| 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 |
| 5.1-a1 |
5.1-a |
$2$ |
$3$ |
4.4.12400.1 |
$4$ |
$[4, 0]$ |
5.1 |
\( 5 \) |
\( - 5^{9} \) |
$12.16804$ |
$(1/2a^3-1/2a^2-7/2a+5/2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 1 \) |
$1$ |
$217.0163666$ |
1.948864504 |
\( \frac{102109}{6250} a^{3} - \frac{1063917}{3125} a^{2} - \frac{972919}{6250} a + \frac{8947842}{3125} \) |
\( \bigl[\frac{1}{2} a^{3} - \frac{7}{2} a\) , \( \frac{1}{2} a^{3} - \frac{5}{2} a + 1\) , \( \frac{1}{2} a^{2} + a - \frac{5}{2}\) , \( \frac{1}{2} a^{3} - \frac{7}{2} a + 8\) , \( a^{3} - 2 a^{2} - 4 a + 9\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-\frac{7}{2}a\right){x}{y}+\left(\frac{1}{2}a^{2}+a-\frac{5}{2}\right){y}={x}^{3}+\left(\frac{1}{2}a^{3}-\frac{5}{2}a+1\right){x}^{2}+\left(\frac{1}{2}a^{3}-\frac{7}{2}a+8\right){x}+a^{3}-2a^{2}-4a+9$ |
| 5.1-a2 |
5.1-a |
$2$ |
$3$ |
4.4.12400.1 |
$4$ |
$[4, 0]$ |
5.1 |
\( 5 \) |
\( - 5^{3} \) |
$12.16804$ |
$(1/2a^3-1/2a^2-7/2a+5/2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 1 \) |
$1$ |
$217.0163666$ |
1.948864504 |
\( \frac{462073577}{25} a^{3} - \frac{1794849939}{50} a^{2} - \frac{3800943272}{25} a + \frac{14755379619}{50} \) |
\( \bigl[\frac{1}{2} a^{2} + a - \frac{7}{2}\) , \( \frac{1}{2} a^{3} - \frac{5}{2} a - 1\) , \( a + 1\) , \( \frac{3}{2} a^{3} + \frac{7}{2} a^{2} - \frac{21}{2} a - \frac{41}{2}\) , \( \frac{19}{2} a^{3} + 25 a^{2} - \frac{85}{2} a - 106\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{2}+a-\frac{7}{2}\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(\frac{1}{2}a^{3}-\frac{5}{2}a-1\right){x}^{2}+\left(\frac{3}{2}a^{3}+\frac{7}{2}a^{2}-\frac{21}{2}a-\frac{41}{2}\right){x}+\frac{19}{2}a^{3}+25a^{2}-\frac{85}{2}a-106$ |
| 5.1-b1 |
5.1-b |
$2$ |
$3$ |
4.4.12400.1 |
$4$ |
$[4, 0]$ |
5.1 |
\( 5 \) |
\( - 5^{9} \) |
$12.16804$ |
$(1/2a^3-1/2a^2-7/2a+5/2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 3^{2} \) |
$0.036476401$ |
$185.1864460$ |
2.183799909 |
\( \frac{102109}{6250} a^{3} - \frac{1063917}{3125} a^{2} - \frac{972919}{6250} a + \frac{8947842}{3125} \) |
\( \bigl[1\) , \( a - 1\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{5}{2} a - \frac{5}{2}\) , \( -\frac{1}{2} a^{3} + \frac{5}{2} a + 3\) , \( -2 a^{2} + 7\bigr] \) |
${y}^2+{x}{y}+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-\frac{5}{2}a-\frac{5}{2}\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-\frac{1}{2}a^{3}+\frac{5}{2}a+3\right){x}-2a^{2}+7$ |
| 5.1-b2 |
5.1-b |
$2$ |
$3$ |
4.4.12400.1 |
$4$ |
$[4, 0]$ |
5.1 |
\( 5 \) |
\( - 5^{3} \) |
$12.16804$ |
$(1/2a^3-1/2a^2-7/2a+5/2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 3 \) |
$0.109429204$ |
$185.1864460$ |
2.183799909 |
\( \frac{462073577}{25} a^{3} - \frac{1794849939}{50} a^{2} - \frac{3800943272}{25} a + \frac{14755379619}{50} \) |
\( \bigl[\frac{1}{2} a^{2} + a - \frac{5}{2}\) , \( -\frac{1}{2} a^{3} + \frac{9}{2} a + 1\) , \( \frac{1}{2} a^{2} - \frac{7}{2}\) , \( \frac{5}{2} a^{3} + \frac{11}{2} a^{2} - \frac{35}{2} a - \frac{73}{2}\) , \( -a^{3} + \frac{1}{2} a^{2} + 19 a + \frac{53}{2}\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{2}+a-\frac{5}{2}\right){x}{y}+\left(\frac{1}{2}a^{2}-\frac{7}{2}\right){y}={x}^{3}+\left(-\frac{1}{2}a^{3}+\frac{9}{2}a+1\right){x}^{2}+\left(\frac{5}{2}a^{3}+\frac{11}{2}a^{2}-\frac{35}{2}a-\frac{73}{2}\right){x}-a^{3}+\frac{1}{2}a^{2}+19a+\frac{53}{2}$ |
| 5.2-a1 |
5.2-a |
$2$ |
$3$ |
4.4.12400.1 |
$4$ |
$[4, 0]$ |
5.2 |
\( 5 \) |
\( - 5^{9} \) |
$12.16804$ |
$(-1/2a^3-3/2a^2+3/2a+11/2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 1 \) |
$1$ |
$217.0163666$ |
1.948864504 |
\( -\frac{102109}{6250} a^{3} - \frac{1063917}{3125} a^{2} + \frac{972919}{6250} a + \frac{8947842}{3125} \) |
\( \bigl[\frac{1}{2} a^{3} - \frac{7}{2} a\) , \( -\frac{1}{2} a^{3} + \frac{5}{2} a + 1\) , \( \frac{1}{2} a^{2} + a - \frac{5}{2}\) , \( -\frac{1}{2} a^{3} + \frac{5}{2} a + 8\) , \( -\frac{3}{2} a^{3} - 2 a^{2} + \frac{13}{2} a + 9\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-\frac{7}{2}a\right){x}{y}+\left(\frac{1}{2}a^{2}+a-\frac{5}{2}\right){y}={x}^{3}+\left(-\frac{1}{2}a^{3}+\frac{5}{2}a+1\right){x}^{2}+\left(-\frac{1}{2}a^{3}+\frac{5}{2}a+8\right){x}-\frac{3}{2}a^{3}-2a^{2}+\frac{13}{2}a+9$ |
| 5.2-a2 |
5.2-a |
$2$ |
$3$ |
4.4.12400.1 |
$4$ |
$[4, 0]$ |
5.2 |
\( 5 \) |
\( - 5^{3} \) |
$12.16804$ |
$(-1/2a^3-3/2a^2+3/2a+11/2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 1 \) |
$1$ |
$217.0163666$ |
1.948864504 |
\( -\frac{462073577}{25} a^{3} - \frac{1794849939}{50} a^{2} + \frac{3800943272}{25} a + \frac{14755379619}{50} \) |
\( \bigl[\frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{7}{2} a - \frac{5}{2}\) , \( \frac{1}{2} a^{3} - \frac{7}{2} a - 1\) , \( \frac{1}{2} a^{2} - \frac{7}{2}\) , \( -\frac{13}{2} a^{3} + 14 a^{2} + \frac{107}{2} a - 112\) , \( -\frac{91}{2} a^{3} + 89 a^{2} + \frac{747}{2} a - 728\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-\frac{7}{2}a-\frac{5}{2}\right){x}{y}+\left(\frac{1}{2}a^{2}-\frac{7}{2}\right){y}={x}^{3}+\left(\frac{1}{2}a^{3}-\frac{7}{2}a-1\right){x}^{2}+\left(-\frac{13}{2}a^{3}+14a^{2}+\frac{107}{2}a-112\right){x}-\frac{91}{2}a^{3}+89a^{2}+\frac{747}{2}a-728$ |
| 5.2-b1 |
5.2-b |
$2$ |
$3$ |
4.4.12400.1 |
$4$ |
$[4, 0]$ |
5.2 |
\( 5 \) |
\( - 5^{9} \) |
$12.16804$ |
$(-1/2a^3-3/2a^2+3/2a+11/2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 3^{2} \) |
$0.036476401$ |
$185.1864460$ |
2.183799909 |
\( -\frac{102109}{6250} a^{3} - \frac{1063917}{3125} a^{2} + \frac{972919}{6250} a + \frac{8947842}{3125} \) |
\( \bigl[1\) , \( -a - 1\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{5}{2} a - \frac{5}{2}\) , \( 3\) , \( -\frac{1}{2} a^{3} - 2 a^{2} + \frac{3}{2} a + 7\bigr] \) |
