frac{5}{2} a + 9\) , \( 453 a^{3} - 1648 a^{2} - 2813 a + 8195\) , \( -\frac{30405}{2} a^{3} + \frac{105847}{2} a^{2} + \frac{187163}{2} a - 263974\bigr] \) |
${y}^2+\left(-\frac{1}{2}a^{3}+\frac{5}{2}a^{2}+\frac{5}{2}a-15\right){x}{y}+\left(\frac{1}{2}a^{3}-\frac{3}{2}a^{2}-\frac{5}{2}a+9\right){y}={x}^{3}+\left(\frac{3}{2}a^{3}-\frac{11}{2}a^{2}-\frac{21}{2}a+30\right){x}^{2}+\left(453a^{3}-1648a^{2}-2813a+8195\right){x}-\frac{30405}{2}a^{3}+\frac{105847}{2}a^{2}+\frac{187163}{2}a-263974$ |
| 16.1-b3 |
16.1-b |
$8$ |
$12$ |
4.4.19225.1 |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{16} \) |
$17.52212$ |
$(-2a^3+7a^2+13a-37), (a^2-6)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$16$ |
\( 2^{2} \) |
$1$ |
$3.190538233$ |
0.368172004 |
\( \frac{736893343255346009698471431}{64} a^{3} - \frac{614552780826746745178292639}{16} a^{2} - \frac{663904503983519760197358457}{8} a + \frac{1735045632450056459307189577}{8} \) |
\( \bigl[-\frac{1}{2} a^{3} + \frac{5}{2} a^{2} + \frac{5}{2} a - 14\) , \( -a^{3} + 4 a^{2} + 6 a - 23\) , \( a + 1\) , \( -88 a^{3} + 551 a^{2} + 258 a - 4205\) , \( -\frac{6657}{2} a^{3} + \frac{5337}{2} a^{2} + \frac{72269}{2} a + 21125\bigr] \) |
${y}^2+\left(-\frac{1}{2}a^{3}+\frac{5}{2}a^{2}+\frac{5}{2}a-14\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a^{3}+4a^{2}+6a-23\right){x}^{2}+\left(-88a^{3}+551a^{2}+258a-4205\right){x}-\frac{6657}{2}a^{3}+\frac{5337}{2}a^{2}+\frac{72269}{2}a+21125$ |
| 16.1-b4 |
16.1-b |
$8$ |
$12$ |
4.4.19225.1 |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( - 2^{28} \) |
$17.52212$ |
$(-2a^3+7a^2+13a-37), (a^2-6)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \) |
$1$ |
$51.04861173$ |
0.368172004 |
\( -\frac{30864285011429}{256} a^{3} - \frac{13816879188073}{128} a^{2} + \frac{102645157841977}{64} a + \frac{716471975519289}{256} \) |
\( \bigl[-\frac{1}{2} a^{3} + \frac{5}{2} a^{2} + \frac{5}{2} a - 14\) , \( a^{3} - 4 a^{2} - 5 a + 24\) , \( -\frac{1}{2} a^{3} + \frac{5}{2} a^{2} + \frac{7}{2} a - 15\) , \( \frac{3845}{2} a^{3} - \frac{13513}{2} a^{2} - \frac{23701}{2} a + 33674\) , \( 72164 a^{3} - 253569 a^{2} - 445193 a + 1263424\bigr] \) |
${y}^2+\left(-\frac{1}{2}a^{3}+\frac{5}{2}a^{2}+\frac{5}{2}a-14\right){x}{y}+\left(-\frac{1}{2}a^{3}+\frac{5}{2}a^{2}+\frac{7}{2}a-15\right){y}={x}^{3}+\left(a^{3}-4a^{2}-5a+24\right){x}^{2}+\left(\frac{3845}{2}a^{3}-\frac{13513}{2}a^{2}-\frac{23701}{2}a+33674\right){x}+72164a^{3}-253569a^{2}-445193a+1263424$ |
| 16.1-b5 |
16.1-b |
$8$ |
$12$ |
