| 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 |
$2$ |
$5$ |
4.4.4913.1 |
$4$ |
$[4, 0]$ |
4.1 |
\( 2^{2} \) |
\( 2^{70} \) |
$7.44851$ |
$(1/2a^3-a^2-2a+5/2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.1.2 |
$25$ |
\( 1 \) |
$1$ |
$2.545438365$ |
0.907881595 |
\( \frac{69419000739757}{34359738368} a^{3} - \frac{69419000739757}{34359738368} a^{2} - \frac{347095003698785}{34359738368} a - \frac{108360928343791}{34359738368} \) |
\( \bigl[a^{2} - 3\) , \( a^{2} - a - 3\) , \( a\) , \( 18 a^{3} - 10 a^{2} - 107 a - 21\) , \( -\frac{251}{2} a^{3} + 210 a^{2} + 668 a - \frac{1203}{2}\bigr] \) |
${y}^2+\left(a^{2}-3\right){x}{y}+a{y}={x}^{3}+\left(a^{2}-a-3\right){x}^{2}+\left(18a^{3}-10a^{2}-107a-21\right){x}-\frac{251}{2}a^{3}+210a^{2}+668a-\frac{1203}{2}$ |
| 4.1-a2 |
4.1-a |
$2$ |
$5$ |
4.4.4913.1 |
$4$ |
$[4, 0]$ |
4.1 |
\( 2^{2} \) |
\( 2^{14} \) |
$7.44851$ |
$(1/2a^3-a^2-2a+5/2)$ |
0 |
$\Z/5\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.1.1 |
$1$ |
\( 1 \) |
$1$ |
$1590.898978$ |
0.907881595 |
\( -\frac{346627}{128} a^{3} + \frac{346627}{128} a^{2} + \frac{1733135}{128} a - \frac{887903}{128} \) |
\( \bigl[a + 1\) , \( a\) , \( a\) , \( 0\) , \( 0\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+a{x}^{2}$ |
| 4.2-a1 |
4.2-a |
$2$ |
$5$ |
4.4.4913.1 |
$4$ |
$[4, 0]$ |
4.2 |
\( 2^{2} \) |
\( 2^{14} \) |
$7.44851$ |
$(-a-1)$ |
0 |
$\Z/5\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.1.1 |
$1$ |
\( 1 \) |
$1$ |
$1590.898978$ |
0.907881595 |
\( \frac{346627}{128} a^{3} - \frac{346627}{128} a^{2} - \frac{1733135}{128} a - \frac{135319}{32} \) |
\( \bigl[\frac{1}{2} a^{3} - 3 a - \frac{1}{2}\) , \( \frac{1}{2} a^{3} - 3 a - \frac{3}{2}\) , \( -\frac{1}{2} a^{3} + a^{2} + 2 a - \frac{3}{2}\) , \( 2 a^{3} - a^{2} - 11 a - 3\) , \( -\frac{7}{2} a^{3} + 2 a^{2} + 23 a + \frac{13}{2}\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-3a-\frac{1}{2}\right){x}{y}+\left(-\frac{1}{2}a^{3}+a^{2}+2a-\frac{3}{2}\right){y}={x}^{3}+\left(\frac{1}{2}a^{3}-3a-\frac{3}{2}\right){x}^{2}+\left(2a^{3}-a^{2}-11a-3\right){x}-\frac{7}{2}a^{3}+2a^{2}+23a+\frac{13}{2}$ |
| 4.2-a2 |
4.2-a |
$2$ |
$5$ |
4.4.4913.1 |
$4$ |
$[4, 0]$ |
4.2 |
\( 2^{2} \) |
\( 2^{70} \) |
$7.44851$ |
$(-a-1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.1.2 |
$25$ |
\( 1 \) |
$1$ |
$2.545438365$ |
0.907881595 |
\( -\frac{69419000739757}{34359738368} a^{3} + \frac{69419000739757}{34359738368} a^{2} + \frac{347095003698785}{34359738368} a - \frac{44444982270887}{8589934592} \) |
\( \bigl[-\frac{1}{2} a^{3} + a^{2} + 2 a - \frac{1}{2}\) , \( -\frac{1}{2} a^{3} + a^{2} + 2 a - \frac{3}{2}\) , \( -\frac{1}{2} a^{3} + a^{2} + 2 a - \frac{3}{2}\) , \( -\frac{35}{2} a^{3} + 25 a^{2} + 90 a - \frac{95}{2}\) , \( -\frac{29}{2} a^{3} - 41 a^{2} + 284 a - \frac{257}{2}\bigr] \) |
${y}^2+\left(-\frac{1}{2}a^{3}+a^{2}+2a-\frac{1}{2}\right){x}{y}+\left(-\frac{1}{2}a^{3}+a^{2}+2a-\frac{3}{2}\right){y}={x}^{3}+\left(-\frac{1}{2}a^{3}+a^{2}+2a-\frac{3}{2}\right){x}^{2}+\left(-\frac{35}{2}a^{3}+25a^{2}+90a-\frac{95}{2}\right){x}-\frac{29}{2}a^{3}-41a^{2}+284a-\frac{257}{2}$ |
| 16.1-a1 |
16.1-a |
$4$ |
$10$ |
4.4.4913.1 |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{60} \) |
$8.85782$ |
$(1/2a^3-a^2-2a+5/2), (-a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 5$ |
2B, 5B.1.2 |
$25$ |
\( 2^{2} \) |
$1$ |
$3.379388771$ |
1.205326717 |
\( \frac{2823303859929}{1048576} a^{3} - \frac{2823303859929}{1048576} a^{2} - \frac{14116519299645}{1048576} a + \frac{7229268910125}{1048576} \) |
\( \bigl[\frac{1}{2} a^{3} - 3 a - \frac{3}{2}\) , \( -a^{2} + 2 a + 4\) , \( 0\) , \( -87 a^{3} + 104 a^{2} + 511 a - 250\) , \( -780 a^{3} + 1005 a^{2} + 4438 a - 2307\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-3a-\frac{3}{2}\right){x}{y}={x}^{3}+\left(-a^{2}+2a+4\right){x}^{2}+\left(-87a^{3}+104a^{2}+511a-250\right){x}-780a^{3}+1005a^{2}+4438a-2307$ |
| 16.1-a2 |
16.1-a |
$4$ |
$10$ |
4.4.4913.1 |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{12} \) |
$8.85782$ |
$(1/2a^3-a^2-2a+5/2), (-a-1)$ |
0 |
$\Z/10\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 5$ |
2B, 5B.1.1 |
$1$ |
\( 2^{2} \) |
$1$ |
$2112.117982$ |
1.205326717 |
\( \frac{750141}{16} a^{3} - \frac{750141}{16} a^{2} - \frac{3750705}{16} a + \frac{1920861}{16} \) |
\( \bigl[\frac{1}{2} a^{3} - 3 a - \frac{3}{2}\) , \( -a^{2} + 2 a + 4\) , \( 0\) , \( -\frac{9}{2} a^{3} + 4 a^{2} + 26 a + \frac{5}{2}\) , \( -2 a^{3} + a^{2} + 12 a + 6\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-3a-\frac{3}{2}\right){x}{y}={x}^{3}+\left(-a^{2}+2a+4\right){x}^{2}+\left(-\frac{9}{2}a^{3}+4a^{2}+26a+\frac{5}{2}\right){x}-2a^{3}+a^{2}+12a+6$ |
