| 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 |
| 3.2-a1 |
3.2-a |
$6$ |
$18$ |
3.3.564.1 |
$3$ |
$[3, 0]$ |
3.2 |
\( 3 \) |
\( - 3^{2} \) |
$2.54858$ |
$(-a+2)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2 \) |
$1$ |
$265.9650826$ |
0.622175014 |
\( -\frac{777670594336}{3} a^{2} + 110949412416 a + 1359579986768 \) |
\( \bigl[a^{2} + a - 4\) , \( -a^{2} - a + 3\) , \( 1\) , \( 192869829633 a^{2} - 82549578611 a - 1011566941119\) , \( -74074904350449806 a^{2} + 31704557718515450 a + 388509315353825421\bigr] \) |
${y}^2+\left(a^{2}+a-4\right){x}{y}+{y}={x}^{3}+\left(-a^{2}-a+3\right){x}^{2}+\left(192869829633a^{2}-82549578611a-1011566941119\right){x}-74074904350449806a^{2}+31704557718515450a+388509315353825421$ |
| 3.2-a2 |
3.2-a |
$6$ |
$18$ |
3.3.564.1 |
$3$ |
$[3, 0]$ |
3.2 |
\( 3 \) |
\( -3 \) |
$2.54858$ |
$(-a+2)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 1 \) |
$1$ |
$531.9301652$ |
0.622175014 |
\( \frac{79273984}{3} a^{2} - \frac{242819072}{3} a + 36495360 \) |
\( \bigl[0\) , \( 1\) , \( a^{2} - 4\) , \( 9242113 a^{2} - 3955935 a - 48473709\) , \( -24587375908 a^{2} + 10523565455 a + 128956292760\bigr] \) |
${y}^2+\left(a^{2}-4\right){y}={x}^{3}+{x}^{2}+\left(9242113a^{2}-3955935a-48473709\right){x}-24587375908a^{2}+10523565455a+128956292760$ |
| 3.2-a3 |
3.2-a |
$6$ |
$18$ |
3.3.564.1 |
$3$ |
$[3, 0]$ |
3.2 |
\( 3 \) |
\( -3 \) |
$2.54858$ |
$(-a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$9$ |
\( 1 \) |
$1$ |
$6.567039076$ |
0.622175014 |
\( \frac{376349800136704}{3} a^{2} + \frac{569845045338112}{3} a - 149693421551616 \) |
\( \bigl[0\) , \( 1\) , \( a^{2} + a - 3\) , \( 63 a^{2} - 27 a - 333\) , \( 1790 a^{2} - 768 a - 9395\bigr] \) |
${y}^2+\left(a^{2}+a-3\right){y}={x}^{3}+{x}^{2}+\left(63a^{2}-27a-333\right){x}+1790a^{2}-768a-9395$ |
| 3.2-a4 |
3.2-a |
$6$ |
$18$ |
3.3.564.1 |
$3$ |
$[3, 0]$ |
3.2 |
\( 3 \) |
\( - 3^{3} \) |
$2.54858$ |
$(-a+2)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3Cs.1.1 |
$1$ |
\( 3 \) |
$1$ |
$177.3100550$ |
0.622175014 |
\( \frac{106496}{9} a^{2} + \frac{155648}{9} a - \frac{40960}{3} \) |
\( \bigl[0\) , \( -a^{2} - a + 4\) , \( a\) , \( -14104 a^{2} + 4647 a + 71075\) , \( -5223079 a^{2} + 2195277 a + 27310155\bigr] \) |
${y}^2+a{y}={x}^{3}+\left(-a^{2}-a+4\right){x}^{2}+\left(-14104a^{2}+4647a+71075\right){x}-5223079a^{2}+2195277a+27310155$ |
| 3.2-a5 |
3.2-a |
$6$ |
$18$ |
3.3.564.1 |
$3$ |
$[3, 0]$ |
3.2 |
\( 3 \) |
\( - 3^{6} \) |
$2.54858$ |
$(-a+2)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3Cs.1.1 |
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$88.65502753$ |
0.622175014 |
\( \frac{335008}{27} a^{2} - \frac{1197760}{27} a + \frac{297872}{9} \) |
\( \bigl[a + 1\) , \( a^{2} - 3\) , \( a^{2} + a - 3\) , \( 260424248 a^{2} - 111493586 a - 1365940630\) , \( -3395664178017 a^{2} + 1453294909707 a + 17809486448856\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{2}+a-3\right){y}={x}^{3}+\left(a^{2}-3\right){x}^{2}+\left(260424248a^{2}-111493586a-1365940630\right){x}-3395664178017a^{2}+1453294909707a+17809486448856$ |
| 3.2-a6 |
3.2-a |
$6$ |
$18$ |
3.3.564.1 |
$3$ |
$[3, 0]$ |
3.2 |
\( 3 \) |
\( - 3^{2} \) |
$2.54858$ |
$(-a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$9$ |
\( 2 \) |
$1$ |
$3.283519538$ |
0.622175014 |
\( \frac{1404573422770144}{3} a^{2} - \frac{4334696507062528}{3} a + 673291363036432 \) |
\( \bigl[a + 1\) , \( -a^{2} + a + 3\) , \( a\) , \( 2240627 a^{2} - 959056 a - 11751786\) , \( 2928528549 a^{2} - 1253430277 a - 15359596949\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(-a^{2}+a+3\right){x}^{2}+\left(2240627a^{2}-959056a-11751786\right){x}+2928528549a^{2}-1253430277a-15359596949$ |
