| 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 |
| 17.1-a1 |
17.1-a |
$2$ |
$2$ |
4.4.7168.1 |
$4$ |
$[4, 0]$ |
17.1 |
\( 17 \) |
\( 17 \) |
$10.78062$ |
$(-a^3+3a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$0.052750052$ |
$1885.029271$ |
1.174470194 |
\( \frac{1382912}{17} a^{3} - \frac{895616}{17} a^{2} - \frac{6535424}{17} a + \frac{4858432}{17} \) |
\( \bigl[a^{3} - 3 a\) , \( -a^{2} - a + 3\) , \( 1\) , \( -a + 1\) , \( 0\bigr] \) |
${y}^2+\left(a^{3}-3a\right){x}{y}+{y}={x}^{3}+\left(-a^{2}-a+3\right){x}^{2}+\left(-a+1\right){x}$ |
| 17.1-a2 |
17.1-a |
$2$ |
$2$ |
4.4.7168.1 |
$4$ |
$[4, 0]$ |
17.1 |
\( 17 \) |
\( 17^{2} \) |
$10.78062$ |
$(-a^3+3a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.026375026$ |
$1885.029271$ |
1.174470194 |
\( -\frac{585784626872}{289} a^{3} - \frac{737663693128}{289} a^{2} + \frac{2585789310328}{289} a + \frac{3256228458192}{289} \) |
\( \bigl[a^{3} + a^{2} - 4 a - 2\) , \( a^{2} - a - 4\) , \( a\) , \( 2 a^{3} - 8 a^{2} + 11\) , \( 7 a^{3} - 15 a^{2} - 10 a + 22\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-4a-2\right){x}{y}+a{y}={x}^{3}+\left(a^{2}-a-4\right){x}^{2}+\left(2a^{3}-8a^{2}+11\right){x}+7a^{3}-15a^{2}-10a+22$ |
| 17.1-b1 |
17.1-b |
$4$ |
$6$ |
4.4.7168.1 |
$4$ |
$[4, 0]$ |
17.1 |
\( 17 \) |
\( 17^{2} \) |
$10.78062$ |
$(-a^3+3a-1)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2 \) |
$1$ |
$2073.149931$ |
1.360376773 |
\( -\frac{10376952}{289} a^{3} + \frac{22222584}{289} a^{2} + \frac{22328024}{289} a - \frac{24869088}{289} \) |
\( \bigl[a^{3} + a^{2} - 4 a - 2\) , \( a^{3} + a^{2} - 3 a - 2\) , \( a^{3} + a^{2} - 3 a - 2\) , \( 3 a^{3} + 4 a^{2} - 11 a - 13\) , \( 3 a^{3} + 4 a^{2} - 12 a - 15\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-4a-2\right){x}{y}+\left(a^{3}+a^{2}-3a-2\right){y}={x}^{3}+\left(a^{3}+a^{2}-3a-2\right){x}^{2}+\left(3a^{3}+4a^{2}-11a-13\right){x}+3a^{3}+4a^{2}-12a-15$ |
| 17.1-b2 |
17.1-b |
$4$ |
$6$ |
4.4.7168.1 |
$4$ |
$[4, 0]$ |
17.1 |
\( 17 \) |
\( 17 \) |
$10.78062$ |
$(-a^3+3a-1)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$4$ |
\( 1 \) |
$1$ |
$1036.574965$ |
1.360376773 |
\( \frac{12544}{17} a^{3} - \frac{13696}{17} a^{2} - \frac{62464}{17} a + \frac{75328}{17} \) |
\( \bigl[a^{3} - 3 a\) , \( a - 1\) , \( a^{2} - 2\) , \( 0\) , \( 0\bigr] \) |
${y}^2+\left(a^{3}-3a\right){x}{y}+\left(a^{2}-2\right){y}={x}^{3}+\left(a-1\right){x}^{2}$ |
| 17.1-b3 |
17.1-b |
$4$ |
$6$ |
4.4.7168.1 |
$4$ |
$[4, 0]$ |
17.1 |
\( 17 \) |
\( 17^{3} \) |
$10.78062$ |
$(-a^3+3a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$36$ |
\( 1 \) |
$1$ |
$12.79722180$ |
1.360376773 |
\( \frac{116397472994048}{4913} a^{3} - \frac{146520715987328}{4913} a^{2} - \frac{513905172598784}{4913} a + \frac{646987758094912}{4913} \) |
\( \bigl[a^{3} - 3 a\) , \( a - 1\) , \( a^{2} - 2\) , \( 5 a^{3} - 20 a^{2} + 25 a - 10\) , \( 51 a^{3} - 139 a^{2} + 21 a + 92\bigr] \) |
${y}^2+\left(a^{3}-3a\right){x}{y}+\left(a^{2}-2\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(5a^{3}-20a^{2}+25a-10\right){x}+51a^{3}-139a^{2}+21a+92$ |
| 17.1-b4 |
17.1-b |
$4$ |
$6$ |
4.4.7168.1 |
$4$ |
$[4, 0]$ |
17.1 |
\( 17 \) |
\( 17^{6} \) |
$10.78062$ |
$(-a^3+3a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$9$ |
\( 2 \) |
$1$ |
$25.59444360$ |
1.360376773 |
\( -\frac{758840120526044865736}{24137569} a^{3} - \frac{955592286541113206856}{24137569} a^{2} + \frac{3349682351847265616232}{24137569} a + \frac{4218188431904389048608}{24137569} \) |
\( \bigl[a^{3} + a^{2} - 4 a - 2\) , \( a^{3} + a^{2} - 3 a - 2\) , \( a^{3} + a^{2} - 3 a - 2\) , \( 123 a^{3} + 154 a^{2} - 546 a - 688\) , \( 1438 a^{3} + 1804 a^{2} - 6375 a - 8022\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-4a-2\right){x}{y}+\left(a^{3}+a^{2}-3a-2\right){y}={x}^{3}+\left(a^{3}+a^{2}-3a-2\right){x}^{2}+\left(123a^{3}+154a^{2}-546a-688\right){x}+1438a^{3}+1804a^{2}-6375a-8022$ |
| 17.1-c1 |
17.1-c |
$4$ |
$6$ |
4.4.7168.1 |
$4$ |
$[4, 0]$ |
17.1 |
\( 17 \) |
\( 17^{2} \) |
$10.78062$ |
$(-a^3+3a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$0.029918731$ |
$2492.098594$ |
