| 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 |
| 300.1-a1 |
300.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{33}) \) |
$2$ |
$[2, 0]$ |
300.1 |
\( 2^{2} \cdot 3 \cdot 5^{2} \) |
\( 2^{16} \cdot 3^{28} \cdot 5^{8} \) |
$2.13637$ |
$(-a-2), (-a+3), (-2a+7), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{7} \) |
$1$ |
$0.293596507$ |
1.635474935 |
\( \frac{1281177907381}{765275040000} \) |
\( \bigl[1\) , \( -a\) , \( 0\) , \( -1810 a + 6112\) , \( 2281556 a - 7693920\bigr] \) |
${y}^2+{x}{y}={x}^{3}-a{x}^{2}+\left(-1810a+6112\right){x}+2281556a-7693920$ |
| 300.1-a2 |
300.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{33}) \) |
$2$ |
$[2, 0]$ |
300.1 |
\( 2^{2} \cdot 3 \cdot 5^{2} \) |
\( 2^{40} \cdot 3^{7} \cdot 5^{2} \) |
$2.13637$ |
$(-a-2), (-a+3), (-2a+7), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2$ |
2B |
$4$ |
\( 2^{4} \) |
$1$ |
$0.587193014$ |
1.635474935 |
\( -\frac{378635697618365323499}{1739461754880} a + \frac{159608856006948603629}{217432719360} \) |
\( \bigl[1\) , \( 1\) , \( a + 1\) , \( -322 a - 1687\) , \( -4182 a - 21123\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(-322a-1687\right){x}-4182a-21123$ |
| 300.1-a3 |
300.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{33}) \) |
$2$ |
$[2, 0]$ |
300.1 |
\( 2^{2} \cdot 3 \cdot 5^{2} \) |
\( 2^{32} \cdot 3^{14} \cdot 5^{4} \) |
$2.13637$ |
$(-a-2), (-a+3), (-2a+7), (5)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{7} \) |
$1$ |
$1.174386028$ |
1.635474935 |
\( \frac{129392980254539}{3583180800} \) |
\( \bigl[1\) , \( -a\) , \( 0\) , \( 8430 a - 28448\) , \( 704596 a - 2376032\bigr] \) |
${y}^2+{x}{y}={x}^{3}-a{x}^{2}+\left(8430a-28448\right){x}+704596a-2376032$ |
| 300.1-a4 |
300.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{33}) \) |
$2$ |
$[2, 0]$ |
300.1 |
\( 2^{2} \cdot 3 \cdot 5^{2} \) |
\( 2^{40} \cdot 3^{7} \cdot 5^{2} \) |
$2.13637$ |
$(-a-2), (-a+3), (-2a+7), (5)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{6} \) |
$1$ |
$2.348772056$ |
1.635474935 |
\( \frac{378635697618365323499}{1739461754880} a + \frac{898235150437223505533}{1739461754880} \) |
\( \bigl[1\) , \( -a\) , \( 0\) , \( -340154 a - 806940\) , \( 183370596 a + 435006640\bigr] \) |
${y}^2+{x}{y}={x}^{3}-a{x}^{2}+\left(-340154a-806940\right){x}+183370596a+435006640$ |
| 300.1-b1 |
300.1-b |
$2$ |
$2$ |
\(\Q(\sqrt{33}) \) |
$2$ |
$[2, 0]$ |
300.1 |
\( 2^{2} \cdot 3 \cdot 5^{2} \) |
\( - 2^{15} \cdot 3^{5} \cdot 5^{4} \) |
$2.13637$ |
$(-a-2), (-a+3), (-2a+7), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \cdot 7 \) |
$1$ |
$3.143096606$ |
3.830000228 |
\( -\frac{142516147786397}{11059200} a + \frac{59998120915403}{1382400} \) |
\( \bigl[1\) , \( -a\) , \( a\) , \( 233 a - 793\) , \( -3116 a + 10503\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}-a{x}^{2}+\left(233a-793\right){x}-3116a+10503$ |
| 300.1-b2 |
300.1-b |
$2$ |
