| 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 |
| 4.1-a1 |
4.1-a |
$6$ |
$8$ |
4.4.9225.1 |
$4$ |
$[4, 0]$ |
4.1 |
\( 2^{2} \) |
\( 2^{4} \) |
$10.20656$ |
$(1/4a^3-5/2a+5/4)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2 \) |
$1$ |
$1286.706389$ |
1.674581477 |
\( -32556416 a^{3} - \frac{140841667}{4} a^{2} + \frac{504596565}{2} a + \frac{1189080877}{4} \) |
\( \bigl[\frac{1}{4} a^{3} + a^{2} - \frac{3}{2} a - \frac{19}{4}\) , \( -\frac{1}{4} a^{3} + \frac{5}{2} a + \frac{3}{4}\) , \( a + 1\) , \( -\frac{5}{4} a^{3} - 2 a^{2} + \frac{15}{2} a + \frac{39}{4}\) , \( -\frac{17}{4} a^{3} - 8 a^{2} + \frac{41}{2} a + \frac{115}{4}\bigr] \) |
${y}^2+\left(\frac{1}{4}a^{3}+a^{2}-\frac{3}{2}a-\frac{19}{4}\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-\frac{1}{4}a^{3}+\frac{5}{2}a+\frac{3}{4}\right){x}^{2}+\left(-\frac{5}{4}a^{3}-2a^{2}+\frac{15}{2}a+\frac{39}{4}\right){x}-\frac{17}{4}a^{3}-8a^{2}+\frac{41}{2}a+\frac{115}{4}$ |
| 4.1-a2 |
4.1-a |
$6$ |
$8$ |
4.4.9225.1 |
$4$ |
$[4, 0]$ |
4.1 |
\( 2^{2} \) |
\( 2^{2} \) |
$10.20656$ |
$(1/4a^3-5/2a+5/4)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 1 \) |
$1$ |
$160.8382987$ |
1.674581477 |
\( -\frac{24506325065924643}{2} a^{3} - 13249114371850221 a^{2} + \frac{189912985144525033}{2} a + 111859025743839833 \) |
\( \bigl[\frac{1}{4} a^{3} + a^{2} - \frac{1}{2} a - \frac{19}{4}\) , \( a^{2} + a - 5\) , \( a + 1\) , \( \frac{135}{4} a^{3} + 60 a^{2} - \frac{331}{2} a - \frac{901}{4}\) , \( -\frac{87}{4} a^{3} - 40 a^{2} + \frac{213}{2} a + \frac{589}{4}\bigr] \) |
${y}^2+\left(\frac{1}{4}a^{3}+a^{2}-\frac{1}{2}a-\frac{19}{4}\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a^{2}+a-5\right){x}^{2}+\left(\frac{135}{4}a^{3}+60a^{2}-\frac{331}{2}a-\frac{901}{4}\right){x}-\frac{87}{4}a^{3}-40a^{2}+\frac{213}{2}a+\frac{589}{4}$ |
| 4.1-a3 |
4.1-a |
$6$ |
$8$ |
4.4.9225.1 |
$4$ |
$[4, 0]$ |
4.1 |
\( 2^{2} \) |
\( 2^{16} \) |
$10.20656$ |
$(1/4a^3-5/2a+5/4)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$321.6765974$ |
1.674581477 |
\( -\frac{2941}{64} a^{3} - \frac{83967}{256} a^{2} + \frac{8735}{128} a + \frac{440389}{256} \) |
\( \bigl[a^{2} - 4\) , \( a^{2} - 5\) , \( \frac{1}{4} a^{3} + a^{2} - \frac{1}{2} a - \frac{15}{4}\) , \( -\frac{5}{4} a^{3} + \frac{9}{2} a + \frac{7}{4}\) , \( -\frac{19}{4} a^{3} - 2 a^{2} + \frac{35}{2} a + \frac{57}{4}\bigr] \) |
${y}^2+\left(a^{2}-4\right){x}{y}+\left(\frac{1}{4}a^{3}+a^{2}-\frac{1}{2}a-\frac{15}{4}\right){y}={x}^{3}+\left(a^{2}-5\right){x}^{2}+\left(-\frac{5}{4}a^{3}+\frac{9}{2}a+\frac{7}{4}\right){x}-\frac{19}{4}a^{3}-2a^{2}+\frac{35}{2}a+\frac{57}{4}$ |
| 4.1-a4 |
4.1-a |
$6$ |
$8$ |
4.4.9225.1 |
$4$ |
$[4, 0]$ |
4.1 |
\( 2^{2} \) |
\( 2^{2} \) |
$10.20656$ |
$(1/4a^3-5/2a+5/4)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$643.3531949$ |
1.674581477 |
\( \frac{254388955}{2} a^{3} - 279826331 a^{2} - \frac{1872226153}{2} a + 2013700075 \) |
\( \bigl[a^{2} - 4\) , \( -a^{2} - a + 6\) , \( \frac{1}{4} a^{3} - \frac{1}{2} a + \frac{5}{4}\) , \( -\frac{9}{4} a^{3} + 3 a^{2} + \frac{25}{2} a - \frac{77}{4}\) , \( -\frac{23}{2} a^{3} + 24 a^{2} + 83 a - \frac{349}{2}\bigr] \) |
${y}^2+\left(a^{2}-4\right){x}{y}+\left(\frac{1}{4}a^{3}-\frac{1}{2}a+\frac{5}{4}\right){y}={x}^{3}+\left(-a^{2}-a+6\right){x}^{2}+\left(-\frac{9}{4}a^{3}+3a^{2}+\frac{25}{2}a-\frac{77}{4}\right){x}-\frac{23}{2}a^{3}+24a^{2}+83a-\frac{349}{2}$ |
| 4.1-a5 |
4.1-a |
$6$ |
$8$ |
4.4.9225.1 |
$4$ |
$[4, 0]$ |
4.1 |
\( 2^{2} \) |
\( 2^{4} \) |
$10.20656$ |
$(1/4a^3-5/2a+5/4)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$321.6765974$ |
1.674581477 |
\( 1983838617590 a^{3} + \frac{14427521023955}{4} a^{2} - \frac{19347816447845}{2} a - \frac{53501248402053}{4} \) |
\( \bigl[a^{2} - 4\) , \( \frac{1}{4} a^{3} - a^{2} - \frac{3}{2} a + \frac{25}{4}\) , \( a^{2} - 5\) , \( \frac{39}{4} a^{3} + 7 a^{2} - \frac{163}{2} a - \frac{333}{4}\) , \( \frac{139}{4} a^{3} + 31 a^{2} - \frac{585}{2} a - \frac{1333}{4}\bigr] \) |
${y}^2+\left(a^{2}-4\right){x}{y}+\left(a^{2}-5\right){y}={x}^{3}+\left(\frac{1}{4}a^{3}-a^{2}-\frac{3}{2}a+\frac{25}{4}\right){x}^{2}+\left(\frac{39}{4}a^{3}+7a^{2}-\frac{163}{2}a-\frac{333}{4}\right){x}+\frac{139}{4}a^{3}+31a^{2}-\frac{585}{2}a-\frac{1333}{4}$ |
| 4.1-a6 |
4.1-a |
$6$ |
$8$ |
4.4.9225.1 |
$4$ |
$[4, 0]$ |
4.1 |
\( 2^{2} \) |
\( 2^{8} \) |
$10.20656$ |
$(1/4a^3-5/2a+5/4)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2 \) |
$1$ |
$1286.706389$ |
1.674581477 |
\( \frac{5543885}{16} a^{3} + 633055 a^{2} - \frac{26990715}{16} a - \frac{18679521}{8} \) |
\( \bigl[a^{2} - 4\) , \( \frac{1}{4} a^{3} - a^{2} - \frac{3}{2} a + \frac{25}{4}\) , \( a^{2} - 5\) , \( \frac{19}{4} a^{3} + 2 a^{2} - \frac{73}{2} a - \frac{93}{4}\) , \( -\frac{35}{4} a^{3} - 12 a^{2} + \frac{135}{2} a + \frac{385}{4}\bigr] \) |
${y}^2+\left(a^{2}-4\right){x}{y}+\left(a^{2}-5\right){y}={x}^{3}+\left(\frac{1}{4}a^{3}-a^{2}-\frac{3}{2}a+\frac{25}{4}\right){x}^{2}+\left(\frac{19}{4}a^{3}+2a^{2}-\frac{73}{2}a-\frac{93}{4}\right){x}-\frac{35}{4}a^{3}-12a^{2}+\frac{135}{2}a+\frac{385}{4}$ |
| 4.1-b1 |
4.1-b |
$6$ |
$8$ |
4.4.9225.1 |
$4$ |
$[4, 0]$ |
4.1 |
\( 2^{2} \) |
\( 2^{2} \) |
$10.20656$ |
$(1/4a^3-5/2a+5/4)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$567.9642993$ |
1.478352020 |
\( \frac{254388955}{2} a^{3} - 279826331 a^{2} - \frac{1872226153}{2} a + 2013700075 \) |