| 16.1-a3 |
16.1-a |
$4$ |
$10$ |
4.4.4913.1 |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{60} \) |
$8.85782$ |
$(1/2a^3-a^2-2a+5/2), (-a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 5$ |
2B, 5B.1.2 |
$25$ |
\( 2^{2} \) |
$1$ |
$3.379388771$ |
1.205326717 |
\( -\frac{2823303859929}{1048576} a^{3} + \frac{2823303859929}{1048576} a^{2} + \frac{14116519299645}{1048576} a + \frac{1101491262549}{262144} \) |
\( \bigl[a\) , \( -a^{2} + 3\) , \( \frac{1}{2} a^{3} - 3 a - \frac{3}{2}\) , \( \frac{113}{2} a^{3} - 11 a^{2} - 364 a - \frac{473}{2}\) , \( 551 a^{3} - 153 a^{2} - 3546 a - 1924\bigr] \) |
${y}^2+a{x}{y}+\left(\frac{1}{2}a^{3}-3a-\frac{3}{2}\right){y}={x}^{3}+\left(-a^{2}+3\right){x}^{2}+\left(\frac{113}{2}a^{3}-11a^{2}-364a-\frac{473}{2}\right){x}+551a^{3}-153a^{2}-3546a-1924$ |
| 16.1-a4 |
16.1-a |
$4$ |
$10$ |
4.4.4913.1 |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{12} \) |
$8.85782$ |
$(1/2a^3-a^2-2a+5/2), (-a-1)$ |
0 |
$\Z/10\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 5$ |
2B, 5B.1.1 |
$1$ |
\( 2^{2} \) |
$1$ |
$2112.117982$ |
1.205326717 |
\( -\frac{750141}{16} a^{3} + \frac{750141}{16} a^{2} + \frac{3750705}{16} a + 73170 \) |
\( \bigl[a\) , \( -a^{2} + 3\) , \( \frac{1}{2} a^{3} - 3 a - \frac{3}{2}\) , \( \frac{3}{2} a^{3} - a^{2} - 9 a - \frac{3}{2}\) , \( \frac{1}{2} a^{3} - a^{2} - 3 a + \frac{5}{2}\bigr] \) |
${y}^2+a{x}{y}+\left(\frac{1}{2}a^{3}-3a-\frac{3}{2}\right){y}={x}^{3}+\left(-a^{2}+3\right){x}^{2}+\left(\frac{3}{2}a^{3}-a^{2}-9a-\frac{3}{2}\right){x}+\frac{1}{2}a^{3}-a^{2}-3a+\frac{5}{2}$ |
| 16.1-b1 |
16.1-b |
$12$ |
$24$ |
4.4.4913.1 |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{54} \) |
$8.85782$ |
$(1/2a^3-a^2-2a+5/2), (-a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2^{3} \cdot 3^{2} \) |
$1$ |
$6.508937725$ |
1.671511001 |
\( -\frac{55573026649}{16777216} a^{3} + \frac{55573026649}{16777216} a^{2} + \frac{277865133245}{16777216} a - \frac{35327972395}{4194304} \) |
\( \bigl[-\frac{1}{2} a^{3} + a^{2} + 3 a - \frac{3}{2}\) , \( 0\) , \( 1\) , \( -\frac{13}{2} a^{3} + 4 a^{2} + 21 a - \frac{21}{2}\) , \( -10 a^{3} - 29 a^{2} + 57 a - 20\bigr] \) |
${y}^2+\left(-\frac{1}{2}a^{3}+a^{2}+3a-\frac{3}{2}\right){x}{y}+{y}={x}^{3}+\left(-\frac{13}{2}a^{3}+4a^{2}+21a-\frac{21}{2}\right){x}-10a^{3}-29a^{2}+57a-20$ |
| 16.1-b2 |
16.1-b |
$12$ |
$24$ |
4.4.4913.1 |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{18} \) |
$8.85782$ |
$(1/2a^3-a^2-2a+5/2), (-a-1)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{3} \) |
$1$ |
$527.2239557$ |
1.671511001 |
\( \frac{110887}{256} a^{3} - \frac{110887}{256} a^{2} - \frac{554435}{256} a + \frac{66933}{64} \) |
\( \bigl[-\frac{1}{2} a^{3} + a^{2} + 3 a - \frac{3}{2}\) , \( 0\) , \( 1\) , \( a^{3} - a^{2} - 4 a + 2\) , \( a^{2} - a\bigr] \) |
${y}^2+\left(-\frac{1}{2}a^{3}+a^{2}+3a-\frac{3}{2}\right){x}{y}+{y}={x}^{3}+\left(a^{3}-a^{2}-4a+2\right){x}+a^{2}-a$ |
| 16.1-b3 |
16.1-b |
$12$ |
$24$ |
4.4.4913.1 |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{18} \) |
$8.85782$ |
$(1/2a^3-a^2-2a+5/2), (-a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$4$ |
\( 2 \cdot 3^{2} \) |
$1$ |
$6.508937725$ |
1.671511001 |
\( -\frac{653762688677050897}{64} a^{3} + \frac{653762688677050897}{64} a^{2} + \frac{3268813443385254485}{64} a + \frac{1020884965413408563}{64} \) |
\( \bigl[-\frac{1}{2} a^{3} + a^{2} + 3 a - \frac{3}{2}\) , \( -\frac{1}{2} a^{3} + 3 a + \frac{3}{2}\) , \( \frac{1}{2} a^{3} - 2 a - \frac{1}{2}\) , \( 49 a^{3} - 295 a^{2} + 229 a - 46\) , \( \frac{4121}{2} a^{3} - 5454 a^{2} - 245 a + \frac{2353}{2}\bigr] \) |
${y}^2+\left(-\frac{1}{2}a^{3}+a^{2}+3a-\frac{3}{2}\right){x}{y}+\left(\frac{1}{2}a^{3}-2a-\frac{1}{2}\right){y}={x}^{3}+\left(-\frac{1}{2}a^{3}+3a+\frac{3}{2}\right){x}^{2}+\left(49a^{3}-295a^{2}+229a-46\right){x}+\frac{4121}{2}a^{3}-5454a^{2}-245a+\frac{2353}{2}$ |
| 16.1-b4 |
16.1-b |
$12$ |
$24$ |
4.4.4913.1 |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{36} \) |
$8.85782$ |
$(1/2a^3-a^2-2a+5/2), (-a-1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2Cs, 3B.1.2 |
$1$ |
\( 2^{3} \cdot 3^{2} \) |
$1$ |
$26.03575090$ |
1.671511001 |
\( -\frac{203862548967}{4096} a^{3} + \frac{203862548967}{4096} a^{2} + \frac{1019312744835}{4096} a + \frac{318403919021}{4096} \) |
\( \bigl[-\frac{1}{2} a^{3} + a^{2} + 3 a - \frac{3}{2}\) , \( -\frac{1}{2} a^{3} + 3 a + \frac{3}{2}\) , \( \frac{1}{2} a^{3} - 2 a - \frac{1}{2}\) , \( -11 a^{3} - 15 a^{2} + 69 a - 26\) , \( -\frac{79}{2} a^{3} - 94 a^{2} + 227 a - \frac{167}{2}\bigr] \) |
