| 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 |
$6$ |
$8$ |
4.4.13625.1 |
$4$ |
$[4, 0]$ |
4.1 |
\( 2^{2} \) |
\( - 2^{2} \) |
$12.40407$ |
$(-1/2a^3-a^2+3a+11/2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 1 \) |
$1$ |
$243.2813374$ |
2.084205507 |
\( \frac{275460243734691826247921669}{4} a^{3} - 241267362169227007085479555 a^{2} - \frac{789550043777683111809568017}{2} a + \frac{5679668289813676572655921593}{4} \) |
\( \bigl[\frac{1}{2} a^{3} - 4 a - \frac{7}{2}\) , \( -\frac{1}{2} a^{2} + \frac{3}{2} a + \frac{9}{2}\) , \( a + 1\) , \( -189 a^{3} + \frac{1289}{2} a^{2} + \frac{2229}{2} a - \frac{7591}{2}\) , \( 4097 a^{3} - \frac{28701}{2} a^{2} - \frac{47203}{2} a + \frac{169657}{2}\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-4a-\frac{7}{2}\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-\frac{1}{2}a^{2}+\frac{3}{2}a+\frac{9}{2}\right){x}^{2}+\left(-189a^{3}+\frac{1289}{2}a^{2}+\frac{2229}{2}a-\frac{7591}{2}\right){x}+4097a^{3}-\frac{28701}{2}a^{2}-\frac{47203}{2}a+\frac{169657}{2}$ |
| 4.1-a2 |
4.1-a |
$6$ |
$8$ |
4.4.13625.1 |
$4$ |
$[4, 0]$ |
4.1 |
\( 2^{2} \) |
\( 2^{4} \) |
$12.40407$ |
$(-1/2a^3-a^2+3a+11/2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2 \) |
$1$ |
$1946.250699$ |
2.084205507 |
\( \frac{15683066265537}{8} a^{3} - \frac{54944149012505}{8} a^{2} - \frac{89904663756199}{8} a + \frac{161679747714421}{4} \) |
\( \bigl[\frac{1}{2} a^{3} - 4 a - \frac{7}{2}\) , \( -\frac{1}{2} a^{2} + \frac{3}{2} a + \frac{9}{2}\) , \( a + 1\) , \( -\frac{23}{2} a^{3} + 22 a^{2} + 102 a - \frac{291}{2}\) , \( \frac{77}{2} a^{3} - 137 a^{2} - 298 a + \frac{2161}{2}\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-4a-\frac{7}{2}\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-\frac{1}{2}a^{2}+\frac{3}{2}a+\frac{9}{2}\right){x}^{2}+\left(-\frac{23}{2}a^{3}+22a^{2}+102a-\frac{291}{2}\right){x}+\frac{77}{2}a^{3}-137a^{2}-298a+\frac{2161}{2}$ |
| 4.1-a3 |
4.1-a |
$6$ |
$8$ |
4.4.13625.1 |
$4$ |
$[4, 0]$ |
4.1 |
\( 2^{2} \) |
\( 2^{8} \) |
$12.40407$ |
$(-1/2a^3-a^2+3a+11/2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2 \) |
$1$ |
$1946.250699$ |
2.084205507 |
\( \frac{10570617}{32} a^{3} - \frac{9262425}{8} a^{2} - \frac{30217737}{16} a + \frac{218496889}{32} \) |
\( \bigl[\frac{1}{2} a^{3} - 4 a - \frac{7}{2}\) , \( -\frac{1}{2} a^{2} + \frac{3}{2} a + \frac{9}{2}\) , \( a + 1\) , \( -4 a^{3} - \frac{1}{2} a^{2} + \frac{79}{2} a + \frac{69}{2}\) , \( -4 a^{3} - \frac{7}{2} a^{2} + \frac{79}{2} a + \frac{133}{2}\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-4a-\frac{7}{2}\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-\frac{1}{2}a^{2}+\frac{3}{2}a+\frac{9}{2}\right){x}^{2}+\left(-4a^{3}-\frac{1}{2}a^{2}+\frac{79}{2}a+\frac{69}{2}\right){x}-4a^{3}-\frac{7}{2}a^{2}+\frac{79}{2}a+\frac{133}{2}$ |
| 4.1-a4 |
4.1-a |
$6$ |
$8$ |
4.4.13625.1 |
$4$ |
$[4, 0]$ |
4.1 |
\( 2^{2} \) |
\( - 2^{2} \) |
$12.40407$ |
$(-1/2a^3-a^2+3a+11/2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$973.1253497$ |
2.084205507 |
\( \frac{90556086177484795}{4} a^{3} + 31991058085523075 a^{2} - \frac{279683635551871727}{2} a - \frac{822495624449110649}{4} \) |
\( \bigl[\frac{1}{2} a^{3} - 3 a - \frac{5}{2}\) , \( -\frac{1}{2} a^{3} + \frac{1}{2} a^{2} + \frac{9}{2} a\) , \( 1\) , \( -\frac{137}{2} a^{3} + \frac{489}{2} a^{2} + \frac{877}{2} a - 1566\) , \( 1234 a^{3} - 4261 a^{2} - 7362 a + 25778\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-3a-\frac{5}{2}\right){x}{y}+{y}={x}^{3}+\left(-\frac{1}{2}a^{3}+\frac{1}{2}a^{2}+\frac{9}{2}a\right){x}^{2}+\left(-\frac{137}{2}a^{3}+\frac{489}{2}a^{2}+\frac{877}{2}a-1566\right){x}+1234a^{3}-4261a^{2}-7362a+25778$ |
| 4.1-a5 |
4.1-a |
$6$ |
$8$ |
4.4.13625.1 |
$4$ |
$[4, 0]$ |
4.1 |
\( 2^{2} \) |
\( 2^{4} \) |
$12.40407$ |
$(-1/2a^3-a^2+3a+11/2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$486.5626748$ |
2.084205507 |
\( -\frac{296537553}{8} a^{3} - \frac{149144911}{8} a^{2} + \frac{2887847071}{8} a + \frac{1835572495}{4} \) |
\( \bigl[\frac{1}{2} a^{3} - \frac{1}{2} a^{2} - \frac{5}{2} a\) , \( -\frac{1}{2} a^{3} + a^{2} + 4 a - \frac{9}{2}\) , \( \frac{1}{2} a^{2} + \frac{1}{2} a - \frac{7}{2}\) , \( \frac{5}{2} a^{3} - \frac{1}{2} a^{2} - \frac{27}{2} a + 4\) , \( 59 a^{3} + \frac{173}{2} a^{2} - \frac{729}{2} a - \frac{1109}{2}\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-\frac{1}{2}a^{2}-\frac{5}{2}a\right){x}{y}+\left(\frac{1}{2}a^{2}+\frac{1}{2}a-\frac{7}{2}\right){y}={x}^{3}+\left(-\frac{1}{2}a^{3}+a^{2}+4a-\frac{9}{2}\right){x}^{2}+\left(\frac{5}{2}a^{3}-\frac{1}{2}a^{2}-\frac{27}{2}a+4\right){x}+59a^{3}+\frac{173}{2}a^{2}-\frac{729}{2}a-\frac{1109}{2}$ |
| 4.1-a6 |
4.1-a |
$6$ |
$8$ |
4.4.13625.1 |
$4$ |
$[4, 0]$ |
4.1 |
\( 2^{2} \) |
\( 2^{16} \) |
$12.40407$ |
$(-1/2a^3-a^2+3a+11/2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$486.5626748$ |
2.084205507 |
\( \frac{123165}{512} a^{3} - \frac{106881}{512} a^{2} - \frac{895575}{512} a + \frac{492203}{256} \) |
\( \bigl[a + 1\) , \( -\frac{1}{2} a^{3} + 4 a + \frac{5}{2}\) , \( \frac{1}{2} a^{3} - \frac{1}{2} a^{2} - \frac{7}{2} a + 1\) , \( -\frac{7}{2} a^{3} - \frac{5}{2} a^{2} + \frac{67}{2} a + 46\) , \( \frac{101}{2} a^{3} + 26 a^{2} - 493 a - \frac{1263}{2}\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(\frac{1}{2}a^{3}-\frac{1}{2}a^{2}-\frac{7}{2}a+1\right){y}={x}^{3}+\left(-\frac{1}{2}a^{3}+4a+\frac{5}{2}\right){x}^{2}+\left(-\frac{7}{2}a^{3}-\frac{5}{2}a^{2}+\frac{67}{2}a+46\right){x}+\frac{101}{2}a^{3}+26a^{2}-493a-\frac{1263}{2}$ |
| 4.1-b1 |
4.1-b |
$6$ |
$8$ |
4.4.13625.1 |
$4$ |
$[4, 0]$ |
4.1 |
\( 2^{2} \) |
