| 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 |
| 2.1-a1 |
2.1-a |
$2$ |
$3$ |
3.3.756.1 |
$3$ |
$[3, 0]$ |
2.1 |
\( 2 \) |
\( -2 \) |
$2.75785$ |
$(-a)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1 |
$1$ |
\( 1 \) |
$0.169476270$ |
$318.3906047$ |
0.654164525 |
\( \frac{950820111}{2} a^{2} - 161579934 a - 2797544034 \) |
\( \bigl[a^{2} + a - 3\) , \( -a^{2} - a + 3\) , \( a^{2} - 4\) , \( -4\) , \( a^{2} - a - 4\bigr] \) |
${y}^2+\left(a^{2}+a-3\right){x}{y}+\left(a^{2}-4\right){y}={x}^{3}+\left(-a^{2}-a+3\right){x}^{2}-4{x}+a^{2}-a-4$ |
| 2.1-a2 |
2.1-a |
$2$ |
$3$ |
3.3.756.1 |
$3$ |
$[3, 0]$ |
2.1 |
\( 2 \) |
\( - 2^{3} \) |
$2.75785$ |
$(-a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.2 |
$1$ |
\( 1 \) |
$0.056492090$ |
$106.1302015$ |
0.654164525 |
\( \frac{243}{2} a^{2} - 810 a - \frac{2133}{2} \) |
\( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( 37 a^{2} - 14 a - 217\) , \( -365 a^{2} + 124 a + 2146\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(37a^{2}-14a-217\right){x}-365a^{2}+124a+2146$ |
| 6.1-a1 |
6.1-a |
$1$ |
$1$ |
3.3.756.1 |
$3$ |
$[3, 0]$ |
6.1 |
\( 2 \cdot 3 \) |
\( - 2 \cdot 3^{13} \) |
$3.31201$ |
$(-a), (-a-1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$1$ |
$54.40253310$ |
1.978600999 |
\( -\frac{159241}{486} a^{2} + \frac{66734}{243} a + \frac{421534}{243} \) |
\( \bigl[a^{2} - 3\) , \( -a^{2} - a + 4\) , \( 0\) , \( -4 a^{2} + 2 a + 23\) , \( -5 a^{2} + a + 31\bigr] \) |
${y}^2+\left(a^{2}-3\right){x}{y}={x}^{3}+\left(-a^{2}-a+4\right){x}^{2}+\left(-4a^{2}+2a+23\right){x}-5a^{2}+a+31$ |
| 6.1-b1 |
6.1-b |
$1$ |
$1$ |
3.3.756.1 |
$3$ |
$[3, 0]$ |
6.1 |
\( 2 \cdot 3 \) |
\( - 2^{17} \cdot 3^{7} \) |
$3.31201$ |
$(-a), (-a-1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 7 \) |
$1$ |
$4.081863800$ |
1.039191658 |
\( \frac{3257021269}{1728} a^{2} - \frac{916834585}{1728} a - \frac{9829877647}{864} \) |
\( \bigl[1\) , \( -a^{2} + 4\) , \( a^{2} + a - 3\) , \( -7 a^{2} + 29 a - 29\) , \( -25 a^{2} + 117 a - 146\bigr] \) |
${y}^2+{x}{y}+\left(a^{2}+a-3\right){y}={x}^{3}+\left(-a^{2}+4\right){x}^{2}+\left(-7a^{2}+29a-29\right){x}-25a^{2}+117a-146$ |
| 7.1-a1 |
7.1-a |
$2$ |
$2$ |
3.3.756.1 |
$3$ |
$[3, 0]$ |
7.1 |
\( 7 \) |
\( - 7^{2} \) |
$3.39820$ |
$(-a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$57.33171247$ |
1.042567111 |
\( -\frac{757137492}{7} a^{2} - \frac{65339609}{7} a + \frac{5294855361}{7} \) |
\( \bigl[a^{2} + a - 3\) , \( a^{2} - a - 4\) , \( 1\) , \( -3 a^{2} + 21 a - 2\) , \( -32 a^{2} + 80 a + 49\bigr] \) |
${y}^2+\left(a^{2}+a-3\right){x}{y}+{y}={x}^{3}+\left(a^{2}-a-4\right){x}^{2}+\left(-3a^{2}+21a-2\right){x}-32a^{2}+80a+49$ |
| 7.1-a2 |
7.1-a |
$2$ |
$2$ |
3.3.756.1 |
$3$ |
$[3, 0]$ |
7.1 |
\( 7 \) |
\( -7 \) |
$3.39820$ |
$(-a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$114.6634249$ |
1.042567111 |
\( -\frac{34801}{7} a^{2} + \frac{63618}{7} a + \frac{222231}{7} \) |
\( \bigl[a^{2} + a - 3\) , \( a^{2} - a - 4\) , \( 1\) , \( 2 a^{2} + 6 a + 3\) , \( 2 a^{2} + 9 a + 3\bigr] \) |
${y}^2+\left(a^{2}+a-3\right){x}{y}+{y}={x}^{3}+\left(a^{2}-a-4\right){x}^{2}+\left(2a^{2}+6a+3\right){x}+2a^{2}+9a+3$ |
| 8.1-a1 |
8.1-a |
$1$ |
$1$ |
3.3.756.1 |
$3$ |
$[3, 0]$ |
8.1 |
\( 2^{3} \) |
\( - 2^{11} \) |
$3.47468$ |
$(-a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
|
|
$1$ |
\( 1 \) |
$0.113861389$ |
$171.0519514$ |
2.125029043 |
\( -8445 a^{2} - 5561 a - 898 \) |
\( \bigl[a\) , \( a + 1\) , \( a^{2} + a - 4\) , \( -19 a^{2} - 49 a - 15\) , \( 90 a^{2} + 232 a + 64\bigr] \) |