\( \bigl[\frac{1}{4} a^{3} + a^{2} - \frac{1}{2} a - \frac{19}{4}\) , \( -\frac{1}{4} a^{3} + a^{2} + \frac{1}{2} a - \frac{21}{4}\) , \( a^{2} + a - 5\) , \( -\frac{1}{2} a^{3} + 9 a^{2} - 4 a - \frac{51}{2}\) , \( -\frac{21}{4} a^{3} + 32 a^{2} - \frac{19}{2} a - \frac{289}{4}\bigr] \) |
${y}^2+\left(\frac{1}{4}a^{3}+a^{2}-\frac{1}{2}a-\frac{19}{4}\right){x}{y}+\left(a^{2}+a-5\right){y}={x}^{3}+\left(-\frac{1}{4}a^{3}+a^{2}+\frac{1}{2}a-\frac{21}{4}\right){x}^{2}+\left(-\frac{1}{2}a^{3}+9a^{2}-4a-\frac{51}{2}\right){x}-\frac{21}{4}a^{3}+32a^{2}-\frac{19}{2}a-\frac{289}{4}$ |
| 4.1-b2 |
4.1-b |
$6$ |
$8$ |
4.4.9225.1 |
$4$ |
$[4, 0]$ |
4.1 |
\( 2^{2} \) |
\( 2^{4} \) |
$10.20656$ |
$(1/4a^3-5/2a+5/4)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$283.9821496$ |
1.478352020 |
\( 1983838617590 a^{3} + \frac{14427521023955}{4} a^{2} - \frac{19347816447845}{2} a - \frac{53501248402053}{4} \) |
\( \bigl[\frac{1}{4} a^{3} + a^{2} - \frac{1}{2} a - \frac{19}{4}\) , \( -a^{2} + a + 6\) , \( \frac{1}{4} a^{3} - \frac{1}{2} a + \frac{5}{4}\) , \( -\frac{179}{2} a^{3} - 170 a^{2} + 419 a + \frac{1213}{2}\) , \( \frac{4213}{4} a^{3} + 1918 a^{2} - \frac{10237}{2} a - \frac{28311}{4}\bigr] \) |
${y}^2+\left(\frac{1}{4}a^{3}+a^{2}-\frac{1}{2}a-\frac{19}{4}\right){x}{y}+\left(\frac{1}{4}a^{3}-\frac{1}{2}a+\frac{5}{4}\right){y}={x}^{3}+\left(-a^{2}+a+6\right){x}^{2}+\left(-\frac{179}{2}a^{3}-170a^{2}+419a+\frac{1213}{2}\right){x}+\frac{4213}{4}a^{3}+1918a^{2}-\frac{10237}{2}a-\frac{28311}{4}$ |
| 4.1-b3 |
4.1-b |
$6$ |
$8$ |
4.4.9225.1 |
$4$ |
$[4, 0]$ |
4.1 |
\( 2^{2} \) |
\( 2^{8} \) |
$10.20656$ |
$(1/4a^3-5/2a+5/4)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2 \) |
$1$ |
$1135.928598$ |
1.478352020 |
\( \frac{5543885}{16} a^{3} + 633055 a^{2} - \frac{26990715}{16} a - \frac{18679521}{8} \) |
\( \bigl[a\) , \( -a^{2} - a + 4\) , \( \frac{1}{4} a^{3} + a^{2} - \frac{3}{2} a - \frac{15}{4}\) , \( -42 a^{3} - 77 a^{2} + 203 a + 287\) , \( 496 a^{3} + 901 a^{2} - 2419 a - 3341\bigr] \) |
${y}^2+a{x}{y}+\left(\frac{1}{4}a^{3}+a^{2}-\frac{3}{2}a-\frac{15}{4}\right){y}={x}^{3}+\left(-a^{2}-a+4\right){x}^{2}+\left(-42a^{3}-77a^{2}+203a+287\right){x}+496a^{3}+901a^{2}-2419a-3341$ |
| 4.1-b4 |
4.1-b |
$6$ |
$8$ |
4.4.9225.1 |
$4$ |
$[4, 0]$ |
4.1 |
\( 2^{2} \) |
\( 2^{2} \) |
$10.20656$ |
$(1/4a^3-5/2a+5/4)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 1 \) |
$1$ |
$141.9910748$ |
1.478352020 |
\( -\frac{24506325065924643}{2} a^{3} - 13249114371850221 a^{2} + \frac{189912985144525033}{2} a + 111859025743839833 \) |
\( \bigl[\frac{1}{4} a^{3} - \frac{1}{2} a + \frac{1}{4}\) , \( \frac{1}{4} a^{3} + a^{2} - \frac{1}{2} a - \frac{23}{4}\) , \( \frac{1}{4} a^{3} - \frac{1}{2} a + \frac{5}{4}\) , \( \frac{17}{2} a^{3} + 9 a^{2} - 59 a - \frac{127}{2}\) , \( \frac{49}{2} a^{3} + 24 a^{2} - 180 a - \frac{359}{2}\bigr] \) |
${y}^2+\left(\frac{1}{4}a^{3}-\frac{1}{2}a+\frac{1}{4}\right){x}{y}+\left(\frac{1}{4}a^{3}-\frac{1}{2}a+\frac{5}{4}\right){y}={x}^{3}+\left(\frac{1}{4}a^{3}+a^{2}-\frac{1}{2}a-\frac{23}{4}\right){x}^{2}+\left(\frac{17}{2}a^{3}+9a^{2}-59a-\frac{127}{2}\right){x}+\frac{49}{2}a^{3}+24a^{2}-180a-\frac{359}{2}$ |
| 4.1-b5 |
4.1-b |
$6$ |
$8$ |
4.4.9225.1 |
$4$ |
$[4, 0]$ |
4.1 |
\( 2^{2} \) |
\( 2^{4} \) |
$10.20656$ |
$(1/4a^3-5/2a+5/4)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2 \) |
$1$ |
$1135.928598$ |
1.478352020 |
\( -32556416 a^{3} - \frac{140841667}{4} a^{2} + \frac{504596565}{2} a + \frac{1189080877}{4} \) |
\( \bigl[\frac{1}{4} a^{3} - \frac{1}{2} a + \frac{1}{4}\) , \( \frac{1}{4} a^{3} + a^{2} - \frac{1}{2} a - \frac{23}{4}\) , \( \frac{1}{4} a^{3} - \frac{1}{2} a + \frac{5}{4}\) , \( \frac{9}{4} a^{3} + 4 a^{2} - \frac{23}{2} a - \frac{79}{4}\) , \( \frac{17}{4} a^{3} + 3 a^{2} - \frac{49}{2} a - \frac{23}{4}\bigr] \) |
${y}^2+\left(\frac{1}{4}a^{3}-\frac{1}{2}a+\frac{1}{4}\right){x}{y}+\left(\frac{1}{4}a^{3}-\frac{1}{2}a+\frac{5}{4}\right){y}={x}^{3}+\left(\frac{1}{4}a^{3}+a^{2}-\frac{1}{2}a-\frac{23}{4}\right){x}^{2}+\left(\frac{9}{4}a^{3}+4a^{2}-\frac{23}{2}a-\frac{79}{4}\right){x}+\frac{17}{4}a^{3}+3a^{2}-\frac{49}{2}a-\frac{23}{4}$ |
| 4.1-b6 |
4.1-b |
$6$ |
$8$ |
4.4.9225.1 |
$4$ |
$[4, 0]$ |
4.1 |
\( 2^{2} \) |
\( 2^{16} \) |
$10.20656$ |
$(1/4a^3-5/2a+5/4)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$283.9821496$ |
1.478352020 |
\( -\frac{2941}{64} a^{3} - \frac{83967}{256} a^{2} + \frac{8735}{128} a + \frac{440389}{256} \) |
\( \bigl[1\) , \( -\frac{1}{4} a^{3} + a^{2} + \frac{3}{2} a - \frac{25}{4}\) , \( a\) , \( \frac{1}{2} a^{3} - a^{2} - 5 a + \frac{19}{2}\) , \( -\frac{1}{4} a^{3} + \frac{7}{2} a - \frac{25}{4}\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(-\frac{1}{4}a^{3}+a^{2}+\frac{3}{2}a-\frac{25}{4}\right){x}^{2}+\left(\frac{1}{2}a^{3}-a^{2}-5a+\frac{19}{2}\right){x}-\frac{1}{4}a^{3}+\frac{7}{2}a-\frac{25}{4}$ |
| 4.2-a1 |
4.2-a |
$6$ |
$8$ |
4.4.9225.1 |
$4$ |
$[4, 0]$ |
4.2 |
\( 2^{2} \) |
\( 2^{16} \) |
$10.20656$ |
$(1/2a^3+a^2-2a-7/2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$321.6765974$ |
1.674581477 |
\( -\frac{16203}{1024} a^{3} + \frac{83967}{256} a^{2} + \frac{154837}{512} a - \frac{1902139}{1024} \) |
\( \bigl[\frac{1}{4} a^{3} + a^{2} - \frac{3}{2} a - \frac{19}{4}\) , \( \frac{1}{4} a^{3} + a^{2} - \frac{3}{2} a - \frac{23}{4}\) , \( \frac{1}{4} a^{3} - \frac{3}{2} a + \frac{1}{4}\) , \( \frac{1}{4} a^{3} + 3 a^{2} + \frac{3}{2} a - \frac{47}{4}\) , \( -\frac{7}{4} a^{3} + 2 a^{2} + \frac{35}{2} a - \frac{7}{4}\bigr] \) |