$2$ |
\(\Q(\sqrt{33}) \) |
$2$ |
$[2, 0]$ |
300.1 |
\( 2^{2} \cdot 3 \cdot 5^{2} \) |
\( - 2^{9} \cdot 3^{10} \cdot 5^{2} \) |
$2.13637$ |
$(-a-2), (-a+3), (-2a+7), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \cdot 7 \) |
$1$ |
$3.143096606$ |
3.830000228 |
\( \frac{87232522733081}{155520} a + \frac{5173471476937}{3888} \) |
\( \bigl[1\) , \( a - 1\) , \( a + 1\) , \( 11886 a - 40083\) , \( -1332528 a + 4493655\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(11886a-40083\right){x}-1332528a+4493655$ |
| 300.1-c1 |
300.1-c |
$2$ |
$2$ |
\(\Q(\sqrt{33}) \) |
$2$ |
$[2, 0]$ |
300.1 |
\( 2^{2} \cdot 3 \cdot 5^{2} \) |
\( - 2^{9} \cdot 3^{10} \cdot 5^{2} \) |
$2.13637$ |
$(-a-2), (-a+3), (-2a+7), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$3.797786755$ |
0.661109816 |
\( -\frac{87232522733081}{155520} a + \frac{98057127270187}{51840} \) |
\( \bigl[1\) , \( 1\) , \( 0\) , \( 57 a - 224\) , \( -447 a + 1416\bigr] \) |
${y}^2+{x}{y}={x}^{3}+{x}^{2}+\left(57a-224\right){x}-447a+1416$ |
| 300.1-c2 |
300.1-c |
$2$ |
$2$ |
\(\Q(\sqrt{33}) \) |
$2$ |
$[2, 0]$ |
300.1 |
\( 2^{2} \cdot 3 \cdot 5^{2} \) |
\( - 2^{15} \cdot 3^{5} \cdot 5^{4} \) |
$2.13637$ |
$(-a-2), (-a+3), (-2a+7), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$3.797786755$ |
0.661109816 |
\( \frac{142516147786397}{11059200} a + \frac{337468819536827}{11059200} \) |
\( \bigl[1\) , \( -a\) , \( a + 1\) , \( 3246 a - 10946\) , \( -170418 a + 574692\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(3246a-10946\right){x}-170418a+574692$ |
| 300.1-d1 |
300.1-d |
$4$ |
$6$ |
\(\Q(\sqrt{33}) \) |
$2$ |
$[2, 0]$ |
300.1 |
\( 2^{2} \cdot 3 \cdot 5^{2} \) |
\( - 2^{7} \cdot 3^{3} \cdot 5^{4} \) |
$2.13637$ |
$(-a-2), (-a+3), (-2a+7), (5)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$17.60019616$ |
1.021266964 |
\( -\frac{208640806561}{1440} a + \frac{3517970171029}{7200} \) |
\( \bigl[1\) , \( a + 1\) , \( a\) , \( -490 a - 1161\) , \( 15731 a + 37317\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-490a-1161\right){x}+15731a+37317$ |
| 300.1-d2 |
300.1-d |
$4$ |
$6$ |
\(\Q(\sqrt{33}) \) |
$2$ |
$[2, 0]$ |
300.1 |
\( 2^{2} \cdot 3 \cdot 5^{2} \) |
\( - 2^{21} \cdot 3 \cdot 5^{12} \) |
$2.13637$ |
$(-a-2), (-a+3), (-2a+7), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$1.955577351$ |
1.021266964 |
\( -\frac{64550919851}{307200000} a + \frac{2182406508623}{1536000000} \) |
\( \bigl[1\) , \( a + 1\) , \( a\) , \( 4090 a + 9704\) , \( -281794 a - 668496\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(4090a+9704\right){x}-281794a-668496$ |
| 300.1-d3 |
300.1-d |
$4$ |
$6$ |
\(\Q(\sqrt{33}) \) |
$2$ |
$[2, 0]$ |
300.1 |
\( 2^{2} \cdot 3 \cdot 5^{2} \) |
\( - 2^{33} \cdot 3^{2} \cdot 5^{6} \) |
$2.13637$ |
$(-a-2), (-a+3), (-2a+7), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$1.955577351$ |
1.021266964 |