1.761324583 |
\( -\frac{10376952}{289} a^{3} + \frac{22222584}{289} a^{2} + \frac{22328024}{289} a - \frac{24869088}{289} \) |
\( \bigl[a^{2} + a - 2\) , \( a^{3} - 4 a\) , \( a^{3} - 4 a\) , \( -4 a^{2} - 2 a + 11\) , \( a^{2} - 2\bigr] \) |
${y}^2+\left(a^{2}+a-2\right){x}{y}+\left(a^{3}-4a\right){y}={x}^{3}+\left(a^{3}-4a\right){x}^{2}+\left(-4a^{2}-2a+11\right){x}+a^{2}-2$ |
| 17.1-c2 |
17.1-c |
$4$ |
$6$ |
4.4.7168.1 |
$4$ |
$[4, 0]$ |
17.1 |
\( 17 \) |
\( 17 \) |
$10.78062$ |
$(-a^3+3a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 1 \) |
$0.059837463$ |
$2492.098594$ |
1.761324583 |
\( \frac{12544}{17} a^{3} - \frac{13696}{17} a^{2} - \frac{62464}{17} a + \frac{75328}{17} \) |
\( \bigl[a^{2} - 3\) , \( a^{3} - 4 a\) , \( a\) , \( -a^{3} + 4 a\) , \( -1\bigr] \) |
${y}^2+\left(a^{2}-3\right){x}{y}+a{y}={x}^{3}+\left(a^{3}-4a\right){x}^{2}+\left(-a^{3}+4a\right){x}-1$ |
| 17.1-c3 |
17.1-c |
$4$ |
$6$ |
4.4.7168.1 |
$4$ |
$[4, 0]$ |
17.1 |
\( 17 \) |
\( 17^{3} \) |
$10.78062$ |
$(-a^3+3a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 3 \) |
$0.179512390$ |
$276.8998438$ |
1.761324583 |
\( \frac{116397472994048}{4913} a^{3} - \frac{146520715987328}{4913} a^{2} - \frac{513905172598784}{4913} a + \frac{646987758094912}{4913} \) |
\( \bigl[a^{2} - 3\) , \( a^{3} - 4 a\) , \( a\) , \( -66 a^{3} + 80 a^{2} + 299 a - 370\) , \( 513 a^{3} - 652 a^{2} - 2247 a + 2840\bigr] \) |
${y}^2+\left(a^{2}-3\right){x}{y}+a{y}={x}^{3}+\left(a^{3}-4a\right){x}^{2}+\left(-66a^{3}+80a^{2}+299a-370\right){x}+513a^{3}-652a^{2}-2247a+2840$ |
| 17.1-c4 |
17.1-c |
$4$ |
$6$ |
4.4.7168.1 |
$4$ |
$[4, 0]$ |
17.1 |
\( 17 \) |
\( 17^{6} \) |
$10.78062$ |
$(-a^3+3a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \cdot 3 \) |
$0.089756195$ |
$276.8998438$ |
1.761324583 |
\( -\frac{758840120526044865736}{24137569} a^{3} - \frac{955592286541113206856}{24137569} a^{2} + \frac{3349682351847265616232}{24137569} a + \frac{4218188431904389048608}{24137569} \) |
\( \bigl[a^{2} + a - 2\) , \( a^{3} - 4 a\) , \( a^{3} - 4 a\) , \( 10 a^{3} - 4 a^{2} - 77 a - 64\) , \( -210 a^{3} - 344 a^{2} + 674 a + 974\bigr] \) |
${y}^2+\left(a^{2}+a-2\right){x}{y}+\left(a^{3}-4a\right){y}={x}^{3}+\left(a^{3}-4a\right){x}^{2}+\left(10a^{3}-4a^{2}-77a-64\right){x}-210a^{3}-344a^{2}+674a+974$ |
| 17.1-d1 |
17.1-d |
$2$ |
$2$ |
4.4.7168.1 |
$4$ |
$[4, 0]$ |
17.1 |
\( 17 \) |
\( 17 \) |
$10.78062$ |
$(-a^3+3a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$1061.052442$ |
3.133125995 |
\( \frac{1382912}{17} a^{3} - \frac{895616}{17} a^{2} - \frac{6535424}{17} a + \frac{4858432}{17} \) |
\( \bigl[a^{2} - 3\) , \( -a^{3} + a^{2} + 5 a - 3\) , \( a^{3} - 4 a\) , \( 2 a^{3} - 3 a^{2} - 7 a + 11\) , \( -a^{3} + 3 a^{2} + 4 a - 9\bigr] \) |
${y}^2+\left(a^{2}-3\right){x}{y}+\left(a^{3}-4a\right){y}={x}^{3}+\left(-a^{3}+a^{2}+5a-3\right){x}^{2}+\left(2a^{3}-3a^{2}-7a+11\right){x}-a^{3}+3a^{2}+4a-9$ |
| 17.1-d2 |
17.1-d |
$2$ |
$2$ |
4.4.7168.1 |
$4$ |
$[4, 0]$ |
17.1 |
\( 17 \) |
\( 17^{2} \) |
$10.78062$ |
$(-a^3+3a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$530.5262214$ |
3.133125995 |
\( -\frac{585784626872}{289} a^{3} - \frac{737663693128}{289} a^{2} + \frac{2585789310328}{289} a + \frac{3256228458192}{289} \) |
\( \bigl[a^{3} - 4 a + 1\) , \( -a^{3} + a^{2} + 4 a - 4\) , \( 1\) , \( -6 a^{3} + 6 a^{2} + 28 a - 31\) , \( 6 a^{3} - 8 a^{2} - 25 a + 32\bigr] \) |
${y}^2+\left(a^{3}-4a+1\right){x}{y}+{y}={x}^{3}+\left(-a^{3}+a^{2}+4a-4\right){x}^{2}+\left(-6a^{3}+6a^{2}+28a-31\right){x}+6a^{3}-8a^{2}-25a+32$ |
| 17.2-a1 |
17.2-a |
$2$ |
$2$ |
4.4.7168.1 |
$4$ |
$[4, 0]$ |
17.2 |
\( 17 \) |
\( 17 \) |
$10.78062$ |
$(a^3-3a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$0.052750052$ |
$1885.029271$ |
1.174470194 |
\( -\frac{1382912}{17} a^{3} - \frac{895616}{17} a^{2} + \frac{6535424}{17} a + \frac{4858432}{17} \) |
\( \bigl[a^{3} - 3 a\) , \( -a^{2} + a + 3\) , \( 1\) , \( -a^{3} + 4 a + 1\) , \( 0\bigr] \) |
${y}^2+\left(a^{3}-3a\right){x}{y}+{y}={x}^{3}+\left(-a^{2}+a+3\right){x}^{2}+\left(-a^{3}+4a+1\right){x}$ |
| 17.2-a2 |
17.2-a |
$2$ |
$2$ |