4.4.19225.1 |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( - 2^{52} \) |
$17.52212$ |
$(-2a^3+7a^2+13a-37), (a^2-6)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \) |
$1$ |
$51.04861173$ |
0.368172004 |
\( -\frac{545960784201}{16777216} a^{3} - \frac{815476527833}{8388608} a^{2} + \frac{464702887749}{4194304} a + \frac{6345922356361}{16777216} \) |
\( \bigl[1\) , \( 0\) , \( \frac{1}{2} a^{3} - \frac{3}{2} a^{2} - \frac{7}{2} a + 8\) , \( \frac{7}{2} a^{3} - \frac{35}{2} a^{2} - \frac{325}{2} a - 242\) , \( -\frac{537}{2} a^{3} - \frac{1031}{2} a^{2} + \frac{4475}{2} a + 4617\bigr] \) |
${y}^2+{x}{y}+\left(\frac{1}{2}a^{3}-\frac{3}{2}a^{2}-\frac{7}{2}a+8\right){y}={x}^{3}+\left(\frac{7}{2}a^{3}-\frac{35}{2}a^{2}-\frac{325}{2}a-242\right){x}-\frac{537}{2}a^{3}-\frac{1031}{2}a^{2}+\frac{4475}{2}a+4617$ |
| 16.1-b6 |
16.1-b |
$8$ |
$12$ |
4.4.19225.1 |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{32} \) |
$17.52212$ |
$(-2a^3+7a^2+13a-37), (a^2-6)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2Cs, 3B |
$4$ |
\( 2^{2} \) |
$1$ |
$51.04861173$ |
0.368172004 |
\( \frac{360757190563215}{4096} a^{3} + \frac{532834151252913}{2048} a^{2} - \frac{149725310219475}{512} a - \frac{4014600289140547}{4096} \) |
\( \bigl[a + 1\) , \( -\frac{3}{2} a^{3} + \frac{11}{2} a^{2} + \frac{19}{2} a - 32\) , \( -a^{3} + 4 a^{2} + 6 a - 22\) , \( 76 a^{3} - 290 a^{2} - 478 a + 1436\) , \( -567 a^{3} + 1807 a^{2} + 3416 a - 9108\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(-a^{3}+4a^{2}+6a-22\right){y}={x}^{3}+\left(-\frac{3}{2}a^{3}+\frac{11}{2}a^{2}+\frac{19}{2}a-32\right){x}^{2}+\left(76a^{3}-290a^{2}-478a+1436\right){x}-567a^{3}+1807a^{2}+3416a-9108$ |
| 16.1-b7 |
16.1-b |
$8$ |
$12$ |
4.4.19225.1 |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( - 2^{52} \) |
$17.52212$ |
$(-2a^3+7a^2+13a-37), (a^2-6)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \) |
$1$ |
$51.04861173$ |
0.368172004 |
\( -\frac{9699506274079}{16777216} a^{3} + \frac{16183677115253}{8388608} a^{2} + \frac{17464864464241}{4194304} a - \frac{713303381989}{65536} \) |
\( \bigl[\frac{1}{2} a^{3} - \frac{3}{2} a^{2} - \frac{7}{2} a + 9\) , \( -\frac{1}{2} a^{3} + \frac{3}{2} a^{2} + \frac{7}{2} a - 8\) , \( \frac{1}{2} a^{3} - \frac{3}{2} a^{2} - \frac{7}{2} a + 8\) , \( \frac{1537}{2} a^{3} - \frac{5411}{2} a^{2} - \frac{9421}{2} a + 13415\) , \( -\frac{36977}{2} a^{3} + \frac{129869}{2} a^{2} + \frac{228395}{2} a - 323835\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-\frac{3}{2}a^{2}-\frac{7}{2}a+9\right){x}{y}+\left(\frac{1}{2}a^{3}-\frac{3}{2}a^{2}-\frac{7}{2}a+8\right){y}={x}^{3}+\left(-\frac{1}{2}a^{3}+\frac{3}{2}a^{2}+\frac{7}{2}a-8\right){x}^{2}+\left(\frac{1537}{2}a^{3}-\frac{5411}{2}a^{2}-\frac{9421}{2}a+13415\right){x}-\frac{36977}{2}a^{3}+\frac{129869}{2}a^{2}+\frac{228395}{2}a-323835$ |