${y}^2+\left(-\frac{1}{2}a^{3}+a^{2}+3a-\frac{3}{2}\right){x}{y}+\left(\frac{1}{2}a^{3}-2a-\frac{1}{2}\right){y}={x}^{3}+\left(-\frac{1}{2}a^{3}+3a+\frac{3}{2}\right){x}^{2}+\left(-11a^{3}-15a^{2}+69a-26\right){x}-\frac{79}{2}a^{3}-94a^{2}+227a-\frac{167}{2}$ |
| 16.1-b5 |
16.1-b |
$12$ |
$24$ |
4.4.4913.1 |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{54} \) |
$8.85782$ |
$(1/2a^3-a^2-2a+5/2), (-a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2^{3} \cdot 3^{2} \) |
$1$ |
$6.508937725$ |
1.671511001 |
\( \frac{55573026649}{16777216} a^{3} - \frac{55573026649}{16777216} a^{2} - \frac{277865133245}{16777216} a - \frac{85738862931}{16777216} \) |
\( \bigl[-\frac{1}{2} a^{3} + a^{2} + 3 a - \frac{1}{2}\) , \( -a^{3} + a^{2} + 6 a\) , \( a + 1\) , \( \frac{527}{2} a^{3} - 135 a^{2} - 1646 a - \frac{1075}{2}\) , \( 4245 a^{3} - 2173 a^{2} - 26530 a - 8703\bigr] \) |
${y}^2+\left(-\frac{1}{2}a^{3}+a^{2}+3a-\frac{1}{2}\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a^{3}+a^{2}+6a\right){x}^{2}+\left(\frac{527}{2}a^{3}-135a^{2}-1646a-\frac{1075}{2}\right){x}+4245a^{3}-2173a^{2}-26530a-8703$ |
| 16.1-b6 |
16.1-b |
$12$ |
$24$ |
4.4.4913.1 |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{18} \) |
$8.85782$ |
$(1/2a^3-a^2-2a+5/2), (-a-1)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{3} \) |
$1$ |
$527.2239557$ |
1.671511001 |
\( -\frac{110887}{256} a^{3} + \frac{110887}{256} a^{2} + \frac{554435}{256} a + \frac{156845}{256} \) |
\( \bigl[-\frac{1}{2} a^{3} + a^{2} + 3 a - \frac{1}{2}\) , \( -a^{3} + a^{2} + 6 a\) , \( a + 1\) , \( -19 a^{3} + 10 a^{2} + 119 a + 40\) , \( -17 a^{3} + 9 a^{2} + 107 a + 35\bigr] \) |
${y}^2+\left(-\frac{1}{2}a^{3}+a^{2}+3a-\frac{1}{2}\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a^{3}+a^{2}+6a\right){x}^{2}+\left(-19a^{3}+10a^{2}+119a+40\right){x}-17a^{3}+9a^{2}+107a+35$ |
| 16.1-b7 |
16.1-b |
$12$ |
$24$ |
4.4.4913.1 |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{18} \) |
$8.85782$ |
$(1/2a^3-a^2-2a+5/2), (-a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$4$ |
\( 2 \cdot 3^{2} \) |
$1$ |
$6.508937725$ |
1.671511001 |
\( \frac{653762688677050897}{64} a^{3} - \frac{653762688677050897}{64} a^{2} - \frac{3268813443385254485}{64} a + \frac{418661913522614865}{16} \) |
\( \bigl[-\frac{1}{2} a^{3} + a^{2} + 3 a - \frac{1}{2}\) , \( -a^{2} + 2 a + 3\) , \( a + 1\) , \( 2251 a^{3} - 1133 a^{2} - 14091 a - 4744\) , \( -\frac{143863}{2} a^{3} + 36944 a^{2} + 449440 a + \frac{293461}{2}\bigr] \) |
${y}^2+\left(-\frac{1}{2}a^{3}+a^{2}+3a-\frac{1}{2}\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a^{2}+2a+3\right){x}^{2}+\left(2251a^{3}-1133a^{2}-14091a-4744\right){x}-\frac{143863}{2}a^{3}+36944a^{2}+449440a+\frac{293461}{2}$ |
| 16.1-b8 |
16.1-b |
$12$ |
$24$ |
4.4.4913.1 |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{36} \) |
$8.85782$ |
$(1/2a^3-a^2-2a+5/2), (-a-1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2Cs, 3B.1.2 |
$1$ |
\( 2^{3} \cdot 3^{2} \) |
$1$ |
$26.03575090$ |
1.671511001 |
\( \frac{203862548967}{4096} a^{3} - \frac{203862548967}{4096} a^{2} - \frac{1019312744835}{4096} a + \frac{130566616997}{1024} \) |
\( \bigl[-\frac{1}{2} a^{3} + a^{2} + 3 a - \frac{1}{2}\) , \( -a^{2} + 2 a + 3\) , \( a + 1\) , \( 731 a^{3} - 373 a^{2} - 4571 a - 1504\) , \( \frac{34473}{2} a^{3} - 8824 a^{2} - 107728 a - \frac{70683}{2}\bigr] \) |
${y}^2+\left(-\frac{1}{2}a^{3}+a^{2}+3a-\frac{1}{2}\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a^{2}+2a+3\right){x}^{2}+\left(731a^{3}-373a^{2}-4571a-1504\right){x}+\frac{34473}{2}a^{3}-8824a^{2}-107728a-\frac{70683}{2}$ |
| 16.1-b9 |
16.1-b |
$12$ |
$24$ |
4.4.4913.1 |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{6} \) |
$8.85782$ |
$(1/2a^3-a^2-2a+5/2), (-a-1)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$4$ |
\( 2 \) |
$1$ |
$527.2239557$ |
1.671511001 |
\( -\frac{54503407609}{4} a^{3} + \frac{54503407609}{4} a^{2} + \frac{272517038045}{4} a + \frac{42555672073}{2} \) |
\( \bigl[1\) , \( -a^{3} + a^{2} + 5 a\) , \( a^{2} - a - 2\) , \( -\frac{23}{2} a^{3} + 11 a^{2} + 58 a - \frac{61}{2}\) , \( -\frac{55}{2} a^{3} + 27 a^{2} + 138 a - \frac{143}{2}\bigr] \) |
${y}^2+{x}{y}+\left(a^{2}-a-2\right){y}={x}^{3}+\left(-a^{3}+a^{2}+5a\right){x}^{2}+\left(-\frac{23}{2}a^{3}+11a^{2}+58a-\frac{61}{2}\right){x}-\frac{55}{2}a^{3}+27a^{2}+138a-\frac{143}{2}$ |
| 16.1-b10 |
16.1-b |
$12$ |
$24$ |
4.4.4913.1 |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{12} \) |