4.4.7168.1 |
$4$ |
$[4, 0]$ |
17.2 |
\( 17 \) |
\( 17^{2} \) |
$10.78062$ |
$(a^3-3a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.026375026$ |
$1885.029271$ |
1.174470194 |
\( \frac{585784626872}{289} a^{3} - \frac{737663693128}{289} a^{2} - \frac{2585789310328}{289} a + \frac{3256228458192}{289} \) |
\( \bigl[a^{3} + a^{2} - 4 a - 2\) , \( a^{2} - 4\) , \( a\) , \( -3 a^{3} - 8 a^{2} + 2 a + 11\) , \( -7 a^{3} - 15 a^{2} + 10 a + 22\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-4a-2\right){x}{y}+a{y}={x}^{3}+\left(a^{2}-4\right){x}^{2}+\left(-3a^{3}-8a^{2}+2a+11\right){x}-7a^{3}-15a^{2}+10a+22$ |
| 17.2-b1 |
17.2-b |
$4$ |
$6$ |
4.4.7168.1 |
$4$ |
$[4, 0]$ |
17.2 |
\( 17 \) |
\( 17^{2} \) |
$10.78062$ |
$(a^3-3a-1)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2 \) |
$1$ |
$2073.149931$ |
1.360376773 |
\( \frac{10376952}{289} a^{3} + \frac{22222584}{289} a^{2} - \frac{22328024}{289} a - \frac{24869088}{289} \) |
\( \bigl[a^{3} + a^{2} - 4 a - 2\) , \( -a^{3} + a^{2} + 5 a - 2\) , \( a^{2} + a - 3\) , \( -2 a^{3} - a^{2} + 11 a + 7\) , \( -2 a^{3} + 10 a + 3\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-4a-2\right){x}{y}+\left(a^{2}+a-3\right){y}={x}^{3}+\left(-a^{3}+a^{2}+5a-2\right){x}^{2}+\left(-2a^{3}-a^{2}+11a+7\right){x}-2a^{3}+10a+3$ |
| 17.2-b2 |
17.2-b |
$4$ |
$6$ |
4.4.7168.1 |
$4$ |
$[4, 0]$ |
17.2 |
\( 17 \) |
\( 17 \) |
$10.78062$ |
$(a^3-3a-1)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$4$ |
\( 1 \) |
$1$ |
$1036.574965$ |
1.360376773 |
\( -\frac{12544}{17} a^{3} - \frac{13696}{17} a^{2} + \frac{62464}{17} a + \frac{75328}{17} \) |
\( \bigl[a^{3} - 3 a\) , \( -a - 1\) , \( a^{2} - 2\) , \( -a^{3} + a\) , \( 0\bigr] \) |
${y}^2+\left(a^{3}-3a\right){x}{y}+\left(a^{2}-2\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-a^{3}+a\right){x}$ |
| 17.2-b3 |
17.2-b |
$4$ |
$6$ |
4.4.7168.1 |
$4$ |
$[4, 0]$ |
17.2 |
\( 17 \) |
\( 17^{3} \) |
$10.78062$ |
$(a^3-3a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$36$ |
\( 1 \) |
$1$ |
$12.79722180$ |
1.360376773 |
\( -\frac{116397472994048}{4913} a^{3} - \frac{146520715987328}{4913} a^{2} + \frac{513905172598784}{4913} a + \frac{646987758094912}{4913} \) |
\( \bigl[a^{3} - 3 a\) , \( -a - 1\) , \( a^{2} - 2\) , \( -6 a^{3} - 20 a^{2} - 24 a - 10\) , \( -51 a^{3} - 139 a^{2} - 21 a + 92\bigr] \) |
${y}^2+\left(a^{3}-3a\right){x}{y}+\left(a^{2}-2\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-6a^{3}-20a^{2}-24a-10\right){x}-51a^{3}-139a^{2}-21a+92$ |
| 17.2-b4 |
17.2-b |
$4$ |
$6$ |
4.4.7168.1 |
$4$ |
$[4, 0]$ |
17.2 |
\( 17 \) |
\( 17^{6} \) |
$10.78062$ |
$(a^3-3a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$9$ |
\( 2 \) |
$1$ |
$25.59444360$ |
1.360376773 |
\( \frac{758840120526044865736}{24137569} a^{3} - \frac{955592286541113206856}{24137569} a^{2} - \frac{3349682351847265616232}{24137569} a + \frac{4218188431904389048608}{24137569} \) |
\( \bigl[a^{3} + a^{2} - 4 a - 2\) , \( -a^{3} + a^{2} + 5 a - 2\) , \( a^{2} + a - 3\) , \( -122 a^{3} + 149 a^{2} + 546 a - 668\) , \( -1287 a^{3} + 1615 a^{2} + 5698 a - 7164\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-4a-2\right){x}{y}+\left(a^{2}+a-3\right){y}={x}^{3}+\left(-a^{3}+a^{2}+5a-2\right){x}^{2}+\left(-122a^{3}+149a^{2}+546a-668\right){x}-1287a^{3}+1615a^{2}+5698a-7164$ |
| 17.2-c1 |
17.2-c |
$4$ |
$6$ |
4.4.7168.1 |
$4$ |
$[4, 0]$ |
17.2 |
\( 17 \) |
\( 17^{2} \) |
$10.78062$ |
$(a^3-3a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$0.029918731$ |
$2492.098594$ |
1.761324583 |
\( \frac{10376952}{289} a^{3} + \frac{22222584}{289} a^{2} - \frac{22328024}{289} a - \frac{24869088}{289} \) |
\( \bigl[a^{2} + a - 2\) , \( a^{3} - 3 a\) , \( a^{2} + a - 3\) , \( 2 a^{3} - a^{2} - 2 a + 1\) , \( -4 a^{3} + 12 a^{2} + 7 a - 20\bigr] \) |
${y}^2+\left(a^{2}+a-2\right){x}{y}+\left(a^{2}+a-3\right){y}={x}^{3}+\left(a^{3}-3a\right){x}^{2}+\left(2a^{3}-a^{2}-2a+1\right){x}-4a^{3}+12a^{2}+7a-20$ |
| 17.2-c2 |
17.2-c |
$4$ |
$6$ |
4.4.7168.1 |
$4$ |
$[4, 0]$ |
17.2 |
\( 17 \) |
\( 17 \) |
$10.78062$ |
$(a^3-3a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 1 \) |