| 16.1-b8 |
16.1-b |
$8$ |
$12$ |
4.4.19225.1 |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{32} \) |
$17.52212$ |
$(-2a^3+7a^2+13a-37), (a^2-6)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2Cs, 3B |
$4$ |
\( 2^{2} \) |
$1$ |
$51.04861173$ |
0.368172004 |
\( \frac{6394355802145245}{4096} a^{3} - \frac{10665503640315603}{2048} a^{2} - \frac{11521997116800855}{1024} a + \frac{3763943620647283}{128} \) |
\( \bigl[\frac{1}{2} a^{3} - \frac{3}{2} a^{2} - \frac{5}{2} a + 9\) , \( -\frac{3}{2} a^{3} + \frac{11}{2} a^{2} + \frac{21}{2} a - 31\) , \( a + 1\) , \( -\frac{95}{2} a^{3} + \frac{415}{2} a^{2} + \frac{559}{2} a - 1363\) , \( -\frac{719}{2} a^{3} + \frac{1705}{2} a^{2} + \frac{6207}{2} a - 3294\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-\frac{3}{2}a^{2}-\frac{5}{2}a+9\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-\frac{3}{2}a^{3}+\frac{11}{2}a^{2}+\frac{21}{2}a-31\right){x}^{2}+\left(-\frac{95}{2}a^{3}+\frac{415}{2}a^{2}+\frac{559}{2}a-1363\right){x}-\frac{719}{2}a^{3}+\frac{1705}{2}a^{2}+\frac{6207}{2}a-3294$ |
| 16.1-c1 |
16.1-c |
$3$ |
$9$ |
4.4.19225.1 |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{24} \) |
$17.52212$ |
$(-2a^3+7a^2+13a-37), (a^2-6)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3Cs |
$1$ |
\( 2^{2} \) |
$1$ |
$58.65070151$ |
1.691998712 |
\( -\frac{6665}{8} a^{3} + \frac{19995}{8} a^{2} + \frac{46655}{8} a - \frac{852225}{64} \) |
\( \bigl[a + 1\) , \( \frac{1}{2} a^{3} - \frac{3}{2} a^{2} - \frac{5}{2} a + 9\) , \( 1\) , \( -\frac{201}{2} a^{3} - \frac{173}{2} a^{2} + \frac{2679}{2} a + 2319\) , \( \frac{3597}{2} a^{3} + \frac{3227}{2} a^{2} - \frac{47837}{2} a - 41754\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(\frac{1}{2}a^{3}-\frac{3}{2}a^{2}-\frac{5}{2}a+9\right){x}^{2}+\left(-\frac{201}{2}a^{3}-\frac{173}{2}a^{2}+\frac{2679}{2}a+2319\right){x}+\frac{3597}{2}a^{3}+\frac{3227}{2}a^{2}-\frac{47837}{2}a-41754$ |
| 16.1-c2 |
16.1-c |
$3$ |
$9$ |
4.4.19225.1 |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{8} \) |
$17.52212$ |
$(-2a^3+7a^2+13a-37), (a^2-6)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 2^{2} \) |
$1$ |
$58.65070151$ |
1.691998712 |