\( 2^{4} \) |
$12.40407$ |
$(-1/2a^3-a^2+3a+11/2)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.552905600$ |
$713.5315913$ |
1.689919216 |
\( -\frac{296537553}{8} a^{3} - \frac{149144911}{8} a^{2} + \frac{2887847071}{8} a + \frac{1835572495}{4} \) |
\( \bigl[\frac{1}{2} a^{2} - \frac{1}{2} a - \frac{7}{2}\) , \( -\frac{1}{2} a^{2} - \frac{1}{2} a + \frac{9}{2}\) , \( \frac{1}{2} a^{3} - 3 a - \frac{7}{2}\) , \( -\frac{3}{2} a^{3} + 6 a^{2} + 8 a - \frac{73}{2}\) , \( -10 a^{3} + \frac{67}{2} a^{2} + \frac{115}{2} a - \frac{399}{2}\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{2}-\frac{1}{2}a-\frac{7}{2}\right){x}{y}+\left(\frac{1}{2}a^{3}-3a-\frac{7}{2}\right){y}={x}^{3}+\left(-\frac{1}{2}a^{2}-\frac{1}{2}a+\frac{9}{2}\right){x}^{2}+\left(-\frac{3}{2}a^{3}+6a^{2}+8a-\frac{73}{2}\right){x}-10a^{3}+\frac{67}{2}a^{2}+\frac{115}{2}a-\frac{399}{2}$ |
| 4.1-b2 |
4.1-b |
$6$ |
$8$ |
4.4.13625.1 |
$4$ |
$[4, 0]$ |
4.1 |
\( 2^{2} \) |
\( 2^{8} \) |
$12.40407$ |
$(-1/2a^3-a^2+3a+11/2)$ |
$1$ |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$1.105811201$ |
$713.5315913$ |
1.689919216 |
\( \frac{10570617}{32} a^{3} - \frac{9262425}{8} a^{2} - \frac{30217737}{16} a + \frac{218496889}{32} \) |
\( \bigl[\frac{1}{2} a^{2} - \frac{1}{2} a - \frac{5}{2}\) , \( -\frac{1}{2} a^{3} + 5 a + \frac{9}{2}\) , \( \frac{1}{2} a^{3} - 4 a - \frac{5}{2}\) , \( -\frac{9}{2} a^{3} - \frac{11}{2} a^{2} + \frac{65}{2} a + 47\) , \( -\frac{29}{2} a^{3} - \frac{39}{2} a^{2} + \frac{185}{2} a + 133\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{2}-\frac{1}{2}a-\frac{5}{2}\right){x}{y}+\left(\frac{1}{2}a^{3}-4a-\frac{5}{2}\right){y}={x}^{3}+\left(-\frac{1}{2}a^{3}+5a+\frac{9}{2}\right){x}^{2}+\left(-\frac{9}{2}a^{3}-\frac{11}{2}a^{2}+\frac{65}{2}a+47\right){x}-\frac{29}{2}a^{3}-\frac{39}{2}a^{2}+\frac{185}{2}a+133$ |
| 4.1-b3 |
4.1-b |
$6$ |
$8$ |
4.4.13625.1 |
$4$ |
$[4, 0]$ |
4.1 |
\( 2^{2} \) |
\( - 2^{2} \) |
$12.40407$ |
$(-1/2a^3-a^2+3a+11/2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$16$ |
\( 1 \) |
$4.423244807$ |
$2.787232778$ |
1.689919216 |
\( \frac{275460243734691826247921669}{4} a^{3} - 241267362169227007085479555 a^{2} - \frac{789550043777683111809568017}{2} a + \frac{5679668289813676572655921593}{4} \) |
\( \bigl[\frac{1}{2} a^{2} - \frac{1}{2} a - \frac{5}{2}\) , \( -\frac{1}{2} a^{3} + 5 a + \frac{9}{2}\) , \( \frac{1}{2} a^{3} - 4 a - \frac{5}{2}\) , \( -\frac{109}{2} a^{3} - \frac{141}{2} a^{2} + \frac{695}{2} a + 482\) , \( -\frac{1547}{2} a^{3} - \frac{2171}{2} a^{2} + \frac{9577}{2} a + 7006\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{2}-\frac{1}{2}a-\frac{5}{2}\right){x}{y}+\left(\frac{1}{2}a^{3}-4a-\frac{5}{2}\right){y}={x}^{3}+\left(-\frac{1}{2}a^{3}+5a+\frac{9}{2}\right){x}^{2}+\left(-\frac{109}{2}a^{3}-\frac{141}{2}a^{2}+\frac{695}{2}a+482\right){x}-\frac{1547}{2}a^{3}-\frac{2171}{2}a^{2}+\frac{9577}{2}a+7006$ |
| 4.1-b4 |
4.1-b |
$6$ |
$8$ |
4.4.13625.1 |
$4$ |
$[4, 0]$ |
4.1 |
\( 2^{2} \) |
\( 2^{16} \) |
$12.40407$ |
$(-1/2a^3-a^2+3a+11/2)$ |
$1$ |
$\Z/8\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.552905600$ |
$713.5315913$ |
1.689919216 |
\( \frac{123165}{512} a^{3} - \frac{106881}{512} a^{2} - \frac{895575}{512} a + \frac{492203}{256} \) |
\( \bigl[\frac{1}{2} a^{3} - \frac{1}{2} a^{2} - \frac{7}{2} a\) , \( -\frac{1}{2} a^{3} + 4 a + \frac{7}{2}\) , \( \frac{1}{2} a^{2} - \frac{1}{2} a - \frac{7}{2}\) , \( -3 a^{3} + \frac{11}{2} a^{2} + \frac{31}{2} a + \frac{5}{2}\) , \( -\frac{3}{2} a^{3} - 3 a^{2} + 19 a + \frac{59}{2}\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-\frac{1}{2}a^{2}-\frac{7}{2}a\right){x}{y}+\left(\frac{1}{2}a^{2}-\frac{1}{2}a-\frac{7}{2}\right){y}={x}^{3}+\left(-\frac{1}{2}a^{3}+4a+\frac{7}{2}\right){x}^{2}+\left(-3a^{3}+\frac{11}{2}a^{2}+\frac{31}{2}a+\frac{5}{2}\right){x}-\frac{3}{2}a^{3}-3a^{2}+19a+\frac{59}{2}$ |
| 4.1-b5 |
4.1-b |
$6$ |
$8$ |
4.4.13625.1 |
$4$ |
$[4, 0]$ |
4.1 |
\( 2^{2} \) |
\( 2^{4} \) |
$12.40407$ |
$(-1/2a^3-a^2+3a+11/2)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$4$ |
\( 2 \) |
$2.211622403$ |
$44.59572445$ |
1.689919216 |
\( \frac{15683066265537}{8} a^{3} - \frac{54944149012505}{8} a^{2} - \frac{89904663756199}{8} a + \frac{161679747714421}{4} \) |
\( \bigl[1\) , \( -a - 1\) , \( a\) , \( -4 a^{3} - 7 a^{2} + 11 a + 13\) , \( -26 a^{3} - \frac{77}{2} a^{2} + \frac{291}{2} a + \frac{417}{2}\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-4a^{3}-7a^{2}+11a+13\right){x}-26a^{3}-\frac{77}{2}a^{2}+\frac{291}{2}a+\frac{417}{2}$ |
| 4.1-b6 |
4.1-b |
$6$ |
$8$ |
4.4.13625.1 |
$4$ |
$[4, 0]$ |
4.1 |
\( 2^{2} \) |
\( - 2^{2} \) |
$12.40407$ |
$(-1/2a^3-a^2+3a+11/2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$16$ |
\( 1 \) |
$4.423244807$ |
$2.787232778$ |
1.689919216 |
\( \frac{90556086177484795}{4} a^{3} + 31991058085523075 a^{2} - \frac{279683635551871727}{2} a - \frac{822495624449110649}{4} \) |
\( \bigl[1\) , \( -a - 1\) , \( a\) , \( -64 a^{3} - \frac{279}{2} a^{2} + \frac{397}{2} a + \frac{781}{2}\) , \( -\frac{3559}{2} a^{3} - \frac{6141}{2} a^{2} + \frac{17623}{2} a + 14132\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-64a^{3}-\frac{279}{2}a^{2}+\frac{397}{2}a+\frac{781}{2}\right){x}-\frac{3559}{2}a^{3}-\frac{6141}{2}a^{2}+\frac{17623}{2}a+14132$ |
| 4.2-a1 |
4.2-a |
$6$ |
$8$ |
4.4.13625.1 |
$4$ |
$[4, 0]$ |
4.2 |
\( 2^{2} \) |
\( 2^{4} \) |
$12.40407$ |
$(1/2a^3-3/2a^2-5/2a+6)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$486.5626748$ |
2.084205507 |
\( \frac{296537553}{8} a^{3} - \frac{519378785}{4} a^{2} - \frac{849972295}{4} a + \frac{6113309597}{8} \) |