$8.85782$ |
$(1/2a^3-a^2-2a+5/2), (-a-1)$ |
0 |
$\Z/2\Z\oplus\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2Cs, 3B.1.1 |
$1$ |
\( 2^{3} \) |
$1$ |
$2108.895823$ |
1.671511001 |
\( -\frac{915957}{16} a^{3} + \frac{915957}{16} a^{2} + \frac{4579785}{16} a + \frac{182257}{2} \) |
\( \bigl[1\) , \( -a^{3} + a^{2} + 5 a\) , \( a^{2} - a - 2\) , \( -\frac{3}{2} a^{3} + a^{2} + 8 a - \frac{1}{2}\) , \( \frac{1}{2} a^{3} - a^{2} - 2 a + \frac{1}{2}\bigr] \) |
${y}^2+{x}{y}+\left(a^{2}-a-2\right){y}={x}^{3}+\left(-a^{3}+a^{2}+5a\right){x}^{2}+\left(-\frac{3}{2}a^{3}+a^{2}+8a-\frac{1}{2}\right){x}+\frac{1}{2}a^{3}-a^{2}-2a+\frac{1}{2}$ |
| 16.1-b11 |
16.1-b |
$12$ |
$24$ |
4.4.4913.1 |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{6} \) |
$8.85782$ |
$(1/2a^3-a^2-2a+5/2), (-a-1)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$4$ |
\( 2 \) |
$1$ |
$527.2239557$ |
1.671511001 |
\( \frac{54503407609}{4} a^{3} - \frac{54503407609}{4} a^{2} - \frac{272517038045}{4} a + \frac{139614751755}{4} \) |
\( \bigl[1\) , \( a^{3} - a^{2} - 5 a + 1\) , \( a^{2} - a - 3\) , \( \frac{23}{2} a^{3} - 12 a^{2} - 57 a - \frac{37}{2}\) , \( 28 a^{3} - 28 a^{2} - 140 a - 45\bigr] \) |
${y}^2+{x}{y}+\left(a^{2}-a-3\right){y}={x}^{3}+\left(a^{3}-a^{2}-5a+1\right){x}^{2}+\left(\frac{23}{2}a^{3}-12a^{2}-57a-\frac{37}{2}\right){x}+28a^{3}-28a^{2}-140a-45$ |
| 16.1-b12 |
16.1-b |
$12$ |
$24$ |
4.4.4913.1 |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{12} \) |
$8.85782$ |
$(1/2a^3-a^2-2a+5/2), (-a-1)$ |
0 |
$\Z/2\Z\oplus\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2Cs, 3B.1.1 |
$1$ |
\( 2^{3} \) |
$1$ |
$2108.895823$ |
1.671511001 |
\( \frac{915957}{16} a^{3} - \frac{915957}{16} a^{2} - \frac{4579785}{16} a + \frac{2374013}{16} \) |
\( \bigl[1\) , \( a^{3} - a^{2} - 5 a + 1\) , \( a^{2} - a - 3\) , \( \frac{3}{2} a^{3} - 2 a^{2} - 7 a + \frac{3}{2}\) , \( -1\bigr] \) |
${y}^2+{x}{y}+\left(a^{2}-a-3\right){y}={x}^{3}+\left(a^{3}-a^{2}-5a+1\right){x}^{2}+\left(\frac{3}{2}a^{3}-2a^{2}-7a+\frac{3}{2}\right){x}-1$ |
| 16.1-c1 |
16.1-c |
$4$ |
$10$ |
4.4.4913.1 |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{30} \) |
$8.85782$ |
$(1/2a^3-a^2-2a+5/2), (-a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 5$ |
2B, 5B.1.2 |
$25$ |
\( 2 \) |
$1$ |
$2.857322084$ |
0.509560586 |
\( \frac{5496753136423}{1024} a^{3} - \frac{5496753136423}{1024} a^{2} - \frac{27483765682115}{1024} a + \frac{3520017969613}{256} \) |
\( \bigl[a^{2} - 2\) , \( a\) , \( -\frac{1}{2} a^{3} + a^{2} + 3 a - \frac{3}{2}\) , \( -\frac{19}{2} a^{3} - 42 a^{2} + 13 a - \frac{3}{2}\) , \( -189 a^{3} - 469 a^{2} + 106 a + 72\bigr] \) |
${y}^2+\left(a^{2}-2\right){x}{y}+\left(-\frac{1}{2}a^{3}+a^{2}+3a-\frac{3}{2}\right){y}={x}^{3}+a{x}^{2}+\left(-\frac{19}{2}a^{3}-42a^{2}+13a-\frac{3}{2}\right){x}-189a^{3}-469a^{2}+106a+72$ |
| 16.1-c2 |
16.1-c |
$4$ |
$10$ |
4.4.4913.1 |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{6} \) |
$8.85782$ |
$(1/2a^3-a^2-2a+5/2), (-a-1)$ |
0 |
$\Z/10\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 5$ |
2B, 5B.1.1 |
$1$ |
\( 2 \) |
$1$ |
$1785.826303$ |
0.509560586 |
\( -\frac{4117}{4} a^{3} + \frac{4117}{4} a^{2} + \frac{20585}{4} a + \frac{8517}{4} \) |
\( \bigl[\frac{1}{2} a^{3} - 3 a - \frac{3}{2}\) , \( a^{3} - a^{2} - 4 a\) , \( \frac{1}{2} a^{3} - 3 a - \frac{1}{2}\) , \( a^{3} - 6 a\) , \( \frac{1}{2} a^{3} - 3 a + \frac{1}{2}\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-3a-\frac{3}{2}\right){x}{y}+\left(\frac{1}{2}a^{3}-3a-\frac{1}{2}\right){y}={x}^{3}+\left(a^{3}-a^{2}-4a\right){x}^{2}+\left(a^{3}-6a\right){x}+\frac{1}{2}a^{3}-3a+\frac{1}{2}$ |
| 16.1-c3 |
16.1-c |
$4$ |
$10$ |
4.4.4913.1 |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{30} \) |
$8.85782$ |
$(1/2a^3-a^2-2a+5/2), (-a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 5$ |
2B, 5B.1.2 |
$25$ |
\( 2 \) |
$1$ |
$2.857322084$ |
0.509560586 |
\( -\frac{5496753136423}{1024} a^{3} + \frac{5496753136423}{1024} a^{2} + \frac{27483765682115}{1024} a + \frac{8583318742029}{1024} \) |
\( \bigl[-\frac{1}{2} a^{3} + a^{2} + 2 a - \frac{3}{2}\) , \( -a^{3} + a^{2} + 4 a + 1\) , \( a^{2} - a - 3\) , \( \frac{223}{2} a^{3} - 62 a^{2} - 718 a - \frac{489}{2}\) , \( \frac{2433}{2} a^{3} - 647 a^{2} - 7657 a - \frac{5039}{2}\bigr] \) |
${y}^2+\left(-\frac{1}{2}a^{3}+a^{2}+2a-\frac{3}{2}\right){x}{y}+\left(a^{2}-a-3\right){y}={x}^{3}+\left(-a^{3}+a^{2}+4a+1\right){x}^{2}+\left(\frac{223}{2}a^{3}-62a^{2}-718a-\frac{489}{2}\right){x}+\frac{2433}{2}a^{3}-647a^{2}-7657a-\frac{5039}{2}$ |