| 3.2-b1 |
3.2-b |
$2$ |
$2$ |
3.3.564.1 |
$3$ |
$[3, 0]$ |
3.2 |
\( 3 \) |
\( -3 \) |
$2.54858$ |
$(-a+2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$0.044489043$ |
$320.4736801$ |
0.450263923 |
\( \frac{4096}{3} a^{2} - \frac{8192}{3} a \) |
\( \bigl[0\) , \( -a + 1\) , \( a^{2} + a - 3\) , \( -2 a^{2} - 4 a + 3\) , \( a^{2} + a - 2\bigr] \) |
${y}^2+\left(a^{2}+a-3\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-2a^{2}-4a+3\right){x}+a^{2}+a-2$ |
| 3.2-b2 |
3.2-b |
$2$ |
$2$ |
3.3.564.1 |
$3$ |
$[3, 0]$ |
3.2 |
\( 3 \) |
\( - 3^{2} \) |
$2.54858$ |
$(-a+2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.022244521$ |
$320.4736801$ |
0.450263923 |
\( -\frac{1785856}{3} a^{2} + 253920 a + 3126032 \) |
\( \bigl[a + 1\) , \( -a^{2} + 3\) , \( a\) , \( 730 a^{2} + 1076 a - 933\) , \( 3125 a^{2} + 4806 a - 3575\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(-a^{2}+3\right){x}^{2}+\left(730a^{2}+1076a-933\right){x}+3125a^{2}+4806a-3575$ |
| 6.1-a1 |
6.1-a |
$1$ |
$1$ |
3.3.564.1 |
$3$ |
$[3, 0]$ |
6.1 |
\( 2 \cdot 3 \) |
\( - 2^{5} \cdot 3^{17} \) |
$2.86068$ |
$(a-1), (-a+2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 5 \) |
$1$ |
$10.98191601$ |
2.312110417 |
\( -\frac{33761589187}{78732} a^{2} - \frac{51061199071}{78732} a + \frac{6729320131}{13122} \) |
\( \bigl[a^{2} - 4\) , \( -a^{2} - a + 5\) , \( 1\) , \( -32 a^{2} - 40 a + 58\) , \( -148 a^{2} - 215 a + 196\bigr] \) |
${y}^2+\left(a^{2}-4\right){x}{y}+{y}={x}^{3}+\left(-a^{2}-a+5\right){x}^{2}+\left(-32a^{2}-40a+58\right){x}-148a^{2}-215a+196$ |
| 6.1-b1 |
6.1-b |
$3$ |
$9$ |
3.3.564.1 |
$3$ |
$[3, 0]$ |
6.1 |
\( 2 \cdot 3 \) |
\( - 2^{3} \cdot 3 \) |
$2.86068$ |
$(a-1), (-a+2)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1 |
$1$ |
\( 1 \) |
$1$ |
$248.3454602$ |
1.161914479 |
\( -\frac{1193658451}{3} a^{2} + \frac{7280702455}{6} a - 563905311 \) |
\( \bigl[a^{2} - 4\) , \( a^{2} - 3\) , \( a^{2} - 4\) , \( -557414 a^{2} + 232434 a + 2910720\) , \( -227476127 a^{2} + 97749322 a + 1193880087\bigr] \) |
${y}^2+\left(a^{2}-4\right){x}{y}+\left(a^{2}-4\right){y}={x}^{3}+\left(a^{2}-3\right){x}^{2}+\left(-557414a^{2}+232434a+2910720\right){x}-227476127a^{2}+97749322a+1193880087$ |
| 6.1-b2 |
6.1-b |
$3$ |
$9$ |
3.3.564.1 |
$3$ |
$[3, 0]$ |
6.1 |
\( 2 \cdot 3 \) |
\( - 2^{9} \cdot 3^{3} \) |
$2.86068$ |
$(a-1), (-a+2)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3Cs.1.1 |
$1$ |
\( 3 \) |
$1$ |
$82.78182006$ |
1.161914479 |
\( \frac{30311}{72} a^{2} + \frac{3485}{72} a - \frac{66871}{24} \) |
\( \bigl[a^{2} + a - 3\) , \( a^{2} + a - 5\) , \( a + 1\) , \( 7401 a^{2} - 3868 a - 40276\) , \( 937143 a^{2} - 62193 a - 4208133\bigr] \) |
${y}^2+\left(a^{2}+a-3\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a^{2}+a-5\right){x}^{2}+\left(7401a^{2}-3868a-40276\right){x}+937143a^{2}-62193a-4208133$ |
| 6.1-b3 |
6.1-b |
$3$ |
$9$ |
3.3.564.1 |
$3$ |
$[3, 0]$ |
6.1 |
\( 2 \cdot 3 \) |
\( - 2^{27} \cdot 3 \) |
$2.86068$ |
$(a-1), (-a+2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.2 |
$9$ |
\( 1 \) |
$1$ |
$3.065993335$ |
1.161914479 |
\( \frac{5381675487107}{768} a^{2} - \frac{4606786915613}{1536} a - \frac{9408634203231}{256} \) |
\( \bigl[a\) , \( a^{2} - a - 5\) , \( a + 1\) , \( 352 a^{2} - 152 a - 1847\) , \( 5215 a^{2} - 2233 a - 27353\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a^{2}-a-5\right){x}^{2}+\left(352a^{2}-152a-1847\right){x}+5215a^{2}-2233a-27353$ |
| 9.1-a1 |
9.1-a |
$4$ |
$4$ |
3.3.564.1 |
$3$ |
$[3, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{10} \) |
$3.06068$ |
$(a), (-a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 3 \) |
$1$ |
$46.93954028$ |
1.482383401 |