\( \bigl[\frac{1}{2} a^{3} - 3 a - \frac{5}{2}\) , \( 0\) , \( a\) , \( \frac{17}{2} a^{2} - \frac{15}{2} a - \frac{63}{2}\) , \( -\frac{105}{2} a^{3} + \frac{497}{2} a^{2} + \frac{3}{2} a - 739\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-3a-\frac{5}{2}\right){x}{y}+a{y}={x}^{3}+\left(\frac{17}{2}a^{2}-\frac{15}{2}a-\frac{63}{2}\right){x}-\frac{105}{2}a^{3}+\frac{497}{2}a^{2}+\frac{3}{2}a-739$ |
| 4.2-a2 |
4.2-a |
$6$ |
$8$ |
4.4.13625.1 |
$4$ |
$[4, 0]$ |
4.2 |
\( 2^{2} \) |
\( - 2^{2} \) |
$12.40407$ |
$(1/2a^3-3/2a^2-5/2a+6)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 1 \) |
$1$ |
$243.2813374$ |
2.084205507 |
\( -\frac{275460243734691826247921669}{4} a^{3} - \frac{138688717472832549598153213}{4} a^{2} + \frac{2682858253705106801559207467}{4} a + 852739749329023536735697252 \) |
\( \bigl[\frac{1}{2} a^{3} - \frac{1}{2} a^{2} - \frac{7}{2} a\) , \( \frac{1}{2} a^{3} - 3 a - \frac{7}{2}\) , \( \frac{1}{2} a^{3} - 4 a - \frac{7}{2}\) , \( \frac{373}{2} a^{3} + \frac{183}{2} a^{2} - \frac{3649}{2} a - 2316\) , \( -\frac{8263}{2} a^{3} - \frac{4129}{2} a^{2} + \frac{80593}{2} a + 51211\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-\frac{1}{2}a^{2}-\frac{7}{2}a\right){x}{y}+\left(\frac{1}{2}a^{3}-4a-\frac{7}{2}\right){y}={x}^{3}+\left(\frac{1}{2}a^{3}-3a-\frac{7}{2}\right){x}^{2}+\left(\frac{373}{2}a^{3}+\frac{183}{2}a^{2}-\frac{3649}{2}a-2316\right){x}-\frac{8263}{2}a^{3}-\frac{4129}{2}a^{2}+\frac{80593}{2}a+51211$ |
| 4.2-a3 |
4.2-a |
$6$ |
$8$ |
4.4.13625.1 |
$4$ |
$[4, 0]$ |
4.2 |
\( 2^{2} \) |
\( 2^{4} \) |
$12.40407$ |
$(1/2a^3-3/2a^2-5/2a+6)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2 \) |
$1$ |
$1946.250699$ |
2.084205507 |
\( -\frac{15683066265537}{8} a^{3} - \frac{3947475107947}{4} a^{2} + \frac{76371881492299}{4} a + \frac{194193748925675}{8} \) |
\( \bigl[\frac{1}{2} a^{3} - \frac{1}{2} a^{2} - \frac{7}{2} a\) , \( \frac{1}{2} a^{3} - 3 a - \frac{7}{2}\) , \( \frac{1}{2} a^{3} - 4 a - \frac{7}{2}\) , \( 9 a^{3} + \frac{3}{2} a^{2} - \frac{199}{2} a - \frac{247}{2}\) , \( -\frac{111}{2} a^{3} - \frac{43}{2} a^{2} + \frac{1123}{2} a + 704\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-\frac{1}{2}a^{2}-\frac{7}{2}a\right){x}{y}+\left(\frac{1}{2}a^{3}-4a-\frac{7}{2}\right){y}={x}^{3}+\left(\frac{1}{2}a^{3}-3a-\frac{7}{2}\right){x}^{2}+\left(9a^{3}+\frac{3}{2}a^{2}-\frac{199}{2}a-\frac{247}{2}\right){x}-\frac{111}{2}a^{3}-\frac{43}{2}a^{2}+\frac{1123}{2}a+704$ |
| 4.2-a4 |
4.2-a |
$6$ |
$8$ |
4.4.13625.1 |
$4$ |
$[4, 0]$ |
4.2 |
\( 2^{2} \) |
\( 2^{8} \) |
$12.40407$ |
$(1/2a^3-3/2a^2-5/2a+6)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2 \) |
$1$ |
$1946.250699$ |
2.084205507 |
\( -\frac{10570617}{32} a^{3} - \frac{5337849}{32} a^{2} + \frac{102823023}{32} a + \frac{32895583}{8} \) |
\( \bigl[\frac{1}{2} a^{3} - \frac{1}{2} a^{2} - \frac{7}{2} a\) , \( \frac{1}{2} a^{3} - 3 a - \frac{7}{2}\) , \( \frac{1}{2} a^{3} - 4 a - \frac{7}{2}\) , \( \frac{3}{2} a^{3} + \frac{3}{2} a^{2} - \frac{29}{2} a - 21\) , \( -\frac{1}{2} a^{3} - \frac{1}{2} a^{2} + \frac{9}{2} a + 6\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-\frac{1}{2}a^{2}-\frac{7}{2}a\right){x}{y}+\left(\frac{1}{2}a^{3}-4a-\frac{7}{2}\right){y}={x}^{3}+\left(\frac{1}{2}a^{3}-3a-\frac{7}{2}\right){x}^{2}+\left(\frac{3}{2}a^{3}+\frac{3}{2}a^{2}-\frac{29}{2}a-21\right){x}-\frac{1}{2}a^{3}-\frac{1}{2}a^{2}+\frac{9}{2}a+6$ |
| 4.2-a5 |
4.2-a |
$6$ |
$8$ |
4.4.13625.1 |
$4$ |
$[4, 0]$ |
4.2 |
\( 2^{2} \) |
\( - 2^{2} \) |
$12.40407$ |
$(1/2a^3-3/2a^2-5/2a+6)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$973.1253497$ |
2.084205507 |
\( -\frac{90556086177484795}{4} a^{3} + \frac{399632490874546685}{4} a^{2} + \frac{31770547887104469}{4} a - 290835644258319252 \) |
\( \bigl[\frac{1}{2} a^{3} - \frac{1}{2} a^{2} - \frac{5}{2} a\) , \( 0\) , \( \frac{1}{2} a^{2} - \frac{1}{2} a - \frac{7}{2}\) , \( \frac{141}{2} a^{3} + \frac{69}{2} a^{2} - \frac{1447}{2} a - 957\) , \( -1128 a^{3} - \frac{1107}{2} a^{2} + \frac{22229}{2} a + \frac{28387}{2}\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-\frac{1}{2}a^{2}-\frac{5}{2}a\right){x}{y}+\left(\frac{1}{2}a^{2}-\frac{1}{2}a-\frac{7}{2}\right){y}={x}^{3}+\left(\frac{141}{2}a^{3}+\frac{69}{2}a^{2}-\frac{1447}{2}a-957\right){x}-1128a^{3}-\frac{1107}{2}a^{2}+\frac{22229}{2}a+\frac{28387}{2}$ |
| 4.2-a6 |
4.2-a |
$6$ |
$8$ |
4.4.13625.1 |
$4$ |
$[4, 0]$ |
4.2 |
\( 2^{2} \) |
\( 2^{16} \) |
$12.40407$ |
$(1/2a^3-3/2a^2-5/2a+6)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$486.5626748$ |
2.084205507 |
\( -\frac{123165}{512} a^{3} + \frac{131307}{256} a^{2} + \frac{369921}{256} a + \frac{105115}{512} \) |
\( \bigl[a\) , \( \frac{1}{2} a^{3} - 5 a - \frac{7}{2}\) , \( \frac{1}{2} a^{2} - \frac{1}{2} a - \frac{5}{2}\) , \( a^{3} - 7 a^{2} - 3 a + 51\) , \( -54 a^{3} + \frac{383}{2} a^{2} + \frac{615}{2} a - \frac{2267}{2}\bigr] \) |
${y}^2+a{x}{y}+\left(\frac{1}{2}a^{2}-\frac{1}{2}a-\frac{5}{2}\right){y}={x}^{3}+\left(\frac{1}{2}a^{3}-5a-\frac{7}{2}\right){x}^{2}+\left(a^{3}-7a^{2}-3a+51\right){x}-54a^{3}+\frac{383}{2}a^{2}+\frac{615}{2}a-\frac{2267}{2}$ |
| 4.2-b1 |
4.2-b |
$6$ |
$8$ |
4.4.13625.1 |
$4$ |
$[4, 0]$ |
4.2 |
\( 2^{2} \) |
\( 2^{16} \) |
$12.40407$ |
$(1/2a^3-3/2a^2-5/2a+6)$ |
$1$ |
$\Z/8\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.552905600$ |
$713.5315913$ |
1.689919216 |
\( -\frac{123165}{512} a^{3} + \frac{131307}{256} a^{2} + \frac{369921}{256} a + \frac{105115}{512} \) |