${y}^2+a{x}{y}+\left(a^{2}+a-4\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-19a^{2}-49a-15\right){x}+90a^{2}+232a+64$ |
| 9.1-a1 |
9.1-a |
$4$ |
$6$ |
3.3.756.1 |
$3$ |
$[3, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{3} \) |
$3.54356$ |
$(-a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-12$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$3$ |
3B.1.2 |
$1$ |
\( 2 \) |
$0.265572092$ |
$99.24662838$ |
1.437899583 |
\( 54000 \) |
\( \bigl[a^{2} + a - 4\) , \( -a^{2} - a + 5\) , \( a + 1\) , \( 3719177 a^{2} - 1264064 a - 21885439\) , \( 6470244265 a^{2} - 2199086477 a - 38074046926\bigr] \) |
${y}^2+\left(a^{2}+a-4\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a^{2}-a+5\right){x}^{2}+\left(3719177a^{2}-1264064a-21885439\right){x}+6470244265a^{2}-2199086477a-38074046926$ |
| 9.1-a2 |
9.1-a |
$4$ |
$6$ |
3.3.756.1 |
$3$ |
$[3, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{9} \) |
$3.54356$ |
$(-a-1)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{potential}$ |
$-12$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$3$ |
3B.1.1 |
$1$ |
\( 2 \) |
$0.796716276$ |
$297.7398851$ |
1.437899583 |
\( 54000 \) |
\( \bigl[a^{2} + a - 4\) , \( a^{2} - 5\) , \( 1\) , \( 14902 a^{2} - 5060 a - 87679\) , \( -1639857 a^{2} + 557355 a + 9649724\bigr] \) |
${y}^2+\left(a^{2}+a-4\right){x}{y}+{y}={x}^{3}+\left(a^{2}-5\right){x}^{2}+\left(14902a^{2}-5060a-87679\right){x}-1639857a^{2}+557355a+9649724$ |
| 9.1-a3 |
9.1-a |
$4$ |
$6$ |
3.3.756.1 |
$3$ |
$[3, 0]$ |
9.1 |
\( 3^{2} \) |
\( - 3^{3} \) |
$3.54356$ |
$(-a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-3$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2 \) |
$0.531144184$ |
$49.62331419$ |
1.437899583 |
\( 0 \) |
\( \bigl[0\) , \( a^{2} - a - 5\) , \( a + 1\) , \( -a^{2} + 7\) , \( 452503 a^{2} - 153796 a - 2662748\bigr] \) |
${y}^2+\left(a+1\right){y}={x}^{3}+\left(a^{2}-a-5\right){x}^{2}+\left(-a^{2}+7\right){x}+452503a^{2}-153796a-2662748$ |
| 9.1-a4 |
9.1-a |
$4$ |
$6$ |
3.3.756.1 |
$3$ |
$[3, 0]$ |
9.1 |
\( 3^{2} \) |
\( - 3^{9} \) |
$3.54356$ |
$(-a-1)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{potential}$ |
$-3$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2 \) |
$1.593432553$ |
$148.8699425$ |
1.437899583 |
\( 0 \) |
\( \bigl[0\) , \( 0\) , \( a^{2} + a - 3\) , \( 0\) , \( -115 a^{2} + 37 a + 672\bigr] \) |
${y}^2+\left(a^{2}+a-3\right){y}={x}^{3}-115a^{2}+37a+672$ |
| 11.1-a1 |
11.1-a |
$2$ |
$2$ |
3.3.756.1 |
$3$ |
$[3, 0]$ |
11.1 |
\( 11 \) |
\( -11 \) |
$3.66408$ |
$(a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$369.9789875$ |
3.364001420 |
\( \frac{56508493824}{11} a^{2} - \frac{127817367552}{11} a - \frac{49969778688}{11} \) |
\( \bigl[0\) , \( -a^{2} + 4\) , \( 1\) , \( 19 a^{2} - 8 a - 115\) , \( -35 a^{2} + 16 a + 215\bigr] \) |
${y}^2+{y}={x}^{3}+\left(-a^{2}+4\right){x}^{2}+\left(19a^{2}-8a-115\right){x}-35a^{2}+16a+215$ |
| 11.1-a2 |
11.1-a |
$2$ |
$2$ |
3.3.756.1 |
$3$ |
$[3, 0]$ |
11.1 |
\( 11 \) |
\( - 11^{2} \) |
$3.66408$ |
$(a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$184.9894937$ |
3.364001420 |
\( \frac{24141029846688}{121} a^{2} + \frac{62807199775200}{121} a + \frac{18558033202224}{121} \) |
\( \bigl[a\) , \( -a^{2} - a + 5\) , \( a^{2} - 3\) , \( -3797 a^{2} + 1288 a + 22344\) , \( -266852 a^{2} + 90697 a + 1570287\bigr] \) |
${y}^2+a{x}{y}+\left(a^{2}-3\right){y}={x}^{3}+\left(-a^{2}-a+5\right){x}^{2}+\left(-3797a^{2}+1288a+22344\right){x}-266852a^{2}+90697a+1570287$ |