\( -\frac{227170}{81} a^{2} + \frac{126290}{81} a + 15429 \) |
\( \bigl[1\) , \( -a\) , \( 0\) , \( 7 a^{2} + 10 a - 8\) , \( 0\bigr] \) |
${y}^2+{x}{y}={x}^{3}-a{x}^{2}+\left(7a^{2}+10a-8\right){x}$ |
| 9.1-a2 |
9.1-a |
$4$ |
$4$ |
3.3.564.1 |
$3$ |
$[3, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{20} \) |
$3.06068$ |
$(a), (-a+2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$46.93954028$ |
1.482383401 |
\( \frac{28186967}{2187} a^{2} - \frac{30015488}{729} a + \frac{17415820}{729} \) |
\( \bigl[1\) , \( -a\) , \( 0\) , \( -28 a^{2} - 40 a + 32\) , \( 61 a^{2} + 98 a - 76\bigr] \) |
${y}^2+{x}{y}={x}^{3}-a{x}^{2}+\left(-28a^{2}-40a+32\right){x}+61a^{2}+98a-76$ |
| 9.1-a3 |
9.1-a |
$4$ |
$4$ |
3.3.564.1 |
$3$ |
$[3, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{19} \) |
$3.06068$ |
$(a), (-a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$11.73488507$ |
1.482383401 |
\( \frac{1183604361947422}{531441} a^{2} - \frac{3656586397186801}{531441} a + \frac{1711800806055574}{531441} \) |
\( \bigl[1\) , \( -a\) , \( 0\) , \( -273 a^{2} - 365 a + 297\) , \( -4726 a^{2} - 6899 a + 5493\bigr] \) |
${y}^2+{x}{y}={x}^{3}-a{x}^{2}+\left(-273a^{2}-365a+297\right){x}-4726a^{2}-6899a+5493$ |
| 9.1-a4 |
9.1-a |
$4$ |
$4$ |
3.3.564.1 |
$3$ |
$[3, 0]$ |
9.1 |
\( 3^{2} \) |
\( - 3^{31} \) |
$3.06068$ |
$(a), (-a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$23.46977014$ |
1.482383401 |
\( \frac{121441416358}{1594323} a^{2} + \frac{549436142201}{4782969} a - \frac{143604752722}{1594323} \) |
\( \bigl[1\) , \( -a\) , \( 0\) , \( -343 a^{2} - 515 a + 407\) , \( 7532 a^{2} + 11407 a - 8989\bigr] \) |
${y}^2+{x}{y}={x}^{3}-a{x}^{2}+\left(-343a^{2}-515a+407\right){x}+7532a^{2}+11407a-8989$ |
| 9.2-a1 |
9.2-a |
$2$ |
$2$ |
3.3.564.1 |
$3$ |
$[3, 0]$ |
9.2 |
\( 3^{2} \) |
\( - 3^{8} \) |
$3.06068$ |
$(-a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$77.81945998$ |
3.276790386 |
\( -\frac{1785856}{3} a^{2} + 253920 a + 3126032 \) |
\( \bigl[a^{2} + a - 4\) , \( -a^{2} + a + 4\) , \( a^{2} - 4\) , \( 4066 a^{2} + 5744 a - 5711\) , \( 51205 a^{2} + 71302 a - 74096\bigr] \) |
${y}^2+\left(a^{2}+a-4\right){x}{y}+\left(a^{2}-4\right){y}={x}^{3}+\left(-a^{2}+a+4\right){x}^{2}+\left(4066a^{2}+5744a-5711\right){x}+51205a^{2}+71302a-74096$ |
| 9.2-a2 |
9.2-a |
$2$ |
$2$ |
3.3.564.1 |
$3$ |
$[3, 0]$ |
9.2 |
\( 3^{2} \) |
\( - 3^{7} \) |
$3.06068$ |
$(-a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$77.81945998$ |
3.276790386 |
\( \frac{4096}{3} a^{2} - \frac{8192}{3} a \) |
\( \bigl[0\) , \( -a - 1\) , \( a^{2} - 4\) , \( -12 a^{2} - 18 a + 15\) , \( 22 a^{2} + 32 a - 29\bigr] \) |
${y}^2+\left(a^{2}-4\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-12a^{2}-18a+15\right){x}+22a^{2}+32a-29$ |
| 9.2-b1 |
9.2-b |
$6$ |
$18$ |
3.3.564.1 |
$3$ |
$[3, 0]$ |
9.2 |
\( 3^{2} \) |
\( - 3^{8} \) |
$3.06068$ |
$(-a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \) |
$1$ |
$34.55346441$ |
1.454963321 |
\( -\frac{777670594336}{3} a^{2} + 110949412416 a + 1359579986768 \) |
\( \bigl[a^{2} + a - 4\) , \( -a + 1\) , \( 1\) , \( 140847 a^{2} - 59482 a - 737039\) , \( 46317141 a^{2} - 19512288 a - 242274553\bigr] \) |
${y}^2+\left(a^{2}+a-4\right){x}{y}+{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(140847a^{2}-59482a-737039\right){x}+46317141a^{2}-19512288a-242274553$ |
| 9.2-b2 |
9.2-b |
$6$ |
$18$ |
3.3.564.1 |
$3$ |
$[3, 0]$ |
9.2 |
\( 3^{2} \) |
\( - 3^{9} \) |
$3.06068$ |
$(-a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3Cs |
$1$ |
\( 2 \) |
$1$ |
$69.10692883$ |
1.454963321 |
\( \frac{106496}{9} a^{2} + \frac{155648}{9} a - \frac{40960}{3} \) |
\( \bigl[0\) , \( a^{2} - 4\) , \( a\) , \( -14539185 a^{2} - 22014279 a + 17348997\) , \( -63263067455 a^{2} - 95788947266 a + 75488807774\bigr] \) |