${y}^2+{x}{y}+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-\frac{5}{2}a-\frac{5}{2}\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+3{x}-\frac{1}{2}a^{3}-2a^{2}+\frac{3}{2}a+7$ |
| 5.2-b2 |
5.2-b |
$2$ |
$3$ |
4.4.12400.1 |
$4$ |
$[4, 0]$ |
5.2 |
\( 5 \) |
\( - 5^{3} \) |
$12.16804$ |
$(-1/2a^3-3/2a^2+3/2a+11/2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 3 \) |
$0.109429204$ |
$185.1864460$ |
2.183799909 |
\( -\frac{462073577}{25} a^{3} - \frac{1794849939}{50} a^{2} + \frac{3800943272}{25} a + \frac{14755379619}{50} \) |
\( \bigl[\frac{1}{2} a^{2} + a - \frac{5}{2}\) , \( a + 1\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{5}{2} a - \frac{5}{2}\) , \( -\frac{5}{2} a^{3} + 6 a^{2} + \frac{45}{2} a - 43\) , \( 7 a^{3} - \frac{19}{2} a^{2} - 62 a + \frac{211}{2}\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{2}+a-\frac{5}{2}\right){x}{y}+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-\frac{5}{2}a-\frac{5}{2}\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-\frac{5}{2}a^{3}+6a^{2}+\frac{45}{2}a-43\right){x}+7a^{3}-\frac{19}{2}a^{2}-62a+\frac{211}{2}$ |
| 9.1-a1 |
9.1-a |
$4$ |
$6$ |
4.4.12400.1 |
$4$ |
$[4, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{8} \) |
$13.09573$ |
$(1/2a^2+a-1/2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$1$ |
$365.8824173$ |
1.642860551 |
\( \frac{8025637785355}{81} a^{3} + \frac{46061580093845}{162} a^{2} - \frac{30209462949730}{81} a - \frac{57788918959565}{54} \) |
\( \bigl[\frac{1}{2} a^{2} - \frac{5}{2}\) , \( -\frac{1}{2} a^{3} + \frac{1}{2} a^{2} + \frac{5}{2} a - \frac{9}{2}\) , \( a\) , \( -\frac{37}{2} a^{3} + 35 a^{2} + \frac{301}{2} a - 289\) , \( -102 a^{3} + \frac{403}{2} a^{2} + 846 a - \frac{3309}{2}\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{2}-\frac{5}{2}\right){x}{y}+a{y}={x}^{3}+\left(-\frac{1}{2}a^{3}+\frac{1}{2}a^{2}+\frac{5}{2}a-\frac{9}{2}\right){x}^{2}+\left(-\frac{37}{2}a^{3}+35a^{2}+\frac{301}{2}a-289\right){x}-102a^{3}+\frac{403}{2}a^{2}+846a-\frac{3309}{2}$ |
| 9.1-a2 |
9.1-a |
$4$ |
$6$ |
4.4.12400.1 |
$4$ |
$[4, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{4} \) |
$13.09573$ |
$(1/2a^2+a-1/2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$1$ |
$365.8824173$ |
1.642860551 |
\( -\frac{29105995}{9} a^{3} + \frac{173474645}{18} a^{2} + \frac{36523615}{3} a - \frac{653017795}{18} \) |
\( \bigl[\frac{1}{2} a^{2} - \frac{5}{2}\) , \( -\frac{1}{2} a^{3} + \frac{1}{2} a^{2} + \frac{5}{2} a - \frac{9}{2}\) , \( a\) , \( -a^{3} + \frac{5}{2} a^{2} + 8 a - \frac{33}{2}\) , \( -\frac{1}{2} a^{3} + \frac{11}{2} a - 8\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{2}-\frac{5}{2}\right){x}{y}+a{y}={x}^{3}+\left(-\frac{1}{2}a^{3}+\frac{1}{2}a^{2}+\frac{5}{2}a-\frac{9}{2}\right){x}^{2}+\left(-a^{3}+\frac{5}{2}a^{2}+8a-\frac{33}{2}\right){x}-\frac{1}{2}a^{3}+\frac{11}{2}a-8$ |
| 9.1-a3 |
9.1-a |
$4$ |
$6$ |
4.4.12400.1 |
$4$ |
$[4, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{24} \) |
$13.09573$ |
$(1/2a^2+a-1/2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$1$ |
$365.8824173$ |
1.642860551 |
\( -\frac{18006809585}{1062882} a^{3} + \frac{25720340240}{531441} a^{2} + \frac{70788991685}{1062882} a - \frac{30982326505}{177147} \) |
\( \bigl[\frac{1}{2} a^{2} + a - \frac{7}{2}\) , \( -\frac{1}{2} a^{3} + \frac{9}{2} a\) , \( \frac{1}{2} a^{3} - \frac{5}{2} a + 1\) , \( 7 a^{3} + \frac{13}{2} a^{2} - 53 a - \frac{143}{2}\) , \( 31 a^{3} + \frac{139}{2} a^{2} - 265 a - \frac{1101}{2}\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{2}+a-\frac{7}{2}\right){x}{y}+\left(\frac{1}{2}a^{3}-\frac{5}{2}a+1\right){y}={x}^{3}+\left(-\frac{1}{2}a^{3}+\frac{9}{2}a\right){x}^{2}+\left(7a^{3}+\frac{13}{2}a^{2}-53a-\frac{143}{2}\right){x}+31a^{3}+\frac{139}{2}a^{2}-265a-\frac{1101}{2}$ |
| 9.1-a4 |
9.1-a |
$4$ |
$6$ |
4.4.12400.1 |
$4$ |
$[4, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{12} \) |
$13.09573$ |
$(1/2a^2+a-1/2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$1$ |
$365.8824173$ |
1.642860551 |
\( \frac{51065}{243} a^{3} + \frac{776305}{1458} a^{2} - \frac{876295}{729} a - \frac{1624405}{1458} \) |
\( \bigl[\frac{1}{2} a^{2} + a - \frac{7}{2}\) , \( -\frac{1}{2} a^{3} + \frac{9}{2} a\) , \( \frac{1}{2} a^{3} - \frac{5}{2} a + 1\) , \( -\frac{1}{2} a^{3} - \frac{7}{2} a^{2} + \frac{9}{2} a + \frac{47}{2}\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{9}{2} a - \frac{17}{2}\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{2}+a-\frac{7}{2}\right){x}{y}+\left(\frac{1}{2}a^{3}-\frac{5}{2}a+1\right){y}={x}^{3}+\left(-\frac{1}{2}a^{3}+\frac{9}{2}a\right){x}^{2}+\left(-\frac{1}{2}a^{3}-\frac{7}{2}a^{2}+\frac{9}{2}a+\frac{47}{2}\right){x}+\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-\frac{9}{2}a-\frac{17}{2}$ |
| 9.1-b1 |
9.1-b |
$4$ |
$6$ |
4.4.12400.1 |
$4$ |
$[4, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{8} \) |
$13.09573$ |
$(1/2a^2+a-1/2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \) |
$0.153200176$ |
$525.2209558$ |
2.890350157 |
\( \frac{8025637785355}{81} a^{3} + \frac{46061580093845}{162} a^{2} - \frac{30209462949730}{81} a - \frac{57788918959565}{54} \) |
\( \bigl[a\) , \( -\frac{1}{2} a^{3} - \frac{1}{2} a^{2} + \frac{9}{2} a + \frac{5}{2}\) , \( 0\) , \( -8 a^{3} + 7 a^{2} + 64 a - 78\) , \( \frac{79}{2} a^{3} - 72 a^{2} - \frac{631}{2} a + 604\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-\frac{1}{2}a^{3}-\frac{1}{2}a^{2}+\frac{9}{2}a+\frac{5}{2}\right){x}^{2}+\left(-8a^{3}+7a^{2}+64a-78\right){x}+\frac{79}{2}a^{3}-72a^{2}-\frac{631}{2}a+604$ |
| 9.1-b2 |
9.1-b |
$4$ |
$6$ |
4.4.12400.1 |
$4$ |
$[4, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{4} \) |
$13.09573$ |
$(1/2a^2+a-1/2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$0.306400352$ |
$525.2209558$ |