$0.059837463$ |
$2492.098594$ |
1.761324583 |
\( -\frac{12544}{17} a^{3} - \frac{13696}{17} a^{2} + \frac{62464}{17} a + \frac{75328}{17} \) |
\( \bigl[a^{2} - 3\) , \( -a^{3} + 4 a\) , \( a\) , \( -a\) , \( -1\bigr] \) |
${y}^2+\left(a^{2}-3\right){x}{y}+a{y}={x}^{3}+\left(-a^{3}+4a\right){x}^{2}-a{x}-1$ |
| 17.2-c3 |
17.2-c |
$4$ |
$6$ |
4.4.7168.1 |
$4$ |
$[4, 0]$ |
17.2 |
\( 17 \) |
\( 17^{3} \) |
$10.78062$ |
$(a^3-3a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 3 \) |
$0.179512390$ |
$276.8998438$ |
1.761324583 |
\( -\frac{116397472994048}{4913} a^{3} - \frac{146520715987328}{4913} a^{2} + \frac{513905172598784}{4913} a + \frac{646987758094912}{4913} \) |
\( \bigl[a^{2} - 3\) , \( -a^{3} + 4 a\) , \( a\) , \( 65 a^{3} + 80 a^{2} - 296 a - 370\) , \( -513 a^{3} - 652 a^{2} + 2247 a + 2840\bigr] \) |
${y}^2+\left(a^{2}-3\right){x}{y}+a{y}={x}^{3}+\left(-a^{3}+4a\right){x}^{2}+\left(65a^{3}+80a^{2}-296a-370\right){x}-513a^{3}-652a^{2}+2247a+2840$ |
| 17.2-c4 |
17.2-c |
$4$ |
$6$ |
4.4.7168.1 |
$4$ |
$[4, 0]$ |
17.2 |
\( 17 \) |
\( 17^{6} \) |
$10.78062$ |
$(a^3-3a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \cdot 3 \) |
$0.089756195$ |
$276.8998438$ |
1.761324583 |
\( \frac{758840120526044865736}{24137569} a^{3} - \frac{955592286541113206856}{24137569} a^{2} - \frac{3349682351847265616232}{24137569} a + \frac{4218188431904389048608}{24137569} \) |
\( \bigl[a^{2} + a - 2\) , \( a^{3} - 3 a\) , \( a^{2} + a - 3\) , \( -8 a^{3} - a^{2} + 73 a - 74\) , \( 131 a^{3} - 218 a^{2} - 442 a + 641\bigr] \) |
${y}^2+\left(a^{2}+a-2\right){x}{y}+\left(a^{2}+a-3\right){y}={x}^{3}+\left(a^{3}-3a\right){x}^{2}+\left(-8a^{3}-a^{2}+73a-74\right){x}+131a^{3}-218a^{2}-442a+641$ |
| 17.2-d1 |
17.2-d |
$2$ |
$2$ |
4.4.7168.1 |
$4$ |
$[4, 0]$ |
17.2 |
\( 17 \) |
\( 17 \) |
$10.78062$ |
$(a^3-3a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$1061.052442$ |
3.133125995 |
\( -\frac{1382912}{17} a^{3} - \frac{895616}{17} a^{2} + \frac{6535424}{17} a + \frac{4858432}{17} \) |
\( \bigl[a^{2} - 3\) , \( a^{3} + a^{2} - 5 a - 3\) , \( a^{3} - 4 a\) , \( -a^{3} - 3 a^{2} + 2 a + 11\) , \( a^{3} + 3 a^{2} - 4 a - 9\bigr] \) |
${y}^2+\left(a^{2}-3\right){x}{y}+\left(a^{3}-4a\right){y}={x}^{3}+\left(a^{3}+a^{2}-5a-3\right){x}^{2}+\left(-a^{3}-3a^{2}+2a+11\right){x}+a^{3}+3a^{2}-4a-9$ |
| 17.2-d2 |
17.2-d |
$2$ |
$2$ |
4.4.7168.1 |
$4$ |
$[4, 0]$ |
17.2 |
\( 17 \) |
\( 17^{2} \) |
$10.78062$ |
$(a^3-3a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$530.5262214$ |
3.133125995 |
\( \frac{585784626872}{289} a^{3} - \frac{737663693128}{289} a^{2} - \frac{2585789310328}{289} a + \frac{3256228458192}{289} \) |
\( \bigl[a^{3} - 4 a + 1\) , \( a^{2} - 4\) , \( 1\) , \( 5 a^{3} + 6 a^{2} - 24 a - 31\) , \( -6 a^{3} - 8 a^{2} + 25 a + 32\bigr] \) |
${y}^2+\left(a^{3}-4a+1\right){x}{y}+{y}={x}^{3}+\left(a^{2}-4\right){x}^{2}+\left(5a^{3}+6a^{2}-24a-31\right){x}-6a^{3}-8a^{2}+25a+32$ |
| 28.1-a1 |
28.1-a |
$12$ |
$24$ |
4.4.7168.1 |
$4$ |
$[4, 0]$ |
28.1 |
\( 2^{2} \cdot 7 \) |
\( 2^{4} \cdot 7^{2} \) |
$11.47446$ |
$(a^2-a-2), (-a)$ |
$1$ |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
|
|
$2, 3$ |
2Cs, 3B |
$1$ |
\( 2 \) |
$0.763731887$ |
$2485.885867$ |
2.803064709 |
\( \frac{1720664028}{7} a^{2} - \frac{2727963232}{7} \) |
\( \bigl[a^{3} + a^{2} - 4 a - 2\) , \( a^{2} - a - 2\) , \( a^{2} + a - 2\) , \( -85 a^{3} + 99 a^{2} + 355 a - 471\) , \( 709 a^{3} - 874 a^{2} - 3093 a + 3940\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-4a-2\right){x}{y}+\left(a^{2}+a-2\right){y}={x}^{3}+\left(a^{2}-a-2\right){x}^{2}+\left(-85a^{3}+99a^{2}+355a-471\right){x}+709a^{3}-874a^{2}-3093a+3940$ |
| 28.1-a2 |
28.1-a |
$12$ |
$24$ |
4.4.7168.1 |
$4$ |
$[4, 0]$ |
28.1 |
\( 2^{2} \cdot 7 \) |
\( 2^{8} \cdot 7 \) |
$11.47446$ |
$(a^2-a-2), (-a)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 1 \) |
$1.527463774$ |
$621.4714669$ |
2.803064709 |
\( \frac{284771259948120952}{7} a^{3} + 85472182194531840 a^{2} - \frac{451586378819525314}{7} a - 135540623175049496 \) |
\( \bigl[a^{2} + a - 2\) , \( -a - 1\) , \( a + 1\) , \( -62 a^{3} + 76 a^{2} + 275 a - 348\) , \( 11784 a^{3} - 14841 a^{2} - 52022 a + 65520\bigr] \) |