\( \bigl[\frac{1}{2} a^{3} - 4 a - \frac{7}{2}\) , \( -\frac{1}{2} a^{3} + a^{2} + 2 a - \frac{7}{2}\) , \( \frac{1}{2} a^{3} - 3 a - \frac{7}{2}\) , \( \frac{1}{2} a^{3} + 2 a^{2} - 2 a - \frac{7}{2}\) , \( -4 a^{3} - \frac{9}{2} a^{2} + \frac{55}{2} a + \frac{75}{2}\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-4a-\frac{7}{2}\right){x}{y}+\left(\frac{1}{2}a^{3}-3a-\frac{7}{2}\right){y}={x}^{3}+\left(-\frac{1}{2}a^{3}+a^{2}+2a-\frac{7}{2}\right){x}^{2}+\left(\frac{1}{2}a^{3}+2a^{2}-2a-\frac{7}{2}\right){x}-4a^{3}-\frac{9}{2}a^{2}+\frac{55}{2}a+\frac{75}{2}$ |
| 4.2-b2 |
4.2-b |
$6$ |
$8$ |
4.4.13625.1 |
$4$ |
$[4, 0]$ |
4.2 |
\( 2^{2} \) |
\( 2^{4} \) |
$12.40407$ |
$(1/2a^3-3/2a^2-5/2a+6)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.552905600$ |
$713.5315913$ |
1.689919216 |
\( \frac{296537553}{8} a^{3} - \frac{519378785}{4} a^{2} - \frac{849972295}{4} a + \frac{6113309597}{8} \) |
\( \bigl[\frac{1}{2} a^{2} - \frac{1}{2} a - \frac{7}{2}\) , \( -\frac{1}{2} a^{2} + \frac{3}{2} a + \frac{7}{2}\) , \( \frac{1}{2} a^{3} - \frac{1}{2} a^{2} - \frac{5}{2} a + 1\) , \( \frac{3}{2} a^{3} + a^{2} - 16 a - \frac{39}{2}\) , \( \frac{19}{2} a^{3} + 4 a^{2} - 93 a - \frac{235}{2}\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{2}-\frac{1}{2}a-\frac{7}{2}\right){x}{y}+\left(\frac{1}{2}a^{3}-\frac{1}{2}a^{2}-\frac{5}{2}a+1\right){y}={x}^{3}+\left(-\frac{1}{2}a^{2}+\frac{3}{2}a+\frac{7}{2}\right){x}^{2}+\left(\frac{3}{2}a^{3}+a^{2}-16a-\frac{39}{2}\right){x}+\frac{19}{2}a^{3}+4a^{2}-93a-\frac{235}{2}$ |
| 4.2-b3 |
4.2-b |
$6$ |
$8$ |
4.4.13625.1 |
$4$ |
$[4, 0]$ |
4.2 |
\( 2^{2} \) |
\( 2^{8} \) |
$12.40407$ |
$(1/2a^3-3/2a^2-5/2a+6)$ |
$1$ |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$1.105811201$ |
$713.5315913$ |
1.689919216 |
\( -\frac{10570617}{32} a^{3} - \frac{5337849}{32} a^{2} + \frac{102823023}{32} a + \frac{32895583}{8} \) |
\( \bigl[\frac{1}{2} a^{2} - \frac{1}{2} a - \frac{5}{2}\) , \( \frac{1}{2} a^{3} - 5 a - \frac{9}{2}\) , \( \frac{1}{2} a^{3} - 4 a - \frac{5}{2}\) , \( \frac{3}{2} a^{3} - \frac{29}{2} a^{2} + \frac{29}{2} a + 57\) , \( 14 a^{3} - \frac{107}{2} a^{2} - \frac{43}{2} a + \frac{273}{2}\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{2}-\frac{1}{2}a-\frac{5}{2}\right){x}{y}+\left(\frac{1}{2}a^{3}-4a-\frac{5}{2}\right){y}={x}^{3}+\left(\frac{1}{2}a^{3}-5a-\frac{9}{2}\right){x}^{2}+\left(\frac{3}{2}a^{3}-\frac{29}{2}a^{2}+\frac{29}{2}a+57\right){x}+14a^{3}-\frac{107}{2}a^{2}-\frac{43}{2}a+\frac{273}{2}$ |
| 4.2-b4 |
4.2-b |
$6$ |
$8$ |
4.4.13625.1 |
$4$ |
$[4, 0]$ |
4.2 |
\( 2^{2} \) |
\( - 2^{2} \) |
$12.40407$ |
$(1/2a^3-3/2a^2-5/2a+6)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$16$ |
\( 1 \) |
$4.423244807$ |
$2.787232778$ |
1.689919216 |
\( -\frac{275460243734691826247921669}{4} a^{3} - \frac{138688717472832549598153213}{4} a^{2} + \frac{2682858253705106801559207467}{4} a + 852739749329023536735697252 \) |
\( \bigl[\frac{1}{2} a^{2} - \frac{1}{2} a - \frac{5}{2}\) , \( \frac{1}{2} a^{3} - 5 a - \frac{9}{2}\) , \( \frac{1}{2} a^{3} - 4 a - \frac{5}{2}\) , \( \frac{103}{2} a^{3} - \frac{459}{2} a^{2} - \frac{41}{2} a + 692\) , \( 748 a^{3} - \frac{6603}{2} a^{2} - \frac{507}{2} a + \frac{19161}{2}\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{2}-\frac{1}{2}a-\frac{5}{2}\right){x}{y}+\left(\frac{1}{2}a^{3}-4a-\frac{5}{2}\right){y}={x}^{3}+\left(\frac{1}{2}a^{3}-5a-\frac{9}{2}\right){x}^{2}+\left(\frac{103}{2}a^{3}-\frac{459}{2}a^{2}-\frac{41}{2}a+692\right){x}+748a^{3}-\frac{6603}{2}a^{2}-\frac{507}{2}a+\frac{19161}{2}$ |
| 4.2-b5 |
4.2-b |
$6$ |
$8$ |
4.4.13625.1 |
$4$ |
$[4, 0]$ |
4.2 |
\( 2^{2} \) |
\( 2^{4} \) |
$12.40407$ |
$(1/2a^3-3/2a^2-5/2a+6)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$4$ |
\( 2 \) |
$2.211622403$ |
$44.59572445$ |
1.689919216 |
\( -\frac{15683066265537}{8} a^{3} - \frac{3947475107947}{4} a^{2} + \frac{76371881492299}{4} a + \frac{194193748925675}{8} \) |
\( \bigl[1\) , \( a + 1\) , \( a\) , \( 4 a^{3} - 19 a^{2} + 16 a + 13\) , \( 30 a^{3} - \frac{271}{2} a^{2} + \frac{49}{2} a + \frac{605}{2}\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(4a^{3}-19a^{2}+16a+13\right){x}+30a^{3}-\frac{271}{2}a^{2}+\frac{49}{2}a+\frac{605}{2}$ |
| 4.2-b6 |
4.2-b |
$6$ |
$8$ |
4.4.13625.1 |
$4$ |
$[4, 0]$ |
4.2 |
\( 2^{2} \) |
\( - 2^{2} \) |
$12.40407$ |
$(1/2a^3-3/2a^2-5/2a+6)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$16$ |
\( 1 \) |
$4.423244807$ |
$2.787232778$ |
1.689919216 |
\( -\frac{90556086177484795}{4} a^{3} + \frac{399632490874546685}{4} a^{2} + \frac{31770547887104469}{4} a - 290835644258319252 \) |
\( \bigl[1\) , \( a + 1\) , \( a\) , \( 64 a^{3} - \frac{663}{2} a^{2} + \frac{547}{2} a + \frac{771}{2}\) , \( \frac{3687}{2} a^{3} - \frac{17481}{2} a^{2} + \frac{5881}{2} a + 18479\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(64a^{3}-\frac{663}{2}a^{2}+\frac{547}{2}a+\frac{771}{2}\right){x}+\frac{3687}{2}a^{3}-\frac{17481}{2}a^{2}+\frac{5881}{2}a+18479$ |
| 11.1-a1 |
11.1-a |
$2$ |
$3$ |
4.4.13625.1 |
$4$ |
$[4, 0]$ |
11.1 |
\( 11 \) |
\( 11 \) |
$14.07605$ |
$(a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.2 |
$9$ |
\( 1 \) |
$6.818180487$ |
$1.537328160$ |
3.232729164 |
\( -\frac{908833236673}{22} a^{3} + \frac{1804251327861}{11} a^{2} + \frac{2358050011412}{11} a - \frac{22402232453999}{22} \) |
\( \bigl[\frac{1}{2} a^{3} - \frac{1}{2} a^{2} - \frac{7}{2} a + 1\) , \( \frac{1}{2} a^{3} - 3 a - \frac{5}{2}\) , \( \frac{1}{2} a^{3} - 4 a - \frac{5}{2}\) , \( \frac{99}{2} a^{3} + \frac{63}{2} a^{2} - \frac{981}{2} a - 642\) , \( 579 a^{3} + \frac{517}{2} a^{2} - \frac{11149}{2} a - \frac{14001}{2}\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-\frac{1}{2}a^{2}-\frac{7}{2}a+1\right){x}{y}+\left(\frac{1}{2}a^{3}-4a-\frac{5}{2}\right){y}={x}^{3}+\left(\frac{1}{2}a^{3}-3a-\frac{5}{2}\right){x}^{2}+\left(\frac{99}{2}a^{3}+\frac{63}{2}a^{2}-\frac{981}{2}a-642\right){x}+579a^{3}+\frac{517}{2}a^{2}-\frac{11149}{2}a-\frac{14001}{2}$ |