${y}^2+a{y}={x}^{3}+\left(a^{2}-4\right){x}^{2}+\left(-14539185a^{2}-22014279a+17348997\right){x}-63263067455a^{2}-95788947266a+75488807774$ |
| 9.2-b3 |
9.2-b |
$6$ |
$18$ |
3.3.564.1 |
$3$ |
$[3, 0]$ |
9.2 |
\( 3^{2} \) |
\( - 3^{7} \) |
$3.06068$ |
$(-a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$9$ |
\( 2 \) |
$1$ |
$7.678547648$ |
1.454963321 |
\( \frac{376349800136704}{3} a^{2} + \frac{569845045338112}{3} a - 149693421551616 \) |
\( \bigl[0\) , \( a^{2} - 4\) , \( a\) , \( -1174957315 a^{2} - 1779046589 a + 1402019987\) , \( -46336375800604 a^{2} - 70159617755850 a + 55290993048396\bigr] \) |
${y}^2+a{y}={x}^{3}+\left(a^{2}-4\right){x}^{2}+\left(-1174957315a^{2}-1779046589a+1402019987\right){x}-46336375800604a^{2}-70159617755850a+55290993048396$ |
| 9.2-b4 |
9.2-b |
$6$ |
$18$ |
3.3.564.1 |
$3$ |
$[3, 0]$ |
9.2 |
\( 3^{2} \) |
\( - 3^{7} \) |
$3.06068$ |
$(-a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$1$ |
$69.10692883$ |
1.454963321 |
\( \frac{79273984}{3} a^{2} - \frac{242819072}{3} a + 36495360 \) |
\( \bigl[0\) , \( a^{2} - 4\) , \( 1\) , \( -9 a^{2} - 25 a - 13\) , \( 61 a^{2} + 78 a - 103\bigr] \) |
${y}^2+{y}={x}^{3}+\left(a^{2}-4\right){x}^{2}+\left(-9a^{2}-25a-13\right){x}+61a^{2}+78a-103$ |
| 9.2-b5 |
9.2-b |
$6$ |
$18$ |
3.3.564.1 |
$3$ |
$[3, 0]$ |
9.2 |
\( 3^{2} \) |
\( - 3^{12} \) |
$3.06068$ |
$(-a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3Cs |
$1$ |
\( 2^{2} \) |
$1$ |
$34.55346441$ |
1.454963321 |
\( \frac{335008}{27} a^{2} - \frac{1197760}{27} a + \frac{297872}{9} \) |
\( \bigl[a + 1\) , \( a + 1\) , \( a\) , \( -315856869 a^{2} - 478955819 a + 375425692\) , \( -107441784047257 a^{2} - 162681916837688 a + 128204452553168\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-315856869a^{2}-478955819a+375425692\right){x}-107441784047257a^{2}-162681916837688a+128204452553168$ |
| 9.2-b6 |
9.2-b |
$6$ |
$18$ |
3.3.564.1 |
$3$ |
$[3, 0]$ |
9.2 |
\( 3^{2} \) |
\( - 3^{8} \) |
$3.06068$ |
$(-a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$9$ |
\( 2^{2} \) |
$1$ |
$3.839273824$ |
1.454963321 |
\( \frac{1404573422770144}{3} a^{2} - \frac{4334696507062528}{3} a + 673291363036432 \) |
\( \bigl[a + 1\) , \( a + 1\) , \( a\) , \( -92817390184 a^{2} - 140549857504 a + 110730336912\) , \( -32537219532762283 a^{2} - 49265780890113512 a + 38825167968431489\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-92817390184a^{2}-140549857504a+110730336912\right){x}-32537219532762283a^{2}-49265780890113512a+38825167968431489$ |
| 9.3-a1 |
9.3-a |
$4$ |
$6$ |
3.3.564.1 |
$3$ |
$[3, 0]$ |
9.3 |
\( 3^{2} \) |
\( - 3^{3} \) |
$3.06068$ |
$(a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-3$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$0.154595273$ |
$148.8699425$ |
1.453633559 |
\( 0 \) |
\( \bigl[0\) , \( -a^{2} - a + 3\) , \( a^{2} + a - 3\) , \( a^{2} + 2 a\) , \( -a^{2} - 3 a - 2\bigr] \) |
${y}^2+\left(a^{2}+a-3\right){y}={x}^{3}+\left(-a^{2}-a+3\right){x}^{2}+\left(a^{2}+2a\right){x}-a^{2}-3a-2$ |
| 9.3-a2 |
9.3-a |
$4$ |
$6$ |
3.3.564.1 |
$3$ |
$[3, 0]$ |
9.3 |
\( 3^{2} \) |
\( - 3^{9} \) |
$3.06068$ |
$(a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-3$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$0.463785821$ |
$49.62331419$ |
1.453633559 |
\( 0 \) |
\( \bigl[0\) , \( -a^{2} - a + 3\) , \( a^{2} + a - 3\) , \( a^{2} + 2 a\) , \( -9778 a^{2} - 13667 a + 14042\bigr] \) |
${y}^2+\left(a^{2}+a-3\right){y}={x}^{3}+\left(-a^{2}-a+3\right){x}^{2}+\left(a^{2}+2a\right){x}-9778a^{2}-13667a+14042$ |
| 9.3-a3 |
9.3-a |
$4$ |
$6$ |
3.3.564.1 |
$3$ |
$[3, 0]$ |
9.3 |
\( 3^{2} \) |
\( 3^{3} \) |
$3.06068$ |