| 11.1-b1 |
11.1-b |
$4$ |
$6$ |
3.3.756.1 |
$3$ |
$[3, 0]$ |
11.1 |
\( 11 \) |
\( - 11^{3} \) |
$3.66408$ |
$(a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 1 \) |
$0.557446061$ |
$111.1058379$ |
1.689429587 |
\( \frac{75644928}{1331} a^{2} - \frac{175841280}{1331} a - \frac{52862976}{1331} \) |
\( \bigl[0\) , \( a^{2} - a - 5\) , \( 1\) , \( 709 a^{2} - 239 a - 4177\) , \( -17110 a^{2} + 5820 a + 100671\bigr] \) |
${y}^2+{y}={x}^{3}+\left(a^{2}-a-5\right){x}^{2}+\left(709a^{2}-239a-4177\right){x}-17110a^{2}+5820a+100671$ |
| 11.1-b2 |
11.1-b |
$4$ |
$6$ |
3.3.756.1 |
$3$ |
$[3, 0]$ |
11.1 |
\( 11 \) |
\( -11 \) |
$3.66408$ |
$(a+3)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 1 \) |
$1.672338183$ |
$333.3175138$ |
1.689429587 |
\( -\frac{2581414060032}{11} a^{2} + \frac{877362831360}{11} a + \frac{15190288736256}{11} \) |
\( \bigl[0\) , \( a + 1\) , \( a^{2} - 3\) , \( 25 a^{2} - 7 a - 147\) , \( -109 a^{2} + 36 a + 642\bigr] \) |
${y}^2+\left(a^{2}-3\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(25a^{2}-7a-147\right){x}-109a^{2}+36a+642$ |
| 11.1-b3 |
11.1-b |
$4$ |
$6$ |
3.3.756.1 |
$3$ |
$[3, 0]$ |
11.1 |
\( 11 \) |
\( - 11^{2} \) |
$3.66408$ |
$(a+3)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2 \) |
$0.836169091$ |
$333.3175138$ |
1.689429587 |
\( \frac{26541559008}{121} a^{2} + \frac{65152755072}{121} a + \frac{18938651184}{121} \) |
\( \bigl[a\) , \( a^{2} - a - 3\) , \( 1\) , \( 1881 a^{2} - 641 a - 11063\) , \( -76250 a^{2} + 25915 a + 448694\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+\left(a^{2}-a-3\right){x}^{2}+\left(1881a^{2}-641a-11063\right){x}-76250a^{2}+25915a+448694$ |
| 11.1-b4 |
11.1-b |
$4$ |
$6$ |
3.3.756.1 |
$3$ |
$[3, 0]$ |
11.1 |
\( 11 \) |
\( - 11^{6} \) |
$3.66408$ |
$(a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2 \) |
$0.278723030$ |
$111.1058379$ |
1.689429587 |
\( \frac{594571104}{1771561} a^{2} - \frac{2711232}{1771561} a + \frac{126904752}{1771561} \) |
\( \bigl[a\) , \( -a + 1\) , \( a + 1\) , \( -57303 a^{2} + 19474 a + 337199\) , \( -47957957 a^{2} + 16299800 a + 282207816\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-57303a^{2}+19474a+337199\right){x}-47957957a^{2}+16299800a+282207816$ |
| 12.1-a1 |
12.1-a |
$6$ |
$8$ |
3.3.756.1 |
$3$ |
$[3, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( 2^{8} \cdot 3^{2} \) |
$3.71760$ |
$(-a), (-a-1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2 \) |
$1$ |
$297.0980244$ |
1.350668835 |
\( -52192 a^{2} + \frac{51296}{3} a + \frac{932096}{3} \) |
\( \bigl[a^{2} - 4\) , \( a^{2} - 5\) , \( 0\) , \( -7 a^{2} - 18 a - 5\) , \( 0\bigr] \) |
${y}^2+\left(a^{2}-4\right){x}{y}={x}^{3}+\left(a^{2}-5\right){x}^{2}+\left(-7a^{2}-18a-5\right){x}$ |
| 12.1-a2 |
12.1-a |
$6$ |
$8$ |
3.3.756.1 |
$3$ |
$[3, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( - 2^{4} \cdot 3 \) |
$3.71760$ |
$(-a), (-a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$148.5490122$ |
1.350668835 |
\( \frac{26432}{3} a^{2} + \frac{47488}{3} a + \frac{12800}{3} \) |
\( \bigl[a^{2} - 4\) , \( a^{2} - a - 3\) , \( a\) , \( 59 a^{2} - 22 a - 343\) , \( -1747 a^{2} + 593 a + 10281\bigr] \) |
${y}^2+\left(a^{2}-4\right){x}{y}+a{y}={x}^{3}+\left(a^{2}-a-3\right){x}^{2}+\left(59a^{2}-22a-343\right){x}-1747a^{2}+593a+10281$ |
| 12.1-a3 |
12.1-a |
$6$ |
$8$ |
3.3.756.1 |
$3$ |
$[3, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( - 2^{8} \cdot 3^{2} \) |
$3.71760$ |