2.890350157 |
\( -\frac{29105995}{9} a^{3} + \frac{173474645}{18} a^{2} + \frac{36523615}{3} a - \frac{653017795}{18} \) |
\( \bigl[\frac{1}{2} a^{3} - \frac{7}{2} a\) , \( -\frac{1}{2} a^{2} - a + \frac{7}{2}\) , \( 1\) , \( -\frac{5}{2} a^{3} + \frac{9}{2} a^{2} + \frac{41}{2} a - \frac{71}{2}\) , \( \frac{7}{2} a^{3} - 7 a^{2} - \frac{57}{2} a + 56\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-\frac{7}{2}a\right){x}{y}+{y}={x}^{3}+\left(-\frac{1}{2}a^{2}-a+\frac{7}{2}\right){x}^{2}+\left(-\frac{5}{2}a^{3}+\frac{9}{2}a^{2}+\frac{41}{2}a-\frac{71}{2}\right){x}+\frac{7}{2}a^{3}-7a^{2}-\frac{57}{2}a+56$ |
| 9.1-b3 |
9.1-b |
$4$ |
$6$ |
4.4.12400.1 |
$4$ |
$[4, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{24} \) |
$13.09573$ |
$(1/2a^2+a-1/2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \cdot 3 \) |
$0.051066725$ |
$525.2209558$ |
2.890350157 |
\( -\frac{18006809585}{1062882} a^{3} + \frac{25720340240}{531441} a^{2} + \frac{70788991685}{1062882} a - \frac{30982326505}{177147} \) |
\( \bigl[\frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{5}{2} a - \frac{7}{2}\) , \( \frac{1}{2} a^{3} - \frac{7}{2} a + 1\) , \( \frac{1}{2} a^{3} - \frac{7}{2} a + 1\) , \( \frac{13}{2} a^{3} - a^{2} - \frac{75}{2} a - 15\) , \( -\frac{21}{2} a^{3} + 10 a^{2} + \frac{129}{2} a + 9\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-\frac{5}{2}a-\frac{7}{2}\right){x}{y}+\left(\frac{1}{2}a^{3}-\frac{7}{2}a+1\right){y}={x}^{3}+\left(\frac{1}{2}a^{3}-\frac{7}{2}a+1\right){x}^{2}+\left(\frac{13}{2}a^{3}-a^{2}-\frac{75}{2}a-15\right){x}-\frac{21}{2}a^{3}+10a^{2}+\frac{129}{2}a+9$ |
| 9.1-b4 |
9.1-b |
$4$ |
$6$ |
4.4.12400.1 |
$4$ |
$[4, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{12} \) |
$13.09573$ |
$(1/2a^2+a-1/2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \cdot 3 \) |
$0.102133450$ |
$525.2209558$ |
2.890350157 |
\( \frac{51065}{243} a^{3} + \frac{776305}{1458} a^{2} - \frac{876295}{729} a - \frac{1624405}{1458} \) |
\( \bigl[\frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{5}{2} a - \frac{7}{2}\) , \( \frac{1}{2} a^{3} - \frac{7}{2} a + 1\) , \( \frac{1}{2} a^{3} - \frac{7}{2} a + 1\) , \( \frac{3}{2} a^{3} + \frac{3}{2} a^{2} - \frac{15}{2} a - \frac{5}{2}\) , \( a^{3} + \frac{5}{2} a^{2} - 2 a - \frac{15}{2}\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-\frac{5}{2}a-\frac{7}{2}\right){x}{y}+\left(\frac{1}{2}a^{3}-\frac{7}{2}a+1\right){y}={x}^{3}+\left(\frac{1}{2}a^{3}-\frac{7}{2}a+1\right){x}^{2}+\left(\frac{3}{2}a^{3}+\frac{3}{2}a^{2}-\frac{15}{2}a-\frac{5}{2}\right){x}+a^{3}+\frac{5}{2}a^{2}-2a-\frac{15}{2}$ |
| 9.2-a1 |
9.2-a |
$4$ |
$6$ |
4.4.12400.1 |
$4$ |
$[4, 0]$ |
9.2 |
\( 3^{2} \) |
\( 3^{8} \) |
$13.09573$ |
$(-1/2a^3+a^2+7/2a-6)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$1$ |
$365.8824173$ |
1.642860551 |
\( -\frac{8025637785355}{81} a^{3} + \frac{46061580093845}{162} a^{2} + \frac{30209462949730}{81} a - \frac{57788918959565}{54} \) |
\( \bigl[\frac{1}{2} a^{2} - \frac{5}{2}\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{5}{2} a - \frac{9}{2}\) , \( a\) , \( 18 a^{3} + 35 a^{2} - 148 a - 289\) , \( 102 a^{3} + \frac{403}{2} a^{2} - 846 a - \frac{3309}{2}\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{2}-\frac{5}{2}\right){x}{y}+a{y}={x}^{3}+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-\frac{5}{2}a-\frac{9}{2}\right){x}^{2}+\left(18a^{3}+35a^{2}-148a-289\right){x}+102a^{3}+\frac{403}{2}a^{2}-846a-\frac{3309}{2}$ |
| 9.2-a2 |
9.2-a |
$4$ |
$6$ |
4.4.12400.1 |
$4$ |
$[4, 0]$ |
9.2 |
\( 3^{2} \) |
\( 3^{4} \) |
$13.09573$ |
$(-1/2a^3+a^2+7/2a-6)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$1$ |
$365.8824173$ |
1.642860551 |
\( \frac{29105995}{9} a^{3} + \frac{173474645}{18} a^{2} - \frac{36523615}{3} a - \frac{653017795}{18} \) |
\( \bigl[\frac{1}{2} a^{2} - \frac{5}{2}\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{5}{2} a - \frac{9}{2}\) , \( a\) , \( \frac{1}{2} a^{3} + \frac{5}{2} a^{2} - \frac{11}{2} a - \frac{33}{2}\) , \( \frac{1}{2} a^{3} - \frac{11}{2} a - 8\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{2}-\frac{5}{2}\right){x}{y}+a{y}={x}^{3}+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-\frac{5}{2}a-\frac{9}{2}\right){x}^{2}+\left(\frac{1}{2}a^{3}+\frac{5}{2}a^{2}-\frac{11}{2}a-\frac{33}{2}\right){x}+\frac{1}{2}a^{3}-\frac{11}{2}a-8$ |
| 9.2-a3 |
9.2-a |
$4$ |
$6$ |
4.4.12400.1 |
$4$ |
$[4, 0]$ |
9.2 |
\( 3^{2} \) |
\( 3^{24} \) |
$13.09573$ |
$(-1/2a^3+a^2+7/2a-6)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$1$ |
$365.8824173$ |
1.642860551 |
\( \frac{18006809585}{1062882} a^{3} + \frac{25720340240}{531441} a^{2} - \frac{70788991685}{1062882} a - \frac{30982326505}{177147} \) |
\( \bigl[\frac{1}{2} a^{2} + a - \frac{7}{2}\) , \( -a\) , \( \frac{1}{2} a^{3} - \frac{5}{2} a + 1\) , \( -7 a^{3} + \frac{13}{2} a^{2} + 51 a - \frac{143}{2}\) , \( -\frac{63}{2} a^{3} + \frac{139}{2} a^{2} + \frac{535}{2} a - \frac{1101}{2}\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{2}+a-\frac{7}{2}\right){x}{y}+\left(\frac{1}{2}a^{3}-\frac{5}{2}a+1\right){y}={x}^{3}-a{x}^{2}+\left(-7a^{3}+\frac{13}{2}a^{2}+51a-\frac{143}{2}\right){x}-\frac{63}{2}a^{3}+\frac{139}{2}a^{2}+\frac{535}{2}a-\frac{1101}{2}$ |
| 9.2-a4 |
9.2-a |
$4$ |
$6$ |
4.4.12400.1 |
$4$ |
$[4, 0]$ |
9.2 |
\( 3^{2} \) |
\( 3^{12} \) |
$13.09573$ |
$(-1/2a^3+a^2+7/2a-6)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$1$ |
$365.8824173$ |
1.642860551 |
\( -\frac{51065}{243} a^{3} + \frac{776305}{1458} a^{2} + \frac{876295}{729} a - \frac{1624405}{1458} \) |