\( \frac{52022105302299}{134217728000} a + \frac{995623501641319}{402653184000} \) |
\( \bigl[1\) , \( -a - 1\) , \( a\) , \( -39 a - 44\) , \( -88 a - 144\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-39a-44\right){x}-88a-144$ |
| 300.1-d4 |
300.1-d |
$4$ |
$6$ |
\(\Q(\sqrt{33}) \) |
$2$ |
$[2, 0]$ |
300.1 |
\( 2^{2} \cdot 3 \cdot 5^{2} \) |
\( - 2^{11} \cdot 3^{6} \cdot 5^{2} \) |
$2.13637$ |
$(-a-2), (-a+3), (-2a+7), (5)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$17.60019616$ |
1.021266964 |
\( \frac{2442771683}{5120} a + \frac{152577105607}{138240} \) |
\( \bigl[1\) , \( -a - 1\) , \( a\) , \( -9 a - 29\) , \( 47 a + 117\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-9a-29\right){x}+47a+117$ |
| 300.1-e1 |
300.1-e |
$4$ |
$6$ |
\(\Q(\sqrt{33}) \) |
$2$ |
$[2, 0]$ |
300.1 |
\( 2^{2} \cdot 3 \cdot 5^{2} \) |
\( - 2^{11} \cdot 3^{6} \cdot 5^{2} \) |
$2.13637$ |
$(-a-2), (-a+3), (-2a+7), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2^{2} \cdot 3 \cdot 5 \) |
$1$ |
$2.283677502$ |
5.963058399 |
\( -\frac{2442771683}{5120} a + \frac{27316492631}{17280} \) |
\( \bigl[1\) , \( -a - 1\) , \( a + 1\) , \( -3574 a - 8477\) , \( -198196 a - 470177\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-3574a-8477\right){x}-198196a-470177$ |
| 300.1-e2 |
300.1-e |
$4$ |
$6$ |
\(\Q(\sqrt{33}) \) |
$2$ |
$[2, 0]$ |
300.1 |
\( 2^{2} \cdot 3 \cdot 5^{2} \) |
\( - 2^{33} \cdot 3^{2} \cdot 5^{6} \) |
$2.13637$ |
$(-a-2), (-a+3), (-2a+7), (5)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{2} \cdot 3^{3} \cdot 5 \) |
$1$ |
$2.283677502$ |
5.963058399 |
\( -\frac{52022105302299}{134217728000} a + \frac{143961227193527}{50331648000} \) |
\( \bigl[1\) , \( -a - 1\) , \( a + 1\) , \( 17096 a + 40558\) , \( -715321 a - 1696943\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(17096a+40558\right){x}-715321a-1696943$ |
| 300.1-e3 |
300.1-e |
$4$ |
$6$ |
\(\Q(\sqrt{33}) \) |
$2$ |
$[2, 0]$ |
300.1 |
\( 2^{2} \cdot 3 \cdot 5^{2} \) |
\( - 2^{21} \cdot 3 \cdot 5^{12} \) |
$2.13637$ |
$(-a-2), (-a+3), (-2a+7), (5)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{2} \cdot 3^{3} \cdot 5 \) |
$1$ |
$2.283677502$ |
5.963058399 |
\( \frac{64550919851}{307200000} a + \frac{232456488671}{192000000} \) |
\( \bigl[1\) , \( 0\) , \( 0\) , \( -89 a - 200\) , \( -247 a - 568\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(-89a-200\right){x}-247a-568$ |
| 300.1-e4 |
300.1-e |
$4$ |
$6$ |
\(\Q(\sqrt{33}) \) |
$2$ |
$[2, 0]$ |
300.1 |
\( 2^{2} \cdot 3 \cdot 5^{2} \) |
\( - 2^{7} \cdot 3^{3} \cdot 5^{4} \) |
$2.13637$ |
$(-a-2), (-a+3), (-2a+7), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2^{2} \cdot 3 \cdot 5 \) |
$1$ |
$2.283677502$ |
5.963058399 |
\( \frac{208640806561}{1440} a + \frac{154672883639}{450} \) |
\( \bigl[1\) , \( 0\) , \( 0\) , \( -69 a - 165\) , \( -537 a - 1275\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(-69a-165\right){x}-537a-1275$ |