| 16.1-c4 |
16.1-c |
$4$ |
$10$ |
4.4.4913.1 |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{6} \) |
$8.85782$ |
$(1/2a^3-a^2-2a+5/2), (-a-1)$ |
0 |
$\Z/10\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 5$ |
2B, 5B.1.1 |
$1$ |
\( 2 \) |
$1$ |
$1785.826303$ |
0.509560586 |
\( \frac{4117}{4} a^{3} - \frac{4117}{4} a^{2} - \frac{20585}{4} a + \frac{6317}{2} \) |
\( \bigl[a\) , \( -a^{2} + a + 2\) , \( -\frac{1}{2} a^{3} + a^{2} + 2 a - \frac{3}{2}\) , \( -\frac{3}{2} a^{3} + 2 a^{2} + 7 a - \frac{1}{2}\) , \( -\frac{1}{2} a^{3} + 4 a + \frac{1}{2}\bigr] \) |
${y}^2+a{x}{y}+\left(-\frac{1}{2}a^{3}+a^{2}+2a-\frac{3}{2}\right){y}={x}^{3}+\left(-a^{2}+a+2\right){x}^{2}+\left(-\frac{3}{2}a^{3}+2a^{2}+7a-\frac{1}{2}\right){x}-\frac{1}{2}a^{3}+4a+\frac{1}{2}$ |
| 16.2-a1 |
16.2-a |
$4$ |
$4$ |
4.4.4913.1 |
$4$ |
$[4, 0]$ |
16.2 |
\( 2^{4} \) |
\( - 2^{16} \) |
$8.85782$ |
$(1/2a^3-a^2-2a+5/2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$502.9366260$ |
1.793824249 |
\( -78828400594 a^{3} + 40366354305 a^{2} + 492667383775 a + 161557746473 \) |
\( \bigl[a^{2} - a - 3\) , \( -a^{3} + a^{2} + 4 a + 1\) , \( \frac{1}{2} a^{3} - 3 a - \frac{1}{2}\) , \( -\frac{15}{2} a^{3} - 8 a^{2} + 8 a + \frac{7}{2}\) , \( -\frac{61}{2} a^{3} - 53 a^{2} + 16 a + \frac{21}{2}\bigr] \) |
${y}^2+\left(a^{2}-a-3\right){x}{y}+\left(\frac{1}{2}a^{3}-3a-\frac{1}{2}\right){y}={x}^{3}+\left(-a^{3}+a^{2}+4a+1\right){x}^{2}+\left(-\frac{15}{2}a^{3}-8a^{2}+8a+\frac{7}{2}\right){x}-\frac{61}{2}a^{3}-53a^{2}+16a+\frac{21}{2}$ |
| 16.2-a2 |
16.2-a |
$4$ |
$4$ |
4.4.4913.1 |
$4$ |
$[4, 0]$ |
16.2 |
\( 2^{4} \) |
\( 2^{8} \) |
$8.85782$ |
$(1/2a^3-a^2-2a+5/2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2Cs |
$1$ |
\( 1 \) |
$1$ |
$2011.746504$ |
1.793824249 |
\( -153101 a^{3} + 153101 a^{2} + 765505 a + 242916 \) |
\( \bigl[a^{2} - a - 3\) , \( -a^{3} + a^{2} + 4 a + 1\) , \( \frac{1}{2} a^{3} - 3 a - \frac{1}{2}\) , \( -\frac{5}{2} a^{3} + 2 a^{2} + 8 a + \frac{7}{2}\) , \( -2 a^{3} + 2 a^{2} + 7 a + 2\bigr] \) |
${y}^2+\left(a^{2}-a-3\right){x}{y}+\left(\frac{1}{2}a^{3}-3a-\frac{1}{2}\right){y}={x}^{3}+\left(-a^{3}+a^{2}+4a+1\right){x}^{2}+\left(-\frac{5}{2}a^{3}+2a^{2}+8a+\frac{7}{2}\right){x}-2a^{3}+2a^{2}+7a+2$ |
| 16.2-a3 |
16.2-a |
$4$ |
$4$ |
4.4.4913.1 |
$4$ |
$[4, 0]$ |
16.2 |
\( 2^{4} \) |
\( - 2^{16} \) |
$8.85782$ |
$(1/2a^3-a^2-2a+5/2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$502.9366260$ |
1.793824249 |
\( -18765066078 a^{3} + 57227112367 a^{2} - 4700050415 a - 9151196745 \) |
\( \bigl[a^{2} - a - 3\) , \( -a^{3} + a^{2} + 4 a + 1\) , \( \frac{1}{2} a^{3} - 3 a - \frac{1}{2}\) , \( -\frac{5}{2} a^{3} - 8 a^{2} + 13 a + \frac{7}{2}\) , \( \frac{11}{2} a^{3} + 22 a^{2} + 7 a - \frac{7}{2}\bigr] \) |
${y}^2+\left(a^{2}-a-3\right){x}{y}+\left(\frac{1}{2}a^{3}-3a-\frac{1}{2}\right){y}={x}^{3}+\left(-a^{3}+a^{2}+4a+1\right){x}^{2}+\left(-\frac{5}{2}a^{3}-8a^{2}+13a+\frac{7}{2}\right){x}+\frac{11}{2}a^{3}+22a^{2}+7a-\frac{7}{2}$ |
| 16.2-a4 |
16.2-a |
$4$ |
$4$ |
4.4.4913.1 |
$4$ |
$[4, 0]$ |
16.2 |
\( 2^{4} \) |
\( 2^{16} \) |
$8.85782$ |
$(1/2a^3-a^2-2a+5/2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$502.9366260$ |
1.793824249 |
\( -273 a^{3} + 273 a^{2} + 1365 a + 1124 \) |
\( \bigl[-\frac{1}{2} a^{3} + a^{2} + 2 a - \frac{1}{2}\) , \( -\frac{1}{2} a^{3} + a^{2} + 3 a - \frac{1}{2}\) , \( \frac{1}{2} a^{3} - 3 a - \frac{1}{2}\) , \( \frac{1}{2} a^{3} - 3 a + \frac{5}{2}\) , \( -\frac{1}{2} a^{3} + a^{2} + 3 a - \frac{5}{2}\bigr] \) |
${y}^2+\left(-\frac{1}{2}a^{3}+a^{2}+2a-\frac{1}{2}\right){x}{y}+\left(\frac{1}{2}a^{3}-3a-\frac{1}{2}\right){y}={x}^{3}+\left(-\frac{1}{2}a^{3}+a^{2}+3a-\frac{1}{2}\right){x}^{2}+\left(\frac{1}{2}a^{3}-3a+\frac{5}{2}\right){x}-\frac{1}{2}a^{3}+a^{2}+3a-\frac{5}{2}$ |
| 16.3-a1 |
16.3-a |
$4$ |
$4$ |
4.4.4913.1 |
$4$ |
$[4, 0]$ |
16.3 |
\( 2^{4} \) |
\( 2^{16} \) |
$8.85782$ |
$(-a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$502.9366260$ |
1.793824249 |
\( 273 a^{3} - 273 a^{2} - 1365 a + 1397 \) |
\( \bigl[a^{2} - 3\) , \( a^{3} - a^{2} - 5 a + 1\) , \( 0\) , \( a^{3} + a^{2} - a + 3\) , \( a^{3} + 2 a^{2} - a - 2\bigr] \) |
${y}^2+\left(a^{2}-3\right){x}{y}={x}^{3}+\left(a^{3}-a^{2}-5a+1\right){x}^{2}+\left(a^{3}+a^{2}-a+3\right){x}+a^{3}+2a^{2}-a-2$ |
| 16.3-a2 |
16.3-a |
$4$ |
$4$ |
4.4.4913.1 |
$4$ |
$[4, 0]$ |
16.3 |
\( 2^{4} \) |
\( - 2^{16} \) |
$8.85782$ |
$(-a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$502.9366260$ |
1.793824249 |
\( 87258779625 a^{3} - 117290446883 a^{2} - 483186323445 a + 253557056263 \) |