| 11.1-a2 |
11.1-a |
$2$ |
$3$ |
4.4.13625.1 |
$4$ |
$[4, 0]$ |
11.1 |
\( 11 \) |
\( 11^{3} \) |
$14.07605$ |
$(a+1)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1 |
$1$ |
\( 3 \) |
$2.272726829$ |
$124.5235809$ |
3.232729164 |
\( -\frac{878327}{2662} a^{3} + \frac{4430313}{2662} a^{2} + \frac{2880331}{2662} a - \frac{15877368}{1331} \) |
\( \bigl[\frac{1}{2} a^{3} - \frac{1}{2} a^{2} - \frac{7}{2} a + 1\) , \( \frac{1}{2} a^{3} - 3 a - \frac{5}{2}\) , \( \frac{1}{2} a^{3} - 4 a - \frac{5}{2}\) , \( 2 a^{3} + \frac{3}{2} a^{2} - \frac{31}{2} a - \frac{39}{2}\) , \( 2 a^{3} + \frac{7}{2} a^{2} - \frac{37}{2} a - \frac{57}{2}\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-\frac{1}{2}a^{2}-\frac{7}{2}a+1\right){x}{y}+\left(\frac{1}{2}a^{3}-4a-\frac{5}{2}\right){y}={x}^{3}+\left(\frac{1}{2}a^{3}-3a-\frac{5}{2}\right){x}^{2}+\left(2a^{3}+\frac{3}{2}a^{2}-\frac{31}{2}a-\frac{39}{2}\right){x}+2a^{3}+\frac{7}{2}a^{2}-\frac{37}{2}a-\frac{57}{2}$ |
| 11.1-b1 |
11.1-b |
$6$ |
$8$ |
4.4.13625.1 |
$4$ |
$[4, 0]$ |
11.1 |
\( 11 \) |
\( 11^{8} \) |
$14.07605$ |
$(a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 2 \) |
$1$ |
$56.37925566$ |
0.966008789 |
\( \frac{2496122044949307}{428717762} a^{3} - \frac{8382565157493245}{428717762} a^{2} - \frac{14342029089905557}{428717762} a + \frac{24638490312231527}{214358881} \) |
\( \bigl[\frac{1}{2} a^{2} - \frac{1}{2} a - \frac{7}{2}\) , \( \frac{1}{2} a^{3} - a^{2} - 2 a + \frac{7}{2}\) , \( 1\) , \( -5 a^{3} + \frac{43}{2} a^{2} + \frac{21}{2} a - \frac{159}{2}\) , \( \frac{55}{2} a^{3} - \frac{257}{2} a^{2} + \frac{55}{2} a + 314\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{2}-\frac{1}{2}a-\frac{7}{2}\right){x}{y}+{y}={x}^{3}+\left(\frac{1}{2}a^{3}-a^{2}-2a+\frac{7}{2}\right){x}^{2}+\left(-5a^{3}+\frac{43}{2}a^{2}+\frac{21}{2}a-\frac{159}{2}\right){x}+\frac{55}{2}a^{3}-\frac{257}{2}a^{2}+\frac{55}{2}a+314$ |
| 11.1-b2 |
11.1-b |
$6$ |
$8$ |
4.4.13625.1 |
$4$ |
$[4, 0]$ |
11.1 |
\( 11 \) |
\( 11^{2} \) |
$14.07605$ |
$(a+1)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$902.0680905$ |
0.966008789 |
\( -\frac{4686475935}{242} a^{3} - \frac{2359181875}{242} a^{2} + \frac{45643501173}{242} a + \frac{29014871499}{121} \) |
\( \bigl[\frac{1}{2} a^{3} - 3 a - \frac{5}{2}\) , \( -\frac{1}{2} a^{3} + \frac{1}{2} a^{2} + \frac{7}{2} a - 1\) , \( \frac{1}{2} a^{3} - \frac{1}{2} a^{2} - \frac{7}{2} a\) , \( 3 a^{3} + \frac{3}{2} a^{2} - \frac{49}{2} a - \frac{53}{2}\) , \( 2 a^{2} + 5 a\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-3a-\frac{5}{2}\right){x}{y}+\left(\frac{1}{2}a^{3}-\frac{1}{2}a^{2}-\frac{7}{2}a\right){y}={x}^{3}+\left(-\frac{1}{2}a^{3}+\frac{1}{2}a^{2}+\frac{7}{2}a-1\right){x}^{2}+\left(3a^{3}+\frac{3}{2}a^{2}-\frac{49}{2}a-\frac{53}{2}\right){x}+2a^{2}+5a$ |
| 11.1-b3 |
11.1-b |
$6$ |
$8$ |
4.4.13625.1 |
$4$ |
$[4, 0]$ |
11.1 |
\( 11 \) |
\( 11^{2} \) |
$14.07605$ |
$(a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2 \) |
$1$ |
$902.0680905$ |
0.966008789 |
\( -\frac{489143943}{242} a^{3} + \frac{2160117515}{242} a^{2} + \frac{170000891}{242} a - \frac{3144082808}{121} \) |
\( \bigl[\frac{1}{2} a^{3} - 3 a - \frac{5}{2}\) , \( \frac{1}{2} a^{3} - a^{2} - 3 a + \frac{5}{2}\) , \( \frac{1}{2} a^{3} - \frac{1}{2} a^{2} - \frac{5}{2} a\) , \( -9 a^{3} - \frac{29}{2} a^{2} + \frac{111}{2} a + \frac{177}{2}\) , \( \frac{49}{2} a^{3} + \frac{67}{2} a^{2} - \frac{301}{2} a - 218\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-3a-\frac{5}{2}\right){x}{y}+\left(\frac{1}{2}a^{3}-\frac{1}{2}a^{2}-\frac{5}{2}a\right){y}={x}^{3}+\left(\frac{1}{2}a^{3}-a^{2}-3a+\frac{5}{2}\right){x}^{2}+\left(-9a^{3}-\frac{29}{2}a^{2}+\frac{111}{2}a+\frac{177}{2}\right){x}+\frac{49}{2}a^{3}+\frac{67}{2}a^{2}-\frac{301}{2}a-218$ |
| 11.1-b4 |
11.1-b |
$6$ |
$8$ |
4.4.13625.1 |
$4$ |
$[4, 0]$ |
11.1 |
\( 11 \) |
\( 11 \) |
$14.07605$ |
$(a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$451.0340452$ |
0.966008789 |
\( \frac{22313123}{22} a^{3} - \frac{62310447}{11} a^{2} - \frac{40719953}{11} a + \frac{842529485}{22} \) |
\( \bigl[1\) , \( \frac{1}{2} a^{3} - \frac{1}{2} a^{2} - \frac{9}{2} a + 1\) , \( \frac{1}{2} a^{3} - 4 a - \frac{7}{2}\) , \( -3 a^{2} + 4 a + 20\) , \( \frac{3}{2} a^{3} - \frac{7}{2} a^{2} - \frac{15}{2} a + 5\bigr] \) |
${y}^2+{x}{y}+\left(\frac{1}{2}a^{3}-4a-\frac{7}{2}\right){y}={x}^{3}+\left(\frac{1}{2}a^{3}-\frac{1}{2}a^{2}-\frac{9}{2}a+1\right){x}^{2}+\left(-3a^{2}+4a+20\right){x}+\frac{3}{2}a^{3}-\frac{7}{2}a^{2}-\frac{15}{2}a+5$ |
| 11.1-b5 |
11.1-b |
$6$ |
$8$ |
4.4.13625.1 |
$4$ |
$[4, 0]$ |
11.1 |
\( 11 \) |
\( 11^{4} \) |
$14.07605$ |
$(a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2 \) |
$1$ |
$902.0680905$ |
0.966008789 |
\( -\frac{19682967}{29282} a^{3} - \frac{16698710}{14641} a^{2} + \frac{94849112}{14641} a + \frac{610818013}{29282} \) |
\( \bigl[1\) , \( -\frac{1}{2} a^{3} + 4 a + \frac{5}{2}\) , \( \frac{1}{2} a^{3} - \frac{1}{2} a^{2} - \frac{5}{2} a + 1\) , \( \frac{29}{2} a^{3} - 66 a^{2} - a + \frac{393}{2}\) , \( 101 a^{3} - \frac{899}{2} a^{2} - \frac{61}{2} a + \frac{2625}{2}\bigr] \) |
${y}^2+{x}{y}+\left(\frac{1}{2}a^{3}-\frac{1}{2}a^{2}-\frac{5}{2}a+1\right){y}={x}^{3}+\left(-\frac{1}{2}a^{3}+4a+\frac{5}{2}\right){x}^{2}+\left(\frac{29}{2}a^{3}-66a^{2}-a+\frac{393}{2}\right){x}+101a^{3}-\frac{899}{2}a^{2}-\frac{61}{2}a+\frac{2625}{2}$ |
| 11.1-b6 |
11.1-b |
$6$ |
$8$ |