| 300.1-f1 |
300.1-f |
$4$ |
$4$ |
\(\Q(\sqrt{33}) \) |
$2$ |
$[2, 0]$ |
300.1 |
\( 2^{2} \cdot 3 \cdot 5^{2} \) |
\( 2^{4} \cdot 3^{20} \cdot 5^{8} \) |
$2.13637$ |
$(-a-2), (-a+3), (-2a+7), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$1$ |
$1.184821298$ |
1.650007314 |
\( -\frac{128864147651}{147622500} \) |
\( \bigl[1\) , \( -a\) , \( 1\) , \( 842 a - 2839\) , \( 39659 a - 133738\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-a{x}^{2}+\left(842a-2839\right){x}+39659a-133738$ |
| 300.1-f2 |
300.1-f |
$4$ |
$4$ |
\(\Q(\sqrt{33}) \) |
$2$ |
$[2, 0]$ |
300.1 |
\( 2^{2} \cdot 3 \cdot 5^{2} \) |
\( 2^{10} \cdot 3^{5} \cdot 5^{2} \) |
$2.13637$ |
$(-a-2), (-a+3), (-2a+7), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2$ |
2B |
$4$ |
\( 2^{2} \) |
$1$ |
$2.369642596$ |
1.650007314 |
\( -\frac{30017554598442983}{34560} a + \frac{101227638824796319}{34560} \) |
\( \bigl[1\) , \( -a\) , \( 1\) , \( -2954 a - 7007\) , \( 80619 a + 191250\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-a{x}^{2}+\left(-2954a-7007\right){x}+80619a+191250$ |
| 300.1-f3 |
300.1-f |
$4$ |
$4$ |
\(\Q(\sqrt{33}) \) |
$2$ |
$[2, 0]$ |
300.1 |
\( 2^{2} \cdot 3 \cdot 5^{2} \) |
\( 2^{8} \cdot 3^{10} \cdot 5^{4} \) |
$2.13637$ |
$(-a-2), (-a+3), (-2a+7), (5)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$1$ |
$4.739285193$ |
1.650007314 |
\( \frac{217190179331}{97200} \) |
\( \bigl[1\) , \( -a\) , \( 1\) , \( 1002 a - 3379\) , \( 30139 a - 101634\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-a{x}^{2}+\left(1002a-3379\right){x}+30139a-101634$ |
| 300.1-f4 |
300.1-f |
$4$ |
$4$ |
\(\Q(\sqrt{33}) \) |
$2$ |
$[2, 0]$ |
300.1 |
\( 2^{2} \cdot 3 \cdot 5^{2} \) |
\( 2^{10} \cdot 3^{5} \cdot 5^{2} \) |
$2.13637$ |
$(-a-2), (-a+3), (-2a+7), (5)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$9.478570387$ |
1.650007314 |
\( \frac{30017554598442983}{34560} a + \frac{8901260528294167}{4320} \) |
\( \bigl[1\) , \( 1\) , \( a\) , \( -394 a - 941\) , \( 7076 a + 16777\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+{x}^{2}+\left(-394a-941\right){x}+7076a+16777$ |
| 300.1-g1 |
300.1-g |
$8$ |
$12$ |
\(\Q(\sqrt{33}) \) |
$2$ |
$[2, 0]$ |
300.1 |
\( 2^{2} \cdot 3 \cdot 5^{2} \) |
\( 2^{24} \cdot 3^{2} \cdot 5^{6} \) |
$2.13637$ |
$(-a-2), (-a+3), (-2a+7), (5)$ |
0 |
$\Z/12\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{5} \cdot 3^{3} \) |
$1$ |
$5.367489134$ |
5.606159561 |
\( -\frac{273359449}{1536000} \) |
\( \bigl[1\) , \( a + 1\) , \( a + 1\) , \( -4975 a - 11801\) , \( 1051929 a + 2495471\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-4975a-11801\right){x}+1051929a+2495471$ |
| 300.1-g2 |
300.1-g |
$8$ |
$12$ |
\(\Q(\sqrt{33}) \) |
$2$ |
$[2, 0]$ |
300.1 |
\( 2^{2} \cdot 3 \cdot 5^{2} \) |
\( 2^{8} \cdot 3^{6} \cdot 5^{2} \) |
$2.13637$ |
$(-a-2), (-a+3), (-2a+7), (5)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2^{5} \cdot 3 \) |