$(a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-12$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2 \) |
$0.077297636$ |
$297.7398851$ |
1.453633559 |
\( 54000 \) |
\( \bigl[a + 1\) , \( a^{2} - 4\) , \( a\) , \( 8365 a^{2} - 3588 a - 43890\) , \( 650317 a^{2} - 278333 a - 3410780\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(a^{2}-4\right){x}^{2}+\left(8365a^{2}-3588a-43890\right){x}+650317a^{2}-278333a-3410780$ |
| 9.3-a4 |
9.3-a |
$4$ |
$6$ |
3.3.564.1 |
$3$ |
$[3, 0]$ |
9.3 |
\( 3^{2} \) |
\( 3^{9} \) |
$3.06068$ |
$(a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-12$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2 \) |
$0.231892910$ |
$99.24662838$ |
1.453633559 |
\( 54000 \) |
\( \bigl[a + 1\) , \( a^{2} - 4\) , \( a\) , \( 542135 a^{2} - 718673 a - 3858585\) , \( -750497147 a^{2} + 44609980 a + 3359180180\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(a^{2}-4\right){x}^{2}+\left(542135a^{2}-718673a-3858585\right){x}-750497147a^{2}+44609980a+3359180180$ |
| 12.1-a1 |
12.1-a |
$8$ |
$12$ |
3.3.564.1 |
$3$ |
$[3, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( 2^{4} \cdot 3^{3} \) |
$3.21101$ |
$(a-1), (a)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 1 \) |
$1$ |
$361.9743051$ |
0.952616738 |
\( \frac{291520468}{27} a^{2} - \frac{866820064}{27} a + \frac{405451276}{27} \) |
\( \bigl[a^{2} + a - 4\) , \( -a + 1\) , \( a^{2} + a - 4\) , \( -65182 a^{2} - 107355 a + 59715\) , \( 20780624 a^{2} + 31959765 a - 23763780\bigr] \) |
${y}^2+\left(a^{2}+a-4\right){x}{y}+\left(a^{2}+a-4\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-65182a^{2}-107355a+59715\right){x}+20780624a^{2}+31959765a-23763780$ |
| 12.1-a2 |
12.1-a |
$8$ |
$12$ |
3.3.564.1 |
$3$ |
$[3, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( 2^{4} \cdot 3^{12} \) |
$3.21101$ |
$(a-1), (a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$1$ |
$45.24678814$ |
0.952616738 |
\( \frac{2527129540}{531441} a^{2} + \frac{4144946720}{531441} a - \frac{2295871508}{531441} \) |
\( \bigl[a^{2} + a - 4\) , \( -a + 1\) , \( 0\) , \( -38604 a^{2} - 55093 a + 53076\) , \( -8036173 a^{2} - 12181226 a + 9561315\bigr] \) |
${y}^2+\left(a^{2}+a-4\right){x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-38604a^{2}-55093a+53076\right){x}-8036173a^{2}-12181226a+9561315$ |
| 12.1-a3 |
12.1-a |
$8$ |
$12$ |
3.3.564.1 |
$3$ |
$[3, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( - 2^{4} \cdot 3^{3} \) |
$3.21101$ |
$(a-1), (a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 1 \) |
$1$ |
$90.49357628$ |
0.952616738 |
\( -\frac{2350144}{27} a^{2} + \frac{980608}{27} a + \frac{12421568}{27} \) |
\( \bigl[a^{2} - 3\) , \( a^{2} + a - 4\) , \( a^{2} + a - 4\) , \( 7985782 a^{2} - 912084 a - 36656362\) , \( 16266023798 a^{2} - 4735213855 a - 80667019236\bigr] \) |
${y}^2+\left(a^{2}-3\right){x}{y}+\left(a^{2}+a-4\right){y}={x}^{3}+\left(a^{2}+a-4\right){x}^{2}+\left(7985782a^{2}-912084a-36656362\right){x}+16266023798a^{2}-4735213855a-80667019236$ |
| 12.1-a4 |
12.1-a |
$8$ |
$12$ |
3.3.564.1 |
$3$ |
$[3, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( - 2^{4} \cdot 3 \) |
$3.21101$ |
$(a-1), (a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 3 \) |
$1$ |
$30.16452542$ |
0.952616738 |
\( \frac{25509749696}{3} a^{2} - \frac{78726427520}{3} a + \frac{36684830144}{3} \) |
\( \bigl[a^{2} - 3\) , \( a^{2} + a - 4\) , \( a^{2} + a - 4\) , \( 2670 a^{2} - 3321 a - 18546\) , \( -246313 a^{2} - 10442 a + 1050155\bigr] \) |
${y}^2+\left(a^{2}-3\right){x}{y}+\left(a^{2}+a-4\right){y}={x}^{3}+\left(a^{2}+a-4\right){x}^{2}+\left(2670a^{2}-3321a-18546\right){x}-246313a^{2}-10442a+1050155$ |
| 12.1-a5 |
12.1-a |
$8$ |
$12$ |