${y}^2+\left(a^{2}+a-2\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-62a^{3}+76a^{2}+275a-348\right){x}+11784a^{3}-14841a^{2}-52022a+65520$ |
| 28.1-a3 |
28.1-a |
$12$ |
$24$ |
4.4.7168.1 |
$4$ |
$[4, 0]$ |
28.1 |
\( 2^{2} \cdot 7 \) |
\( 2^{8} \cdot 7 \) |
$11.47446$ |
$(a^2-a-2), (-a)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 1 \) |
$1.527463774$ |
$621.4714669$ |
2.803064709 |
\( -\frac{284771259948120952}{7} a^{3} + 85472182194531840 a^{2} + \frac{451586378819525314}{7} a - 135540623175049496 \) |
\( \bigl[a^{2} + a - 2\) , \( -a^{3} + 3 a - 1\) , \( a + 1\) , \( 61 a^{3} + 76 a^{2} - 274 a - 348\) , \( -11784 a^{3} - 14841 a^{2} + 52021 a + 65520\bigr] \) |
${y}^2+\left(a^{2}+a-2\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a^{3}+3a-1\right){x}^{2}+\left(61a^{3}+76a^{2}-274a-348\right){x}-11784a^{3}-14841a^{2}+52021a+65520$ |
| 28.1-a4 |
28.1-a |
$12$ |
$24$ |
4.4.7168.1 |
$4$ |
$[4, 0]$ |
28.1 |
\( 2^{2} \cdot 7 \) |
\( 2^{8} \cdot 7^{12} \) |
$11.47446$ |
$(a^2-a-2), (-a)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
|
|
$2, 3$ |
2Cs, 3B |
$1$ |
\( 2 \cdot 3 \) |
$1.145597830$ |
$138.1047704$ |
2.803064709 |
\( -\frac{1137747277344}{117649} a^{2} + \frac{5035628450000}{117649} \) |
\( \bigl[a^{3} - 3 a\) , \( -a^{2} + 4\) , \( 0\) , \( 9 a^{2} - 56\) , \( -38 a^{2} + 130\bigr] \) |
${y}^2+\left(a^{3}-3a\right){x}{y}={x}^{3}+\left(-a^{2}+4\right){x}^{2}+\left(9a^{2}-56\right){x}-38a^{2}+130$ |
| 28.1-a5 |
28.1-a |
$12$ |
$24$ |
4.4.7168.1 |
$4$ |
$[4, 0]$ |
28.1 |
\( 2^{2} \cdot 7 \) |
\( 2^{8} \cdot 7^{4} \) |
$11.47446$ |
$(a^2-a-2), (-a)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
|
|
$2, 3$ |
2Cs, 3B |
$1$ |
\( 2 \) |
$0.381865943$ |
$1242.942933$ |
2.803064709 |
\( \frac{435744}{49} a^{2} - \frac{594544}{49} \) |
\( \bigl[a^{3} - 3 a\) , \( -a^{2} + 4\) , \( 0\) , \( -a^{2} + 4\) , \( 0\bigr] \) |
${y}^2+\left(a^{3}-3a\right){x}{y}={x}^{3}+\left(-a^{2}+4\right){x}^{2}+\left(-a^{2}+4\right){x}$ |
| 28.1-a6 |
28.1-a |
$12$ |
$24$ |
4.4.7168.1 |
$4$ |
$[4, 0]$ |
28.1 |
\( 2^{2} \cdot 7 \) |
\( 2^{4} \cdot 7^{2} \) |
$11.47446$ |
$(a^2-a-2), (-a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$0.190932971$ |
$621.4714669$ |
2.803064709 |
\( \frac{4096}{7} a^{2} + \frac{4096}{7} \) |
\( \bigl[0\) , \( -a\) , \( a^{3} + a^{2} - 4 a - 2\) , \( 8 a^{3} - 12 a^{2} - 36 a + 53\) , \( -6 a^{3} + 9 a^{2} + 26 a - 41\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-4a-2\right){y}={x}^{3}-a{x}^{2}+\left(8a^{3}-12a^{2}-36a+53\right){x}-6a^{3}+9a^{2}+26a-41$ |
| 28.1-a7 |
28.1-a |
$12$ |
$24$ |
4.4.7168.1 |
$4$ |
$[4, 0]$ |
28.1 |
\( 2^{2} \cdot 7 \) |
\( 2^{4} \cdot 7^{6} \) |
$11.47446$ |
$(a^2-a-2), (-a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \cdot 3 \) |
$0.572798915$ |
$69.05238521$ |
2.803064709 |
\( \frac{1545435312128}{343} a^{2} - \frac{2450731913216}{343} \) |
\( \bigl[0\) , \( -a\) , \( a^{3} + a^{2} - 4 a - 2\) , \( -112 a^{3} + 98 a^{2} + 444 a - 537\) , \( 1068 a^{3} - 1696 a^{2} - 4962 a + 6966\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-4a-2\right){y}={x}^{3}-a{x}^{2}+\left(-112a^{3}+98a^{2}+444a-537\right){x}+1068a^{3}-1696a^{2}-4962a+6966$ |
| 28.1-a8 |
28.1-a |
$12$ |
$24$ |
4.4.7168.1 |
$4$ |
$[4, 0]$ |
28.1 |
\( 2^{2} \cdot 7 \) |
\( 2^{8} \cdot 7^{3} \) |
$11.47446$ |
$(a^2-a-2), (-a)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 3 \) |
$4.582391323$ |
$69.05238521$ |
2.803064709 |
\( -\frac{3914388170038407466610901238990}{49} a^{3} - 100598188385994848717558770176 a^{2} + \frac{17278945348576339145325144222568}{49} a + 444061887523622038076420848360 \) |
\( \bigl[a^{3} - 4 a + 1\) , \( a^{2} + a - 3\) , \( a^{3} - 3 a\) , \( -893 a^{3} + 1279 a^{2} + 3280 a - 4390\) , \( 15899 a^{3} - 18838 a^{2} - 73669 a + 90907\bigr] \) |
${y}^2+\left(a^{3}-4a+1\right){x}{y}+\left(a^{3}-3a\right){y}={x}^{3}+\left(a^{2}+a-3\right){x}^{2}+\left(-893a^{3}+1279a^{2}+3280a-4390\right){x}+15899a^{3}-18838a^{2}-73669a+90907$ |
| 28.1-a9 |
28.1-a |
$12$ |
$24$ |
4.4.7168.1 |
$4$ |