$1$ |
$5.367489134$ |
5.606159561 |
\( \frac{357911}{2160} \) |
\( \bigl[1\) , \( a + 1\) , \( a + 1\) , \( 545 a + 1294\) , \( -35136 a - 83353\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(545a+1294\right){x}-35136a-83353$ |
| 300.1-g3 |
300.1-g |
$8$ |
$12$ |
\(\Q(\sqrt{33}) \) |
$2$ |
$[2, 0]$ |
300.1 |
\( 2^{2} \cdot 3 \cdot 5^{2} \) |
\( 2^{6} \cdot 3^{2} \cdot 5^{24} \) |
$2.13637$ |
$(-a-2), (-a+3), (-2a+7), (5)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$4$ |
\( 2^{3} \cdot 3^{3} \) |
$1$ |
$1.341872283$ |
5.606159561 |
\( \frac{10316097499609}{5859375000} \) |
\( \bigl[1\) , \( a + 1\) , \( a + 1\) , \( -166895 a - 395921\) , \( 8303649 a + 19698591\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-166895a-395921\right){x}+8303649a+19698591$ |
| 300.1-g4 |
300.1-g |
$8$ |
$12$ |
\(\Q(\sqrt{33}) \) |
$2$ |
$[2, 0]$ |
300.1 |
\( 2^{2} \cdot 3 \cdot 5^{2} \) |
\( 2^{2} \cdot 3^{24} \cdot 5^{2} \) |
$2.13637$ |
$(-a-2), (-a+3), (-2a+7), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2^{3} \cdot 3 \) |
$1$ |
$5.367489134$ |
5.606159561 |
\( \frac{35578826569}{5314410} \) |
\( \bigl[1\) , \( -a - 1\) , \( a + 1\) , \( 25216 a - 85032\) , \( -3168011 a + 10683417\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(25216a-85032\right){x}-3168011a+10683417$ |
| 300.1-g5 |
300.1-g |
$8$ |
$12$ |
\(\Q(\sqrt{33}) \) |
$2$ |
$[2, 0]$ |
300.1 |
\( 2^{2} \cdot 3 \cdot 5^{2} \) |
\( 2^{4} \cdot 3^{12} \cdot 5^{4} \) |
$2.13637$ |
$(-a-2), (-a+3), (-2a+7), (5)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2Cs, 3B.1.2 |
$1$ |
\( 2^{5} \cdot 3 \) |
$1$ |
$5.367489134$ |
5.606159561 |
\( \frac{702595369}{72900} \) |
\( \bigl[1\) , \( -a - 1\) , \( a + 1\) , \( 6816 a - 22982\) , \( 473939 a - 1598263\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(6816a-22982\right){x}+473939a-1598263$ |
| 300.1-g6 |
300.1-g |
$8$ |
$12$ |
\(\Q(\sqrt{33}) \) |
$2$ |
$[2, 0]$ |
300.1 |
\( 2^{2} \cdot 3 \cdot 5^{2} \) |
\( 2^{12} \cdot 3^{4} \cdot 5^{12} \) |
$2.13637$ |
$(-a-2), (-a+3), (-2a+7), (5)$ |
0 |
$\Z/2\Z\oplus\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2Cs, 3B.1.1 |
$1$ |
\( 2^{5} \cdot 3^{3} \) |
$1$ |
$5.367489134$ |
5.606159561 |
\( \frac{4102915888729}{9000000} \) |
\( \bigl[1\) , \( -a - 1\) , \( a + 1\) , \( 122736 a - 413897\) , \( -39525706 a + 133291793\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(122736a-413897\right){x}-39525706a+133291793$ |
| 300.1-g7 |
300.1-g |
$8$ |
$12$ |
\(\Q(\sqrt{33}) \) |
$2$ |
$[2, 0]$ |
300.1 |
\( 2^{2} \cdot 3 \cdot 5^{2} \) |
\( 2^{2} \cdot 3^{6} \cdot 5^{8} \) |
$2.13637$ |
$(-a-2), (-a+3), (-2a+7), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$4$ |
\( 2^{3} \cdot 3 \) |
$1$ |
$1.341872283$ |
5.606159561 |
\( \frac{2656166199049}{33750} \) |
\( \bigl[1\) , \( -a - 1\) , \( a + 1\) , \( 106176 a - 358052\) , \( 31973489 a - 107823607\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(106176a-358052\right){x}+31973489a-107823607$ |