${y}^2+\left(\frac{1}{4}a^{3}+a^{2}-\frac{3}{2}a-\frac{19}{4}\right){x}{y}+\left(\frac{1}{4}a^{3}-\frac{3}{2}a+\frac{1}{4}\right){y}={x}^{3}+\left(\frac{1}{4}a^{3}+a^{2}-\frac{3}{2}a-\frac{23}{4}\right){x}^{2}+\left(\frac{1}{4}a^{3}+3a^{2}+\frac{3}{2}a-\frac{47}{4}\right){x}-\frac{7}{4}a^{3}+2a^{2}+\frac{35}{2}a-\frac{7}{4}$ |
| 4.2-a2 |
4.2-a |
$6$ |
$8$ |
4.4.9225.1 |
$4$ |
$[4, 0]$ |
4.2 |
\( 2^{2} \) |
\( 2^{2} \) |
$10.20656$ |
$(1/2a^3+a^2-2a-7/2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$643.3531949$ |
1.674581477 |
\( \frac{1231316059}{8} a^{3} + 279826331 a^{2} - \frac{3002163331}{4} a - \frac{8301356289}{8} \) |
\( \bigl[\frac{1}{4} a^{3} + a^{2} - \frac{3}{2} a - \frac{19}{4}\) , \( -\frac{1}{4} a^{3} + \frac{5}{2} a + \frac{3}{4}\) , \( a + 1\) , \( -\frac{13}{4} a^{3} - 5 a^{2} + \frac{37}{2} a + \frac{95}{4}\) , \( -\frac{55}{4} a^{3} - 25 a^{2} + \frac{135}{2} a + \frac{373}{4}\bigr] \) |
${y}^2+\left(\frac{1}{4}a^{3}+a^{2}-\frac{3}{2}a-\frac{19}{4}\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-\frac{1}{4}a^{3}+\frac{5}{2}a+\frac{3}{4}\right){x}^{2}+\left(-\frac{13}{4}a^{3}-5a^{2}+\frac{37}{2}a+\frac{95}{4}\right){x}-\frac{55}{4}a^{3}-25a^{2}+\frac{135}{2}a+\frac{373}{4}$ |
| 4.2-a3 |
4.2-a |
$6$ |
$8$ |
4.4.9225.1 |
$4$ |
$[4, 0]$ |
4.2 |
\( 2^{2} \) |
\( 2^{4} \) |
$10.20656$ |
$(1/2a^3+a^2-2a-7/2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$321.6765974$ |
1.674581477 |
\( \frac{26230390783955}{16} a^{3} - \frac{14427521023955}{4} a^{2} - \frac{96524160204805}{8} a + \frac{415294904348323}{16} \) |
\( \bigl[\frac{1}{4} a^{3} + a^{2} - \frac{3}{2} a - \frac{19}{4}\) , \( \frac{1}{4} a^{3} - \frac{3}{2} a + \frac{5}{4}\) , \( \frac{1}{4} a^{3} + a^{2} - \frac{3}{2} a - \frac{15}{4}\) , \( \frac{7}{4} a^{3} - 9 a^{2} + \frac{25}{2} a - \frac{13}{4}\) , \( \frac{23}{4} a^{3} - 32 a^{2} + \frac{99}{2} a - \frac{65}{4}\bigr] \) |
${y}^2+\left(\frac{1}{4}a^{3}+a^{2}-\frac{3}{2}a-\frac{19}{4}\right){x}{y}+\left(\frac{1}{4}a^{3}+a^{2}-\frac{3}{2}a-\frac{15}{4}\right){y}={x}^{3}+\left(\frac{1}{4}a^{3}-\frac{3}{2}a+\frac{5}{4}\right){x}^{2}+\left(\frac{7}{4}a^{3}-9a^{2}+\frac{25}{2}a-\frac{13}{4}\right){x}+\frac{23}{4}a^{3}-32a^{2}+\frac{99}{2}a-\frac{65}{4}$ |
| 4.2-a4 |
4.2-a |
$6$ |
$8$ |
4.4.9225.1 |
$4$ |
$[4, 0]$ |
4.2 |
\( 2^{2} \) |
\( 2^{8} \) |
$10.20656$ |
$(1/2a^3+a^2-2a-7/2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2 \) |
$1$ |
$1286.706389$ |
1.674581477 |
\( \frac{18319255}{64} a^{3} - 633055 a^{2} - \frac{67502955}{32} a + \frac{292378267}{64} \) |
\( \bigl[\frac{1}{4} a^{3} + a^{2} - \frac{3}{2} a - \frac{19}{4}\) , \( \frac{1}{4} a^{3} - \frac{3}{2} a + \frac{5}{4}\) , \( \frac{1}{4} a^{3} + a^{2} - \frac{3}{2} a - \frac{15}{4}\) , \( \frac{7}{4} a^{3} - 4 a^{2} - \frac{5}{2} a + \frac{27}{4}\) , \( -\frac{9}{4} a^{3} + 11 a^{2} - \frac{3}{2} a - \frac{97}{4}\bigr] \) |
${y}^2+\left(\frac{1}{4}a^{3}+a^{2}-\frac{3}{2}a-\frac{19}{4}\right){x}{y}+\left(\frac{1}{4}a^{3}+a^{2}-\frac{3}{2}a-\frac{15}{4}\right){y}={x}^{3}+\left(\frac{1}{4}a^{3}-\frac{3}{2}a+\frac{5}{4}\right){x}^{2}+\left(\frac{7}{4}a^{3}-4a^{2}-\frac{5}{2}a+\frac{27}{4}\right){x}-\frac{9}{4}a^{3}+11a^{2}-\frac{3}{2}a-\frac{97}{4}$ |
| 4.2-a5 |
4.2-a |
$6$ |
$8$ |
4.4.9225.1 |
$4$ |
$[4, 0]$ |
4.2 |
\( 2^{2} \) |
\( 2^{4} \) |
$10.20656$ |
$(1/2a^3+a^2-2a-7/2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2 \) |
$1$ |
$1286.706389$ |
1.674581477 |
\( -\frac{152221843}{16} a^{3} + \frac{140841667}{4} a^{2} + \frac{987237}{8} a - \frac{1072029027}{16} \) |
\( \bigl[a^{2} - 4\) , \( -a^{2} - a + 6\) , \( \frac{1}{4} a^{3} - \frac{1}{2} a + \frac{5}{4}\) , \( -\frac{3}{4} a^{3} + \frac{5}{2} a - \frac{3}{4}\) , \( -\frac{15}{4} a^{3} + 7 a^{2} + \frac{53}{2} a - \frac{215}{4}\bigr] \) |
${y}^2+\left(a^{2}-4\right){x}{y}+\left(\frac{1}{4}a^{3}-\frac{1}{2}a+\frac{5}{4}\right){y}={x}^{3}+\left(-a^{2}-a+6\right){x}^{2}+\left(-\frac{3}{4}a^{3}+\frac{5}{2}a-\frac{3}{4}\right){x}-\frac{15}{4}a^{3}+7a^{2}+\frac{53}{2}a-\frac{215}{4}$ |
| 4.2-a6 |
4.2-a |
$6$ |
$8$ |
4.4.9225.1 |
$4$ |
$[4, 0]$ |
4.2 |
\( 2^{2} \) |
\( 2^{2} \) |
$10.20656$ |
$(1/2a^3+a^2-2a-7/2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 1 \) |
$1$ |
$160.8382987$ |
1.674581477 |
\( -\frac{28652036771020955}{8} a^{3} + 13249114371850221 a^{2} + \frac{206040815108515}{4} a - \frac{201676595279423167}{8} \) |
\( \bigl[\frac{1}{4} a^{3} + a^{2} - \frac{1}{2} a - \frac{15}{4}\) , \( -\frac{1}{4} a^{3} - a^{2} + \frac{3}{2} a + \frac{15}{4}\) , \( \frac{1}{4} a^{3} + a^{2} - \frac{1}{2} a - \frac{15}{4}\) , \( 23 a^{3} - 46 a^{2} - 167 a + 334\) , \( -\frac{307}{2} a^{3} + 351 a^{2} + 1135 a - \frac{5009}{2}\bigr] \) |
${y}^2+\left(\frac{1}{4}a^{3}+a^{2}-\frac{1}{2}a-\frac{15}{4}\right){x}{y}+\left(\frac{1}{4}a^{3}+a^{2}-\frac{1}{2}a-\frac{15}{4}\right){y}={x}^{3}+\left(-\frac{1}{4}a^{3}-a^{2}+\frac{3}{2}a+\frac{15}{4}\right){x}^{2}+\left(23a^{3}-46a^{2}-167a+334\right){x}-\frac{307}{2}a^{3}+351a^{2}+1135a-\frac{5009}{2}$ |
| 4.2-b1 |
4.2-b |
$6$ |
$8$ |
4.4.9225.1 |
$4$ |
$[4, 0]$ |
4.2 |
\( 2^{2} \) |
\( 2^{4} \) |
$10.20656$ |
$(1/2a^3+a^2-2a-7/2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$283.9821496$ |
1.478352020 |
\( \frac{26230390783955}{16} a^{3} - \frac{14427521023955}{4} a^{2} - \frac{96524160204805}{8} a + \frac{415294904348323}{16} \) |