\( \bigl[a^{2} - a - 2\) , \( -a^{3} + a^{2} + 5 a - 1\) , \( a + 1\) , \( \frac{83}{2} a^{3} - 20 a^{2} - 265 a - \frac{177}{2}\) , \( 291 a^{3} - 149 a^{2} - 1820 a - 593\bigr] \) |
${y}^2+\left(a^{2}-a-2\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a^{3}+a^{2}+5a-1\right){x}^{2}+\left(\frac{83}{2}a^{3}-20a^{2}-265a-\frac{177}{2}\right){x}+291a^{3}-149a^{2}-1820a-593$ |
| 16.3-a3 |
16.3-a |
$4$ |
$4$ |
4.4.4913.1 |
$4$ |
$[4, 0]$ |
16.3 |
\( 2^{4} \) |
\( - 2^{16} \) |
$8.85782$ |
$(-a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$502.9366260$ |
1.793824249 |
\( 10334687047 a^{3} + 19696980211 a^{2} - 4781009915 a - 3557039863 \) |
\( \bigl[a^{2} - a - 2\) , \( -a^{3} + a^{2} + 5 a - 1\) , \( a + 1\) , \( 14 a^{3} - 10 a^{2} - 100 a - 31\) , \( -37 a^{3} + 28 a^{2} + 253 a + 82\bigr] \) |
${y}^2+\left(a^{2}-a-2\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a^{3}+a^{2}+5a-1\right){x}^{2}+\left(14a^{3}-10a^{2}-100a-31\right){x}-37a^{3}+28a^{2}+253a+82$ |
| 16.3-a4 |
16.3-a |
$4$ |
$4$ |
4.4.4913.1 |
$4$ |
$[4, 0]$ |
16.3 |
\( 2^{4} \) |
\( 2^{8} \) |
$8.85782$ |
$(-a-1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2Cs |
$1$ |
\( 1 \) |
$1$ |
$2011.746504$ |
1.793824249 |
\( 153101 a^{3} - 153101 a^{2} - 765505 a + 396017 \) |
\( \bigl[a^{2} - a - 2\) , \( -a^{3} + a^{2} + 5 a - 1\) , \( a + 1\) , \( \frac{3}{2} a^{3} - 15 a - \frac{7}{2}\) , \( \frac{11}{2} a^{3} - 2 a^{2} - 37 a - \frac{25}{2}\bigr] \) |
${y}^2+\left(a^{2}-a-2\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a^{3}+a^{2}+5a-1\right){x}^{2}+\left(\frac{3}{2}a^{3}-15a-\frac{7}{2}\right){x}+\frac{11}{2}a^{3}-2a^{2}-37a-\frac{25}{2}$ |
| 17.1-a1 |
17.1-a |
$8$ |
$16$ |
4.4.4913.1 |
$4$ |
$[4, 0]$ |
17.1 |
\( 17 \) |
\( 17^{2} \) |
$8.92520$ |
$(1/2a^3-2a-3/2)$ |
$1$ |
$\Z/8\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.379407022$ |
$1466.529406$ |
0.992276649 |
\( \frac{5821794}{17} a^{3} - \frac{5821794}{17} a^{2} - \frac{29108970}{17} a + \frac{14936697}{17} \) |
\( \bigl[-\frac{1}{2} a^{3} + a^{2} + 3 a - \frac{3}{2}\) , \( a^{2} - 2 a - 2\) , \( \frac{1}{2} a^{3} - 2 a - \frac{1}{2}\) , \( -\frac{5}{2} a^{3} + 4 a^{2} + 5 a - \frac{1}{2}\) , \( -2 a^{3} + 6 a^{2} - 3 a - 1\bigr] \) |
${y}^2+\left(-\frac{1}{2}a^{3}+a^{2}+3a-\frac{3}{2}\right){x}{y}+\left(\frac{1}{2}a^{3}-2a-\frac{1}{2}\right){y}={x}^{3}+\left(a^{2}-2a-2\right){x}^{2}+\left(-\frac{5}{2}a^{3}+4a^{2}+5a-\frac{1}{2}\right){x}-2a^{3}+6a^{2}-3a-1$ |
| 17.1-a2 |
17.1-a |
$8$ |
$16$ |
4.4.4913.1 |
$4$ |
$[4, 0]$ |
17.1 |
\( 17 \) |
\( 17^{2} \) |
$8.92520$ |
$(1/2a^3-2a-3/2)$ |
$1$ |
$\Z/8\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.379407022$ |
$1466.529406$ |
0.992276649 |
\( -\frac{5821794}{17} a^{3} + \frac{5821794}{17} a^{2} + \frac{29108970}{17} a + \frac{9114903}{17} \) |
\( \bigl[-\frac{1}{2} a^{3} + a^{2} + 3 a - \frac{1}{2}\) , \( a^{3} - a^{2} - 5 a\) , \( \frac{1}{2} a^{3} - 3 a - \frac{3}{2}\) , \( 26 a^{3} - 13 a^{2} - 161 a - 51\) , \( -134 a^{3} + 69 a^{2} + 839 a + 276\bigr] \) |
${y}^2+\left(-\frac{1}{2}a^{3}+a^{2}+3a-\frac{1}{2}\right){x}{y}+\left(\frac{1}{2}a^{3}-3a-\frac{3}{2}\right){y}={x}^{3}+\left(a^{3}-a^{2}-5a\right){x}^{2}+\left(26a^{3}-13a^{2}-161a-51\right){x}-134a^{3}+69a^{2}+839a+276$ |
| 17.1-a3 |
17.1-a |
$8$ |
$16$ |
4.4.4913.1 |
$4$ |
$[4, 0]$ |
17.1 |
\( 17 \) |
\( 17^{2} \) |
$8.92520$ |
$(1/2a^3-2a-3/2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$64$ |
\( 2 \) |
$1.517628088$ |
$0.358039405$ |
0.992276649 |
\( \frac{97064067741644382786}{17} a^{3} - \frac{97064067741644382786}{17} a^{2} - \frac{485320338708221913930}{17} a + \frac{248634735746274843273}{17} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -330 a^{3} + 330 a^{2} + 1650 a - 936\) , \( -4996 a^{3} + 4996 a^{2} + 24980 a - 13110\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}+\left(-330a^{3}+330a^{2}+1650a-936\right){x}-4996a^{3}+4996a^{2}+24980a-13110$ |
| 17.1-a4 |
17.1-a |
$8$ |
$16$ |
4.4.4913.1 |
$4$ |
$[4, 0]$ |
17.1 |
\( 17 \) |
\( 17^{2} \) |
$8.92520$ |
$(1/2a^3-2a-3/2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$64$ |
\( 2 \) |
$1.517628088$ |
$0.358039405$ |
0.992276649 |
\( -\frac{97064067741644382786}{17} a^{3} + \frac{97064067741644382786}{17} a^{2} + \frac{485320338708221913930}{17} a + \frac{151570668004630460487}{17} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( 330 a^{3} - 330 a^{2} - 1650 a - 606\) , \( 4996 a^{3} - 4996 a^{2} - 24980 a - 8114\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}+\left(330a^{3}-330a^{2}-1650a-606\right){x}+4996a^{3}-4996a^{2}-24980a-8114$ |