$[4, 0]$ |
28.1 |
\( 2^{2} \cdot 7 \) |
\( 2^{8} \cdot 7^{3} \) |
$11.47446$ |
$(a^2-a-2), (-a)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 3 \) |
$4.582391323$ |
$69.05238521$ |
2.803064709 |
\( \frac{3914388170038407466610901238990}{49} a^{3} - 100598188385994848717558770176 a^{2} - \frac{17278945348576339145325144222568}{49} a + 444061887523622038076420848360 \) |
\( \bigl[a^{3} - 4 a + 1\) , \( -a^{3} + a^{2} + 3 a - 3\) , \( a^{3} - 3 a\) , \( 892 a^{3} + 1279 a^{2} - 3277 a - 4390\) , \( -15899 a^{3} - 18838 a^{2} + 73669 a + 90907\bigr] \) |
${y}^2+\left(a^{3}-4a+1\right){x}{y}+\left(a^{3}-3a\right){y}={x}^{3}+\left(-a^{3}+a^{2}+3a-3\right){x}^{2}+\left(892a^{3}+1279a^{2}-3277a-4390\right){x}-15899a^{3}-18838a^{2}+73669a+90907$ |
| 28.1-a10 |
28.1-a |
$12$ |
$24$ |
4.4.7168.1 |
$4$ |
$[4, 0]$ |
28.1 |
\( 2^{2} \cdot 7 \) |
\( 2^{4} \cdot 7^{8} \) |
$11.47446$ |
$(a^2-a-2), (-a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$0.763731887$ |
$155.3678667$ |
2.803064709 |
\( -\frac{861093316}{2401} a^{2} + \frac{3801070960}{2401} \) |
\( \bigl[a + 1\) , \( -a^{3} - a^{2} + 4 a + 2\) , \( a^{3} + a^{2} - 3 a - 3\) , \( 12 a^{2} + 13 a - 26\) , \( 209 a^{3} + 452 a^{2} - 321 a - 732\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{3}+a^{2}-3a-3\right){y}={x}^{3}+\left(-a^{3}-a^{2}+4a+2\right){x}^{2}+\left(12a^{2}+13a-26\right){x}+209a^{3}+452a^{2}-321a-732$ |
| 28.1-a11 |
28.1-a |
$12$ |
$24$ |
4.4.7168.1 |
$4$ |
$[4, 0]$ |
28.1 |
\( 2^{2} \cdot 7 \) |
\( 2^{4} \cdot 7^{24} \) |
$11.47446$ |
$(a^2-a-2), (-a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \cdot 3 \) |
$2.291195661$ |
$17.26309630$ |
2.803064709 |
\( -\frac{29518306565684}{13841287201} a^{2} + \frac{130177642092184}{13841287201} \) |
\( \bigl[a + 1\) , \( -a^{3} - a^{2} + 4 a + 2\) , \( a^{3} + a^{2} - 3 a - 3\) , \( -60 a^{3} - 83 a^{2} + 133 a + 89\) , \( -5753 a^{3} - 12262 a^{2} + 8975 a + 19628\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{3}+a^{2}-3a-3\right){y}={x}^{3}+\left(-a^{3}-a^{2}+4a+2\right){x}^{2}+\left(-60a^{3}-83a^{2}+133a+89\right){x}-5753a^{3}-12262a^{2}+8975a+19628$ |
| 28.1-a12 |
28.1-a |
$12$ |
$24$ |
4.4.7168.1 |
$4$ |
$[4, 0]$ |
28.1 |
\( 2^{2} \cdot 7 \) |
\( 2^{4} \cdot 7^{6} \) |
$11.47446$ |
$(a^2-a-2), (-a)$ |
$1$ |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
|
|
$2, 3$ |
2Cs, 3B |
$1$ |
\( 2 \cdot 3 \) |
$2.291195661$ |
$276.2095408$ |
2.803064709 |
\( -\frac{91481168031853524}{343} a^{2} + \frac{403817412628584968}{343} \) |
\( \bigl[a + 1\) , \( -a^{3} - a^{2} + 4 a + 2\) , \( 0\) , \( -449 a^{3} - 286 a^{2} + 1240 a - 296\) , \( 4710 a^{3} - 343 a^{2} - 16028 a + 11521\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-a^{3}-a^{2}+4a+2\right){x}^{2}+\left(-449a^{3}-286a^{2}+1240a-296\right){x}+4710a^{3}-343a^{2}-16028a+11521$ |
| 28.1-b1 |
28.1-b |
$12$ |
$24$ |
4.4.7168.1 |
$4$ |
$[4, 0]$ |
28.1 |
\( 2^{2} \cdot 7 \) |
\( 2^{8} \cdot 7^{4} \) |
$11.47446$ |
$(a^2-a-2), (-a)$ |
0 |
$\Z/2\Z\oplus\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
|
|
$2, 3$ |
2Cs, 3B.1.1 |
$1$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$1505.280068$ |
1.481620801 |
\( \frac{435744}{49} a^{2} - \frac{594544}{49} \) |
\( \bigl[a^{2} - 3\) , \( -1\) , \( a^{2} - 3\) , \( 2 a^{2} - 10\) , \( -a^{2} + 4\bigr] \) |
${y}^2+\left(a^{2}-3\right){x}{y}+\left(a^{2}-3\right){y}={x}^{3}-{x}^{2}+\left(2a^{2}-10\right){x}-a^{2}+4$ |
| 28.1-b2 |
28.1-b |
$12$ |
$24$ |
4.4.7168.1 |
$4$ |
$[4, 0]$ |
28.1 |
\( 2^{2} \cdot 7 \) |
\( 2^{8} \cdot 7^{12} \) |
$11.47446$ |
$(a^2-a-2), (-a)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
|
|
$2, 3$ |
2Cs, 3B.1.2 |
$9$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$18.58370454$ |
1.481620801 |
\( -\frac{1137747277344}{117649} a^{2} + \frac{5035628450000}{117649} \) |
\( \bigl[a^{2} - 3\) , \( -a^{2} + 4\) , \( 0\) , \( -34 a^{2} + 49\) , \( -133 a^{2} + 196\bigr] \) |
${y}^2+\left(a^{2}-3\right){x}{y}={x}^{3}+\left(-a^{2}+4\right){x}^{2}+\left(-34a^{2}+49\right){x}-133a^{2}+196$ |
| 28.1-b3 |
28.1-b |
$12$ |
$24$ |
4.4.7168.1 |
$4$ |
$[4, 0]$ |
28.1 |