\( \bigl[\frac{1}{4} a^{3} + a^{2} - \frac{1}{2} a - \frac{15}{4}\) , \( \frac{1}{4} a^{3} + a^{2} - \frac{3}{2} a - \frac{15}{4}\) , \( \frac{1}{4} a^{3} - \frac{3}{2} a + \frac{1}{4}\) , \( -69 a^{3} + 193 a^{2} + 546 a - 1356\) , \( 1285 a^{3} - 2709 a^{2} - 9407 a + 19721\bigr] \) |
${y}^2+\left(\frac{1}{4}a^{3}+a^{2}-\frac{1}{2}a-\frac{15}{4}\right){x}{y}+\left(\frac{1}{4}a^{3}-\frac{3}{2}a+\frac{1}{4}\right){y}={x}^{3}+\left(\frac{1}{4}a^{3}+a^{2}-\frac{3}{2}a-\frac{15}{4}\right){x}^{2}+\left(-69a^{3}+193a^{2}+546a-1356\right){x}+1285a^{3}-2709a^{2}-9407a+19721$ |
| 4.2-b2 |
4.2-b |
$6$ |
$8$ |
4.4.9225.1 |
$4$ |
$[4, 0]$ |
4.2 |
\( 2^{2} \) |
\( 2^{2} \) |
$10.20656$ |
$(1/2a^3+a^2-2a-7/2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$567.9642993$ |
1.478352020 |
\( \frac{1231316059}{8} a^{3} + 279826331 a^{2} - \frac{3002163331}{4} a - \frac{8301356289}{8} \) |
\( \bigl[\frac{1}{4} a^{3} + a^{2} - \frac{1}{2} a - \frac{15}{4}\) , \( -\frac{1}{4} a^{3} - a^{2} + \frac{1}{2} a + \frac{15}{4}\) , \( 1\) , \( -\frac{11}{4} a^{3} - 2 a^{2} + \frac{51}{2} a + \frac{117}{4}\) , \( -\frac{53}{4} a^{3} - 12 a^{2} + \frac{215}{2} a + \frac{467}{4}\bigr] \) |
${y}^2+\left(\frac{1}{4}a^{3}+a^{2}-\frac{1}{2}a-\frac{15}{4}\right){x}{y}+{y}={x}^{3}+\left(-\frac{1}{4}a^{3}-a^{2}+\frac{1}{2}a+\frac{15}{4}\right){x}^{2}+\left(-\frac{11}{4}a^{3}-2a^{2}+\frac{51}{2}a+\frac{117}{4}\right){x}-\frac{53}{4}a^{3}-12a^{2}+\frac{215}{2}a+\frac{467}{4}$ |
| 4.2-b3 |
4.2-b |
$6$ |
$8$ |
4.4.9225.1 |
$4$ |
$[4, 0]$ |
4.2 |
\( 2^{2} \) |
\( 2^{4} \) |
$10.20656$ |
$(1/2a^3+a^2-2a-7/2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2 \) |
$1$ |
$1135.928598$ |
1.478352020 |
\( -\frac{152221843}{16} a^{3} + \frac{140841667}{4} a^{2} + \frac{987237}{8} a - \frac{1072029027}{16} \) |
\( \bigl[a\) , \( \frac{1}{4} a^{3} + a^{2} - \frac{5}{2} a - \frac{15}{4}\) , \( 0\) , \( -\frac{1}{2} a^{3} + a^{2} + a - \frac{3}{2}\) , \( 0\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(\frac{1}{4}a^{3}+a^{2}-\frac{5}{2}a-\frac{15}{4}\right){x}^{2}+\left(-\frac{1}{2}a^{3}+a^{2}+a-\frac{3}{2}\right){x}$ |
| 4.2-b4 |
4.2-b |
$6$ |
$8$ |
4.4.9225.1 |
$4$ |
$[4, 0]$ |
4.2 |
\( 2^{2} \) |
\( 2^{2} \) |
$10.20656$ |
$(1/2a^3+a^2-2a-7/2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 1 \) |
$1$ |
$141.9910748$ |
1.478352020 |
\( -\frac{28652036771020955}{8} a^{3} + 13249114371850221 a^{2} + \frac{206040815108515}{4} a - \frac{201676595279423167}{8} \) |
\( \bigl[a\) , \( \frac{1}{4} a^{3} + a^{2} - \frac{5}{2} a - \frac{15}{4}\) , \( 0\) , \( 2 a^{3} - 4 a^{2} - 4 a + 6\) , \( \frac{23}{2} a^{3} - 31 a^{2} - 10 a + \frac{107}{2}\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(\frac{1}{4}a^{3}+a^{2}-\frac{5}{2}a-\frac{15}{4}\right){x}^{2}+\left(2a^{3}-4a^{2}-4a+6\right){x}+\frac{23}{2}a^{3}-31a^{2}-10a+\frac{107}{2}$ |
| 4.2-b5 |
4.2-b |
$6$ |
$8$ |
4.4.9225.1 |
$4$ |
$[4, 0]$ |
4.2 |
\( 2^{2} \) |
\( 2^{8} \) |
$10.20656$ |
$(1/2a^3+a^2-2a-7/2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2 \) |
$1$ |
$1135.928598$ |
1.478352020 |
\( \frac{18319255}{64} a^{3} - 633055 a^{2} - \frac{67502955}{32} a + \frac{292378267}{64} \) |
\( \bigl[\frac{1}{4} a^{3} - \frac{1}{2} a + \frac{1}{4}\) , \( -\frac{1}{4} a^{3} + \frac{5}{2} a + \frac{3}{4}\) , \( \frac{1}{4} a^{3} + a^{2} - \frac{1}{2} a - \frac{19}{4}\) , \( -\frac{141}{4} a^{3} + 76 a^{2} + \frac{521}{2} a - \frac{2193}{4}\) , \( 375 a^{3} - 826 a^{2} - 2759 a + 5942\bigr] \) |
${y}^2+\left(\frac{1}{4}a^{3}-\frac{1}{2}a+\frac{1}{4}\right){x}{y}+\left(\frac{1}{4}a^{3}+a^{2}-\frac{1}{2}a-\frac{19}{4}\right){y}={x}^{3}+\left(-\frac{1}{4}a^{3}+\frac{5}{2}a+\frac{3}{4}\right){x}^{2}+\left(-\frac{141}{4}a^{3}+76a^{2}+\frac{521}{2}a-\frac{2193}{4}\right){x}+375a^{3}-826a^{2}-2759a+5942$ |
| 4.2-b6 |
4.2-b |
$6$ |
$8$ |
4.4.9225.1 |
$4$ |
$[4, 0]$ |
4.2 |
\( 2^{2} \) |
\( 2^{16} \) |
$10.20656$ |
$(1/2a^3+a^2-2a-7/2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$283.9821496$ |
1.478352020 |
\( -\frac{16203}{1024} a^{3} + \frac{83967}{256} a^{2} + \frac{154837}{512} a - \frac{1902139}{1024} \) |
\( \bigl[1\) , \( \frac{1}{4} a^{3} - a^{2} - \frac{3}{2} a + \frac{21}{4}\) , \( a\) , \( \frac{1}{4} a^{3} - a^{2} - \frac{5}{2} a + \frac{37}{4}\) , \( \frac{5}{4} a^{3} - \frac{19}{2} a - \frac{15}{4}\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(\frac{1}{4}a^{3}-a^{2}-\frac{3}{2}a+\frac{21}{4}\right){x}^{2}+\left(\frac{1}{4}a^{3}-a^{2}-\frac{5}{2}a+\frac{37}{4}\right){x}+\frac{5}{4}a^{3}-\frac{19}{2}a-\frac{15}{4}$ |
| 11.1-a1 |
11.1-a |
$4$ |
$4$ |
4.4.9225.1 |
$4$ |
$[4, 0]$ |
11.1 |
\( 11 \) |
\( 11^{2} \) |
$11.58233$ |
$(-1/4a^3+1/2a+7/4)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2 \) |
$1$ |
$1014.004460$ |
1.319674093 |
\( -\frac{1109833}{484} a^{3} + \frac{1060017}{121} a^{2} - \frac{459263}{242} a - \frac{4955969}{484} \) |
\( \bigl[a^{2} - 4\) , \( -\frac{1}{4} a^{3} + \frac{1}{2} a + \frac{3}{4}\) , \( 0\) , \( -\frac{1}{4} a^{3} + a^{2} - \frac{1}{2} a - \frac{5}{4}\) , \( 0\bigr] \) |
${y}^2+\left(a^{2}-4\right){x}{y}={x}^{3}+\left(-\frac{1}{4}a^{3}+\frac{1}{2}a+\frac{3}{4}\right){x}^{2}+\left(-\frac{1}{4}a^{3}+a^{2}-\frac{1}{2}a-\frac{5}{4}\right){x}$ |
| 11.1-a2 |
11.1-a |
$4$ |
$4$ |
4.4.9225.1 |
$4$ |
$[4, 0]$ |
11.1 |
\( 11 \) |
\( 11^{4} \) |
$11.58233$ |
$(-1/4a^3+1/2a+7/4)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 2 \) |
$1$ |
$63.37527880$ |
1.319674093 |
\( -\frac{15549813030215}{58564} a^{3} + \frac{14449314416335}{14641} a^{2} - \frac{558404903085}{29282} a - \frac{107847613689483}{58564} \) |