\( -\frac{32389647605}{4} a^{3} + \frac{108048993915}{4} a^{2} + \frac{116725923955}{2} a - \frac{610102138125}{4} \) |
\( \bigl[\frac{1}{2} a^{3} - \frac{3}{2} a^{2} - \frac{7}{2} a + 8\) , \( -\frac{3}{2} a^{3} + \frac{11}{2} a^{2} + \frac{21}{2} a - 32\) , \( -a^{3} + 4 a^{2} + 6 a - 22\) , \( \frac{3}{2} a^{3} - \frac{13}{2} a^{2} - \frac{3}{2} a + 17\) , \( \frac{35}{2} a^{3} - \frac{125}{2} a^{2} - \frac{201}{2} a + 293\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-\frac{3}{2}a^{2}-\frac{7}{2}a+8\right){x}{y}+\left(-a^{3}+4a^{2}+6a-22\right){y}={x}^{3}+\left(-\frac{3}{2}a^{3}+\frac{11}{2}a^{2}+\frac{21}{2}a-32\right){x}^{2}+\left(\frac{3}{2}a^{3}-\frac{13}{2}a^{2}-\frac{3}{2}a+17\right){x}+\frac{35}{2}a^{3}-\frac{125}{2}a^{2}-\frac{201}{2}a+293$ |
| 16.1-c3 |
16.1-c |
$3$ |
$9$ |
4.4.19225.1 |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{8} \) |
$17.52212$ |
$(-2a^3+7a^2+13a-37), (a^2-6)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 2^{2} \) |
$1$ |
$58.65070151$ |
1.691998712 |
\( -\frac{3654725035}{8} a^{3} - \frac{10795927095}{8} a^{2} + \frac{12134445895}{8} a + \frac{20335087575}{4} \) |
\( \bigl[\frac{1}{2} a^{3} - \frac{3}{2} a^{2} - \frac{7}{2} a + 8\) , \( a^{3} - 4 a^{2} - 7 a + 24\) , \( -\frac{1}{2} a^{3} + \frac{5}{2} a^{2} + \frac{5}{2} a - 15\) , \( \frac{7}{2} a^{3} - \frac{21}{2} a^{2} - \frac{69}{2} a + 36\) , \( 6 a^{3} - 7 a^{2} - 74 a - 48\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-\frac{3}{2}a^{2}-\frac{7}{2}a+8\right){x}{y}+\left(-\frac{1}{2}a^{3}+\frac{5}{2}a^{2}+\frac{5}{2}a-15\right){y}={x}^{3}+\left(a^{3}-4a^{2}-7a+24\right){x}^{2}+\left(\frac{7}{2}a^{3}-\frac{21}{2}a^{2}-\frac{69}{2}a+36\right){x}+6a^{3}-7a^{2}-74a-48$ |
| 16.1-d1 |
16.1-d |
$2$ |
$2$ |
4.4.19225.1 |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{10} \) |
$17.52212$ |
$(-2a^3+7a^2+13a-37), (a^2-6)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.109256890$ |
$868.9965230$ |
2.739010459 |
\( \frac{105917}{32} a^{3} - \frac{336075}{32} a^{2} - \frac{753085}{32} a + \frac{478387}{8} \) |
\( \bigl[-a^{3} + 4 a^{2} + 7 a - 23\) , \( \frac{3}{2} a^{3} - \frac{11}{2} a^{2} - \frac{19}{2} a + 30\) , \( \frac{1}{2} a^{3} - \frac{3}{2} a^{2} - \frac{7}{2} a + 8\) , \( 4 a^{3} - 13 a^{2} - 29 a + 80\) , \( \frac{3}{2} a^{3} - \frac{23}{2} a^{2} + \frac{1}{2} a + 94\bigr] \) |
${y}^2+\left(-a^{3}+4a^{2}+7a-23\right){x}{y}+\left(\frac{1}{2}a^{3}-\frac{3}{2}a^{2}-\frac{7}{2}a+8\right){y}={x}^{3}+\left(\frac{3}{2}a^{3}-\frac{11}{2}a^{2}-\frac{19}{2}a+30\right){x}^{2}+\left(4a^{3}-13a^{2}-29a+80\right){x}+\frac{3}{2}a^{3}-\frac{23}{2}a^{2}+\frac{1}{2}a+94$ |