3.3.564.1 |
$3$ |
$[3, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( 2^{8} \cdot 3^{2} \) |
$3.21101$ |
$(a-1), (a)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2Cs, 3B |
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$60.32905085$ |
0.952616738 |
\( -\frac{128976128}{9} a^{2} + \frac{72997664}{9} a + \frac{716487712}{9} \) |
\( \bigl[a^{2} - 3\) , \( a^{2} + a - 4\) , \( a^{2} - 3\) , \( -79 a^{2} - 120 a + 91\) , \( -1042 a^{2} - 1578 a + 1242\bigr] \) |
${y}^2+\left(a^{2}-3\right){x}{y}+\left(a^{2}-3\right){y}={x}^{3}+\left(a^{2}+a-4\right){x}^{2}+\left(-79a^{2}-120a+91\right){x}-1042a^{2}-1578a+1242$ |
| 12.1-a6 |
12.1-a |
$8$ |
$12$ |
3.3.564.1 |
$3$ |
$[3, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( 2^{8} \cdot 3^{6} \) |
$3.21101$ |
$(a-1), (a)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2Cs, 3B |
$1$ |
\( 2 \) |
$1$ |
$180.9871525$ |
0.952616738 |
\( \frac{675712}{729} a^{2} - \frac{1817824}{729} a + \frac{2101408}{729} \) |
\( \bigl[a^{2} - 3\) , \( a^{2} + a - 4\) , \( 0\) , \( -26317 a^{2} - 39876 a + 31344\) , \( 2630825 a^{2} + 3983429 a - 3139239\bigr] \) |
${y}^2+\left(a^{2}-3\right){x}{y}={x}^{3}+\left(a^{2}+a-4\right){x}^{2}+\left(-26317a^{2}-39876a+31344\right){x}+2630825a^{2}+3983429a-3139239$ |
| 12.1-a7 |
12.1-a |
$8$ |
$12$ |
3.3.564.1 |
$3$ |
$[3, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( 2^{4} \cdot 3^{4} \) |
$3.21101$ |
$(a-1), (a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$15.08226271$ |
0.952616738 |
\( \frac{804188335428820}{81} a^{2} + \frac{1217651256566960}{81} a - \frac{959599685860868}{81} \) |
\( \bigl[a + 1\) , \( a + 1\) , \( a^{2} + a - 4\) , \( -244 a^{2} - 373 a + 283\) , \( -4999 a^{2} - 7565 a + 5973\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{2}+a-4\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-244a^{2}-373a+283\right){x}-4999a^{2}-7565a+5973$ |
| 12.1-a8 |
12.1-a |
$8$ |
$12$ |
3.3.564.1 |
$3$ |
$[3, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( 2^{4} \cdot 3 \) |
$3.21101$ |
$(a-1), (a)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 3 \) |
$1$ |
$120.6581017$ |
0.952616738 |
\( -\frac{3678332413180796}{3} a^{2} + \frac{1574351034213488}{3} a + \frac{19292180259448060}{3} \) |
\( \bigl[a + 1\) , \( a + 1\) , \( a^{2} - 3\) , \( 29 a^{2} - 43 a - 215\) , \( -327 a^{2} - 42 a + 1335\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{2}-3\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(29a^{2}-43a-215\right){x}-327a^{2}-42a+1335$ |
| 12.1-b1 |
12.1-b |
$4$ |
$6$ |
3.3.564.1 |
$3$ |
$[3, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( 2^{4} \cdot 3^{6} \) |
$3.21101$ |
$(a-1), (a)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2 \cdot 3^{2} \) |
$0.121863684$ |
$210.2879676$ |
1.618603355 |
\( \frac{15042880}{729} a^{2} + \frac{33763712}{729} a - \frac{23706560}{729} \) |
\( \bigl[a^{2} - 3\) , \( a^{2} - a - 5\) , \( a^{2} + a - 4\) , \( -208603 a^{2} + 89168 a + 1093846\) , \( -97847436 a^{2} + 41880294 a + 513193838\bigr] \) |
${y}^2+\left(a^{2}-3\right){x}{y}+\left(a^{2}+a-4\right){y}={x}^{3}+\left(a^{2}-a-5\right){x}^{2}+\left(-208603a^{2}+89168a+1093846\right){x}-97847436a^{2}+41880294a+513193838$ |
| 12.1-b2 |
12.1-b |
$4$ |
$6$ |
3.3.564.1 |
$3$ |
$[3, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( - 2^{8} \cdot 3 \) |
$3.21101$ |
$(a-1), (a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 1 \) |
$0.731182108$ |
$70.09598921$ |
1.618603355 |
\( -\frac{1625152}{3} a^{2} + \frac{694240}{3} a + \frac{8527136}{3} \) |
\( \bigl[a^{2} - 3\) , \( a^{2} - a - 5\) , \( a^{2} - 3\) , \( 0\) , \( -2 a^{2} - 4 a\bigr] \) |