\( 2^{2} \cdot 7 \) |
\( 2^{4} \cdot 7^{24} \) |
$11.47446$ |
$(a^2-a-2), (-a)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
|
|
$2, 3$ |
2B, 3B.1.2 |
$9$ |
\( 2^{3} \cdot 3 \) |
$1$ |
$9.291852272$ |
1.481620801 |
\( -\frac{29518306565684}{13841287201} a^{2} + \frac{130177642092184}{13841287201} \) |
\( \bigl[a^{2} + a - 2\) , \( -a^{3} + 5 a\) , \( a^{2} + a - 2\) , \( -79 a^{3} + 84 a^{2} + 327 a - 416\) , \( -895 a^{3} - 276 a^{2} + 2735 a - 1336\bigr] \) |
${y}^2+\left(a^{2}+a-2\right){x}{y}+\left(a^{2}+a-2\right){y}={x}^{3}+\left(-a^{3}+5a\right){x}^{2}+\left(-79a^{3}+84a^{2}+327a-416\right){x}-895a^{3}-276a^{2}+2735a-1336$ |
| 28.1-b4 |
28.1-b |
$12$ |
$24$ |
4.4.7168.1 |
$4$ |
$[4, 0]$ |
28.1 |
\( 2^{2} \cdot 7 \) |
\( 2^{4} \cdot 7^{8} \) |
$11.47446$ |
$(a^2-a-2), (-a)$ |
0 |
$\Z/12\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
|
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{3} \cdot 3 \) |
$1$ |
$752.6400340$ |
1.481620801 |
\( -\frac{861093316}{2401} a^{2} + \frac{3801070960}{2401} \) |
\( \bigl[a^{2} + a - 2\) , \( -a^{3} + 5 a\) , \( a^{2} + a - 2\) , \( -19 a^{3} + 29 a^{2} + 87 a - 121\) , \( 141 a^{3} - 119 a^{2} - 573 a + 629\bigr] \) |
${y}^2+\left(a^{2}+a-2\right){x}{y}+\left(a^{2}+a-2\right){y}={x}^{3}+\left(-a^{3}+5a\right){x}^{2}+\left(-19a^{3}+29a^{2}+87a-121\right){x}+141a^{3}-119a^{2}-573a+629$ |
| 28.1-b5 |
28.1-b |
$12$ |
$24$ |
4.4.7168.1 |
$4$ |
$[4, 0]$ |
28.1 |
\( 2^{2} \cdot 7 \) |
\( 2^{4} \cdot 7^{6} \) |
$11.47446$ |
$(a^2-a-2), (-a)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
|
|
$2, 3$ |
2Cs, 3B.1.2 |
$36$ |
\( 2 \cdot 3 \) |
$1$ |
$9.291852272$ |
1.481620801 |
\( -\frac{91481168031853524}{343} a^{2} + \frac{403817412628584968}{343} \) |
\( \bigl[a^{2} + a - 2\) , \( -a^{3} + 5 a\) , \( a^{3} - 3 a\) , \( 51937 a^{3} - 109122 a^{2} - 82363 a + 173047\) , \( -4497906 a^{3} + 9450115 a^{2} + 7132713 a - 14985873\bigr] \) |
${y}^2+\left(a^{2}+a-2\right){x}{y}+\left(a^{3}-3a\right){y}={x}^{3}+\left(-a^{3}+5a\right){x}^{2}+\left(51937a^{3}-109122a^{2}-82363a+173047\right){x}-4497906a^{3}+9450115a^{2}+7132713a-14985873$ |
| 28.1-b6 |
28.1-b |
$12$ |
$24$ |
4.4.7168.1 |
$4$ |
$[4, 0]$ |
28.1 |
\( 2^{2} \cdot 7 \) |
\( 2^{4} \cdot 7^{2} \) |
$11.47446$ |
$(a^2-a-2), (-a)$ |
0 |
$\Z/2\Z\oplus\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
|
|
$2, 3$ |
2Cs, 3B.1.1 |
$4$ |
\( 2 \cdot 3 \) |
$1$ |
$752.6400340$ |
1.481620801 |
\( \frac{1720664028}{7} a^{2} - \frac{2727963232}{7} \) |
\( \bigl[a^{2} + a - 2\) , \( -a^{3} + 5 a\) , \( a^{3} - 4 a + 1\) , \( -48 a^{3} - 56 a^{2} + 114 a + 42\) , \( 168 a^{3} + 482 a^{2} - 162 a - 910\bigr] \) |
${y}^2+\left(a^{2}+a-2\right){x}{y}+\left(a^{3}-4a+1\right){y}={x}^{3}+\left(-a^{3}+5a\right){x}^{2}+\left(-48a^{3}-56a^{2}+114a+42\right){x}+168a^{3}+482a^{2}-162a-910$ |
| 28.1-b7 |
28.1-b |
$12$ |
$24$ |
4.4.7168.1 |
$4$ |
$[4, 0]$ |
28.1 |
\( 2^{2} \cdot 7 \) |
\( 2^{4} \cdot 7^{6} \) |
$11.47446$ |
$(a^2-a-2), (-a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
|
|
$2, 3$ |
2B, 3B.1.2 |
$9$ |
\( 2 \cdot 3 \) |
$1$ |
$9.291852272$ |
1.481620801 |
\( \frac{1545435312128}{343} a^{2} - \frac{2450731913216}{343} \) |
\( \bigl[0\) , \( a^{2} - a - 2\) , \( a + 1\) , \( 34 a^{3} + 24 a^{2} - 216 a - 242\) , \( 344 a^{3} + 305 a^{2} - 1941 a - 2241\bigr] \) |
${y}^2+\left(a+1\right){y}={x}^{3}+\left(a^{2}-a-2\right){x}^{2}+\left(34a^{3}+24a^{2}-216a-242\right){x}+344a^{3}+305a^{2}-1941a-2241$ |
| 28.1-b8 |
28.1-b |
$12$ |
$24$ |
4.4.7168.1 |
$4$ |
$[4, 0]$ |
28.1 |
\( 2^{2} \cdot 7 \) |
\( 2^{4} \cdot 7^{2} \) |
$11.47446$ |
$(a^2-a-2), (-a)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
|
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$752.6400340$ |
1.481620801 |
\( \frac{4096}{7} a^{2} + \frac{4096}{7} \) |
\( \bigl[0\) , \( a^{2} - a - 2\) , \( a + 1\) , \( -6 a^{3} - 6 a^{2} + 24 a + 28\) , \( -2 a^{3} - 2 a^{2} + 7 a + 8\bigr] \) |
${y}^2+\left(a+1\right){y}={x}^{3}+\left(a^{2}-a-2\right){x}^{2}+\left(-6a^{3}-6a^{2}+24a+28\right){x}-2a^{3}-2a^{2}+7a+8$ |
| 28.1-b9 |
28.1-b |
$12$ |
$24$ |
4.4.7168.1 |
$4$ |
$[4, 0]$ |