| 16.1-d2 |
16.1-d |
$2$ |
$2$ |
4.4.19225.1 |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( - 2^{8} \) |
$17.52212$ |
$(-2a^3+7a^2+13a-37), (a^2-6)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.054628445$ |
$1737.993046$ |
2.739010459 |
\( -\frac{34099}{8} a^{3} + \frac{87211}{8} a^{2} + \frac{274435}{8} a - \frac{134475}{4} \) |
\( \bigl[1\) , \( -\frac{1}{2} a^{3} + \frac{3}{2} a^{2} + \frac{5}{2} a - 8\) , \( -\frac{1}{2} a^{3} + \frac{5}{2} a^{2} + \frac{5}{2} a - 14\) , \( \frac{21}{2} a^{3} - \frac{73}{2} a^{2} - \frac{129}{2} a + 184\) , \( -\frac{33}{2} a^{3} + \frac{115}{2} a^{2} + \frac{203}{2} a - 290\bigr] \) |
${y}^2+{x}{y}+\left(-\frac{1}{2}a^{3}+\frac{5}{2}a^{2}+\frac{5}{2}a-14\right){y}={x}^{3}+\left(-\frac{1}{2}a^{3}+\frac{3}{2}a^{2}+\frac{5}{2}a-8\right){x}^{2}+\left(\frac{21}{2}a^{3}-\frac{73}{2}a^{2}-\frac{129}{2}a+184\right){x}-\frac{33}{2}a^{3}+\frac{115}{2}a^{2}+\frac{203}{2}a-290$ |
| 25.1-a1 |
25.1-a |
$1$ |
$1$ |
4.4.19225.1 |
$4$ |
$[4, 0]$ |
25.1 |
\( 5^{2} \) |
\( 5^{4} \) |
$18.52739$ |
$(a^3-3a^2-7a+15)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \) |
$0.424678925$ |
$107.5410594$ |
2.635068041 |
\( -\frac{947083}{2} a^{3} + \frac{15795853}{10} a^{2} + \frac{34133251}{10} a - \frac{44592797}{5} \) |
\( \bigl[\frac{1}{2} a^{3} - \frac{3}{2} a^{2} - \frac{5}{2} a + 9\) , \( -\frac{1}{2} a^{3} + \frac{5}{2} a^{2} + \frac{7}{2} a - 14\) , \( -a^{3} + 4 a^{2} + 6 a - 23\) , \( -a^{3} + 11 a^{2} + 13 a - 48\) , \( \frac{5}{2} a^{3} + \frac{21}{2} a^{2} - \frac{13}{2} a - 45\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-\frac{3}{2}a^{2}-\frac{5}{2}a+9\right){x}{y}+\left(-a^{3}+4a^{2}+6a-23\right){y}={x}^{3}+\left(-\frac{1}{2}a^{3}+\frac{5}{2}a^{2}+\frac{7}{2}a-14\right){x}^{2}+\left(-a^{3}+11a^{2}+13a-48\right){x}+\frac{5}{2}a^{3}+\frac{21}{2}a^{2}-\frac{13}{2}a-45$ |
| 25.1-b1 |
25.1-b |
$1$ |
$1$ |
4.4.19225.1 |
$4$ |
$[4, 0]$ |
25.1 |
\( 5^{2} \) |
\( 5^{4} \) |
$18.52739$ |
$(a^3-3a^2-7a+15)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \) |
$0.424678925$ |
$107.5410594$ |
2.635068041 |
\( -\frac{134361}{5} a^{3} - \frac{391721}{5} a^{2} + \frac{447854}{5} a + \frac{1473199}{5} \) |
\( \bigl[-\frac{1}{2} a^{3} + \frac{5}{2} a^{2} + \frac{5}{2} a - 15\) , \( \frac{1}{2} a^{3} - \frac{5}{2} a^{2} - \frac{7}{2} a + 14\) , \( -a^{3} + 4 a^{2} + 7 a - 23\) , \( -\frac{13}{2} a^{3} + \frac{43}{2} a^{2} + \frac{85}{2} a - 101\) , \( -11 a^{3} + 36 a^{2} + 71 a - 176\bigr] \) |