${y}^2+\left(a^{2}-3\right){x}{y}+\left(a^{2}-3\right){y}={x}^{3}+\left(a^{2}-a-5\right){x}^{2}-2a^{2}-4a$ |
| 12.1-b3 |
12.1-b |
$4$ |
$6$ |
3.3.564.1 |
$3$ |
$[3, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( 2^{4} \cdot 3^{2} \) |
$3.21101$ |
$(a-1), (a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2 \) |
$0.365591054$ |
$70.09598921$ |
1.618603355 |
\( \frac{19264}{9} a^{2} + \frac{20864}{9} a - \frac{27584}{9} \) |
\( \bigl[a^{2} - 3\) , \( a + 1\) , \( a + 1\) , \( 2520 a^{2} - 1393 a - 13872\) , \( 198755 a^{2} - 90108 a - 1052947\bigr] \) |
${y}^2+\left(a^{2}-3\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(2520a^{2}-1393a-13872\right){x}+198755a^{2}-90108a-1052947$ |
| 12.1-b4 |
12.1-b |
$4$ |
$6$ |
3.3.564.1 |
$3$ |
$[3, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( - 2^{8} \cdot 3^{3} \) |
$3.21101$ |
$(a-1), (a)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 3^{2} \) |
$0.243727369$ |
$210.2879676$ |
1.618603355 |
\( \frac{3546214208}{27} a^{2} - \frac{10944131360}{27} a + \frac{5099832992}{27} \) |
\( \bigl[a^{2} - 3\) , \( -a^{2} + 4\) , \( 0\) , \( -1\) , \( a^{2} - 4\bigr] \) |
${y}^2+\left(a^{2}-3\right){x}{y}={x}^{3}+\left(-a^{2}+4\right){x}^{2}-{x}+a^{2}-4$ |
| 12.2-a1 |
12.2-a |
$4$ |
$4$ |
3.3.564.1 |
$3$ |
$[3, 0]$ |
12.2 |
\( 2^{2} \cdot 3 \) |
\( 2^{8} \cdot 3^{2} \) |
$3.21101$ |
$(a-1), (-a+2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2 \) |
$1$ |
$166.1605286$ |
0.874577552 |
\( -1024 a^{2} - \frac{1952}{3} a + 12064 \) |
\( \bigl[a^{2} - 3\) , \( a^{2} - 3\) , \( a^{2} - 3\) , \( 3 a^{2} - 13\) , \( 2 a^{2} - 9\bigr] \) |
${y}^2+\left(a^{2}-3\right){x}{y}+\left(a^{2}-3\right){y}={x}^{3}+\left(a^{2}-3\right){x}^{2}+\left(3a^{2}-13\right){x}+2a^{2}-9$ |
| 12.2-a2 |
12.2-a |
$4$ |
$4$ |
3.3.564.1 |
$3$ |
$[3, 0]$ |
12.2 |
\( 2^{2} \cdot 3 \) |
\( - 2^{4} \cdot 3 \) |
$3.21101$ |
$(a-1), (-a+2)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$332.3210572$ |
0.874577552 |
\( \frac{3008}{3} a^{2} + \frac{10880}{3} a + 3392 \) |
\( \bigl[a^{2} - 3\) , \( -a^{2} + a + 3\) , \( a + 1\) , \( 227015 a^{2} - 97181 a - 1190684\) , \( -78867445 a^{2} + 33755834 a + 413645389\bigr] \) |
${y}^2+\left(a^{2}-3\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a^{2}+a+3\right){x}^{2}+\left(227015a^{2}-97181a-1190684\right){x}-78867445a^{2}+33755834a+413645389$ |
| 12.2-a3 |
12.2-a |
$4$ |
$4$ |
3.3.564.1 |
$3$ |
$[3, 0]$ |
12.2 |
\( 2^{2} \cdot 3 \) |
\( - 2^{4} \cdot 3 \) |
$3.21101$ |
$(a-1), (-a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$83.08026430$ |
0.874577552 |
\( \frac{19808332}{3} a^{2} - \frac{45834272}{3} a + 6578812 \) |
\( \bigl[a + 1\) , \( a^{2} + a - 4\) , \( 0\) , \( -54 a^{2} + 27 a + 292\) , \( 1384 a^{2} - 590 a - 7254\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a^{2}+a-4\right){x}^{2}+\left(-54a^{2}+27a+292\right){x}+1384a^{2}-590a-7254$ |
| 12.2-a4 |
12.2-a |
$4$ |
$4$ |
3.3.564.1 |
$3$ |
$[3, 0]$ |
12.2 |
\( 2^{2} \cdot 3 \) |
\( - 2^{4} \cdot 3^{4} \) |
$3.21101$ |
$(a-1), (-a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$41.54013215$ |
0.874577552 |
\( -\frac{195657764}{9} a^{2} + \frac{27910048}{3} a + 114025236 \) |
\( \bigl[a + 1\) , \( a^{2} + a - 4\) , \( a + 1\) , \( 788 a^{2} - 334 a - 4126\) , \( 18639 a^{2} - 7974 a - 97751\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a^{2}+a-4\right){x}^{2}+\left(788a^{2}-334a-4126\right){x}+18639a^{2}-7974a-97751$ |
| 18.1-a1 |
18.1-a |
$4$ |
$4$ |
3.3.564.1 |
$3$ |
$[3, 0]$ |
18.1 |
\( 2 \cdot 3^{2} \) |
\( 2^{4} \cdot 3^{8} \) |
$3.43550$ |
$(a-1), (a), (-a+2)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$143.1623178$ |
1.507055262 |
\( -\frac{4062005}{8748} a^{2} - \frac{740135}{4374} a + \frac{19740427}{8748} \) |