\( \bigl[\frac{1}{2} a^{2} + a - \frac{7}{2}\) , \( -a\) , \( \frac{1}{2} a^{3} - \frac{5}{2} a + 1\) , \( \frac{1}{2} a^{3} - \frac{7}{2} a^{2} - \frac{13}{2} a + \frac{47}{2}\) , \( -a^{3} + \frac{1}{2} a^{2} + 7 a - \frac{17}{2}\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{2}+a-\frac{7}{2}\right){x}{y}+\left(\frac{1}{2}a^{3}-\frac{5}{2}a+1\right){y}={x}^{3}-a{x}^{2}+\left(\frac{1}{2}a^{3}-\frac{7}{2}a^{2}-\frac{13}{2}a+\frac{47}{2}\right){x}-a^{3}+\frac{1}{2}a^{2}+7a-\frac{17}{2}$ |
| 9.2-b1 |
9.2-b |
$4$ |
$6$ |
4.4.12400.1 |
$4$ |
$[4, 0]$ |
9.2 |
\( 3^{2} \) |
\( 3^{8} \) |
$13.09573$ |
$(-1/2a^3+a^2+7/2a-6)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \) |
$0.153200176$ |
$525.2209558$ |
2.890350157 |
\( -\frac{8025637785355}{81} a^{3} + \frac{46061580093845}{162} a^{2} + \frac{30209462949730}{81} a - \frac{57788918959565}{54} \) |
\( \bigl[a\) , \( \frac{1}{2} a^{3} - \frac{1}{2} a^{2} - \frac{9}{2} a + \frac{5}{2}\) , \( 0\) , \( 8 a^{3} + 7 a^{2} - 64 a - 78\) , \( -\frac{79}{2} a^{3} - 72 a^{2} + \frac{631}{2} a + 604\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(\frac{1}{2}a^{3}-\frac{1}{2}a^{2}-\frac{9}{2}a+\frac{5}{2}\right){x}^{2}+\left(8a^{3}+7a^{2}-64a-78\right){x}-\frac{79}{2}a^{3}-72a^{2}+\frac{631}{2}a+604$ |
| 9.2-b2 |
9.2-b |
$4$ |
$6$ |
4.4.12400.1 |
$4$ |
$[4, 0]$ |
9.2 |
\( 3^{2} \) |
\( 3^{4} \) |
$13.09573$ |
$(-1/2a^3+a^2+7/2a-6)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$0.306400352$ |
$525.2209558$ |
2.890350157 |
\( \frac{29105995}{9} a^{3} + \frac{173474645}{18} a^{2} - \frac{36523615}{3} a - \frac{653017795}{18} \) |
\( \bigl[a\) , \( \frac{1}{2} a^{3} - \frac{1}{2} a^{2} - \frac{9}{2} a + \frac{5}{2}\) , \( 0\) , \( \frac{1}{2} a^{3} - 3 a^{2} - \frac{13}{2} a + 17\) , \( -a^{3} - 5 a^{2} + 5 a + 32\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(\frac{1}{2}a^{3}-\frac{1}{2}a^{2}-\frac{9}{2}a+\frac{5}{2}\right){x}^{2}+\left(\frac{1}{2}a^{3}-3a^{2}-\frac{13}{2}a+17\right){x}-a^{3}-5a^{2}+5a+32$ |
| 9.2-b3 |
9.2-b |
$4$ |
$6$ |
4.4.12400.1 |
$4$ |
$[4, 0]$ |
9.2 |
\( 3^{2} \) |
\( 3^{24} \) |
$13.09573$ |
$(-1/2a^3+a^2+7/2a-6)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \cdot 3 \) |
$0.051066725$ |
$525.2209558$ |
2.890350157 |
\( \frac{18006809585}{1062882} a^{3} + \frac{25720340240}{531441} a^{2} - \frac{70788991685}{1062882} a - \frac{30982326505}{177147} \) |
\( \bigl[\frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{5}{2} a - \frac{7}{2}\) , \( -\frac{1}{2} a^{3} + \frac{5}{2} a + 1\) , \( \frac{1}{2} a^{3} - \frac{7}{2} a + 1\) , \( -\frac{13}{2} a^{3} - a^{2} + \frac{71}{2} a - 15\) , \( 10 a^{3} + 10 a^{2} - 61 a + 9\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-\frac{5}{2}a-\frac{7}{2}\right){x}{y}+\left(\frac{1}{2}a^{3}-\frac{7}{2}a+1\right){y}={x}^{3}+\left(-\frac{1}{2}a^{3}+\frac{5}{2}a+1\right){x}^{2}+\left(-\frac{13}{2}a^{3}-a^{2}+\frac{71}{2}a-15\right){x}+10a^{3}+10a^{2}-61a+9$ |
| 9.2-b4 |
9.2-b |
$4$ |
$6$ |
4.4.12400.1 |
$4$ |
$[4, 0]$ |
9.2 |
\( 3^{2} \) |
\( 3^{12} \) |
$13.09573$ |
$(-1/2a^3+a^2+7/2a-6)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \cdot 3 \) |
$0.102133450$ |
$525.2209558$ |
2.890350157 |
\( -\frac{51065}{243} a^{3} + \frac{776305}{1458} a^{2} + \frac{876295}{729} a - \frac{1624405}{1458} \) |
\( \bigl[\frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{5}{2} a - \frac{7}{2}\) , \( -\frac{1}{2} a^{3} + \frac{5}{2} a + 1\) , \( \frac{1}{2} a^{3} - \frac{7}{2} a + 1\) , \( -\frac{3}{2} a^{3} + \frac{3}{2} a^{2} + \frac{11}{2} a - \frac{5}{2}\) , \( -\frac{3}{2} a^{3} + \frac{5}{2} a^{2} + \frac{11}{2} a - \frac{15}{2}\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-\frac{5}{2}a-\frac{7}{2}\right){x}{y}+\left(\frac{1}{2}a^{3}-\frac{7}{2}a+1\right){y}={x}^{3}+\left(-\frac{1}{2}a^{3}+\frac{5}{2}a+1\right){x}^{2}+\left(-\frac{3}{2}a^{3}+\frac{3}{2}a^{2}+\frac{11}{2}a-\frac{5}{2}\right){x}-\frac{3}{2}a^{3}+\frac{5}{2}a^{2}+\frac{11}{2}a-\frac{15}{2}$ |
| 19.1-a1 |
19.1-a |
$4$ |
$6$ |
4.4.12400.1 |
$4$ |
$[4, 0]$ |
19.1 |
\( 19 \) |
\( - 19^{3} \) |
$14.37784$ |
$(1/2a^3-7/2a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 3 \) |
$0.188035883$ |
$453.8575537$ |
2.299168041 |
\( \frac{43567442560}{6859} a^{3} + \frac{129020350240}{6859} a^{2} - \frac{163951874560}{6859} a - \frac{485555172640}{6859} \) |
\( \bigl[\frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{5}{2} a - \frac{5}{2}\) , \( -\frac{1}{2} a^{3} + \frac{1}{2} a^{2} + \frac{7}{2} a - \frac{5}{2}\) , \( \frac{1}{2} a^{3} - \frac{5}{2} a + 1\) , \( -\frac{1}{2} a^{2} - a + \frac{9}{2}\) , \( \frac{1}{2} a^{2} - \frac{11}{2}\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-\frac{5}{2}a-\frac{5}{2}\right){x}{y}+\left(\frac{1}{2}a^{3}-\frac{5}{2}a+1\right){y}={x}^{3}+\left(-\frac{1}{2}a^{3}+\frac{1}{2}a^{2}+\frac{7}{2}a-\frac{5}{2}\right){x}^{2}+\left(-\frac{1}{2}a^{2}-a+\frac{9}{2}\right){x}+\frac{1}{2}a^{2}-\frac{11}{2}$ |
| 19.1-a2 |
19.1-a |
$4$ |
$6$ |
4.4.12400.1 |
$4$ |
$[4, 0]$ |
19.1 |
\( 19 \) |
\( 19^{6} \) |
$14.37784$ |
$(1/2a^3-7/2a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \cdot 3 \) |
$0.094017941$ |
$453.8575537$ |
2.299168041 |
\( -\frac{20257762240}{47045881} a^{3} - \frac{110308292960}{47045881} a^{2} + \frac{75361538240}{47045881} a + \frac{599800342560}{47045881} \) |
\( \bigl[a + 1\) , \( \frac{1}{2} a^{3} - \frac{9}{2} a - 1\) , \( \frac{1}{2} a^{3} - \frac{7}{2} a + 1\) , \( 32 a^{3} - 96 a^{2} - 114 a + 357\) , \( 642 a^{3} - 1842 a^{2} - 2417 a + 6931\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(\frac{1}{2}a^{3}-\frac{7}{2}a+1\right){y}={x}^{3}+\left(\frac{1}{2}a^{3}-\frac{9}{2}a-1\right){x}^{2}+\left(32a^{3}-96a^{2}-114a+357\right){x}+642a^{3}-1842a^{2}-2417a+6931$ |
| 19.1-a3 |
19.1-a |
$4$ |
$6$ |
4.4.12400.1 |
$4$ |
$[4, 0]$ |
19.1 |
\( 19 \) |
\( 19^{2} \) |
$14.37784$ |
$(1/2a^3-7/2a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$0.282053824$ |
$453.8575537$ |
2.299168041 |