${y}^2+\left(-\frac{1}{2}a^{3}+\frac{5}{2}a^{2}+\frac{5}{2}a-15\right){x}{y}+\left(-a^{3}+4a^{2}+7a-23\right){y}={x}^{3}+\left(\frac{1}{2}a^{3}-\frac{5}{2}a^{2}-\frac{7}{2}a+14\right){x}^{2}+\left(-\frac{13}{2}a^{3}+\frac{43}{2}a^{2}+\frac{85}{2}a-101\right){x}-11a^{3}+36a^{2}+71a-176$ |
| 29.1-a1 |
29.1-a |
$1$ |
$1$ |
4.4.19225.1 |
$4$ |
$[4, 0]$ |
29.1 |
\( 29 \) |
\( - 29^{3} \) |
$18.87433$ |
$(a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3Ns |
$1$ |
\( 3 \) |
$0.385648991$ |
$71.87203199$ |
2.398833998 |
\( -\frac{66138876736}{24389} a^{3} - \frac{59701564825}{24389} a^{2} + \frac{880560775027}{24389} a + \frac{1539517303357}{24389} \) |
\( \bigl[\frac{1}{2} a^{3} - \frac{3}{2} a^{2} - \frac{5}{2} a + 8\) , \( \frac{3}{2} a^{3} - \frac{11}{2} a^{2} - \frac{21}{2} a + 32\) , \( -\frac{1}{2} a^{3} + \frac{5}{2} a^{2} + \frac{7}{2} a - 14\) , \( -59 a^{3} + 194 a^{2} + 433 a - 1112\) , \( 406 a^{3} - 1360 a^{2} - 2899 a + 7616\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-\frac{3}{2}a^{2}-\frac{5}{2}a+8\right){x}{y}+\left(-\frac{1}{2}a^{3}+\frac{5}{2}a^{2}+\frac{7}{2}a-14\right){y}={x}^{3}+\left(\frac{3}{2}a^{3}-\frac{11}{2}a^{2}-\frac{21}{2}a+32\right){x}^{2}+\left(-59a^{3}+194a^{2}+433a-1112\right){x}+406a^{3}-1360a^{2}-2899a+7616$ |
| 29.2-a1 |
29.2-a |
$1$ |
$1$ |
4.4.19225.1 |
$4$ |
$[4, 0]$ |
29.2 |
\( 29 \) |
\( - 29^{3} \) |
$18.87433$ |
$(-3/2a^3+11/2a^2+19/2a-30)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3Ns |
$1$ |
\( 3 \) |
$0.385648991$ |
$71.87203199$ |
2.398833998 |
\( -\frac{502640045381}{24389} a^{3} + \frac{1766038331176}{24389} a^{2} + \frac{3100891679792}{24389} a - \frac{8800037930392}{24389} \) |
\( \bigl[a\) , \( \frac{1}{2} a^{3} - \frac{3}{2} a^{2} - \frac{7}{2} a + 7\) , \( -a^{3} + 4 a^{2} + 6 a - 23\) , \( -4 a^{3} - 7 a^{2} + 7 a + 2\) , \( 28 a^{3} + 76 a^{2} - 119 a - 337\bigr] \) |
${y}^2+a{x}{y}+\left(-a^{3}+4a^{2}+6a-23\right){y}={x}^{3}+\left(\frac{1}{2}a^{3}-\frac{3}{2}a^{2}-\frac{7}{2}a+7\right){x}^{2}+\left(-4a^{3}-7a^{2}+7a+2\right){x}+28a^{3}+76a^{2}-119a-337$ |
| 31.1-a1 |
31.1-a |
$6$ |
$8$ |
4.4.19225.1 |
$4$ |
$[4, 0]$ |
31.1 |
\( 31 \) |
\( - 31^{2} \) |
$19.03233$ |
$(-1/2a^3+5/2a^2+5/2a-16)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$64$ |
\( 2 \) |
$1$ |
$5.870985733$ |
1.354964226 |
\( -\frac{5759284472245575}{1922} a^{3} + \frac{20375783248458071}{1922} a^{2} + \frac{35592827975115379}{1922} a - \frac{50722737470071888}{961} \) |