4.4.13625.1 |
$4$ |
$[4, 0]$ |
11.1 |
\( 11 \) |
\( 11 \) |
$14.07605$ |
$(a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 1 \) |
$1$ |
$112.7585113$ |
0.966008789 |
\( -\frac{2344826527481875}{22} a^{3} + \frac{5173962366746867}{11} a^{2} + \frac{411334723993445}{11} a - \frac{30123117616811269}{22} \) |
\( \bigl[a + 1\) , \( -\frac{1}{2} a^{3} + 3 a + \frac{7}{2}\) , \( \frac{1}{2} a^{3} - 3 a - \frac{7}{2}\) , \( -\frac{63}{2} a^{3} - \frac{79}{2} a^{2} + \frac{427}{2} a + 305\) , \( \frac{547}{2} a^{3} + \frac{755}{2} a^{2} - \frac{3443}{2} a - 2510\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(\frac{1}{2}a^{3}-3a-\frac{7}{2}\right){y}={x}^{3}+\left(-\frac{1}{2}a^{3}+3a+\frac{7}{2}\right){x}^{2}+\left(-\frac{63}{2}a^{3}-\frac{79}{2}a^{2}+\frac{427}{2}a+305\right){x}+\frac{547}{2}a^{3}+\frac{755}{2}a^{2}-\frac{3443}{2}a-2510$ |
| 11.1-c1 |
11.1-c |
$6$ |
$8$ |
4.4.13625.1 |
$4$ |
$[4, 0]$ |
11.1 |
\( 11 \) |
\( 11^{2} \) |
$14.07605$ |
$(a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2 \) |
$1$ |
$1458.097494$ |
1.561450860 |
\( -\frac{489143943}{242} a^{3} + \frac{2160117515}{242} a^{2} + \frac{170000891}{242} a - \frac{3144082808}{121} \) |
\( \bigl[\frac{1}{2} a^{3} - \frac{1}{2} a^{2} - \frac{7}{2} a\) , \( -\frac{1}{2} a^{2} + \frac{3}{2} a + \frac{7}{2}\) , \( a\) , \( -3 a^{3} + \frac{9}{2} a^{2} + \frac{47}{2} a - \frac{25}{2}\) , \( -5 a^{3} + 13 a^{2} + 33 a - 67\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-\frac{1}{2}a^{2}-\frac{7}{2}a\right){x}{y}+a{y}={x}^{3}+\left(-\frac{1}{2}a^{2}+\frac{3}{2}a+\frac{7}{2}\right){x}^{2}+\left(-3a^{3}+\frac{9}{2}a^{2}+\frac{47}{2}a-\frac{25}{2}\right){x}-5a^{3}+13a^{2}+33a-67$ |
| 11.1-c2 |
11.1-c |
$6$ |
$8$ |
4.4.13625.1 |
$4$ |
$[4, 0]$ |
11.1 |
\( 11 \) |
\( 11 \) |
$14.07605$ |
$(a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 1 \) |
$1$ |
$182.2621868$ |
1.561450860 |
\( -\frac{2344826527481875}{22} a^{3} + \frac{5173962366746867}{11} a^{2} + \frac{411334723993445}{11} a - \frac{30123117616811269}{22} \) |
\( \bigl[\frac{1}{2} a^{3} - \frac{1}{2} a^{2} - \frac{7}{2} a\) , \( -\frac{1}{2} a^{2} + \frac{3}{2} a + \frac{7}{2}\) , \( a\) , \( 2 a^{3} - \frac{31}{2} a^{2} - \frac{3}{2} a + \frac{195}{2}\) , \( -19 a^{3} + \frac{117}{2} a^{2} + \frac{211}{2} a - \frac{625}{2}\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-\frac{1}{2}a^{2}-\frac{7}{2}a\right){x}{y}+a{y}={x}^{3}+\left(-\frac{1}{2}a^{2}+\frac{3}{2}a+\frac{7}{2}\right){x}^{2}+\left(2a^{3}-\frac{31}{2}a^{2}-\frac{3}{2}a+\frac{195}{2}\right){x}-19a^{3}+\frac{117}{2}a^{2}+\frac{211}{2}a-\frac{625}{2}$ |
| 11.1-c3 |
11.1-c |
$6$ |
$8$ |
4.4.13625.1 |
$4$ |
$[4, 0]$ |
11.1 |
\( 11 \) |
\( 11^{4} \) |
$14.07605$ |
$(a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2 \) |
$1$ |
$1458.097494$ |
1.561450860 |
\( -\frac{19682967}{29282} a^{3} - \frac{16698710}{14641} a^{2} + \frac{94849112}{14641} a + \frac{610818013}{29282} \) |
\( \bigl[\frac{1}{2} a^{3} - \frac{1}{2} a^{2} - \frac{5}{2} a\) , \( \frac{1}{2} a^{3} - \frac{1}{2} a^{2} - \frac{5}{2} a\) , \( \frac{1}{2} a^{3} - 3 a - \frac{5}{2}\) , \( \frac{15}{2} a^{3} + 4 a^{2} - 66 a - \frac{165}{2}\) , \( \frac{45}{2} a^{3} + \frac{27}{2} a^{2} - \frac{419}{2} a - 269\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-\frac{1}{2}a^{2}-\frac{5}{2}a\right){x}{y}+\left(\frac{1}{2}a^{3}-3a-\frac{5}{2}\right){y}={x}^{3}+\left(\frac{1}{2}a^{3}-\frac{1}{2}a^{2}-\frac{5}{2}a\right){x}^{2}+\left(\frac{15}{2}a^{3}+4a^{2}-66a-\frac{165}{2}\right){x}+\frac{45}{2}a^{3}+\frac{27}{2}a^{2}-\frac{419}{2}a-269$ |
| 11.1-c4 |
11.1-c |
$6$ |
$8$ |
4.4.13625.1 |
$4$ |
$[4, 0]$ |
11.1 |
\( 11 \) |
\( 11^{8} \) |
$14.07605$ |
$(a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$364.5243736$ |
1.561450860 |
\( \frac{2496122044949307}{428717762} a^{3} - \frac{8382565157493245}{428717762} a^{2} - \frac{14342029089905557}{428717762} a + \frac{24638490312231527}{214358881} \) |
\( \bigl[\frac{1}{2} a^{3} - \frac{1}{2} a^{2} - \frac{5}{2} a\) , \( \frac{1}{2} a^{3} - \frac{1}{2} a^{2} - \frac{5}{2} a\) , \( \frac{1}{2} a^{3} - 3 a - \frac{5}{2}\) , \( -\frac{5}{2} a^{3} - a^{2} + 29 a + \frac{75}{2}\) , \( 88 a^{3} + \frac{91}{2} a^{2} - \frac{1705}{2} a - \frac{2171}{2}\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-\frac{1}{2}a^{2}-\frac{5}{2}a\right){x}{y}+\left(\frac{1}{2}a^{3}-3a-\frac{5}{2}\right){y}={x}^{3}+\left(\frac{1}{2}a^{3}-\frac{1}{2}a^{2}-\frac{5}{2}a\right){x}^{2}+\left(-\frac{5}{2}a^{3}-a^{2}+29a+\frac{75}{2}\right){x}+88a^{3}+\frac{91}{2}a^{2}-\frac{1705}{2}a-\frac{2171}{2}$ |
| 11.1-c5 |
11.1-c |
$6$ |
$8$ |
4.4.13625.1 |
$4$ |
$[4, 0]$ |
11.1 |
\( 11 \) |
\( 11 \) |
$14.07605$ |
$(a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$729.0487473$ |
1.561450860 |
\( \frac{22313123}{22} a^{3} - \frac{62310447}{11} a^{2} - \frac{40719953}{11} a + \frac{842529485}{22} \) |
\( \bigl[\frac{1}{2} a^{3} - \frac{1}{2} a^{2} - \frac{5}{2} a\) , \( -a + 1\) , \( \frac{1}{2} a^{2} + \frac{1}{2} a - \frac{5}{2}\) , \( \frac{23}{2} a^{3} + 8 a^{2} - 117 a - \frac{303}{2}\) , \( -\frac{149}{2} a^{3} - 37 a^{2} + 712 a + \frac{1801}{2}\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-\frac{1}{2}a^{2}-\frac{5}{2}a\right){x}{y}+\left(\frac{1}{2}a^{2}+\frac{1}{2}a-\frac{5}{2}\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(\frac{23}{2}a^{3}+8a^{2}-117a-\frac{303}{2}\right){x}-\frac{149}{2}a^{3}-37a^{2}+712a+\frac{1801}{2}$ |
| 11.1-c6 |
11.1-c |
$6$ |
$8$ |
4.4.13625.1 |
$4$ |
$[4, 0]$ |
11.1 |
\( 11 \) |
\( 11^{2} \) |
$14.07605$ |
$(a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$364.5243736$ |