\( \bigl[a^{2} - 4\) , \( -\frac{1}{4} a^{3} + \frac{1}{2} a + \frac{3}{4}\) , \( 0\) , \( a^{3} - 4 a^{2} + 2 a + 5\) , \( \frac{33}{4} a^{3} - 31 a^{2} + \frac{7}{2} a + \frac{209}{4}\bigr] \) |
${y}^2+\left(a^{2}-4\right){x}{y}={x}^{3}+\left(-\frac{1}{4}a^{3}+\frac{1}{2}a+\frac{3}{4}\right){x}^{2}+\left(a^{3}-4a^{2}+2a+5\right){x}+\frac{33}{4}a^{3}-31a^{2}+\frac{7}{2}a+\frac{209}{4}$ |
| 11.1-a3 |
11.1-a |
$4$ |
$4$ |
4.4.9225.1 |
$4$ |
$[4, 0]$ |
11.1 |
\( 11 \) |
\( -11 \) |
$11.58233$ |
$(-1/4a^3+1/2a+7/4)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$2028.008921$ |
1.319674093 |
\( \frac{8694701}{44} a^{3} + \frac{3955311}{11} a^{2} - \frac{21064073}{22} a - \frac{57988167}{44} \) |
\( \bigl[\frac{1}{4} a^{3} - \frac{3}{2} a + \frac{5}{4}\) , \( -\frac{1}{4} a^{3} + a^{2} + \frac{1}{2} a - \frac{17}{4}\) , \( \frac{1}{4} a^{3} + a^{2} - \frac{1}{2} a - \frac{15}{4}\) , \( \frac{7}{4} a^{3} + 5 a^{2} - \frac{37}{2} a - \frac{149}{4}\) , \( -9 a^{3} - 13 a^{2} + 65 a + 104\bigr] \) |
${y}^2+\left(\frac{1}{4}a^{3}-\frac{3}{2}a+\frac{5}{4}\right){x}{y}+\left(\frac{1}{4}a^{3}+a^{2}-\frac{1}{2}a-\frac{15}{4}\right){y}={x}^{3}+\left(-\frac{1}{4}a^{3}+a^{2}+\frac{1}{2}a-\frac{17}{4}\right){x}^{2}+\left(\frac{7}{4}a^{3}+5a^{2}-\frac{37}{2}a-\frac{149}{4}\right){x}-9a^{3}-13a^{2}+65a+104$ |
| 11.1-a4 |
11.1-a |
$4$ |
$4$ |
4.4.9225.1 |
$4$ |
$[4, 0]$ |
11.1 |
\( 11 \) |
\( -11 \) |
$11.58233$ |
$(-1/4a^3+1/2a+7/4)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$507.0022304$ |
1.319674093 |
\( -\frac{19167933}{44} a^{3} - \frac{5160383}{11} a^{2} + \frac{74410861}{22} a + \frac{175206015}{44} \) |
\( \bigl[\frac{1}{4} a^{3} - \frac{3}{2} a + \frac{5}{4}\) , \( -\frac{1}{4} a^{3} - a^{2} + \frac{3}{2} a + \frac{15}{4}\) , \( 0\) , \( \frac{13}{4} a^{3} - 6 a^{2} - \frac{45}{2} a + \frac{173}{4}\) , \( -\frac{75}{4} a^{3} + 41 a^{2} + \frac{273}{2} a - \frac{1171}{4}\bigr] \) |
${y}^2+\left(\frac{1}{4}a^{3}-\frac{3}{2}a+\frac{5}{4}\right){x}{y}={x}^{3}+\left(-\frac{1}{4}a^{3}-a^{2}+\frac{3}{2}a+\frac{15}{4}\right){x}^{2}+\left(\frac{13}{4}a^{3}-6a^{2}-\frac{45}{2}a+\frac{173}{4}\right){x}-\frac{75}{4}a^{3}+41a^{2}+\frac{273}{2}a-\frac{1171}{4}$ |
| 11.1-b1 |
11.1-b |
$4$ |
$4$ |
4.4.9225.1 |
$4$ |
$[4, 0]$ |
11.1 |
\( 11 \) |
\( -11 \) |
$11.58233$ |
$(-1/4a^3+1/2a+7/4)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$0.335501623$ |
$684.2037721$ |
2.389994504 |
\( \frac{8694701}{44} a^{3} + \frac{3955311}{11} a^{2} - \frac{21064073}{22} a - \frac{57988167}{44} \) |
\( \bigl[\frac{1}{4} a^{3} + a^{2} - \frac{1}{2} a - \frac{15}{4}\) , \( -\frac{1}{4} a^{3} + a^{2} + \frac{1}{2} a - \frac{25}{4}\) , \( a\) , \( \frac{11}{2} a^{3} + 9 a^{2} - 33 a - \frac{79}{2}\) , \( \frac{17}{2} a^{3} + 15 a^{2} - 46 a - \frac{129}{2}\bigr] \) |
${y}^2+\left(\frac{1}{4}a^{3}+a^{2}-\frac{1}{2}a-\frac{15}{4}\right){x}{y}+a{y}={x}^{3}+\left(-\frac{1}{4}a^{3}+a^{2}+\frac{1}{2}a-\frac{25}{4}\right){x}^{2}+\left(\frac{11}{2}a^{3}+9a^{2}-33a-\frac{79}{2}\right){x}+\frac{17}{2}a^{3}+15a^{2}-46a-\frac{129}{2}$ |
| 11.1-b2 |
11.1-b |
$4$ |
$4$ |
4.4.9225.1 |
$4$ |
$[4, 0]$ |
11.1 |
\( 11 \) |
\( 11^{4} \) |
$11.58233$ |
$(-1/4a^3+1/2a+7/4)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.083875405$ |
$684.2037721$ |
2.389994504 |
\( -\frac{15549813030215}{58564} a^{3} + \frac{14449314416335}{14641} a^{2} - \frac{558404903085}{29282} a - \frac{107847613689483}{58564} \) |
\( \bigl[a\) , \( -\frac{1}{4} a^{3} + a^{2} + \frac{5}{2} a - \frac{17}{4}\) , \( a + 1\) , \( \frac{51}{2} a^{3} + 27 a^{2} - 109 a - \frac{235}{2}\) , \( -\frac{311}{4} a^{3} - 80 a^{2} + \frac{653}{2} a + \frac{1473}{4}\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-\frac{1}{4}a^{3}+a^{2}+\frac{5}{2}a-\frac{17}{4}\right){x}^{2}+\left(\frac{51}{2}a^{3}+27a^{2}-109a-\frac{235}{2}\right){x}-\frac{311}{4}a^{3}-80a^{2}+\frac{653}{2}a+\frac{1473}{4}$ |
| 11.1-b3 |
11.1-b |
$4$ |
$4$ |
4.4.9225.1 |
$4$ |
$[4, 0]$ |
11.1 |
\( 11 \) |
\( 11^{2} \) |
$11.58233$ |
$(-1/4a^3+1/2a+7/4)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2 \) |
$0.167750811$ |
$2736.815088$ |
2.389994504 |
\( -\frac{1109833}{484} a^{3} + \frac{1060017}{121} a^{2} - \frac{459263}{242} a - \frac{4955969}{484} \) |
\( \bigl[\frac{1}{4} a^{3} - \frac{3}{2} a + \frac{1}{4}\) , \( \frac{1}{4} a^{3} + a^{2} - \frac{3}{2} a - \frac{15}{4}\) , \( \frac{1}{4} a^{3} - \frac{1}{2} a + \frac{1}{4}\) , \( -\frac{23}{4} a^{3} + 15 a^{2} + \frac{87}{2} a - \frac{415}{4}\) , \( 25 a^{3} - 54 a^{2} - 183 a + 389\bigr] \) |
${y}^2+\left(\frac{1}{4}a^{3}-\frac{3}{2}a+\frac{1}{4}\right){x}{y}+\left(\frac{1}{4}a^{3}-\frac{1}{2}a+\frac{1}{4}\right){y}={x}^{3}+\left(\frac{1}{4}a^{3}+a^{2}-\frac{3}{2}a-\frac{15}{4}\right){x}^{2}+\left(-\frac{23}{4}a^{3}+15a^{2}+\frac{87}{2}a-\frac{415}{4}\right){x}+25a^{3}-54a^{2}-183a+389$ |
| 11.1-b4 |
11.1-b |
$4$ |
$4$ |
4.4.9225.1 |
$4$ |
$[4, 0]$ |
11.1 |
\( 11 \) |
\( -11 \) |
$11.58233$ |
$(-1/4a^3+1/2a+7/4)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$0.083875405$ |
$2736.815088$ |
2.389994504 |
\( -\frac{19167933}{44} a^{3} - \frac{5160383}{11} a^{2} + \frac{74410861}{22} a + \frac{175206015}{44} \) |
\( \bigl[\frac{1}{4} a^{3} - \frac{1}{2} a + \frac{1}{4}\) , \( a^{2} + a - 6\) , \( \frac{1}{4} a^{3} + a^{2} - \frac{3}{2} a - \frac{19}{4}\) , \( 2 a^{3} - 10 a + 4\) , \( \frac{3}{2} a^{3} + 3 a^{2} - 5 a - \frac{33}{2}\bigr] \) |