$(-a), (-a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$74.27450611$ |
1.350668835 |
\( 34314114514876 a^{2} - \frac{232835224044038}{3} a - \frac{91026828654464}{3} \) |
\( \bigl[a^{2} + a - 4\) , \( -a^{2} + a + 3\) , \( a^{2} + a - 4\) , \( 19 a^{2} - 12 a - 121\) , \( 144 a^{2} - 39 a - 825\bigr] \) |
${y}^2+\left(a^{2}+a-4\right){x}{y}+\left(a^{2}+a-4\right){y}={x}^{3}+\left(-a^{2}+a+3\right){x}^{2}+\left(19a^{2}-12a-121\right){x}+144a^{2}-39a-825$ |
| 12.1-a4 |
12.1-a |
$6$ |
$8$ |
3.3.756.1 |
$3$ |
$[3, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( 2^{4} \cdot 3^{4} \) |
$3.71760$ |
$(-a), (-a-1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2 \) |
$1$ |
$297.0980244$ |
1.350668835 |
\( \frac{17784004}{9} a^{2} - \frac{37592800}{9} a - \frac{14815712}{9} \) |
\( \bigl[a^{2} + a - 4\) , \( -a^{2} + a + 3\) , \( a^{2} + a - 4\) , \( -a^{2} - 7 a - 6\) , \( 3 a^{2} - 18\bigr] \) |
${y}^2+\left(a^{2}+a-4\right){x}{y}+\left(a^{2}+a-4\right){y}={x}^{3}+\left(-a^{2}+a+3\right){x}^{2}+\left(-a^{2}-7a-6\right){x}+3a^{2}-18$ |
| 12.1-a5 |
12.1-a |
$6$ |
$8$ |
3.3.756.1 |
$3$ |
$[3, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( 2^{8} \cdot 3^{8} \) |
$3.71760$ |
$(-a), (-a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$74.27450611$ |
1.350668835 |
\( \frac{1398867890476}{27} a^{2} + \frac{3639405472822}{27} a + \frac{358452602576}{9} \) |
\( \bigl[a^{2} + a - 4\) , \( -a^{2} + a + 3\) , \( a^{2} + a - 4\) , \( -41 a^{2} - 82 a + 29\) , \( 180 a^{2} + 529 a + 273\bigr] \) |
${y}^2+\left(a^{2}+a-4\right){x}{y}+\left(a^{2}+a-4\right){y}={x}^{3}+\left(-a^{2}+a+3\right){x}^{2}+\left(-41a^{2}-82a+29\right){x}+180a^{2}+529a+273$ |
| 12.1-a6 |
12.1-a |
$6$ |
$8$ |
3.3.756.1 |
$3$ |
$[3, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( 2^{4} \cdot 3 \) |
$3.71760$ |
$(-a), (-a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$148.5490122$ |
1.350668835 |
\( -\frac{47159697452}{3} a^{2} + \frac{16028491808}{3} a + \frac{277510474000}{3} \) |
\( \bigl[a^{2} + a - 4\) , \( -a^{2} + a + 3\) , \( 0\) , \( 21 a^{2} - 4 a - 111\) , \( -43 a^{2} + 21 a + 265\bigr] \) |
${y}^2+\left(a^{2}+a-4\right){x}{y}={x}^{3}+\left(-a^{2}+a+3\right){x}^{2}+\left(21a^{2}-4a-111\right){x}-43a^{2}+21a+265$ |
| 12.1-b1 |
12.1-b |
$2$ |
$2$ |
3.3.756.1 |
$3$ |
$[3, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( 2^{4} \cdot 3^{2} \) |
$3.71760$ |
$(-a), (-a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \cdot 3 \) |
$0.154549830$ |
$98.50820151$ |
2.491681562 |
\( -576 a^{2} + \frac{896}{3} a + \frac{10496}{3} \) |
\( \bigl[a^{2} - 4\) , \( a^{2} + a - 5\) , \( a^{2} + a - 4\) , \( 14287 a^{2} - 4855 a - 84068\) , \( 1076968 a^{2} - 366036 a - 6337400\bigr] \) |
${y}^2+\left(a^{2}-4\right){x}{y}+\left(a^{2}+a-4\right){y}={x}^{3}+\left(a^{2}+a-5\right){x}^{2}+\left(14287a^{2}-4855a-84068\right){x}+1076968a^{2}-366036a-6337400$ |
| 12.1-b2 |
12.1-b |
$2$ |
$2$ |
3.3.756.1 |
$3$ |
$[3, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( - 2^{8} \cdot 3 \) |
$3.71760$ |
$(-a), (-a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 3 \) |
$0.309099660$ |
$98.50820151$ |
2.491681562 |
\( \frac{113696}{3} a^{2} - \frac{251936}{3} a - \frac{96256}{3} \) |
\( \bigl[a^{2} - 4\) , \( -a^{2} - a + 4\) , \( a^{2} - 4\) , \( -4 a^{2} - 2 a + 16\) , \( -a^{2} + 8 a + 23\bigr] \) |
${y}^2+\left(a^{2}-4\right){x}{y}+\left(a^{2}-4\right){y}={x}^{3}+\left(-a^{2}-a+4\right){x}^{2}+\left(-4a^{2}-2a+16\right){x}-a^{2}+8a+23$ |
| 13.1-a1 |
13.1-a |
$1$ |
$1$ |
3.3.756.1 |
$3$ |
$[3, 0]$ |