\( \bigl[-\frac{1}{2} a^{3} + \frac{5}{2} a^{2} + \frac{5}{2} a - 14\) , \( -a - 1\) , \( \frac{1}{2} a^{3} - \frac{3}{2} a^{2} - \frac{7}{2} a + 9\) , \( -236 a^{3} + 821 a^{2} + 1650 a - 4782\) , \( -\frac{12223}{2} a^{3} + \frac{41255}{2} a^{2} + \frac{87405}{2} a - 117506\bigr] \) |
${y}^2+\left(-\frac{1}{2}a^{3}+\frac{5}{2}a^{2}+\frac{5}{2}a-14\right){x}{y}+\left(\frac{1}{2}a^{3}-\frac{3}{2}a^{2}-\frac{7}{2}a+9\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-236a^{3}+821a^{2}+1650a-4782\right){x}-\frac{12223}{2}a^{3}+\frac{41255}{2}a^{2}+\frac{87405}{2}a-117506$ |
| 31.1-a2 |
31.1-a |
$6$ |
$8$ |
4.4.19225.1 |
$4$ |
$[4, 0]$ |
31.1 |
\( 31 \) |
\( -31 \) |
$19.03233$ |
$(-1/2a^3+5/2a^2+5/2a-16)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$3005.944695$ |
1.354964226 |
\( \frac{507035}{62} a^{3} - \frac{1182047}{62} a^{2} - \frac{3803495}{62} a + \frac{4025985}{31} \) |
\( \bigl[1\) , \( -\frac{3}{2} a^{3} + \frac{11}{2} a^{2} + \frac{19}{2} a - 32\) , \( \frac{1}{2} a^{3} - \frac{3}{2} a^{2} - \frac{7}{2} a + 9\) , \( -3 a^{3} - 6 a^{2} + 41 a + 96\) , \( -\frac{23}{2} a^{3} - \frac{9}{2} a^{2} + \frac{301}{2} a + 225\bigr] \) |
${y}^2+{x}{y}+\left(\frac{1}{2}a^{3}-\frac{3}{2}a^{2}-\frac{7}{2}a+9\right){y}={x}^{3}+\left(-\frac{3}{2}a^{3}+\frac{11}{2}a^{2}+\frac{19}{2}a-32\right){x}^{2}+\left(-3a^{3}-6a^{2}+41a+96\right){x}-\frac{23}{2}a^{3}-\frac{9}{2}a^{2}+\frac{301}{2}a+225$ |
| 31.1-a3 |
31.1-a |
$6$ |
$8$ |
4.4.19225.1 |
$4$ |
$[4, 0]$ |
31.1 |
\( 31 \) |
\( - 31^{8} \) |
$19.03233$ |
$(-1/2a^3+5/2a^2+5/2a-16)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$64$ |
\( 2 \) |
$1$ |
$5.870985733$ |
1.354964226 |
\( \frac{889176966465519982283783}{1705782074882} a^{3} - \frac{2966215843392610636661783}{1705782074882} a^{2} - \frac{6408836212056448797519923}{1705782074882} a + \frac{8374414703206531220962848}{852891037441} \) |
\( \bigl[1\) , \( \frac{3}{2} a^{3} - \frac{11}{2} a^{2} - \frac{19}{2} a + 30\) , \( -\frac{1}{2} a^{3} + \frac{5}{2} a^{2} + \frac{5}{2} a - 14\) , \( 54 a^{3} - 195 a^{2} - 335 a + 973\) , \( \frac{907}{2} a^{3} - \frac{3247}{2} a^{2} - \frac{5625}{2} a + 8070\bigr] \) |
${y}^2+{x}{y}+\left(-\frac{1}{2}a^{3}+\frac{5}{2}a^{2}+\frac{5}{2}a-14\right){y}={x}^{3}+\left(\frac{3}{2}a^{3}-\frac{11}{2}a^{2}-\frac{19}{2}a+30\right){x}^{2}+\left(54a^{3}-195a^{2}-335a+973\right){x}+\frac{907}{2}a^{3}-\frac{3247}{2}a^{2}-\frac{5625}{2}a+8070$ |
*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.