\( \frac{651376965440}{361} a^{3} - \frac{1263931654240}{361} a^{2} - \frac{5364784901440}{361} a + \frac{10409827460640}{361} \) |
\( \bigl[\frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{7}{2} a - \frac{7}{2}\) , \( -\frac{1}{2} a^{3} - \frac{1}{2} a^{2} + \frac{9}{2} a + \frac{9}{2}\) , \( \frac{1}{2} a^{2} + a - \frac{7}{2}\) , \( \frac{7}{2} a^{3} + \frac{27}{2} a^{2} + \frac{5}{2} a - \frac{45}{2}\) , \( 3 a^{3} + 11 a^{2} + 8 a + 2\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-\frac{7}{2}a-\frac{7}{2}\right){x}{y}+\left(\frac{1}{2}a^{2}+a-\frac{7}{2}\right){y}={x}^{3}+\left(-\frac{1}{2}a^{3}-\frac{1}{2}a^{2}+\frac{9}{2}a+\frac{9}{2}\right){x}^{2}+\left(\frac{7}{2}a^{3}+\frac{27}{2}a^{2}+\frac{5}{2}a-\frac{45}{2}\right){x}+3a^{3}+11a^{2}+8a+2$ |
| 19.1-a4 |
19.1-a |
$4$ |
$6$ |
4.4.12400.1 |
$4$ |
$[4, 0]$ |
19.1 |
\( 19 \) |
\( -19 \) |
$14.37784$ |
$(1/2a^3-7/2a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 1 \) |
$0.564107649$ |
$453.8575537$ |
2.299168041 |
\( -\frac{7038892130560}{19} a^{3} - \frac{13656052294240}{19} a^{2} + \frac{57972794066560}{19} a + \frac{112472175052640}{19} \) |
\( \bigl[a + 1\) , \( -\frac{1}{2} a^{2} + a + \frac{5}{2}\) , \( \frac{1}{2} a^{2} - \frac{7}{2}\) , \( \frac{5}{2} a^{3} - 10 a^{2} + \frac{3}{2} a + 26\) , \( -\frac{33}{2} a^{3} + 52 a^{2} + \frac{83}{2} a - 153\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(\frac{1}{2}a^{2}-\frac{7}{2}\right){y}={x}^{3}+\left(-\frac{1}{2}a^{2}+a+\frac{5}{2}\right){x}^{2}+\left(\frac{5}{2}a^{3}-10a^{2}+\frac{3}{2}a+26\right){x}-\frac{33}{2}a^{3}+52a^{2}+\frac{83}{2}a-153$ |
| 19.1-b1 |
19.1-b |
$4$ |
$6$ |
4.4.12400.1 |
$4$ |
$[4, 0]$ |
19.1 |
\( 19 \) |
\( - 19^{3} \) |
$14.37784$ |
$(1/2a^3-7/2a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 1 \) |
$1$ |
$553.8502367$ |
1.243430488 |
\( \frac{43567442560}{6859} a^{3} + \frac{129020350240}{6859} a^{2} - \frac{163951874560}{6859} a - \frac{485555172640}{6859} \) |
\( \bigl[\frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{7}{2} a - \frac{7}{2}\) , \( -\frac{1}{2} a^{3} + \frac{5}{2} a - 1\) , \( \frac{1}{2} a^{3} - \frac{5}{2} a + 1\) , \( -\frac{1}{2} a^{3} - a^{2} + \frac{5}{2} a + 6\) , \( \frac{1}{2} a^{2} + a - \frac{7}{2}\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-\frac{7}{2}a-\frac{7}{2}\right){x}{y}+\left(\frac{1}{2}a^{3}-\frac{5}{2}a+1\right){y}={x}^{3}+\left(-\frac{1}{2}a^{3}+\frac{5}{2}a-1\right){x}^{2}+\left(-\frac{1}{2}a^{3}-a^{2}+\frac{5}{2}a+6\right){x}+\frac{1}{2}a^{2}+a-\frac{7}{2}$ |
| 19.1-b2 |
19.1-b |
$4$ |
$6$ |
4.4.12400.1 |
$4$ |
$[4, 0]$ |
19.1 |
\( 19 \) |
\( 19^{6} \) |
$14.37784$ |
$(1/2a^3-7/2a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$1$ |
$276.9251183$ |
1.243430488 |
\( -\frac{20257762240}{47045881} a^{3} - \frac{110308292960}{47045881} a^{2} + \frac{75361538240}{47045881} a + \frac{599800342560}{47045881} \) |
\( \bigl[\frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{5}{2} a - \frac{5}{2}\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{7}{2} a - \frac{9}{2}\) , \( \frac{1}{2} a^{3} - \frac{7}{2} a + 1\) , \( 10 a^{3} - \frac{53}{2} a^{2} - 19 a + \frac{139}{2}\) , \( 142 a^{3} - 404 a^{2} - 492 a + 1433\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-\frac{5}{2}a-\frac{5}{2}\right){x}{y}+\left(\frac{1}{2}a^{3}-\frac{7}{2}a+1\right){y}={x}^{3}+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-\frac{7}{2}a-\frac{9}{2}\right){x}^{2}+\left(10a^{3}-\frac{53}{2}a^{2}-19a+\frac{139}{2}\right){x}+142a^{3}-404a^{2}-492a+1433$ |
| 19.1-b3 |
19.1-b |
$4$ |
$6$ |
4.4.12400.1 |
$4$ |
$[4, 0]$ |
19.1 |
\( 19 \) |
\( 19^{2} \) |
$14.37784$ |
$(1/2a^3-7/2a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$1$ |
$276.9251183$ |
1.243430488 |
\( \frac{651376965440}{361} a^{3} - \frac{1263931654240}{361} a^{2} - \frac{5364784901440}{361} a + \frac{10409827460640}{361} \) |
\( \bigl[\frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{5}{2} a - \frac{5}{2}\) , \( \frac{1}{2} a^{3} - \frac{9}{2} a - 1\) , \( \frac{1}{2} a^{2} + a - \frac{7}{2}\) , \( \frac{37}{2} a^{3} + 52 a^{2} - \frac{137}{2} a - 189\) , \( 50 a^{3} + \frac{289}{2} a^{2} - 188 a - \frac{1097}{2}\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-\frac{5}{2}a-\frac{5}{2}\right){x}{y}+\left(\frac{1}{2}a^{2}+a-\frac{7}{2}\right){y}={x}^{3}+\left(\frac{1}{2}a^{3}-\frac{9}{2}a-1\right){x}^{2}+\left(\frac{37}{2}a^{3}+52a^{2}-\frac{137}{2}a-189\right){x}+50a^{3}+\frac{289}{2}a^{2}-188a-\frac{1097}{2}$ |
| 19.1-b4 |
19.1-b |
$4$ |
$6$ |
4.4.12400.1 |
$4$ |
$[4, 0]$ |
19.1 |
\( 19 \) |
\( -19 \) |
$14.37784$ |
$(1/2a^3-7/2a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 1 \) |
$1$ |
$553.8502367$ |
1.243430488 |
\( -\frac{7038892130560}{19} a^{3} - \frac{13656052294240}{19} a^{2} + \frac{57972794066560}{19} a + \frac{112472175052640}{19} \) |
\( \bigl[\frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{5}{2} a - \frac{5}{2}\) , \( \frac{1}{2} a^{3} - \frac{1}{2} a^{2} - \frac{9}{2} a + \frac{9}{2}\) , \( \frac{1}{2} a^{3} - \frac{7}{2} a\) , \( -a^{3} + 5 a^{2} + 20 a - 53\) , \( -\frac{59}{2} a^{3} + 64 a^{2} + \frac{483}{2} a - 496\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-\frac{5}{2}a-\frac{5}{2}\right){x}{y}+\left(\frac{1}{2}a^{3}-\frac{7}{2}a\right){y}={x}^{3}+\left(\frac{1}{2}a^{3}-\frac{1}{2}a^{2}-\frac{9}{2}a+\frac{9}{2}\right){x}^{2}+\left(-a^{3}+5a^{2}+20a-53\right){x}-\frac{59}{2}a^{3}+64a^{2}+\frac{483}{2}a-496$ |
| 19.2-a1 |
19.2-a |
$4$ |
$6$ |
4.4.12400.1 |
$4$ |
$[4, 0]$ |
19.2 |
\( 19 \) |
\( - 19^{3} \) |
$14.37784$ |
$(1/2a^2+a-5/2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 3 \) |
$0.188035883$ |
$453.8575537$ |
2.299168041 |
\( -\frac{43567442560}{6859} a^{3} + \frac{129020350240}{6859} a^{2} + \frac{163951874560}{6859} a - \frac{485555172640}{6859} \) |