13.1 |
\( 13 \) |
\( -13 \) |
$3.76753$ |
$(a^2-a-3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$0.070708284$ |
$251.6374387$ |
1.941359271 |
\( -\frac{25206}{13} a^{2} - \frac{73469}{13} a - \frac{22785}{13} \) |
\( \bigl[a^{2} + a - 3\) , \( -a^{2} + a + 4\) , \( a^{2} + a - 4\) , \( a + 6\) , \( 3 a + 5\bigr] \) |
${y}^2+\left(a^{2}+a-3\right){x}{y}+\left(a^{2}+a-4\right){y}={x}^{3}+\left(-a^{2}+a+4\right){x}^{2}+\left(a+6\right){x}+3a+5$ |
| 14.1-a1 |
14.1-a |
$2$ |
$2$ |
3.3.756.1 |
$3$ |
$[3, 0]$ |
14.1 |
\( 2 \cdot 7 \) |
\( - 2^{26} \cdot 7^{5} \) |
$3.81435$ |
$(-a), (-a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1.725046078$ |
$22.02258670$ |
2.072523149 |
\( \frac{426197161}{175616} a^{2} + \frac{1321023327}{175616} a + \frac{48451365}{10976} \) |
\( \bigl[a^{2} + a - 3\) , \( -a^{2} + 3\) , \( a^{2} + a - 4\) , \( 5598742 a^{2} - 1902884 a - 32945707\) , \( 5319497132 a^{2} - 1807974123 a - 31302494175\bigr] \) |
${y}^2+\left(a^{2}+a-3\right){x}{y}+\left(a^{2}+a-4\right){y}={x}^{3}+\left(-a^{2}+3\right){x}^{2}+\left(5598742a^{2}-1902884a-32945707\right){x}+5319497132a^{2}-1807974123a-31302494175$ |
| 14.1-a2 |
14.1-a |
$2$ |
$2$ |
3.3.756.1 |
$3$ |
$[3, 0]$ |
14.1 |
\( 2 \cdot 7 \) |
\( 2^{13} \cdot 7^{10} \) |
$3.81435$ |
$(-a), (-a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$3.450092156$ |
$11.01129335$ |
2.072523149 |
\( \frac{59025432903567}{537824} a^{2} + \frac{38462279603579}{134456} a + \frac{1652453166465}{19208} \) |
\( \bigl[1\) , \( -a\) , \( a^{2} + a - 3\) , \( -250 a^{2} + 583 a + 166\) , \( -5116 a^{2} + 11643 a + 4342\bigr] \) |
${y}^2+{x}{y}+\left(a^{2}+a-3\right){y}={x}^{3}-a{x}^{2}+\left(-250a^{2}+583a+166\right){x}-5116a^{2}+11643a+4342$ |
| 14.1-b1 |
14.1-b |
$4$ |
$6$ |
3.3.756.1 |
$3$ |
$[3, 0]$ |
14.1 |
\( 2 \cdot 7 \) |
\( - 2^{2} \cdot 7^{9} \) |
$3.81435$ |
$(-a), (-a+3)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2 \cdot 3^{2} \) |
$1$ |
$52.33430598$ |
0.951690153 |
\( \frac{432748702683}{33614} a^{2} + \frac{1125908180091}{33614} a + \frac{166374042318}{16807} \) |
\( \bigl[a^{2} - 3\) , \( a^{2} + a - 4\) , \( a^{2} - 3\) , \( -a^{2} - 5 a - 8\) , \( 2 a + 2\bigr] \) |
${y}^2+\left(a^{2}-3\right){x}{y}+\left(a^{2}-3\right){y}={x}^{3}+\left(a^{2}+a-4\right){x}^{2}+\left(-a^{2}-5a-8\right){x}+2a+2$ |
| 14.1-b2 |
14.1-b |
$4$ |
$6$ |
3.3.756.1 |
$3$ |
$[3, 0]$ |
14.1 |
\( 2 \cdot 7 \) |
\( - 2 \cdot 7^{18} \) |
$3.81435$ |
$(-a), (-a+3)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$4$ |
\( 2 \cdot 3^{2} \) |
$1$ |
$13.08357649$ |
0.951690153 |
\( \frac{285231962511}{80707214} a^{2} - \frac{146329580889}{40353607} a - \frac{6358370292}{40353607} \) |
\( \bigl[a^{2} - 3\) , \( a^{2} + a - 4\) , \( a^{2} - 3\) , \( -6 a^{2} + 12\) , \( -2 a^{2} + 6 a - 2\bigr] \) |
${y}^2+\left(a^{2}-3\right){x}{y}+\left(a^{2}-3\right){y}={x}^{3}+\left(a^{2}+a-4\right){x}^{2}+\left(-6a^{2}+12\right){x}-2a^{2}+6a-2$ |
| 14.1-b3 |
14.1-b |
$4$ |
$6$ |
3.3.756.1 |
$3$ |
$[3, 0]$ |
14.1 |
\( 2 \cdot 7 \) |
\( - 2^{6} \cdot 7^{3} \) |
$3.81435$ |
$(-a), (-a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$17.44476866$ |
0.951690153 |
\( -\frac{232863336}{49} a^{2} + \frac{119872791}{49} a + \frac{5057617185}{196} \) |
\( \bigl[1\) , \( a^{2} - a - 3\) , \( a^{2} + a - 4\) , \( 811 a^{2} - 275 a - 4776\) , \( 20565 a^{2} - 6984 a - 121036\bigr] \) |
${y}^2+{x}{y}+\left(a^{2}+a-4\right){y}={x}^{3}+\left(a^{2}-a-3\right){x}^{2}+\left(811a^{2}-275a-4776\right){x}+20565a^{2}-6984a-121036$ |