\( \bigl[a^{2} - 4\) , \( -a + 1\) , \( a + 1\) , \( 193026079394562391289 a^{2} - 82616641518757898258 a - 1012386832540196026144\) , \( -875592806319826658126643629012 a^{2} + 374759618515916131212460990275 a + 4592324015467867994086217671064\bigr] \) |
${y}^2+\left(a^{2}-4\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(193026079394562391289a^{2}-82616641518757898258a-1012386832540196026144\right){x}-875592806319826658126643629012a^{2}+374759618515916131212460990275a+4592324015467867994086217671064$ |
| 18.1-a2 |
18.1-a |
$4$ |
$4$ |
3.3.564.1 |
$3$ |
$[3, 0]$ |
18.1 |
\( 2 \cdot 3^{2} \) |
\( 2^{2} \cdot 3^{16} \) |
$3.43550$ |
$(a-1), (a), (-a+2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1$ |
$71.58115891$ |
1.507055262 |
\( \frac{1547712339889}{4782969} a^{2} + \frac{4975989133009}{9565938} a - \frac{3048769095955}{9565938} \) |
\( \bigl[a\) , \( a - 1\) , \( a^{2} - 3\) , \( 46862272886 a^{2} - 20480794232 a - 246667365763\) , \( 8845870692389547 a^{2} - 3778901758233568 a - 46379972509892306\bigr] \) |
${y}^2+a{x}{y}+\left(a^{2}-3\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(46862272886a^{2}-20480794232a-246667365763\right){x}+8845870692389547a^{2}-3778901758233568a-46379972509892306$ |
| 18.1-a3 |
18.1-a |
$4$ |
$4$ |
3.3.564.1 |
$3$ |
$[3, 0]$ |
18.1 |
\( 2 \cdot 3^{2} \) |
\( - 2 \cdot 3^{32} \) |
$3.43550$ |
$(a-1), (a), (-a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 2^{2} \) |
$1$ |
$8.947644864$ |
1.507055262 |
\( \frac{74477037111927089}{45753584909922} a^{2} - \frac{84201883409075761}{22876792454961} a + \frac{71865168970913423}{45753584909922} \) |
\( \bigl[a\) , \( a - 1\) , \( a^{2} - 3\) , \( 9006598131 a^{2} - 4336919257 a - 48243545703\) , \( 22653787918099788 a^{2} - 9690902869143747 a - 118804392822284928\bigr] \) |
${y}^2+a{x}{y}+\left(a^{2}-3\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(9006598131a^{2}-4336919257a-48243545703\right){x}+22653787918099788a^{2}-9690902869143747a-118804392822284928$ |
| 18.1-a4 |
18.1-a |
$4$ |
$4$ |
3.3.564.1 |
$3$ |
$[3, 0]$ |
18.1 |
\( 2 \cdot 3^{2} \) |
\( 2 \cdot 3^{8} \) |
$3.43550$ |
$(a-1), (a), (-a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 1 \) |
$1$ |
$35.79057945$ |
1.507055262 |
\( \frac{4499726629994869}{4374} a^{2} + \frac{3412389347130763}{2187} a - \frac{5345104179542741}{4374} \) |
\( \bigl[1\) , \( a^{2} + a - 5\) , \( a^{2} + a - 3\) , \( -422 a^{2} - 677 a + 422\) , \( 10152 a^{2} + 15255 a - 12350\bigr] \) |
${y}^2+{x}{y}+\left(a^{2}+a-3\right){y}={x}^{3}+\left(a^{2}+a-5\right){x}^{2}+\left(-422a^{2}-677a+422\right){x}+10152a^{2}+15255a-12350$ |
| 18.1-b1 |
18.1-b |
$2$ |
$2$ |
3.3.564.1 |
$3$ |
$[3, 0]$ |
18.1 |
\( 2 \cdot 3^{2} \) |
\( 2^{2} \cdot 3^{6} \) |
$3.43550$ |
$(a-1), (a), (-a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$48.72420879$ |
1.025829650 |
\( -\frac{8628137}{243} a^{2} + \frac{28137547}{486} a + \frac{38744807}{486} \) |
\( \bigl[a^{2} - 4\) , \( 1\) , \( 0\) , \( a^{2} + a - 2\) , \( 0\bigr] \) |
${y}^2+\left(a^{2}-4\right){x}{y}={x}^{3}+{x}^{2}+\left(a^{2}+a-2\right){x}$ |
| 18.1-b2 |
18.1-b |
$2$ |
$2$ |
3.3.564.1 |
$3$ |
$[3, 0]$ |
18.1 |
\( 2 \cdot 3^{2} \) |
\( - 2 \cdot 3^{12} \) |
$3.43550$ |
$(a-1), (a), (-a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$24.36210439$ |
1.025829650 |
\( \frac{372244392642017}{118098} a^{2} - \frac{574397230241389}{59049} a + \frac{535313154727535}{118098} \) |
\( \bigl[a^{2} - 4\) , \( 1\) , \( 0\) , \( -4 a^{2} - 4 a + 8\) , \( -11 a^{2} - 9 a + 28\bigr] \) |
${y}^2+\left(a^{2}-4\right){x}{y}={x}^{3}+{x}^{2}+\left(-4a^{2}-4a+8\right){x}-11a^{2}-9a+28$ |
*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.