\( \bigl[\frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{5}{2} a - \frac{5}{2}\) , \( \frac{1}{2} a^{2} + a - \frac{5}{2}\) , \( \frac{1}{2} a^{2} - \frac{7}{2}\) , \( 3 a^{3} + \frac{11}{2} a^{2} - 11 a - \frac{41}{2}\) , \( 3 a^{3} + 13 a^{2} - 11 a - 49\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-\frac{5}{2}a-\frac{5}{2}\right){x}{y}+\left(\frac{1}{2}a^{2}-\frac{7}{2}\right){y}={x}^{3}+\left(\frac{1}{2}a^{2}+a-\frac{5}{2}\right){x}^{2}+\left(3a^{3}+\frac{11}{2}a^{2}-11a-\frac{41}{2}\right){x}+3a^{3}+13a^{2}-11a-49$ |
| 19.2-a2 |
19.2-a |
$4$ |
$6$ |
4.4.12400.1 |
$4$ |
$[4, 0]$ |
19.2 |
\( 19 \) |
\( 19^{6} \) |
$14.37784$ |
$(1/2a^2+a-5/2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \cdot 3 \) |
$0.094017941$ |
$453.8575537$ |
2.299168041 |
\( \frac{20257762240}{47045881} a^{3} - \frac{110308292960}{47045881} a^{2} - \frac{75361538240}{47045881} a + \frac{599800342560}{47045881} \) |
\( \bigl[a + 1\) , \( -\frac{1}{2} a^{3} + \frac{7}{2} a - 1\) , \( \frac{1}{2} a^{3} - \frac{7}{2} a + 1\) , \( -\frac{65}{2} a^{3} - 96 a^{2} + \frac{233}{2} a + 357\) , \( -\frac{1285}{2} a^{3} - 1842 a^{2} + \frac{4841}{2} a + 6931\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(\frac{1}{2}a^{3}-\frac{7}{2}a+1\right){y}={x}^{3}+\left(-\frac{1}{2}a^{3}+\frac{7}{2}a-1\right){x}^{2}+\left(-\frac{65}{2}a^{3}-96a^{2}+\frac{233}{2}a+357\right){x}-\frac{1285}{2}a^{3}-1842a^{2}+\frac{4841}{2}a+6931$ |
| 19.2-a3 |
19.2-a |
$4$ |
$6$ |
4.4.12400.1 |
$4$ |
$[4, 0]$ |
19.2 |
\( 19 \) |
\( 19^{2} \) |
$14.37784$ |
$(1/2a^2+a-5/2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$0.282053824$ |
$453.8575537$ |
2.299168041 |
\( -\frac{651376965440}{361} a^{3} - \frac{1263931654240}{361} a^{2} + \frac{5364784901440}{361} a + \frac{10409827460640}{361} \) |
\( \bigl[\frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{7}{2} a - \frac{7}{2}\) , \( -\frac{1}{2} a^{3} - \frac{1}{2} a^{2} + \frac{9}{2} a + \frac{9}{2}\) , \( \frac{1}{2} a^{2} - \frac{5}{2}\) , \( -10 a^{3} + \frac{29}{2} a^{2} + 51 a - \frac{57}{2}\) , \( -\frac{7}{2} a^{3} - \frac{17}{2} a^{2} + \frac{61}{2} a + \frac{131}{2}\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-\frac{7}{2}a-\frac{7}{2}\right){x}{y}+\left(\frac{1}{2}a^{2}-\frac{5}{2}\right){y}={x}^{3}+\left(-\frac{1}{2}a^{3}-\frac{1}{2}a^{2}+\frac{9}{2}a+\frac{9}{2}\right){x}^{2}+\left(-10a^{3}+\frac{29}{2}a^{2}+51a-\frac{57}{2}\right){x}-\frac{7}{2}a^{3}-\frac{17}{2}a^{2}+\frac{61}{2}a+\frac{131}{2}$ |
| 19.2-a4 |
19.2-a |
$4$ |
$6$ |
4.4.12400.1 |
$4$ |
$[4, 0]$ |
19.2 |
\( 19 \) |
\( -19 \) |
$14.37784$ |
$(1/2a^2+a-5/2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 1 \) |
$0.564107649$ |
$453.8575537$ |
2.299168041 |
\( \frac{7038892130560}{19} a^{3} - \frac{13656052294240}{19} a^{2} - \frac{57972794066560}{19} a + \frac{112472175052640}{19} \) |
\( \bigl[a + 1\) , \( -\frac{1}{2} a^{2} + a + \frac{5}{2}\) , \( \frac{1}{2} a^{2} + a - \frac{5}{2}\) , \( -\frac{7}{2} a^{3} - \frac{21}{2} a^{2} + \frac{13}{2} a + \frac{51}{2}\) , \( 6 a^{3} + \frac{37}{2} a^{2} - 16 a - \frac{117}{2}\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(\frac{1}{2}a^{2}+a-\frac{5}{2}\right){y}={x}^{3}+\left(-\frac{1}{2}a^{2}+a+\frac{5}{2}\right){x}^{2}+\left(-\frac{7}{2}a^{3}-\frac{21}{2}a^{2}+\frac{13}{2}a+\frac{51}{2}\right){x}+6a^{3}+\frac{37}{2}a^{2}-16a-\frac{117}{2}$ |
| 19.2-b1 |
19.2-b |
$4$ |
$6$ |
4.4.12400.1 |
$4$ |
$[4, 0]$ |
19.2 |
\( 19 \) |
\( - 19^{3} \) |
$14.37784$ |
$(1/2a^2+a-5/2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 1 \) |
$1$ |
$553.8502367$ |
1.243430488 |
\( -\frac{43567442560}{6859} a^{3} + \frac{129020350240}{6859} a^{2} + \frac{163951874560}{6859} a - \frac{485555172640}{6859} \) |
\( \bigl[\frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{7}{2} a - \frac{7}{2}\) , \( -\frac{1}{2} a^{3} + \frac{7}{2} a - 1\) , \( \frac{1}{2} a^{2} - \frac{7}{2}\) , \( -a^{3} - \frac{5}{2} a^{2} + 9 a + \frac{35}{2}\) , \( -\frac{1}{2} a^{3} - \frac{7}{2} a^{2} + \frac{7}{2} a + \frac{61}{2}\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-\frac{7}{2}a-\frac{7}{2}\right){x}{y}+\left(\frac{1}{2}a^{2}-\frac{7}{2}\right){y}={x}^{3}+\left(-\frac{1}{2}a^{3}+\frac{7}{2}a-1\right){x}^{2}+\left(-a^{3}-\frac{5}{2}a^{2}+9a+\frac{35}{2}\right){x}-\frac{1}{2}a^{3}-\frac{7}{2}a^{2}+\frac{7}{2}a+\frac{61}{2}$ |
| 19.2-b2 |
19.2-b |
$4$ |
$6$ |
4.4.12400.1 |
$4$ |
$[4, 0]$ |
19.2 |
\( 19 \) |
\( 19^{6} \) |
$14.37784$ |
$(1/2a^2+a-5/2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$1$ |
$276.9251183$ |
1.243430488 |
\( \frac{20257762240}{47045881} a^{3} - \frac{110308292960}{47045881} a^{2} - \frac{75361538240}{47045881} a + \frac{599800342560}{47045881} \) |
\( \bigl[\frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{7}{2} a - \frac{7}{2}\) , \( \frac{1}{2} a^{3} - \frac{1}{2} a^{2} - \frac{9}{2} a + \frac{7}{2}\) , \( \frac{1}{2} a^{3} - \frac{7}{2} a + 1\) , \( -\frac{173}{2} a^{3} - 253 a^{2} + \frac{637}{2} a + 953\) , \( -\frac{5327}{2} a^{3} - \frac{15295}{2} a^{2} + \frac{20037}{2} a + \frac{57563}{2}\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-\frac{7}{2}a-\frac{7}{2}\right){x}{y}+\left(\frac{1}{2}a^{3}-\frac{7}{2}a+1\right){y}={x}^{3}+\left(\frac{1}{2}a^{3}-\frac{1}{2}a^{2}-\frac{9}{2}a+\frac{7}{2}\right){x}^{2}+\left(-\frac{173}{2}a^{3}-253a^{2}+\frac{637}{2}a+953\right){x}-\frac{5327}{2}a^{3}-\frac{15295}{2}a^{2}+\frac{20037}{2}a+\frac{57563}{2}$ |
| 19.2-b3 |
19.2-b |
$4$ |
$6$ |
4.4.12400.1 |
$4$ |
$[4, 0]$ |
19.2 |
\( 19 \) |
\( 19^{2} \) |
$14.37784$ |
$(1/2a^2+a-5/2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$1$ |
$276.9251183$ |
1.243430488 |