| 300.1-g8 |
300.1-g |
$8$ |
$12$ |
\(\Q(\sqrt{33}) \) |
$2$ |
$[2, 0]$ |
300.1 |
\( 2^{2} \cdot 3 \cdot 5^{2} \) |
\( 2^{6} \cdot 3^{8} \cdot 5^{6} \) |
$2.13637$ |
$(-a-2), (-a+3), (-2a+7), (5)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{3} \cdot 3^{3} \) |
$1$ |
$5.367489134$ |
5.606159561 |
\( \frac{16778985534208729}{81000} \) |
\( \bigl[1\) , \( -a - 1\) , \( a + 1\) , \( 1962736 a - 6618897\) , \( -2535640706 a + 8550893793\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(1962736a-6618897\right){x}-2535640706a+8550893793$ |
| 300.1-h1 |
300.1-h |
$8$ |
$12$ |
\(\Q(\sqrt{33}) \) |
$2$ |
$[2, 0]$ |
300.1 |
\( 2^{2} \cdot 3 \cdot 5^{2} \) |
\( 2^{24} \cdot 3^{2} \cdot 5^{6} \) |
$2.13637$ |
$(-a-2), (-a+3), (-2a+7), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2^{3} \cdot 3 \) |
$1$ |
$1.248395236$ |
1.303906299 |
\( -\frac{273359449}{1536000} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -14\) , \( -64\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-14{x}-64$ |
| 300.1-h2 |
300.1-h |
$8$ |
$12$ |
\(\Q(\sqrt{33}) \) |
$2$ |
$[2, 0]$ |
300.1 |
\( 2^{2} \cdot 3 \cdot 5^{2} \) |
\( 2^{8} \cdot 3^{6} \cdot 5^{2} \) |
$2.13637$ |
$(-a-2), (-a+3), (-2a+7), (5)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{3} \cdot 3 \) |
$1$ |
$11.23555713$ |
1.303906299 |
\( \frac{357911}{2160} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( 1\) , \( 2\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}+2$ |
| 300.1-h3 |
300.1-h |
$8$ |
$12$ |
\(\Q(\sqrt{33}) \) |
$2$ |
$[2, 0]$ |
300.1 |
\( 2^{2} \cdot 3 \cdot 5^{2} \) |
\( 2^{6} \cdot 3^{2} \cdot 5^{24} \) |
$2.13637$ |
$(-a-2), (-a+3), (-2a+7), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2^{3} \cdot 3 \) |
$1$ |
$1.248395236$ |
1.303906299 |
\( \frac{10316097499609}{5859375000} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -454\) , \( -544\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-454{x}-544$ |
| 300.1-h4 |
300.1-h |
$8$ |
$12$ |
\(\Q(\sqrt{33}) \) |
$2$ |
$[2, 0]$ |
300.1 |
\( 2^{2} \cdot 3 \cdot 5^{2} \) |
\( 2^{2} \cdot 3^{24} \cdot 5^{2} \) |
$2.13637$ |
$(-a-2), (-a+3), (-2a+7), (5)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$4$ |
\( 2^{3} \cdot 3 \) |
$1$ |
$2.808889283$ |
1.303906299 |
\( \frac{35578826569}{5314410} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -69\) , \( -194\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-69{x}-194$ |
| 300.1-h5 |
300.1-h |
$8$ |
$12$ |
\(\Q(\sqrt{33}) \) |
$2$ |
$[2, 0]$ |
300.1 |
\( 2^{2} \cdot 3 \cdot 5^{2} \) |
\( 2^{4} \cdot 3^{12} \cdot 5^{4} \) |
$2.13637$ |
$(-a-2), (-a+3), (-2a+7), (5)$ |
0 |
$\Z/2\Z\oplus\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2Cs, 3B.1.1 |
$1$ |
\( 2^{5} \cdot 3 \) |
$1$ |
$11.23555713$ |
1.303906299 |