${y}^2+\left(\frac{1}{4}a^{3}-\frac{1}{2}a+\frac{1}{4}\right){x}{y}+\left(\frac{1}{4}a^{3}+a^{2}-\frac{3}{2}a-\frac{19}{4}\right){y}={x}^{3}+\left(a^{2}+a-6\right){x}^{2}+\left(2a^{3}-10a+4\right){x}+\frac{3}{2}a^{3}+3a^{2}-5a-\frac{33}{2}$ |
| 11.2-a1 |
11.2-a |
$4$ |
$4$ |
4.4.9225.1 |
$4$ |
$[4, 0]$ |
11.2 |
\( 11 \) |
\( 11^{4} \) |
$11.58233$ |
$(-1/2a^3+4a+3/2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 2 \) |
$1$ |
$63.37527880$ |
1.319674093 |
\( -\frac{53603049443415}{58564} a^{3} - \frac{14449314416335}{14641} a^{2} + \frac{208016992323975}{29282} a + \frac{489868984216057}{58564} \) |
\( \bigl[\frac{1}{4} a^{3} + a^{2} - \frac{3}{2} a - \frac{19}{4}\) , \( -a^{2} + a + 4\) , \( a\) , \( \frac{19}{4} a^{3} + 6 a^{2} - \frac{81}{2} a - \frac{189}{4}\) , \( \frac{85}{4} a^{3} + 21 a^{2} - \frac{331}{2} a - \frac{763}{4}\bigr] \) |
${y}^2+\left(\frac{1}{4}a^{3}+a^{2}-\frac{3}{2}a-\frac{19}{4}\right){x}{y}+a{y}={x}^{3}+\left(-a^{2}+a+4\right){x}^{2}+\left(\frac{19}{4}a^{3}+6a^{2}-\frac{81}{2}a-\frac{189}{4}\right){x}+\frac{85}{4}a^{3}+21a^{2}-\frac{331}{2}a-\frac{763}{4}$ |
| 11.2-a2 |
11.2-a |
$4$ |
$4$ |
4.4.9225.1 |
$4$ |
$[4, 0]$ |
11.2 |
\( 11 \) |
\( 11^{2} \) |
$11.58233$ |
$(-1/2a^3+4a+3/2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2 \) |
$1$ |
$1014.004460$ |
1.319674093 |
\( -\frac{4064231}{484} a^{3} - \frac{1060017}{121} a^{2} + \frac{15981455}{242} a + \frac{38730381}{484} \) |
\( \bigl[\frac{1}{4} a^{3} + a^{2} - \frac{3}{2} a - \frac{19}{4}\) , \( -a^{2} + a + 4\) , \( a\) , \( -\frac{1}{4} a^{3} + a^{2} - \frac{1}{2} a - \frac{9}{4}\) , \( \frac{3}{4} a^{3} - \frac{9}{2} a - \frac{17}{4}\bigr] \) |
${y}^2+\left(\frac{1}{4}a^{3}+a^{2}-\frac{3}{2}a-\frac{19}{4}\right){x}{y}+a{y}={x}^{3}+\left(-a^{2}+a+4\right){x}^{2}+\left(-\frac{1}{4}a^{3}+a^{2}-\frac{1}{2}a-\frac{9}{4}\right){x}+\frac{3}{4}a^{3}-\frac{9}{2}a-\frac{17}{4}$ |
| 11.2-a3 |
11.2-a |
$4$ |
$4$ |
4.4.9225.1 |
$4$ |
$[4, 0]$ |
11.2 |
\( 11 \) |
\( -11 \) |
$11.58233$ |
$(-1/2a^3+4a+3/2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$507.0022304$ |
1.319674093 |
\( -\frac{5554019}{44} a^{3} + \frac{5160383}{11} a^{2} - \frac{245005}{22} a - \frac{38236923}{44} \) |
\( \bigl[\frac{1}{4} a^{3} - \frac{3}{2} a + \frac{5}{4}\) , \( a^{2} - 4\) , \( \frac{1}{4} a^{3} - \frac{3}{2} a + \frac{5}{4}\) , \( 4 a^{3} + 8 a^{2} - 21 a - 33\) , \( -19 a^{3} - 34 a^{2} + 93 a + 126\bigr] \) |
${y}^2+\left(\frac{1}{4}a^{3}-\frac{3}{2}a+\frac{5}{4}\right){x}{y}+\left(\frac{1}{4}a^{3}-\frac{3}{2}a+\frac{5}{4}\right){y}={x}^{3}+\left(a^{2}-4\right){x}^{2}+\left(4a^{3}+8a^{2}-21a-33\right){x}-19a^{3}-34a^{2}+93a+126$ |
| 11.2-a4 |
11.2-a |
$4$ |
$4$ |
4.4.9225.1 |
$4$ |
$[4, 0]$ |
11.2 |
\( 11 \) |
\( -11 \) |
$11.58233$ |
$(-1/2a^3+4a+3/2)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$2028.008921$ |
1.319674093 |
\( \frac{7249405}{44} a^{3} - \frac{3955311}{11} a^{2} - \frac{26768245}{22} a + \frac{114600221}{44} \) |
\( \bigl[\frac{1}{4} a^{3} - \frac{3}{2} a + \frac{5}{4}\) , \( -a^{2} + a + 4\) , \( a^{2} + a - 5\) , \( -\frac{1}{4} a^{3} - 6 a^{2} + \frac{7}{2} a + \frac{87}{4}\) , \( -\frac{15}{4} a^{3} + 16 a^{2} - \frac{1}{2} a - \frac{139}{4}\bigr] \) |
${y}^2+\left(\frac{1}{4}a^{3}-\frac{3}{2}a+\frac{5}{4}\right){x}{y}+\left(a^{2}+a-5\right){y}={x}^{3}+\left(-a^{2}+a+4\right){x}^{2}+\left(-\frac{1}{4}a^{3}-6a^{2}+\frac{7}{2}a+\frac{87}{4}\right){x}-\frac{15}{4}a^{3}+16a^{2}-\frac{1}{2}a-\frac{139}{4}$ |
| 11.2-b1 |
11.2-b |
$4$ |
$4$ |
4.4.9225.1 |
$4$ |
$[4, 0]$ |
11.2 |
\( 11 \) |
\( -11 \) |
$11.58233$ |
$(-1/2a^3+4a+3/2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$0.335501623$ |
$684.2037721$ |
2.389994504 |
\( \frac{7249405}{44} a^{3} - \frac{3955311}{11} a^{2} - \frac{26768245}{22} a + \frac{114600221}{44} \) |
\( \bigl[\frac{1}{4} a^{3} + a^{2} - \frac{1}{2} a - \frac{19}{4}\) , \( -a^{2} - a + 4\) , \( 1\) , \( \frac{7}{4} a^{3} - 2 a^{2} - \frac{15}{2} a + \frac{39}{4}\) , \( \frac{7}{4} a^{3} - 2 a^{2} - \frac{11}{2} a + \frac{15}{4}\bigr] \) |
${y}^2+\left(\frac{1}{4}a^{3}+a^{2}-\frac{1}{2}a-\frac{19}{4}\right){x}{y}+{y}={x}^{3}+\left(-a^{2}-a+4\right){x}^{2}+\left(\frac{7}{4}a^{3}-2a^{2}-\frac{15}{2}a+\frac{39}{4}\right){x}+\frac{7}{4}a^{3}-2a^{2}-\frac{11}{2}a+\frac{15}{4}$ |
| 11.2-b2 |
11.2-b |
$4$ |
$4$ |
4.4.9225.1 |
$4$ |
$[4, 0]$ |
11.2 |
\( 11 \) |
\( -11 \) |
$11.58233$ |
$(-1/2a^3+4a+3/2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$0.083875405$ |
$2736.815088$ |
2.389994504 |
\( -\frac{5554019}{44} a^{3} + \frac{5160383}{11} a^{2} - \frac{245005}{22} a - \frac{38236923}{44} \) |
\( \bigl[a\) , \( a^{2} - a - 4\) , \( a^{2} + a - 5\) , \( \frac{1}{4} a^{3} + 3 a^{2} - \frac{13}{2} a - \frac{59}{4}\) , \( -\frac{3}{4} a^{3} + 2 a^{2} + \frac{3}{2} a - \frac{31}{4}\bigr] \) |
${y}^2+a{x}{y}+\left(a^{2}+a-5\right){y}={x}^{3}+\left(a^{2}-a-4\right){x}^{2}+\left(\frac{1}{4}a^{3}+3a^{2}-\frac{13}{2}a-\frac{59}{4}\right){x}-\frac{3}{4}a^{3}+2a^{2}+\frac{3}{2}a-\frac{31}{4}$ |
| 11.2-b3 |
11.2-b |
$4$ |
$4$ |
4.4.9225.1 |
$4$ |
$[4, 0]$ |
11.2 |
\( 11 \) |
\( 11^{2} \) |
$11.58233$ |
$(-1/2a^3+4a+3/2)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2 \) |
$0.167750811$ |
$2736.815088$ |
2.389994504 |
\( -\frac{4064231}{484} a^{3} - \frac{1060017}{121} a^{2} + \frac{15981455}{242} a + \frac{38730381}{484} \) |
\( \bigl[\frac{1}{4} a^{3} - \frac{3}{2} a + \frac{1}{4}\) , \( -a^{2} + 4\) , \( \frac{1}{4} a^{3} - \frac{1}{2} a + \frac{1}{4}\) , \( -\frac{15}{2} a^{3} - 14 a^{2} + 36 a + \frac{107}{2}\) , \( \frac{149}{4} a^{3} + 67 a^{2} - \frac{363}{2} a - \frac{995}{4}\bigr] \) |