1.561450860 |
\( -\frac{4686475935}{242} a^{3} - \frac{2359181875}{242} a^{2} + \frac{45643501173}{242} a + \frac{29014871499}{121} \) |
\( \bigl[a\) , \( -\frac{1}{2} a^{3} + 4 a + \frac{7}{2}\) , \( 1\) , \( 2 a^{3} - \frac{27}{2} a^{2} + \frac{15}{2} a + \frac{101}{2}\) , \( \frac{21}{2} a^{3} - 50 a^{2} + 3 a + \frac{309}{2}\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+\left(-\frac{1}{2}a^{3}+4a+\frac{7}{2}\right){x}^{2}+\left(2a^{3}-\frac{27}{2}a^{2}+\frac{15}{2}a+\frac{101}{2}\right){x}+\frac{21}{2}a^{3}-50a^{2}+3a+\frac{309}{2}$ |
| 11.1-d1 |
11.1-d |
$2$ |
$3$ |
4.4.13625.1 |
$4$ |
$[4, 0]$ |
11.1 |
\( 11 \) |
\( 11^{3} \) |
$14.07605$ |
$(a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 3 \) |
$0.022444057$ |
$1166.899218$ |
2.692450388 |
\( -\frac{878327}{2662} a^{3} + \frac{4430313}{2662} a^{2} + \frac{2880331}{2662} a - \frac{15877368}{1331} \) |
\( \bigl[\frac{1}{2} a^{3} - 3 a - \frac{7}{2}\) , \( -\frac{1}{2} a^{3} + a^{2} + 3 a - \frac{5}{2}\) , \( \frac{1}{2} a^{3} - \frac{1}{2} a^{2} - \frac{5}{2} a\) , \( \frac{15}{2} a^{3} - \frac{67}{2} a^{2} + \frac{1}{2} a + 100\) , \( \frac{297}{2} a^{3} - \frac{1305}{2} a^{2} - \frac{111}{2} a + 1905\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-3a-\frac{7}{2}\right){x}{y}+\left(\frac{1}{2}a^{3}-\frac{1}{2}a^{2}-\frac{5}{2}a\right){y}={x}^{3}+\left(-\frac{1}{2}a^{3}+a^{2}+3a-\frac{5}{2}\right){x}^{2}+\left(\frac{15}{2}a^{3}-\frac{67}{2}a^{2}+\frac{1}{2}a+100\right){x}+\frac{297}{2}a^{3}-\frac{1305}{2}a^{2}-\frac{111}{2}a+1905$ |
| 11.1-d2 |
11.1-d |
$2$ |
$3$ |
4.4.13625.1 |
$4$ |
$[4, 0]$ |
11.1 |
\( 11 \) |
\( 11 \) |
$14.07605$ |
$(a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 1 \) |
$0.067332172$ |
$1166.899218$ |
2.692450388 |
\( -\frac{908833236673}{22} a^{3} + \frac{1804251327861}{11} a^{2} + \frac{2358050011412}{11} a - \frac{22402232453999}{22} \) |
\( \bigl[\frac{1}{2} a^{3} - \frac{1}{2} a^{2} - \frac{7}{2} a + 1\) , \( a\) , \( \frac{1}{2} a^{2} - \frac{1}{2} a - \frac{7}{2}\) , \( -483 a^{3} + \frac{4261}{2} a^{2} + \frac{371}{2} a - \frac{12475}{2}\) , \( -\frac{114973}{2} a^{3} + \frac{507405}{2} a^{2} + \frac{40239}{2} a - 738444\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-\frac{1}{2}a^{2}-\frac{7}{2}a+1\right){x}{y}+\left(\frac{1}{2}a^{2}-\frac{1}{2}a-\frac{7}{2}\right){y}={x}^{3}+a{x}^{2}+\left(-483a^{3}+\frac{4261}{2}a^{2}+\frac{371}{2}a-\frac{12475}{2}\right){x}-\frac{114973}{2}a^{3}+\frac{507405}{2}a^{2}+\frac{40239}{2}a-738444$ |
| 11.2-a1 |
11.2-a |
$2$ |
$3$ |
4.4.13625.1 |
$4$ |
$[4, 0]$ |
11.2 |
\( 11 \) |
\( 11 \) |
$14.07605$ |
$(1/2a^3-3/2a^2-5/2a+7)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.2 |
$9$ |
\( 1 \) |
$6.818180487$ |
$1.537328160$ |
3.232729164 |
\( \frac{908833236673}{22} a^{3} + \frac{80182085973}{2} a^{2} - \frac{836964147659}{2} a - \frac{7493231506063}{11} \) |
\( \bigl[\frac{1}{2} a^{3} - 4 a - \frac{5}{2}\) , \( -\frac{1}{2} a^{3} + 5 a + \frac{5}{2}\) , \( \frac{1}{2} a^{3} - \frac{1}{2} a^{2} - \frac{7}{2} a + 1\) , \( -51 a^{3} + \frac{347}{2} a^{2} + \frac{605}{2} a - \frac{2001}{2}\) , \( -\frac{1073}{2} a^{3} + 1841 a^{2} + 3092 a - \frac{21597}{2}\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-4a-\frac{5}{2}\right){x}{y}+\left(\frac{1}{2}a^{3}-\frac{1}{2}a^{2}-\frac{7}{2}a+1\right){y}={x}^{3}+\left(-\frac{1}{2}a^{3}+5a+\frac{5}{2}\right){x}^{2}+\left(-51a^{3}+\frac{347}{2}a^{2}+\frac{605}{2}a-\frac{2001}{2}\right){x}-\frac{1073}{2}a^{3}+1841a^{2}+3092a-\frac{21597}{2}$ |
| 11.2-a2 |
11.2-a |
$2$ |
$3$ |
4.4.13625.1 |
$4$ |
$[4, 0]$ |
11.2 |
\( 11 \) |
\( 11^{3} \) |
$14.07605$ |
$(1/2a^3-3/2a^2-5/2a+7)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1 |
$1$ |
\( 3 \) |
$2.272726829$ |
$124.5235809$ |
3.232729164 |
\( \frac{878327}{2662} a^{3} + \frac{81606}{121} a^{2} - \frac{37628}{11} a - \frac{25322419}{2662} \) |
\( \bigl[\frac{1}{2} a^{3} - 4 a - \frac{5}{2}\) , \( -\frac{1}{2} a^{3} + 5 a + \frac{5}{2}\) , \( \frac{1}{2} a^{3} - \frac{1}{2} a^{2} - \frac{7}{2} a + 1\) , \( -\frac{7}{2} a^{3} + a^{2} + 30 a + \frac{39}{2}\) , \( -\frac{9}{2} a^{3} + 42 a + \frac{75}{2}\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-4a-\frac{5}{2}\right){x}{y}+\left(\frac{1}{2}a^{3}-\frac{1}{2}a^{2}-\frac{7}{2}a+1\right){y}={x}^{3}+\left(-\frac{1}{2}a^{3}+5a+\frac{5}{2}\right){x}^{2}+\left(-\frac{7}{2}a^{3}+a^{2}+30a+\frac{39}{2}\right){x}-\frac{9}{2}a^{3}+42a+\frac{75}{2}$ |
| 11.2-b1 |
11.2-b |
$6$ |
$8$ |
4.4.13625.1 |
$4$ |
$[4, 0]$ |
11.2 |
\( 11 \) |
\( 11^{8} \) |
$14.07605$ |
$(1/2a^3-3/2a^2-5/2a+7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 2 \) |
$1$ |
$56.37925566$ |
0.966008789 |
\( -\frac{2496122044949307}{428717762} a^{3} - \frac{40645410120242}{19487171} a^{2} + \frac{97598319297703}{1771561} a + \frac{29048508422013559}{428717762} \) |
\( \bigl[\frac{1}{2} a^{2} - \frac{1}{2} a - \frac{7}{2}\) , \( -\frac{1}{2} a^{3} + \frac{1}{2} a^{2} + \frac{5}{2} a + 1\) , \( 1\) , \( 5 a^{3} + \frac{13}{2} a^{2} - \frac{77}{2} a - \frac{105}{2}\) , \( -\frac{55}{2} a^{3} - 46 a^{2} + 147 a + \frac{481}{2}\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{2}-\frac{1}{2}a-\frac{7}{2}\right){x}{y}+{y}={x}^{3}+\left(-\frac{1}{2}a^{3}+\frac{1}{2}a^{2}+\frac{5}{2}a+1\right){x}^{2}+\left(5a^{3}+\frac{13}{2}a^{2}-\frac{77}{2}a-\frac{105}{2}\right){x}-\frac{55}{2}a^{3}-46a^{2}+147a+\frac{481}{2}$ |
| 11.2-b2 |
11.2-b |
$6$ |
$8$ |
4.4.13625.1 |
$4$ |
$[4, 0]$ |
11.2 |
\( 11 \) |
\( 11^{2} \) |
$14.07605$ |
$(1/2a^3-3/2a^2-5/2a+7)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2 \) |
$1$ |
$902.0680905$ |
0.966008789 |