| 14.1-b4 |
14.1-b |
$4$ |
$6$ |
3.3.756.1 |
$3$ |
$[3, 0]$ |
14.1 |
\( 2 \cdot 7 \) |
\( - 2^{3} \cdot 7^{6} \) |
$3.81435$ |
$(-a), (-a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$4$ |
\( 2 \cdot 3 \) |
$1$ |
$4.361192165$ |
0.951690153 |
\( \frac{85622377457727}{49} a^{2} - \frac{1355626168815087}{343} a - \frac{1059962927321079}{686} \) |
\( \bigl[1\) , \( a^{2} - a - 3\) , \( a^{2} + a - 4\) , \( 751 a^{2} - 215 a - 4526\) , \( 22591 a^{2} - 7382 a - 133714\bigr] \) |
${y}^2+{x}{y}+\left(a^{2}+a-4\right){y}={x}^{3}+\left(a^{2}-a-3\right){x}^{2}+\left(751a^{2}-215a-4526\right){x}+22591a^{2}-7382a-133714$ |
| 14.1-c1 |
14.1-c |
$1$ |
$1$ |
3.3.756.1 |
$3$ |
$[3, 0]$ |
14.1 |
\( 2 \cdot 7 \) |
\( - 2 \cdot 7^{4} \) |
$3.81435$ |
$(-a), (-a+3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \) |
$0.070523660$ |
$99.84367027$ |
1.536546601 |
\( -\frac{287013}{14} a^{2} + \frac{2368271}{49} a + \frac{629136}{49} \) |
\( \bigl[a^{2} - 3\) , \( a^{2} + a - 5\) , \( a^{2} + a - 4\) , \( 13 a^{2} - 2 a - 72\) , \( 32 a^{2} - 9 a - 182\bigr] \) |
${y}^2+\left(a^{2}-3\right){x}{y}+\left(a^{2}+a-4\right){y}={x}^{3}+\left(a^{2}+a-5\right){x}^{2}+\left(13a^{2}-2a-72\right){x}+32a^{2}-9a-182$ |
| 14.2-a1 |
14.2-a |
$2$ |
$3$ |
3.3.756.1 |
$3$ |
$[3, 0]$ |
14.2 |
\( 2 \cdot 7 \) |
\( - 2^{7} \cdot 7^{9} \) |
$3.81435$ |
$(-a), (a-1)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1 |
$1$ |
\( 3^{2} \) |
$1$ |
$61.91245147$ |
2.251734090 |
\( -\frac{159986040807231}{322828856} a^{2} - \frac{210952612789731}{161414428} a - \frac{33820719875685}{80707214} \) |
\( \bigl[a^{2} + a - 3\) , \( a^{2} - 4\) , \( 1\) , \( 36 a^{2} - 70 a - 26\) , \( 63 a^{2} - 131 a - 52\bigr] \) |
${y}^2+\left(a^{2}+a-3\right){x}{y}+{y}={x}^{3}+\left(a^{2}-4\right){x}^{2}+\left(36a^{2}-70a-26\right){x}+63a^{2}-131a-52$ |
| 14.2-a2 |
14.2-a |
$2$ |
$3$ |
3.3.756.1 |
$3$ |
$[3, 0]$ |
14.2 |
\( 2 \cdot 7 \) |
\( - 2^{21} \cdot 7^{3} \) |
$3.81435$ |
$(-a), (a-1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.2 |
$1$ |
\( 3 \) |
$1$ |
$20.63748382$ |
2.251734090 |
\( -\frac{5464341}{5488} a^{2} + \frac{9560025}{5488} a + \frac{96965559}{43904} \) |
\( \bigl[a + 1\) , \( 0\) , \( a^{2} + a - 3\) , \( -70 a^{2} + 146 a + 86\) , \( -694 a^{2} + 1560 a + 630\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{2}+a-3\right){y}={x}^{3}+\left(-70a^{2}+146a+86\right){x}-694a^{2}+1560a+630$ |
| 14.2-b1 |
14.2-b |
$2$ |
$2$ |
3.3.756.1 |
$3$ |
$[3, 0]$ |
14.2 |
\( 2 \cdot 7 \) |
\( 2 \cdot 7^{2} \) |
$3.81435$ |
$(-a), (a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$49.14299502$ |
0.893656724 |
\( -\frac{126008104190785}{98} a^{2} + \frac{21413621072019}{49} a + \frac{370746317902690}{49} \) |
\( \bigl[a^{2} + a - 3\) , \( -a^{2} + a + 3\) , \( a^{2} + a - 4\) , \( -12 a^{2} - 4 a + 2\) , \( 22 a^{2} - 47 a - 18\bigr] \) |
${y}^2+\left(a^{2}+a-3\right){x}{y}+\left(a^{2}+a-4\right){y}={x}^{3}+\left(-a^{2}+a+3\right){x}^{2}+\left(-12a^{2}-4a+2\right){x}+22a^{2}-47a-18$ |
| 14.2-b2 |
14.2-b |
$2$ |
$2$ |
3.3.756.1 |
$3$ |
$[3, 0]$ |
14.2 |
\( 2 \cdot 7 \) |
\( - 2^{2} \cdot 7 \) |
$3.81435$ |
$(-a), (a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$49.14299502$ |
0.893656724 |
\( \frac{6676487}{14} a^{2} - \frac{2269261}{14} a - \frac{19639054}{7} \) |
\( \bigl[a^{2} + a - 3\) , \( -a^{2} + a + 3\) , \( a^{2} + a - 4\) , \( 3 a^{2} + a + 2\) , \( 6 a^{2} + 18 a + 6\bigr] \) |
${y}^2+\left(a^{2}+a-3\right){x}{y}+\left(a^{2}+a-4\right){y}={x}^{3}+\left(-a^{2}+a+3\right){x}^{2}+\left(3a^{2}+a+2\right){x}+6a^{2}+18a+6$ |