${y}^2+\left(\frac{1}{4}a^{3}-\frac{3}{2}a+\frac{1}{4}\right){x}{y}+\left(\frac{1}{4}a^{3}-\frac{1}{2}a+\frac{1}{4}\right){y}={x}^{3}+\left(-a^{2}+4\right){x}^{2}+\left(-\frac{15}{2}a^{3}-14a^{2}+36a+\frac{107}{2}\right){x}+\frac{149}{4}a^{3}+67a^{2}-\frac{363}{2}a-\frac{995}{4}$ |
| 11.2-b4 |
11.2-b |
$4$ |
$4$ |
4.4.9225.1 |
$4$ |
$[4, 0]$ |
11.2 |
\( 11 \) |
\( 11^{4} \) |
$11.58233$ |
$(-1/2a^3+4a+3/2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.083875405$ |
$684.2037721$ |
2.389994504 |
\( -\frac{53603049443415}{58564} a^{3} - \frac{14449314416335}{14641} a^{2} + \frac{208016992323975}{29282} a + \frac{489868984216057}{58564} \) |
\( \bigl[\frac{1}{4} a^{3} - \frac{1}{2} a + \frac{1}{4}\) , \( \frac{1}{4} a^{3} + a^{2} - \frac{5}{2} a - \frac{23}{4}\) , \( 0\) , \( \frac{115}{4} a^{3} - 25 a^{2} - \frac{433}{2} a + \frac{703}{4}\) , \( -170 a^{3} + 170 a^{2} + 1275 a - 1132\bigr] \) |
${y}^2+\left(\frac{1}{4}a^{3}-\frac{1}{2}a+\frac{1}{4}\right){x}{y}={x}^{3}+\left(\frac{1}{4}a^{3}+a^{2}-\frac{5}{2}a-\frac{23}{4}\right){x}^{2}+\left(\frac{115}{4}a^{3}-25a^{2}-\frac{433}{2}a+\frac{703}{4}\right){x}-170a^{3}+170a^{2}+1275a-1132$ |
| 19.1-a1 |
19.1-a |
$8$ |
$12$ |
4.4.9225.1 |
$4$ |
$[4, 0]$ |
19.1 |
\( 19 \) |
\( 19 \) |
$12.40126$ |
$(-1/4a^3-a^2+3/2a+19/4)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 1 \) |
$0.998455273$ |
$1778.235949$ |
2.053961523 |
\( -\frac{207913801}{76} a^{3} - \frac{51982800}{19} a^{2} + \frac{792005199}{38} a + \frac{1841805899}{76} \) |
\( \bigl[\frac{1}{4} a^{3} + a^{2} - \frac{3}{2} a - \frac{19}{4}\) , \( a^{2} - 5\) , \( \frac{1}{4} a^{3} - \frac{1}{2} a + \frac{1}{4}\) , \( -\frac{39}{4} a^{3} + 25 a^{2} + \frac{145}{2} a - \frac{691}{4}\) , \( \frac{255}{4} a^{3} - 137 a^{2} - \frac{933}{2} a + \frac{3963}{4}\bigr] \) |
${y}^2+\left(\frac{1}{4}a^{3}+a^{2}-\frac{3}{2}a-\frac{19}{4}\right){x}{y}+\left(\frac{1}{4}a^{3}-\frac{1}{2}a+\frac{1}{4}\right){y}={x}^{3}+\left(a^{2}-5\right){x}^{2}+\left(-\frac{39}{4}a^{3}+25a^{2}+\frac{145}{2}a-\frac{691}{4}\right){x}+\frac{255}{4}a^{3}-137a^{2}-\frac{933}{2}a+\frac{3963}{4}$ |
| 19.1-a2 |
19.1-a |
$8$ |
$12$ |
4.4.9225.1 |
$4$ |
$[4, 0]$ |
19.1 |
\( 19 \) |
\( 19^{3} \) |
$12.40126$ |
$(-1/4a^3-a^2+3/2a+19/4)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 3 \) |
$2.995365819$ |
$21.95353023$ |
2.053961523 |
\( -\frac{4356469732590452386431}{27436} a^{3} + \frac{4028988670414948922426}{6859} a^{2} + \frac{31327979731445344745}{13718} a - \frac{30664416311634343116999}{27436} \) |
\( \bigl[a\) , \( a^{2} - a - 4\) , \( \frac{1}{4} a^{3} - \frac{1}{2} a + \frac{1}{4}\) , \( -\frac{87}{4} a^{3} + 51 a^{2} + \frac{365}{2} a - \frac{1743}{4}\) , \( -\frac{421}{2} a^{3} + 427 a^{2} + 1740 a - \frac{7175}{2}\bigr] \) |
${y}^2+a{x}{y}+\left(\frac{1}{4}a^{3}-\frac{1}{2}a+\frac{1}{4}\right){y}={x}^{3}+\left(a^{2}-a-4\right){x}^{2}+\left(-\frac{87}{4}a^{3}+51a^{2}+\frac{365}{2}a-\frac{1743}{4}\right){x}-\frac{421}{2}a^{3}+427a^{2}+1740a-\frac{7175}{2}$ |
| 19.1-a3 |
19.1-a |
$8$ |
$12$ |
4.4.9225.1 |
$4$ |
$[4, 0]$ |
19.1 |
\( 19 \) |
\( 19^{3} \) |
$12.40126$ |
$(-1/4a^3-a^2+3/2a+19/4)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 3 \) |
$11.98146327$ |
$5.488382559$ |
2.053961523 |
\( \frac{6495779048452187797423531}{27436} a^{3} + \frac{2952518215236153479381310}{6859} a^{2} - \frac{15837823924102104876447349}{13718} a - \frac{43795162739491488634800477}{27436} \) |
\( \bigl[\frac{1}{4} a^{3} - \frac{3}{2} a + \frac{1}{4}\) , \( \frac{1}{4} a^{3} - \frac{5}{2} a + \frac{1}{4}\) , \( \frac{1}{4} a^{3} + a^{2} - \frac{3}{2} a - \frac{15}{4}\) , \( 192 a^{3} + 30 a^{2} - 2175 a - 2322\) , \( \frac{22571}{4} a^{3} + 1883 a^{2} - \frac{120325}{2} a - \frac{260637}{4}\bigr] \) |
${y}^2+\left(\frac{1}{4}a^{3}-\frac{3}{2}a+\frac{1}{4}\right){x}{y}+\left(\frac{1}{4}a^{3}+a^{2}-\frac{3}{2}a-\frac{15}{4}\right){y}={x}^{3}+\left(\frac{1}{4}a^{3}-\frac{5}{2}a+\frac{1}{4}\right){x}^{2}+\left(192a^{3}+30a^{2}-2175a-2322\right){x}+\frac{22571}{4}a^{3}+1883a^{2}-\frac{120325}{2}a-\frac{260637}{4}$ |
| 19.1-a4 |
19.1-a |
$8$ |
$12$ |
4.4.9225.1 |
$4$ |
$[4, 0]$ |
19.1 |
\( 19 \) |
\( 19 \) |
$12.40126$ |
$(-1/4a^3-a^2+3/2a+19/4)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 1 \) |
$3.993821092$ |
$444.5589872$ |
2.053961523 |
\( \frac{26646409466412669}{76} a^{3} - \frac{14656064320831548}{19} a^{2} - \frac{98055120182770347}{38} a + \frac{421873026365255561}{76} \) |
\( \bigl[\frac{1}{4} a^{3} - \frac{3}{2} a + \frac{1}{4}\) , \( \frac{1}{4} a^{3} - \frac{5}{2} a + \frac{1}{4}\) , \( \frac{1}{4} a^{3} + a^{2} - \frac{3}{2} a - \frac{15}{4}\) , \( 2 a^{3} - 25 a - 27\) , \( \frac{11}{4} a^{3} - 3 a^{2} - \frac{87}{2} a - \frac{173}{4}\bigr] \) |
${y}^2+\left(\frac{1}{4}a^{3}-\frac{3}{2}a+\frac{1}{4}\right){x}{y}+\left(\frac{1}{4}a^{3}+a^{2}-\frac{3}{2}a-\frac{15}{4}\right){y}={x}^{3}+\left(\frac{1}{4}a^{3}-\frac{5}{2}a+\frac{1}{4}\right){x}^{2}+\left(2a^{3}-25a-27\right){x}+\frac{11}{4}a^{3}-3a^{2}-\frac{87}{2}a-\frac{173}{4}$ |
| 19.1-a5 |
19.1-a |
$8$ |
$12$ |
4.4.9225.1 |
$4$ |
$[4, 0]$ |
19.1 |
\( 19 \) |
\( 19^{2} \) |
$12.40126$ |
$(-1/4a^3-a^2+3/2a+19/4)$ |
$1$ |
$\Z/2\Z\oplus\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2Cs, 3B.1.1 |
$1$ |
\( 2 \) |
$1.996910546$ |
$1778.235949$ |
2.053961523 |
\( \frac{6080981355}{1444} a^{3} - \frac{3344860896}{361} a^{2} - \frac{22376800713}{722} a + \frac{96286765763}{1444} \) |