\( -\frac{651376965440}{361} a^{3} - \frac{1263931654240}{361} a^{2} + \frac{5364784901440}{361} a + \frac{10409827460640}{361} \) |
\( \bigl[\frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{5}{2} a - \frac{5}{2}\) , \( \frac{1}{2} a^{3} - \frac{9}{2} a - 1\) , \( \frac{1}{2} a^{2} - \frac{5}{2}\) , \( -18 a^{3} + \frac{107}{2} a^{2} + 68 a - \frac{391}{2}\) , \( -16 a^{3} + \frac{101}{2} a^{2} + 59 a - \frac{381}{2}\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-\frac{5}{2}a-\frac{5}{2}\right){x}{y}+\left(\frac{1}{2}a^{2}-\frac{5}{2}\right){y}={x}^{3}+\left(\frac{1}{2}a^{3}-\frac{9}{2}a-1\right){x}^{2}+\left(-18a^{3}+\frac{107}{2}a^{2}+68a-\frac{391}{2}\right){x}-16a^{3}+\frac{101}{2}a^{2}+59a-\frac{381}{2}$ |
| 19.2-b4 |
19.2-b |
$4$ |
$6$ |
4.4.12400.1 |
$4$ |
$[4, 0]$ |
19.2 |
\( 19 \) |
\( -19 \) |
$14.37784$ |
$(1/2a^2+a-5/2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 1 \) |
$1$ |
$553.8502367$ |
1.243430488 |
\( \frac{7038892130560}{19} a^{3} - \frac{13656052294240}{19} a^{2} - \frac{57972794066560}{19} a + \frac{112472175052640}{19} \) |
\( \bigl[\frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{7}{2} a - \frac{7}{2}\) , \( -\frac{1}{2} a^{3} - \frac{1}{2} a^{2} + \frac{9}{2} a + \frac{5}{2}\) , \( \frac{1}{2} a^{3} - \frac{5}{2} a + 1\) , \( -\frac{29}{2} a^{3} - 41 a^{2} + \frac{123}{2} a + 171\) , \( 62 a^{3} + \frac{355}{2} a^{2} - 235 a - \frac{1349}{2}\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-\frac{7}{2}a-\frac{7}{2}\right){x}{y}+\left(\frac{1}{2}a^{3}-\frac{5}{2}a+1\right){y}={x}^{3}+\left(-\frac{1}{2}a^{3}-\frac{1}{2}a^{2}+\frac{9}{2}a+\frac{5}{2}\right){x}^{2}+\left(-\frac{29}{2}a^{3}-41a^{2}+\frac{123}{2}a+171\right){x}+62a^{3}+\frac{355}{2}a^{2}-235a-\frac{1349}{2}$ |
| 20.1-a1 |
20.1-a |
$4$ |
$6$ |
4.4.12400.1 |
$4$ |
$[4, 0]$ |
20.1 |
\( 2^{2} \cdot 5 \) |
\( 2^{36} \cdot 5^{4} \) |
$14.47032$ |
$(1/2a^3-1/2a^2-7/2a+5/2), (-a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \) |
$1$ |
$189.1172742$ |
1.698323258 |
\( -\frac{2062826524589}{25600} a^{3} + \frac{4002071809497}{25600} a^{2} + \frac{16989585953303}{25600} a - \frac{32961272479261}{25600} \) |
\( \bigl[\frac{1}{2} a^{3} - \frac{7}{2} a\) , \( -\frac{1}{2} a^{3} - \frac{1}{2} a^{2} + \frac{9}{2} a + \frac{9}{2}\) , \( \frac{1}{2} a^{3} - \frac{7}{2} a\) , \( -\frac{25}{2} a^{3} - 31 a^{2} + \frac{213}{2} a + 227\) , \( -100 a^{3} - \frac{385}{2} a^{2} + 824 a + \frac{3181}{2}\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-\frac{7}{2}a\right){x}{y}+\left(\frac{1}{2}a^{3}-\frac{7}{2}a\right){y}={x}^{3}+\left(-\frac{1}{2}a^{3}-\frac{1}{2}a^{2}+\frac{9}{2}a+\frac{9}{2}\right){x}^{2}+\left(-\frac{25}{2}a^{3}-31a^{2}+\frac{213}{2}a+227\right){x}-100a^{3}-\frac{385}{2}a^{2}+824a+\frac{3181}{2}$ |
| 20.1-a2 |
20.1-a |
$4$ |
$6$ |
4.4.12400.1 |
$4$ |
$[4, 0]$ |
20.1 |
\( 2^{2} \cdot 5 \) |
\( 2^{12} \cdot 5^{12} \) |
$14.47032$ |
$(1/2a^3-1/2a^2-7/2a+5/2), (-a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \) |
$1$ |
$189.1172742$ |
1.698323258 |
\( -\frac{2028817931053}{250000} a^{3} + \frac{3032952547803}{125000} a^{2} + \frac{7629088540237}{250000} a - \frac{1142292115229}{12500} \) |
\( \bigl[\frac{1}{2} a^{3} - \frac{5}{2} a + 1\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{5}{2} a - \frac{7}{2}\) , \( 0\) , \( 57 a^{3} - \frac{143}{2} a^{2} - 287 a + \frac{247}{2}\) , \( -597 a^{3} + \frac{2261}{2} a^{2} + 2805 a - \frac{6329}{2}\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-\frac{5}{2}a+1\right){x}{y}={x}^{3}+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-\frac{5}{2}a-\frac{7}{2}\right){x}^{2}+\left(57a^{3}-\frac{143}{2}a^{2}-287a+\frac{247}{2}\right){x}-597a^{3}+\frac{2261}{2}a^{2}+2805a-\frac{6329}{2}$ |
| 20.1-a3 |
20.1-a |
$4$ |
$6$ |
4.4.12400.1 |
$4$ |
$[4, 0]$ |
20.1 |
\( 2^{2} \cdot 5 \) |
\( 2^{6} \cdot 5^{24} \) |
$14.47032$ |
$(1/2a^3-1/2a^2-7/2a+5/2), (-a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$4$ |
\( 2 \) |
$1$ |
$94.55863714$ |
1.698323258 |
\( -\frac{1455229050566292019}{1953125000} a^{3} - \frac{2823809491238563383}{1953125000} a^{2} + \frac{11985361149037390153}{1953125000} a + \frac{23257104737525574349}{1953125000} \) |
\( \bigl[\frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{7}{2} a - \frac{5}{2}\) , \( -\frac{1}{2} a^{2} + a + \frac{9}{2}\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{5}{2} a - \frac{5}{2}\) , \( \frac{611}{2} a^{3} - 695 a^{2} - \frac{2631}{2} a + 2280\) , \( -8588 a^{3} + \frac{46545}{2} a^{2} + 33599 a - \frac{170223}{2}\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-\frac{7}{2}a-\frac{5}{2}\right){x}{y}+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-\frac{5}{2}a-\frac{5}{2}\right){y}={x}^{3}+\left(-\frac{1}{2}a^{2}+a+\frac{9}{2}\right){x}^{2}+\left(\frac{611}{2}a^{3}-695a^{2}-\frac{2631}{2}a+2280\right){x}-8588a^{3}+\frac{46545}{2}a^{2}+33599a-\frac{170223}{2}$ |
| 20.1-a4 |
20.1-a |
$4$ |
$6$ |
4.4.12400.1 |
$4$ |
$[4, 0]$ |
20.1 |
\( 2^{2} \cdot 5 \) |
\( 2^{18} \cdot 5^{8} \) |
$14.47032$ |
$(1/2a^3-1/2a^2-7/2a+5/2), (-a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$4$ |
\( 2 \) |
$1$ |
$94.55863714$ |
1.698323258 |
\( \frac{4506837263097866069597}{40000} a^{3} - \frac{8743649944588441599153}{40000} a^{2} - \frac{7423723612473221373661}{8000} a + \frac{72013295315208218404901}{40000} \) |
\( \bigl[\frac{1}{2} a^{3} - \frac{7}{2} a\) , \( -\frac{1}{2} a^{3} - \frac{1}{2} a^{2} + \frac{9}{2} a + \frac{9}{2}\) , \( \frac{1}{2} a^{3} - \frac{7}{2} a\) , \( \frac{135}{2} a^{3} + 49 a^{2} - \frac{1067}{2} a - 733\) , \( -172 a^{3} - \frac{1681}{2} a^{2} + 2192 a + \frac{12317}{2}\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-\frac{7}{2}a\right){x}{y}+\left(\frac{1}{2}a^{3}-\frac{7}{2}a\right){y}={x}^{3}+\left(-\frac{1}{2}a^{3}-\frac{1}{2}a^{2}+\frac{9}{2}a+\frac{9}{2}\right){x}^{2}+\left(\frac{135}{2}a^{3}+49a^{2}-\frac{1067}{2}a-733\right){x}-172a^{3}-\frac{1681}{2}a^{2}+2192a+\frac{12317}{2}$ |