| 14.2-c1 |
14.2-c |
$1$ |
$1$ |
3.3.756.1 |
$3$ |
$[3, 0]$ |
14.2 |
\( 2 \cdot 7 \) |
\( - 2^{5} \cdot 7^{8} \) |
$3.81435$ |
$(-a), (a-1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \) |
$0.233209744$ |
$36.39376971$ |
1.852098533 |
\( -\frac{15701355727}{23059204} a^{2} - \frac{25459219073}{23059204} a + \frac{1949533557}{11529602} \) |
\( \bigl[a^{2} + a - 3\) , \( -a^{2} - a + 4\) , \( a^{2} + a - 3\) , \( -4 a^{2} + 11\) , \( -5 a^{2} + 5 a + 12\bigr] \) |
${y}^2+\left(a^{2}+a-3\right){x}{y}+\left(a^{2}+a-3\right){y}={x}^{3}+\left(-a^{2}-a+4\right){x}^{2}+\left(-4a^{2}+11\right){x}-5a^{2}+5a+12$ |
| 16.1-a1 |
16.1-a |
$1$ |
$1$ |
3.3.756.1 |
$3$ |
$[3, 0]$ |
16.1 |
\( 2^{4} \) |
\( - 2^{11} \) |
$3.90019$ |
$(-a)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
|
|
$1$ |
\( 2^{2} \) |
$1$ |
$14.51683547$ |
2.111888806 |
\( -8445 a^{2} - 5561 a - 898 \) |
\( \bigl[a^{2} + a - 4\) , \( a + 1\) , \( a^{2} + a - 4\) , \( -5 a^{2} - 10 a - 3\) , \( -42 a^{2} - 107 a - 31\bigr] \) |
${y}^2+\left(a^{2}+a-4\right){x}{y}+\left(a^{2}+a-4\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-5a^{2}-10a-3\right){x}-42a^{2}-107a-31$ |
| 16.1-b1 |
16.1-b |
$2$ |
$3$ |
3.3.756.1 |
$3$ |
$[3, 0]$ |
16.1 |
\( 2^{4} \) |
\( - 2^{15} \) |
$3.90019$ |
$(-a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B |
$1$ |
\( 2 \) |
$0.035827204$ |
$153.1146159$ |
1.197071042 |
\( \frac{243}{2} a^{2} - 810 a - \frac{2133}{2} \) |
\( \bigl[a\) , \( -a + 1\) , \( a\) , \( 12 a^{2} - 6 a - 69\) , \( -60 a^{2} + 19 a + 355\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(12a^{2}-6a-69\right){x}-60a^{2}+19a+355$ |
| 16.1-b2 |
16.1-b |
$2$ |
$3$ |
3.3.756.1 |
$3$ |
$[3, 0]$ |
16.1 |
\( 2^{4} \) |
\( - 2^{13} \) |
$3.90019$ |
$(-a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B |
$1$ |
\( 2 \) |
$0.107481613$ |
$51.03820532$ |
1.197071042 |
\( \frac{950820111}{2} a^{2} - 161579934 a - 2797544034 \) |
\( \bigl[a\) , \( -a^{2} + a + 4\) , \( a^{2} + a - 4\) , \( a + 1\) , \( -2 a - 5\bigr] \) |
${y}^2+a{x}{y}+\left(a^{2}+a-4\right){y}={x}^{3}+\left(-a^{2}+a+4\right){x}^{2}+\left(a+1\right){x}-2a-5$ |
| 18.1-a1 |
18.1-a |
$3$ |
$9$ |
3.3.756.1 |
$3$ |
$[3, 0]$ |
18.1 |
\( 2 \cdot 3^{2} \) |
\( - 2^{3} \cdot 3^{3} \) |
$3.97751$ |
$(-a), (-a-1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$3$ |
3B.1.2 |
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$9.849498594$ |
2.149336803 |
\( -\frac{132651}{2} \) |
\( \bigl[a^{2} - 3\) , \( a^{2} - 5\) , \( 1\) , \( 140 a^{2} - 45 a - 823\) , \( 1416 a^{2} - 479 a - 8333\bigr] \) |
${y}^2+\left(a^{2}-3\right){x}{y}+{y}={x}^{3}+\left(a^{2}-5\right){x}^{2}+\left(140a^{2}-45a-823\right){x}+1416a^{2}-479a-8333$ |
| 18.1-a2 |
18.1-a |
$3$ |
$9$ |
3.3.756.1 |
$3$ |
$[3, 0]$ |
18.1 |
\( 2 \cdot 3^{2} \) |
\( - 2^{27} \cdot 3^{3} \) |
$3.97751$ |
$(-a), (-a-1)$ |
0 |
$\Z/9\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$3$ |
3B.1.1 |
$1$ |
\( 2 \cdot 3^{3} \) |
$1$ |
$88.64548734$ |
2.149336803 |
\( -\frac{1167051}{512} \) |
\( \bigl[a^{2} + a - 3\) , \( a + 1\) , \( a^{2} - 3\) , \( 16 a^{2} + 6 a - 73\) , \( -34 a^{2} + 29 a + 247\bigr] \) |
${y}^2+\left(a^{2}+a-3\right){x}{y}+\left(a^{2}-3\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(16a^{2}+6a-73\right){x}-34a^{2}+29a+247$ |
| 18.1-a3 |
18.1-a |
$3$ |
$9$ |
3.3.756.1 |
$3$ |
$[3, 0]$ |
18.1 |
\( 2 \cdot 3^{2} \) |
\( - 2^{9} \cdot 3^{9} \) |
$3.97751$ |