| 17.1-a5 |
17.1-a |
$8$ |
$16$ |
4.4.4913.1 |
$4$ |
$[4, 0]$ |
17.1 |
\( 17 \) |
\( 17^{4} \) |
$8.92520$ |
$(1/2a^3-2a-3/2)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$16$ |
\( 2^{2} \) |
$0.758814044$ |
$5.728630493$ |
0.992276649 |
\( \frac{82483294977}{17} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -91\) , \( -310\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}-91{x}-310$ |
| 17.1-a6 |
17.1-a |
$8$ |
$16$ |
4.4.4913.1 |
$4$ |
$[4, 0]$ |
17.1 |
\( 17 \) |
\( 17^{8} \) |
$8.92520$ |
$(1/2a^3-2a-3/2)$ |
$1$ |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$4$ |
\( 2^{3} \) |
$0.379407022$ |
$91.65808789$ |
0.992276649 |
\( \frac{20346417}{289} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -6\) , \( -4\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}-6{x}-4$ |
| 17.1-a7 |
17.1-a |
$8$ |
$16$ |
4.4.4913.1 |
$4$ |
$[4, 0]$ |
17.1 |
\( 17 \) |
\( 17^{16} \) |
$8.92520$ |
$(1/2a^3-2a-3/2)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$4$ |
\( 2^{4} \) |
$0.758814044$ |
$5.728630493$ |
0.992276649 |
\( -\frac{35937}{83521} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -1\) , \( -14\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}-{x}-14$ |
| 17.1-a8 |
17.1-a |
$8$ |
$16$ |
4.4.4913.1 |
$4$ |
$[4, 0]$ |
17.1 |
\( 17 \) |
\( 17^{4} \) |
$8.92520$ |
$(1/2a^3-2a-3/2)$ |
$1$ |
$\Z/2\Z\oplus\Z/8\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$0.758814044$ |
$1466.529406$ |
0.992276649 |
\( \frac{35937}{17} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -1\) , \( 0\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}-{x}$ |
| 47.1-a1 |
47.1-a |
$4$ |
$4$ |
4.4.4913.1 |
$4$ |
$[4, 0]$ |
47.1 |
\( 47 \) |
\( 47^{4} \) |
$10.13501$ |
$(a^2-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$311.2963543$ |
2.220601643 |
\( -\frac{854106486661303}{9759362} a^{3} + \frac{1309708070168852}{4879681} a^{2} - \frac{107768209049327}{4879681} a - \frac{419232771807451}{9759362} \) |
\( \bigl[-\frac{1}{2} a^{3} + a^{2} + 3 a - \frac{3}{2}\) , \( -a^{2} + 2\) , \( a^{2} - a - 3\) , \( -\frac{11}{2} a^{3} + 41 a + \frac{31}{2}\) , \( 95 a^{3} - 43 a^{2} - 609 a - 201\bigr] \) |
${y}^2+\left(-\frac{1}{2}a^{3}+a^{2}+3a-\frac{3}{2}\right){x}{y}+\left(a^{2}-a-3\right){y}={x}^{3}+\left(-a^{2}+2\right){x}^{2}+\left(-\frac{11}{2}a^{3}+41a+\frac{31}{2}\right){x}+95a^{3}-43a^{2}-609a-201$ |
| 47.1-a2 |
47.1-a |
$4$ |
$4$ |
4.4.4913.1 |
$4$ |
$[4, 0]$ |
47.1 |
\( 47 \) |
\( 47^{2} \) |
$10.13501$ |
$(a^2-2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2 \) |
$1$ |
$1245.185417$ |
2.220601643 |
\( -\frac{14995779}{4418} a^{3} + \frac{11982345}{2209} a^{2} + \frac{22108274}{2209} a + \frac{55891815}{4418} \) |
\( \bigl[-\frac{1}{2} a^{3} + a^{2} + 3 a - \frac{1}{2}\) , \( a^{2} - a - 3\) , \( a\) , \( -6 a^{3} + 9 a^{2} + 33 a - 15\) , \( -6 a^{3} + 9 a^{2} + 34 a - 19\bigr] \) |
${y}^2+\left(-\frac{1}{2}a^{3}+a^{2}+3a-\frac{1}{2}\right){x}{y}+a{y}={x}^{3}+\left(a^{2}-a-3\right){x}^{2}+\left(-6a^{3}+9a^{2}+33a-15\right){x}-6a^{3}+9a^{2}+34a-19$ |
| 47.1-a3 |
47.1-a |
$4$ |
$4$ |
4.4.4913.1 |
$4$ |
$[4, 0]$ |
47.1 |
\( 47 \) |
\( 47 \) |
$10.13501$ |
$(a^2-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$622.5927087$ |
2.220601643 |
\( \frac{1733458109}{94} a^{3} - \frac{1164969528}{47} a^{2} - \frac{4799335457}{47} a + \frac{5037175485}{94} \) |
\( \bigl[a\) , \( \frac{1}{2} a^{3} - a^{2} - 3 a + \frac{3}{2}\) , \( a^{2} - 2\) , \( \frac{17}{2} a^{3} - 5 a^{2} - 55 a - \frac{33}{2}\) , \( -17 a^{3} + 8 a^{2} + 105 a + 34\bigr] \) |
${y}^2+a{x}{y}+\left(a^{2}-2\right){y}={x}^{3}+\left(\frac{1}{2}a^{3}-a^{2}-3a+\frac{3}{2}\right){x}^{2}+\left(\frac{17}{2}a^{3}-5a^{2}-55a-\frac{33}{2}\right){x}-17a^{3}+8a^{2}+105a+34$ |
| 47.1-a4 |
47.1-a |
$4$ |
$4$ |
4.4.4913.1 |
$4$ |
$[4, 0]$ |
47.1 |
\( 47 \) |
\( 47 \) |
$10.13501$ |
$(a^2-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$622.5927087$ |
2.220601643 |
\( -\frac{5753380329}{94} a^{3} + \frac{1473018244}{47} a^{2} + \frac{17978945643}{47} a + \frac{11792101919}{94} \) |
\( \bigl[1\) , \( a^{3} - a^{2} - 5 a\) , \( -\frac{1}{2} a^{3} + a^{2} + 3 a - \frac{3}{2}\) , \( -\frac{3}{2} a^{3} + 2 a^{2} + 8 a - \frac{5}{2}\) , \( -\frac{3}{2} a^{3} + 5 a^{2} - 2 a - \frac{1}{2}\bigr] \) |
${y}^2+{x}{y}+\left(-\frac{1}{2}a^{3}+a^{2}+3a-\frac{3}{2}\right){y}={x}^{3}+\left(a^{3}-a^{2}-5a\right){x}^{2}+\left(-\frac{3}{2}a^{3}+2a^{2}+8a-\frac{5}{2}\right){x}-\frac{3}{2}a^{3}+5a^{2}-2a-\frac{1}{2}$ |
| 47.1-b1 |
47.1-b |
$4$ |
$4$ |
4.4.4913.1 |
$4$ |