\( \frac{489143943}{242} a^{3} + \frac{31485713}{11} a^{2} - 12490926 a - \frac{4447191153}{242} \) |
\( \bigl[\frac{1}{2} a^{3} - \frac{1}{2} a^{2} - \frac{5}{2} a\) , \( \frac{1}{2} a^{3} - 3 a - \frac{5}{2}\) , \( a + 1\) , \( 13 a^{3} - 45 a^{2} - 15 a + 119\) , \( -60 a^{3} + 291 a^{2} - 5 a - 873\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-\frac{1}{2}a^{2}-\frac{5}{2}a\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(\frac{1}{2}a^{3}-3a-\frac{5}{2}\right){x}^{2}+\left(13a^{3}-45a^{2}-15a+119\right){x}-60a^{3}+291a^{2}-5a-873$ |
| 11.2-b3 |
11.2-b |
$6$ |
$8$ |
4.4.13625.1 |
$4$ |
$[4, 0]$ |
11.2 |
\( 11 \) |
\( 11^{2} \) |
$14.07605$ |
$(1/2a^3-3/2a^2-5/2a+7)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$902.0680905$ |
0.966008789 |
\( \frac{4686475935}{242} a^{3} - \frac{746300440}{11} a^{2} - 111015329 a + \frac{96627586361}{242} \) |
\( \bigl[\frac{1}{2} a^{3} - \frac{1}{2} a^{2} - \frac{5}{2} a\) , \( a + 1\) , \( a + 1\) , \( -a^{3} + \frac{17}{2} a^{2} + \frac{13}{2} a - \frac{91}{2}\) , \( \frac{13}{2} a^{3} - \frac{23}{2} a^{2} - \frac{77}{2} a + 66\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-\frac{1}{2}a^{2}-\frac{5}{2}a\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-a^{3}+\frac{17}{2}a^{2}+\frac{13}{2}a-\frac{91}{2}\right){x}+\frac{13}{2}a^{3}-\frac{23}{2}a^{2}-\frac{77}{2}a+66$ |
| 11.2-b4 |
11.2-b |
$6$ |
$8$ |
4.4.13625.1 |
$4$ |
$[4, 0]$ |
11.2 |
\( 11 \) |
\( 11 \) |
$14.07605$ |
$(1/2a^3-3/2a^2-5/2a+7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 1 \) |
$1$ |
$112.7585113$ |
0.966008789 |
\( \frac{2344826527481875}{22} a^{3} + \frac{301222286458919}{2} a^{2} - \frac{1316730848411703}{2} a - \frac{10648674981406260}{11} \) |
\( \bigl[a\) , \( \frac{1}{2} a^{3} - 4 a - \frac{7}{2}\) , \( a + 1\) , \( 30 a^{3} - \frac{257}{2} a^{2} - \frac{67}{2} a + \frac{843}{2}\) , \( -265 a^{3} + \frac{2313}{2} a^{2} + \frac{357}{2} a - \frac{7087}{2}\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(\frac{1}{2}a^{3}-4a-\frac{7}{2}\right){x}^{2}+\left(30a^{3}-\frac{257}{2}a^{2}-\frac{67}{2}a+\frac{843}{2}\right){x}-265a^{3}+\frac{2313}{2}a^{2}+\frac{357}{2}a-\frac{7087}{2}$ |
| 11.2-b5 |
11.2-b |
$6$ |
$8$ |
4.4.13625.1 |
$4$ |
$[4, 0]$ |
11.2 |
\( 11 \) |
\( 11^{4} \) |
$14.07605$ |
$(1/2a^3-3/2a^2-5/2a+7)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2 \) |
$1$ |
$902.0680905$ |
0.966008789 |
\( \frac{19682967}{29282} a^{3} - \frac{8404211}{2662} a^{2} - \frac{527723}{242} a + \frac{373717925}{14641} \) |
\( \bigl[1\) , \( \frac{1}{2} a^{3} - 4 a - \frac{9}{2}\) , \( \frac{1}{2} a^{3} - \frac{1}{2} a^{2} - \frac{5}{2} a\) , \( -16 a^{3} - 21 a^{2} + 101 a + 144\) , \( -\frac{221}{2} a^{3} - \frac{315}{2} a^{2} + \frac{1363}{2} a + 1005\bigr] \) |
${y}^2+{x}{y}+\left(\frac{1}{2}a^{3}-\frac{1}{2}a^{2}-\frac{5}{2}a\right){y}={x}^{3}+\left(\frac{1}{2}a^{3}-4a-\frac{9}{2}\right){x}^{2}+\left(-16a^{3}-21a^{2}+101a+144\right){x}-\frac{221}{2}a^{3}-\frac{315}{2}a^{2}+\frac{1363}{2}a+1005$ |
| 11.2-b6 |
11.2-b |
$6$ |
$8$ |
4.4.13625.1 |
$4$ |
$[4, 0]$ |
11.2 |
\( 11 \) |
\( 11 \) |
$14.07605$ |
$(1/2a^3-3/2a^2-5/2a+7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$451.0340452$ |
0.966008789 |
\( -\frac{22313123}{22} a^{3} - \frac{5243775}{2} a^{2} + \frac{23976575}{2} a + \frac{329390904}{11} \) |
\( \bigl[1\) , \( -\frac{1}{2} a^{3} + a^{2} + 4 a - \frac{7}{2}\) , \( \frac{1}{2} a^{3} - \frac{1}{2} a^{2} - \frac{7}{2} a\) , \( -\frac{1}{2} a^{3} - 2 a^{2} + 5 a + \frac{35}{2}\) , \( -a^{3} + 6 a\bigr] \) |
${y}^2+{x}{y}+\left(\frac{1}{2}a^{3}-\frac{1}{2}a^{2}-\frac{7}{2}a\right){y}={x}^{3}+\left(-\frac{1}{2}a^{3}+a^{2}+4a-\frac{7}{2}\right){x}^{2}+\left(-\frac{1}{2}a^{3}-2a^{2}+5a+\frac{35}{2}\right){x}-a^{3}+6a$ |
| 11.2-c1 |
11.2-c |
$6$ |
$8$ |
4.4.13625.1 |
$4$ |
$[4, 0]$ |
11.2 |
\( 11 \) |
\( 11^{2} \) |
$14.07605$ |
$(1/2a^3-3/2a^2-5/2a+7)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2 \) |
$1$ |
$1458.097494$ |
1.561450860 |
\( \frac{489143943}{242} a^{3} + \frac{31485713}{11} a^{2} - 12490926 a - \frac{4447191153}{242} \) |
\( \bigl[\frac{1}{2} a^{3} - 4 a - \frac{7}{2}\) , \( \frac{1}{2} a^{3} - a^{2} - 2 a + \frac{9}{2}\) , \( \frac{1}{2} a^{2} + \frac{1}{2} a - \frac{5}{2}\) , \( \frac{1}{2} a^{3} - 3 a + \frac{5}{2}\) , \( 7 a^{3} + \frac{7}{2} a^{2} - \frac{133}{2} a - \frac{167}{2}\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-4a-\frac{7}{2}\right){x}{y}+\left(\frac{1}{2}a^{2}+\frac{1}{2}a-\frac{5}{2}\right){y}={x}^{3}+\left(\frac{1}{2}a^{3}-a^{2}-2a+\frac{9}{2}\right){x}^{2}+\left(\frac{1}{2}a^{3}-3a+\frac{5}{2}\right){x}+7a^{3}+\frac{7}{2}a^{2}-\frac{133}{2}a-\frac{167}{2}$ |
| 11.2-c2 |
11.2-c |
$6$ |
$8$ |
4.4.13625.1 |
$4$ |
$[4, 0]$ |
11.2 |
\( 11 \) |
\( 11 \) |
$14.07605$ |
$(1/2a^3-3/2a^2-5/2a+7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 1 \) |
$1$ |
$182.2621868$ |
1.561450860 |
\( \frac{2344826527481875}{22} a^{3} + \frac{301222286458919}{2} a^{2} - \frac{1316730848411703}{2} a - \frac{10648674981406260}{11} \) |
\( \bigl[\frac{1}{2} a^{3} - 4 a - \frac{7}{2}\) , \( \frac{1}{2} a^{3} - a^{2} - 2 a + \frac{9}{2}\) , \( \frac{1}{2} a^{2} + \frac{1}{2} a - \frac{5}{2}\) , \( -\frac{9}{2} a^{3} - 5 a^{2} + 47 a + \frac{145}{2}\) , \( 6 a^{3} + 2 a^{2} - 58 a - 70\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-4a-\frac{7}{2}\right){x}{y}+\left(\frac{1}{2}a^{2}+\frac{1}{2}a-\frac{5}{2}\right){y}={x}^{3}+\left(\frac{1}{2}a^{3}-a^{2}-2a+\frac{9}{2}\right){x}^{2}+\left(-\frac{9}{2}a^{3}-5a^{2}+47a+\frac{145}{2}\right){x}+6a^{3}+2a^{2}-58a-70$ |
*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.