$(-a), (-a-1)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$3$ |
3Cs.1.1 |
$1$ |
\( 2 \cdot 3^{2} \) |
$1$ |
$29.54849578$ |
2.149336803 |
\( \frac{9261}{8} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( 1\) , \( -1\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}+{x}-1$ |
| 18.1-b1 |
18.1-b |
$1$ |
$1$ |
3.3.756.1 |
$3$ |
$[3, 0]$ |
18.1 |
\( 2 \cdot 3^{2} \) |
\( - 2^{17} \cdot 3^{13} \) |
$3.97751$ |
$(-a), (-a-1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2^{2} \cdot 17 \) |
$0.011801086$ |
$38.46514991$ |
3.367896125 |
\( \frac{3257021269}{1728} a^{2} - \frac{916834585}{1728} a - \frac{9829877647}{864} \) |
\( \bigl[a^{2} - 3\) , \( a^{2} + a - 4\) , \( a\) , \( 22 a^{2} + 105 a + 34\) , \( -258 a^{2} - 852 a - 260\bigr] \) |
${y}^2+\left(a^{2}-3\right){x}{y}+a{y}={x}^{3}+\left(a^{2}+a-4\right){x}^{2}+\left(22a^{2}+105a+34\right){x}-258a^{2}-852a-260$ |
| 18.1-c1 |
18.1-c |
$3$ |
$9$ |
3.3.756.1 |
$3$ |
$[3, 0]$ |
18.1 |
\( 2 \cdot 3^{2} \) |
\( - 2^{3} \cdot 3^{9} \) |
$3.97751$ |
$(-a), (-a-1)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$3$ |
3B.1.1 |
$1$ |
\( 2 \) |
$0.276051149$ |
$251.7384296$ |
1.684949629 |
\( -\frac{132651}{2} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -3\) , \( 3\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}-3{x}+3$ |
| 18.1-c2 |
18.1-c |
$3$ |
$9$ |
3.3.756.1 |
$3$ |
$[3, 0]$ |
18.1 |
\( 2 \cdot 3^{2} \) |
\( - 2^{27} \cdot 3^{9} \) |
$3.97751$ |
$(-a), (-a-1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$3$ |
3B.1.2 |
$1$ |
\( 2 \) |
$2.484460348$ |
$3.107881847$ |
1.684949629 |
\( -\frac{1167051}{512} \) |
\( \bigl[a + 1\) , \( 0\) , \( a^{2} + a - 3\) , \( -19 a^{2} - 47 a - 13\) , \( -166 a^{2} - 431 a - 130\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{2}+a-3\right){y}={x}^{3}+\left(-19a^{2}-47a-13\right){x}-166a^{2}-431a-130$ |
| 18.1-c3 |
18.1-c |
$3$ |
$9$ |
3.3.756.1 |
$3$ |
$[3, 0]$ |
18.1 |
\( 2 \cdot 3^{2} \) |
\( - 2^{9} \cdot 3^{3} \) |
$3.97751$ |
$(-a), (-a-1)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$3$ |
3Cs.1.1 |
$1$ |
\( 2 \) |
$0.828153449$ |
$83.91280988$ |
1.684949629 |
\( \frac{9261}{8} \) |
\( \bigl[a + 1\) , \( 0\) , \( a^{2} + a - 3\) , \( a^{2} + 3 a + 2\) , \( 4 a^{2} + 9 a\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{2}+a-3\right){y}={x}^{3}+\left(a^{2}+3a+2\right){x}+4a^{2}+9a$ |
| 18.1-d1 |
18.1-d |
$1$ |
$1$ |
3.3.756.1 |
$3$ |
$[3, 0]$ |
18.1 |
\( 2 \cdot 3^{2} \) |
\( - 2 \cdot 3^{19} \) |
$3.97751$ |
$(-a), (-a-1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2 \) |
$1$ |
$18.43156569$ |
1.340699126 |
\( -\frac{159241}{486} a^{2} + \frac{66734}{243} a + \frac{421534}{243} \) |
\( \bigl[1\) , \( a^{2} + a - 4\) , \( 1\) , \( 5 a^{2} + 17 a + 10\) , \( 58 a^{2} + 151 a + 42\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(a^{2}+a-4\right){x}^{2}+\left(5a^{2}+17a+10\right){x}+58a^{2}+151a+42$ |
| 18.1-e1 |
18.1-e |
$2$ |
$3$ |
3.3.756.1 |
$3$ |
$[3, 0]$ |
18.1 |
\( 2 \cdot 3^{2} \) |
\( - 2^{3} \cdot 3^{6} \) |
$3.97751$ |
$(-a), (-a-1)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.1 |
$1$ |
\( 3 \) |
$1.204228157$ |
$76.74643457$ |
3.361290812 |
\( \frac{243}{2} a^{2} - 810 a - \frac{2133}{2} \) |
\( \bigl[a^{2} + a - 3\) , \( -a^{2} + a + 5\) , \( a^{2} + a - 3\) , \( 3 a + 12\) , \( a^{2} + 8 a + 11\bigr] \) |
${y}^2+\left(a^{2}+a-3\right){x}{y}+\left(a^{2}+a-3\right){y}={x}^{3}+\left(-a^{2}+a+5\right){x}^{2}+\left(3a+12\right){x}+a^{2}+8a+11$ |
*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.