$[4, 0]$ |
47.1 |
\( 47 \) |
\( 47^{4} \) |
$10.13501$ |
$(a^2-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$442.3767078$ |
3.155650333 |
\( \frac{1453216775921384890493283}{4879681} a^{3} - \frac{1953342392250408271604268}{4879681} a^{2} - \frac{8047056442543374755402460}{4879681} a + \frac{4222617136311468914616572}{4879681} \) |
\( \bigl[\frac{1}{2} a^{3} - 3 a - \frac{3}{2}\) , \( -a^{3} + a^{2} + 6 a\) , \( \frac{1}{2} a^{3} - 3 a - \frac{3}{2}\) , \( \frac{605}{2} a^{3} - 160 a^{2} - 1893 a - \frac{1239}{2}\) , \( -5374 a^{3} + 2761 a^{2} + 33596 a + 11016\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-3a-\frac{3}{2}\right){x}{y}+\left(\frac{1}{2}a^{3}-3a-\frac{3}{2}\right){y}={x}^{3}+\left(-a^{3}+a^{2}+6a\right){x}^{2}+\left(\frac{605}{2}a^{3}-160a^{2}-1893a-\frac{1239}{2}\right){x}-5374a^{3}+2761a^{2}+33596a+11016$ |
| 47.1-b2 |
47.1-b |
$4$ |
$4$ |
4.4.4913.1 |
$4$ |
$[4, 0]$ |
47.1 |
\( 47 \) |
\( 47 \) |
$10.13501$ |
$(a^2-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$884.7534156$ |
3.155650333 |
\( \frac{10396814922808000}{47} a^{3} + \frac{19813247048187918}{47} a^{2} - \frac{4809467368048720}{47} a - \frac{3578071461053471}{47} \) |
\( \bigl[-\frac{1}{2} a^{3} + a^{2} + 3 a - \frac{1}{2}\) , \( -\frac{1}{2} a^{3} + 3 a + \frac{3}{2}\) , \( -\frac{1}{2} a^{3} + a^{2} + 2 a - \frac{1}{2}\) , \( \frac{141}{2} a^{3} - 36 a^{2} - 442 a - \frac{291}{2}\) , \( -\frac{651}{2} a^{3} + 166 a^{2} + 2036 a + \frac{1335}{2}\bigr] \) |
${y}^2+\left(-\frac{1}{2}a^{3}+a^{2}+3a-\frac{1}{2}\right){x}{y}+\left(-\frac{1}{2}a^{3}+a^{2}+2a-\frac{1}{2}\right){y}={x}^{3}+\left(-\frac{1}{2}a^{3}+3a+\frac{3}{2}\right){x}^{2}+\left(\frac{141}{2}a^{3}-36a^{2}-442a-\frac{291}{2}\right){x}-\frac{651}{2}a^{3}+166a^{2}+2036a+\frac{1335}{2}$ |
| 47.1-b3 |
47.1-b |
$4$ |
$4$ |
4.4.4913.1 |
$4$ |
$[4, 0]$ |
47.1 |
\( 47 \) |
\( 47 \) |
$10.13501$ |
$(a^2-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$884.7534156$ |
3.155650333 |
\( -\frac{1209607162149525}{47} a^{3} + \frac{619405527522758}{47} a^{2} + \frac{7559868467694644}{47} a + \frac{2479067102596890}{47} \) |
\( \bigl[1\) , \( \frac{1}{2} a^{3} - a^{2} - 2 a + \frac{3}{2}\) , \( a\) , \( -\frac{7}{2} a^{3} - 2 a^{2} + 9 a - \frac{9}{2}\) , \( \frac{15}{2} a^{3} + 11 a^{2} - 8 a + \frac{1}{2}\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(\frac{1}{2}a^{3}-a^{2}-2a+\frac{3}{2}\right){x}^{2}+\left(-\frac{7}{2}a^{3}-2a^{2}+9a-\frac{9}{2}\right){x}+\frac{15}{2}a^{3}+11a^{2}-8a+\frac{1}{2}$ |
| 47.1-b4 |
47.1-b |
$4$ |
$4$ |
4.4.4913.1 |
$4$ |
$[4, 0]$ |
47.1 |
\( 47 \) |
\( 47^{2} \) |
$10.13501$ |
$(a^2-2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2 \) |
$1$ |
$1769.506831$ |
3.155650333 |
\( \frac{561671912500}{2209} a^{3} - \frac{741986957344}{2209} a^{2} - \frac{3079953887744}{2209} a + \frac{1639520290065}{2209} \) |
\( \bigl[1\) , \( -\frac{1}{2} a^{3} + 4 a + \frac{5}{2}\) , \( a^{2} - a - 2\) , \( 10 a^{3} - 23 a^{2} - 18 a - 2\) , \( 11 a^{3} - 39 a^{2} + 16 a + 10\bigr] \) |
${y}^2+{x}{y}+\left(a^{2}-a-2\right){y}={x}^{3}+\left(-\frac{1}{2}a^{3}+4a+\frac{5}{2}\right){x}^{2}+\left(10a^{3}-23a^{2}-18a-2\right){x}+11a^{3}-39a^{2}+16a+10$ |
| 47.1-c1 |
47.1-c |
$6$ |
$8$ |
4.4.4913.1 |
$4$ |
$[4, 0]$ |
47.1 |
\( 47 \) |
\( 47 \) |
$10.13501$ |
$(a^2-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 1 \) |
$1$ |
$122.6360895$ |
1.749624743 |
\( -\frac{23492516568527}{94} a^{3} + \frac{236890947384951}{47} a^{2} - \frac{685295657774263}{47} a + \frac{558684150026963}{94} \) |
\( \bigl[a^{2} - 2\) , \( a^{2} - 2 a - 4\) , \( a + 1\) , \( 2 a^{3} - 4 a^{2} + 12 a\) , \( -\frac{7}{2} a^{3} + 20 a^{2} + 4 a - \frac{7}{2}\bigr] \) |
${y}^2+\left(a^{2}-2\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a^{2}-2a-4\right){x}^{2}+\left(2a^{3}-4a^{2}+12a\right){x}-\frac{7}{2}a^{3}+20a^{2}+4a-\frac{7}{2}$ |
| 47.1-c2 |
47.1-c |
$6$ |
$8$ |
4.4.4913.1 |
$4$ |
$[4, 0]$ |
47.1 |
\( 47 \) |
\( 47^{2} \) |
$10.13501$ |
$(a^2-2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2 \) |
$1$ |
$981.0887166$ |
1.749624743 |
\( \frac{1491164587}{4418} a^{3} + \frac{273178879}{2209} a^{2} - \frac{8648506911}{2209} a + \frac{9073350511}{4418} \) |
\( \bigl[a^{2} - 2\) , \( a^{2} - 2 a - 4\) , \( a + 1\) , \( -\frac{1}{2} a^{3} + a^{2} + 2 a + \frac{5}{2}\) , \( -a^{3} + 4 a + 1\bigr] \) |
${y}^2+\left(a^{2}-2\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a^{2}-2a-4\right){x}^{2}+\left(-\frac{1}{2}a^{3}+a^{2}+2a+\frac{5}{2}\right){x}-a^{3}+4a+1$ |
*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.