\( \bigl[\frac{1}{4} a^{3} - \frac{3}{2} a + \frac{1}{4}\) , \( \frac{1}{4} a^{3} - \frac{5}{2} a + \frac{1}{4}\) , \( \frac{1}{4} a^{3} + a^{2} - \frac{3}{2} a - \frac{15}{4}\) , \( \frac{3}{4} a^{3} - \frac{15}{2} a - \frac{13}{4}\) , \( -3 a^{3} - 4 a^{2} + 22 a + 28\bigr] \) |
${y}^2+\left(\frac{1}{4}a^{3}-\frac{3}{2}a+\frac{1}{4}\right){x}{y}+\left(\frac{1}{4}a^{3}+a^{2}-\frac{3}{2}a-\frac{15}{4}\right){y}={x}^{3}+\left(\frac{1}{4}a^{3}-\frac{5}{2}a+\frac{1}{4}\right){x}^{2}+\left(\frac{3}{4}a^{3}-\frac{15}{2}a-\frac{13}{4}\right){x}-3a^{3}-4a^{2}+22a+28$ |
| 19.1-a6 |
19.1-a |
$8$ |
$12$ |
4.4.9225.1 |
$4$ |
$[4, 0]$ |
19.1 |
\( 19 \) |
\( 19^{4} \) |
$12.40126$ |
$(-1/4a^3-a^2+3/2a+19/4)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{2} \) |
$0.998455273$ |
$444.5589872$ |
2.053961523 |
\( -\frac{237446951}{521284} a^{3} + \frac{141231612}{130321} a^{2} + \frac{834222165}{260642} a - \frac{3601307379}{521284} \) |
\( \bigl[\frac{1}{4} a^{3} - \frac{1}{2} a + \frac{1}{4}\) , \( -a^{2} - a + 6\) , \( \frac{1}{4} a^{3} - \frac{3}{2} a + \frac{5}{4}\) , \( -\frac{9}{4} a^{3} + 4 a^{2} + \frac{27}{2} a - \frac{101}{4}\) , \( \frac{7}{4} a^{3} - 4 a^{2} - \frac{29}{2} a + \frac{127}{4}\bigr] \) |
${y}^2+\left(\frac{1}{4}a^{3}-\frac{1}{2}a+\frac{1}{4}\right){x}{y}+\left(\frac{1}{4}a^{3}-\frac{3}{2}a+\frac{5}{4}\right){y}={x}^{3}+\left(-a^{2}-a+6\right){x}^{2}+\left(-\frac{9}{4}a^{3}+4a^{2}+\frac{27}{2}a-\frac{101}{4}\right){x}+\frac{7}{4}a^{3}-4a^{2}-\frac{29}{2}a+\frac{127}{4}$ |
| 19.1-a7 |
19.1-a |
$8$ |
$12$ |
4.4.9225.1 |
$4$ |
$[4, 0]$ |
19.1 |
\( 19 \) |
\( 19^{12} \) |
$12.40126$ |
$(-1/4a^3-a^2+3/2a+19/4)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2^{2} \cdot 3 \) |
$2.995365819$ |
$5.488382559$ |
2.053961523 |
\( -\frac{122643560239701514649}{8853259676264644} a^{3} - \frac{71796327871227530792}{2213314919066161} a^{2} + \frac{324484472244359149395}{4426629838132322} a + \frac{995507401176695403135}{8853259676264644} \) |
\( \bigl[\frac{1}{4} a^{3} - \frac{1}{2} a + \frac{1}{4}\) , \( -a^{2} - a + 6\) , \( \frac{1}{4} a^{3} - \frac{3}{2} a + \frac{5}{4}\) , \( \frac{33}{2} a^{3} - 41 a^{2} - 104 a + \frac{487}{2}\) , \( \frac{121}{4} a^{3} - 88 a^{2} - \frac{235}{2} a + \frac{1405}{4}\bigr] \) |
${y}^2+\left(\frac{1}{4}a^{3}-\frac{1}{2}a+\frac{1}{4}\right){x}{y}+\left(\frac{1}{4}a^{3}-\frac{3}{2}a+\frac{5}{4}\right){y}={x}^{3}+\left(-a^{2}-a+6\right){x}^{2}+\left(\frac{33}{2}a^{3}-41a^{2}-104a+\frac{487}{2}\right){x}+\frac{121}{4}a^{3}-88a^{2}-\frac{235}{2}a+\frac{1405}{4}$ |
| 19.1-a8 |
19.1-a |
$8$ |
$12$ |
4.4.9225.1 |
$4$ |
$[4, 0]$ |
19.1 |
\( 19 \) |
\( 19^{6} \) |
$12.40126$ |
$(-1/4a^3-a^2+3/2a+19/4)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2Cs, 3B.1.2 |
$1$ |
\( 2 \cdot 3 \) |
$5.990731638$ |
$21.95353023$ |
2.053961523 |
\( \frac{704481118633505045}{188183524} a^{3} + \frac{336657958520594316}{47045881} a^{2} - \frac{1746612902622704687}{94091762} a - \frac{4913975098503879047}{188183524} \) |
\( \bigl[\frac{1}{4} a^{3} - \frac{3}{2} a + \frac{5}{4}\) , \( \frac{1}{4} a^{3} - a^{2} - \frac{5}{2} a + \frac{25}{4}\) , \( \frac{1}{4} a^{3} + a^{2} - \frac{3}{2} a - \frac{15}{4}\) , \( -\frac{391}{4} a^{3} - 186 a^{2} + \frac{925}{2} a + \frac{2717}{4}\) , \( -1558 a^{3} - 2843 a^{2} + 7570 a + 10503\bigr] \) |
${y}^2+\left(\frac{1}{4}a^{3}-\frac{3}{2}a+\frac{5}{4}\right){x}{y}+\left(\frac{1}{4}a^{3}+a^{2}-\frac{3}{2}a-\frac{15}{4}\right){y}={x}^{3}+\left(\frac{1}{4}a^{3}-a^{2}-\frac{5}{2}a+\frac{25}{4}\right){x}^{2}+\left(-\frac{391}{4}a^{3}-186a^{2}+\frac{925}{2}a+\frac{2717}{4}\right){x}-1558a^{3}-2843a^{2}+7570a+10503$ |
| 19.1-b1 |
19.1-b |
$8$ |
$12$ |
4.4.9225.1 |
$4$ |
$[4, 0]$ |
19.1 |
\( 19 \) |
\( 19 \) |
$12.40126$ |
$(-1/4a^3-a^2+3/2a+19/4)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 1 \) |
$1.308375881$ |
$168.8813610$ |
2.300546749 |
\( \frac{26646409466412669}{76} a^{3} - \frac{14656064320831548}{19} a^{2} - \frac{98055120182770347}{38} a + \frac{421873026365255561}{76} \) |
\( \bigl[\frac{1}{4} a^{3} + a^{2} - \frac{3}{2} a - \frac{19}{4}\) , \( a^{2} - 4\) , \( 0\) , \( \frac{255}{4} a^{3} + 108 a^{2} - \frac{989}{2} a - \frac{3453}{4}\) , \( -792 a^{3} - 659 a^{2} + 6119 a + 5743\bigr] \) |
${y}^2+\left(\frac{1}{4}a^{3}+a^{2}-\frac{3}{2}a-\frac{19}{4}\right){x}{y}={x}^{3}+\left(a^{2}-4\right){x}^{2}+\left(\frac{255}{4}a^{3}+108a^{2}-\frac{989}{2}a-\frac{3453}{4}\right){x}-792a^{3}-659a^{2}+6119a+5743$ |
| 19.1-b2 |
19.1-b |
$8$ |
$12$ |
4.4.9225.1 |
$4$ |
$[4, 0]$ |
19.1 |
\( 19 \) |
\( 19^{4} \) |
$12.40126$ |
$(-1/4a^3-a^2+3/2a+19/4)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2^{2} \) |
$0.327093970$ |
$168.8813610$ |
2.300546749 |
\( -\frac{237446951}{521284} a^{3} + \frac{141231612}{130321} a^{2} + \frac{834222165}{260642} a - \frac{3601307379}{521284} \) |
\( \bigl[\frac{1}{4} a^{3} + a^{2} - \frac{1}{2} a - \frac{19}{4}\) , \( -\frac{1}{4} a^{3} + a^{2} + \frac{3}{2} a - \frac{25}{4}\) , \( a\) , \( \frac{13}{4} a^{3} + 7 a^{2} - \frac{35}{2} a - \frac{95}{4}\) , \( 6 a^{3} + 13 a^{2} - 31 a - 47\bigr] \) |
${y}^2+\left(\frac{1}{4}a^{3}+a^{2}-\frac{1}{2}a-\frac{19}{4}\right){x}{y}+a{y}={x}^{3}+\left(-\frac{1}{4}a^{3}+a^{2}+\frac{3}{2}a-\frac{25}{4}\right){x}^{2}+\left(\frac{13}{4}a^{3}+7a^{2}-\frac{35}{2}a-\frac{95}{4}\right){x}+6a^{3}+13a^{2}-31a-47$ |
*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.