| 20.1-b1 |
20.1-b |
$2$ |
$3$ |
4.4.12400.1 |
$4$ |
$[4, 0]$ |
20.1 |
\( 2^{2} \cdot 5 \) |
\( - 2^{2} \cdot 5^{3} \) |
$14.47032$ |
$(1/2a^3-1/2a^2-7/2a+5/2), (-a+3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 3 \) |
$0.038685298$ |
$778.1746306$ |
3.244093983 |
\( -\frac{45736318}{25} a^{3} + \frac{177288981}{50} a^{2} + \frac{753945911}{50} a - \frac{730980408}{25} \) |
\( \bigl[a\) , \( -\frac{1}{2} a^{3} + \frac{9}{2} a - 1\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{5}{2} a - \frac{5}{2}\) , \( -4 a^{2} + 24\) , \( -\frac{1}{2} a^{3} - \frac{3}{2} a^{2} + \frac{7}{2} a + \frac{9}{2}\bigr] \) |
${y}^2+a{x}{y}+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-\frac{5}{2}a-\frac{5}{2}\right){y}={x}^{3}+\left(-\frac{1}{2}a^{3}+\frac{9}{2}a-1\right){x}^{2}+\left(-4a^{2}+24\right){x}-\frac{1}{2}a^{3}-\frac{3}{2}a^{2}+\frac{7}{2}a+\frac{9}{2}$ |
| 20.1-b2 |
20.1-b |
$2$ |
$3$ |
4.4.12400.1 |
$4$ |
$[4, 0]$ |
20.1 |
\( 2^{2} \cdot 5 \) |
\( - 2^{6} \cdot 5 \) |
$14.47032$ |
$(1/2a^3-1/2a^2-7/2a+5/2), (-a+3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 1 \) |
$0.116055896$ |
$778.1746306$ |
3.244093983 |
\( -\frac{2135237909}{40} a^{3} - \frac{4142533731}{40} a^{2} + \frac{17585965949}{40} a + \frac{34118238951}{40} \) |
\( \bigl[\frac{1}{2} a^{2} + a - \frac{7}{2}\) , \( \frac{1}{2} a^{3} - \frac{1}{2} a^{2} - \frac{7}{2} a + \frac{7}{2}\) , \( \frac{1}{2} a^{2} - \frac{5}{2}\) , \( -a^{3} + \frac{9}{2} a^{2} - a - \frac{15}{2}\) , \( \frac{13}{2} a^{3} - 17 a^{2} - \frac{61}{2} a + 76\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{2}+a-\frac{7}{2}\right){x}{y}+\left(\frac{1}{2}a^{2}-\frac{5}{2}\right){y}={x}^{3}+\left(\frac{1}{2}a^{3}-\frac{1}{2}a^{2}-\frac{7}{2}a+\frac{7}{2}\right){x}^{2}+\left(-a^{3}+\frac{9}{2}a^{2}-a-\frac{15}{2}\right){x}+\frac{13}{2}a^{3}-17a^{2}-\frac{61}{2}a+76$ |
| 20.1-c1 |
20.1-c |
$2$ |
$3$ |
4.4.12400.1 |
$4$ |
$[4, 0]$ |
20.1 |
\( 2^{2} \cdot 5 \) |
\( - 2^{2} \cdot 5^{3} \) |
$14.47032$ |
$(1/2a^3-1/2a^2-7/2a+5/2), (-a+3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 1 \) |
$1$ |
$129.2017712$ |
1.160266157 |
\( -\frac{45736318}{25} a^{3} + \frac{177288981}{50} a^{2} + \frac{753945911}{50} a - \frac{730980408}{25} \) |
\( \bigl[\frac{1}{2} a^{2} - \frac{5}{2}\) , \( -\frac{1}{2} a^{3} + \frac{5}{2} a\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{7}{2} a - \frac{5}{2}\) , \( \frac{3}{2} a^{2} - a - \frac{15}{2}\) , \( \frac{1}{2} a^{2} - a - \frac{11}{2}\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{2}-\frac{5}{2}\right){x}{y}+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-\frac{7}{2}a-\frac{5}{2}\right){y}={x}^{3}+\left(-\frac{1}{2}a^{3}+\frac{5}{2}a\right){x}^{2}+\left(\frac{3}{2}a^{2}-a-\frac{15}{2}\right){x}+\frac{1}{2}a^{2}-a-\frac{11}{2}$ |
| 20.1-c2 |
20.1-c |
$2$ |
$3$ |
4.4.12400.1 |
$4$ |
$[4, 0]$ |
20.1 |
\( 2^{2} \cdot 5 \) |
\( - 2^{6} \cdot 5 \) |
$14.47032$ |
$(1/2a^3-1/2a^2-7/2a+5/2), (-a+3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 1 \) |
$1$ |
$129.2017712$ |
1.160266157 |
\( -\frac{2135237909}{40} a^{3} - \frac{4142533731}{40} a^{2} + \frac{17585965949}{40} a + \frac{34118238951}{40} \) |
\( \bigl[\frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{5}{2} a - \frac{7}{2}\) , \( a\) , \( \frac{1}{2} a^{2} - \frac{7}{2}\) , \( -\frac{9}{2} a^{3} + 19 a^{2} + \frac{35}{2} a - 70\) , \( 17 a^{3} - \frac{83}{2} a^{2} - 63 a + \frac{311}{2}\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-\frac{5}{2}a-\frac{7}{2}\right){x}{y}+\left(\frac{1}{2}a^{2}-\frac{7}{2}\right){y}={x}^{3}+a{x}^{2}+\left(-\frac{9}{2}a^{3}+19a^{2}+\frac{35}{2}a-70\right){x}+17a^{3}-\frac{83}{2}a^{2}-63a+\frac{311}{2}$ |
| 20.1-d1 |
20.1-d |
$4$ |
$6$ |
4.4.12400.1 |
$4$ |
$[4, 0]$ |
20.1 |
\( 2^{2} \cdot 5 \) |
\( 2^{36} \cdot 5^{4} \) |
$14.47032$ |
$(1/2a^3-1/2a^2-7/2a+5/2), (-a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \) |
$1.511945060$ |
$22.84119804$ |
2.481041532 |
\( -\frac{2062826524589}{25600} a^{3} + \frac{4002071809497}{25600} a^{2} + \frac{16989585953303}{25600} a - \frac{32961272479261}{25600} \) |
\( \bigl[1\) , \( -\frac{1}{2} a^{3} + \frac{1}{2} a^{2} + \frac{5}{2} a - \frac{5}{2}\) , \( \frac{1}{2} a^{3} - \frac{7}{2} a + 1\) , \( -30 a^{3} - 58 a^{2} + 246 a + 475\) , \( 245 a^{3} + 473 a^{2} - 2013 a - 3901\bigr] \) |
${y}^2+{x}{y}+\left(\frac{1}{2}a^{3}-\frac{7}{2}a+1\right){y}={x}^{3}+\left(-\frac{1}{2}a^{3}+\frac{1}{2}a^{2}+\frac{5}{2}a-\frac{5}{2}\right){x}^{2}+\left(-30a^{3}-58a^{2}+246a+475\right){x}+245a^{3}+473a^{2}-2013a-3901$ |
| 20.1-d2 |
20.1-d |
$4$ |
$6$ |
4.4.12400.1 |
$4$ |
$[4, 0]$ |
20.1 |
\( 2^{2} \cdot 5 \) |
\( 2^{12} \cdot 5^{12} \) |
$14.47032$ |
$(1/2a^3-1/2a^2-7/2a+5/2), (-a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \cdot 3 \) |
$0.503981686$ |
$22.84119804$ |
2.481041532 |
\( -\frac{2028817931053}{250000} a^{3} + \frac{3032952547803}{125000} a^{2} + \frac{7629088540237}{250000} a - \frac{1142292115229}{12500} \) |
\( \bigl[\frac{1}{2} a^{3} - \frac{7}{2} a + 1\) , \( \frac{1}{2} a^{3} - \frac{1}{2} a^{2} - \frac{7}{2} a + \frac{7}{2}\) , \( \frac{1}{2} a^{2} + a - \frac{7}{2}\) , \( 109 a^{3} - 281 a^{2} - 447 a + 1019\) , \( -\frac{4051}{2} a^{3} + 5934 a^{2} + \frac{15015}{2} a - 22545\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-\frac{7}{2}a+1\right){x}{y}+\left(\frac{1}{2}a^{2}+a-\frac{7}{2}\right){y}={x}^{3}+\left(\frac{1}{2}a^{3}-\frac{1}{2}a^{2}-\frac{7}{2}a+\frac{7}{2}\right){x}^{2}+\left(109a^{3}-281a^{2}-447a+1019\right){x}-\frac{4051}{2}a^{3}+5934a^{2}+\frac{15015}{2}a-22545$ |
*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.