28.1 |
\( 2^{2} \cdot 7 \) |
\( 2^{8} \cdot 7^{3} \) |
$11.47446$ |
$(a^2-a-2), (-a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B.1.2 |
$144$ |
\( 3 \) |
$1$ |
$1.161481534$ |
1.481620801 |
\( \frac{3914388170038407466610901238990}{49} a^{3} - 100598188385994848717558770176 a^{2} - \frac{17278945348576339145325144222568}{49} a + 444061887523622038076420848360 \) |
\( \bigl[a + 1\) , \( a^{2} - a - 2\) , \( a^{2} + a - 2\) , \( 3879 a^{3} + 4939 a^{2} - 17012 a - 21585\) , \( 245032 a^{3} + 308773 a^{2} - 1081264 a - 1362224\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{2}+a-2\right){y}={x}^{3}+\left(a^{2}-a-2\right){x}^{2}+\left(3879a^{3}+4939a^{2}-17012a-21585\right){x}+245032a^{3}+308773a^{2}-1081264a-1362224$ |
| 28.1-b10 |
28.1-b |
$12$ |
$24$ |
4.4.7168.1 |
$4$ |
$[4, 0]$ |
28.1 |
\( 2^{2} \cdot 7 \) |
\( 2^{8} \cdot 7 \) |
$11.47446$ |
$(a^2-a-2), (-a)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B.1.1 |
$16$ |
\( 3 \) |
$1$ |
$94.08000425$ |
1.481620801 |
\( -\frac{284771259948120952}{7} a^{3} + 85472182194531840 a^{2} + \frac{451586378819525314}{7} a - 135540623175049496 \) |
\( \bigl[a + 1\) , \( a^{2} - a - 2\) , \( a^{2} + a - 2\) , \( 4 a^{3} - 6 a^{2} - 37 a - 30\) , \( 859 a^{3} + 1104 a^{2} - 3731 a - 4735\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{2}+a-2\right){y}={x}^{3}+\left(a^{2}-a-2\right){x}^{2}+\left(4a^{3}-6a^{2}-37a-30\right){x}+859a^{3}+1104a^{2}-3731a-4735$ |
| 28.1-b11 |
28.1-b |
$12$ |
$24$ |
4.4.7168.1 |
$4$ |
$[4, 0]$ |
28.1 |
\( 2^{2} \cdot 7 \) |
\( 2^{8} \cdot 7^{3} \) |
$11.47446$ |
$(a^2-a-2), (-a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B.1.2 |
$144$ |
\( 3 \) |
$1$ |
$1.161481534$ |
1.481620801 |
\( -\frac{3914388170038407466610901238990}{49} a^{3} - 100598188385994848717558770176 a^{2} + \frac{17278945348576339145325144222568}{49} a + 444061887523622038076420848360 \) |
\( \bigl[a + 1\) , \( a^{2} - 2\) , \( a^{2} + a - 2\) , \( -3880 a^{3} + 4939 a^{2} + 17013 a - 21585\) , \( -245033 a^{3} + 308773 a^{2} + 1081266 a - 1362224\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{2}+a-2\right){y}={x}^{3}+\left(a^{2}-2\right){x}^{2}+\left(-3880a^{3}+4939a^{2}+17013a-21585\right){x}-245033a^{3}+308773a^{2}+1081266a-1362224$ |
| 28.1-b12 |
28.1-b |
$12$ |
$24$ |
4.4.7168.1 |
$4$ |
$[4, 0]$ |
28.1 |
\( 2^{2} \cdot 7 \) |
\( 2^{8} \cdot 7 \) |
$11.47446$ |
$(a^2-a-2), (-a)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B.1.1 |
$16$ |
\( 3 \) |
$1$ |
$94.08000425$ |
1.481620801 |
\( \frac{284771259948120952}{7} a^{3} + 85472182194531840 a^{2} - \frac{451586378819525314}{7} a - 135540623175049496 \) |
\( \bigl[a + 1\) , \( a^{2} - 2\) , \( a^{2} + a - 2\) , \( -5 a^{3} - 6 a^{2} + 38 a - 30\) , \( -860 a^{3} + 1104 a^{2} + 3733 a - 4735\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{2}+a-2\right){y}={x}^{3}+\left(a^{2}-2\right){x}^{2}+\left(-5a^{3}-6a^{2}+38a-30\right){x}-860a^{3}+1104a^{2}+3733a-4735$ |
| 32.1-a1 |
32.1-a |
$2$ |
$2$ |
4.4.7168.1 |
$4$ |
$[4, 0]$ |
32.1 |
\( 2^{5} \) |
\( 2^{12} \) |
$11.66759$ |
$(a^2-a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$314.7722181$ |
1.858948680 |
\( 43136 a^{2} - 68416 \) |
\( \bigl[a^{3} + a^{2} - 3 a - 3\) , \( -a^{3} + 4 a\) , \( 0\) , \( 12 a^{3} - 28 a^{2} - 16 a + 51\) , \( 65 a^{3} - 139 a^{2} - 100 a + 223\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-3a-3\right){x}{y}={x}^{3}+\left(-a^{3}+4a\right){x}^{2}+\left(12a^{3}-28a^{2}-16a+51\right){x}+65a^{3}-139a^{2}-100a+223$ |
| 32.1-a2 |
32.1-a |
$2$ |
$2$ |
4.4.7168.1 |
$4$ |
$[4, 0]$ |
32.1 |
\( 2^{5} \) |
\( 2^{12} \) |
$11.66759$ |
$(a^2-a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$314.7722181$ |
1.858948680 |
\( -43136 a^{2} + 190400 \) |
\( \bigl[a^{3} + a^{2} - 3 a - 3\) , \( a^{3} - a^{2} - 3 a + 2\) , \( 0\) , \( a^{3} + a^{2} - a - 2\) , \( 16 a^{3} - 32 a^{2} - 24 a + 49\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-3a-3\right){x}{y}={x}^{3}+\left(a^{3}-a^{2}-3a+2\right){x}^{2}+\left(a^{3}+a^{2}-a-2\right){x}+16a^{3}-32a^{2}-24a+49$ |
*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.