\( \frac{702595369}{72900} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -19\) , \( 26\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-19{x}+26$ |
| 300.1-h6 |
300.1-h |
$8$ |
$12$ |
\(\Q(\sqrt{33}) \) |
$2$ |
$[2, 0]$ |
300.1 |
\( 2^{2} \cdot 3 \cdot 5^{2} \) |
\( 2^{12} \cdot 3^{4} \cdot 5^{12} \) |
$2.13637$ |
$(-a-2), (-a+3), (-2a+7), (5)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2Cs, 3B.1.2 |
$1$ |
\( 2^{5} \cdot 3 \) |
$1$ |
$1.248395236$ |
1.303906299 |
\( \frac{4102915888729}{9000000} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -334\) , \( -2368\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-334{x}-2368$ |
| 300.1-h7 |
300.1-h |
$8$ |
$12$ |
\(\Q(\sqrt{33}) \) |
$2$ |
$[2, 0]$ |
300.1 |
\( 2^{2} \cdot 3 \cdot 5^{2} \) |
\( 2^{2} \cdot 3^{6} \cdot 5^{8} \) |
$2.13637$ |
$(-a-2), (-a+3), (-2a+7), (5)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{3} \cdot 3 \) |
$1$ |
$11.23555713$ |
1.303906299 |
\( \frac{2656166199049}{33750} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -289\) , \( 1862\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-289{x}+1862$ |
| 300.1-h8 |
300.1-h |
$8$ |
$12$ |
\(\Q(\sqrt{33}) \) |
$2$ |
$[2, 0]$ |
300.1 |
\( 2^{2} \cdot 3 \cdot 5^{2} \) |
\( 2^{6} \cdot 3^{8} \cdot 5^{6} \) |
$2.13637$ |
$(-a-2), (-a+3), (-2a+7), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$4$ |
\( 2^{3} \cdot 3 \) |
$1$ |
$0.312098809$ |
1.303906299 |
\( \frac{16778985534208729}{81000} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -5334\) , \( -150368\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-5334{x}-150368$ |
| 300.1-i1 |
300.1-i |
$4$ |
$4$ |
\(\Q(\sqrt{33}) \) |
$2$ |
$[2, 0]$ |
300.1 |
\( 2^{2} \cdot 3 \cdot 5^{2} \) |
\( 2^{4} \cdot 3^{20} \cdot 5^{8} \) |
$2.13637$ |
$(-a-2), (-a+3), (-2a+7), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$1$ |
$1.184821298$ |
1.650007314 |
\( -\frac{128864147651}{147622500} \) |
\( \bigl[1\) , \( a - 1\) , \( 1\) , \( -842 a - 1997\) , \( -39659 a - 94079\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-842a-1997\right){x}-39659a-94079$ |
| 300.1-i2 |
300.1-i |
$4$ |
$4$ |
\(\Q(\sqrt{33}) \) |
$2$ |
$[2, 0]$ |
300.1 |
\( 2^{2} \cdot 3 \cdot 5^{2} \) |
\( 2^{10} \cdot 3^{5} \cdot 5^{2} \) |
$2.13637$ |
$(-a-2), (-a+3), (-2a+7), (5)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$9.478570387$ |
1.650007314 |
\( -\frac{30017554598442983}{34560} a + \frac{101227638824796319}{34560} \) |
\( \bigl[1\) , \( 1\) , \( a + 1\) , \( 393 a - 1335\) , \( -7077 a + 23853\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(393a-1335\right){x}-7077a+23853$ |
| 300.1-i3 |
300.1-i |
$4$ |
$4$ |
\(\Q(\sqrt{33}) \) |
$2$ |
$[2, 0]$ |
300.1 |
\( 2^{2} \cdot 3 \cdot 5^{2} \) |
\( 2^{8} \cdot 3^{10} \cdot 5^{4} \) |
$2.13637$ |
$(-a-2), (-a+3), (-2a+7), (5)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$1$ |
$4.739285193$ |
1.650007314 |
\( \frac{217190179331}{97200} \) |
\( \bigl[1\) , \( a - 1\) , \( 1\) , \( -1002 a - 2377\) , \( -30139 a - 71495\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-1002a-2377\right){x}-30139a-71495$ |
| 300.1-i4 |
300.1-i |
$4$ |
$4$ |
\(\Q(\sqrt{33}) \) |
$2$ |
$[2, 0]$ |
300.1 |
\( 2^{2} \cdot 3 \cdot 5^{2} \) |
\( 2^{10} \cdot 3^{5} \cdot 5^{2} \) |
$2.13637$ |
$(-a-2), (-a+3), (-2a+7), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2$ |
2B |
$4$ |
\( 2^{2} \) |
$1$ |
$2.369642596$ |
1.650007314 |
\( \frac{30017554598442983}{34560} a + \frac{8901260528294167}{4320} \) |
\( \bigl[1\) , \( a - 1\) , \( 1\) , \( 2954 a - 9961\) , \( -80619 a + 271869\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(2954a-9961\right){x}-80619a+271869$ |
| 300.1-j1 |
300.1-j |
$4$ |
$6$ |
\(\Q(\sqrt{33}) \) |
$2$ |
$[2, 0]$ |
300.1 |
\( 2^{2} \cdot 3 \cdot 5^{2} \) |
\( - 2^{11} \cdot 3^{6} \cdot 5^{2} \) |
$2.13637$ |
$(-a-2), (-a+3), (-2a+7), (5)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$17.60019616$ |
1.021266964 |
\( -\frac{2442771683}{5120} a + \frac{27316492631}{17280} \) |
\( \bigl[1\) , \( a + 1\) , \( a\) , \( 10 a - 38\) , \( -38 a + 126\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(10a-38\right){x}-38a+126$ |
| 300.1-j2 |
300.1-j |
$4$ |
$6$ |
\(\Q(\sqrt{33}) \) |
$2$ |
$[2, 0]$ |
300.1 |
\( 2^{2} \cdot 3 \cdot 5^{2} \) |
\( - 2^{33} \cdot 3^{2} \cdot 5^{6} \) |
$2.13637$ |
$(-a-2), (-a+3), (-2a+7), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$1.955577351$ |
1.021266964 |
\( -\frac{52022105302299}{134217728000} a + \frac{143961227193527}{50331648000} \) |
\( \bigl[1\) , \( a + 1\) , \( a\) , \( 40 a - 83\) , \( 127 a - 315\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(40a-83\right){x}+127a-315$ |
| 300.1-j3 |
300.1-j |
$4$ |
$6$ |
\(\Q(\sqrt{33}) \) |
$2$ |
$[2, 0]$ |
300.1 |
\( 2^{2} \cdot 3 \cdot 5^{2} \) |
\( - 2^{21} \cdot 3 \cdot 5^{12} \) |
$2.13637$ |
$(-a-2), (-a+3), (-2a+7), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$1.955577351$ |
1.021266964 |
\( \frac{64550919851}{307200000} a + \frac{232456488671}{192000000} \) |
\( \bigl[1\) , \( -a - 1\) , \( a\) , \( -4089 a + 13793\) , \( 285883 a - 964083\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-4089a+13793\right){x}+285883a-964083$ |
| 300.1-j4 |
300.1-j |
$4$ |
$6$ |
\(\Q(\sqrt{33}) \) |
$2$ |
$[2, 0]$ |
300.1 |
\( 2^{2} \cdot 3 \cdot 5^{2} \) |
\( - 2^{7} \cdot 3^{3} \cdot 5^{4} \) |
$2.13637$ |
$(-a-2), (-a+3), (-2a+7), (5)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$17.60019616$ |
1.021266964 |
\( \frac{208640806561}{1440} a + \frac{154672883639}{450} \) |
\( \bigl[1\) , \( -a - 1\) , \( a\) , \( 491 a - 1652\) , \( -16222 a + 54700\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(491a-1652\right){x}-16222a+54700$ |
| 300.1-k1 |
300.1-k |
$4$ |
$6$ |
\(\Q(\sqrt{33}) \) |
$2$ |
$[2, 0]$ |
300.1 |
\( 2^{2} \cdot 3 \cdot 5^{2} \) |
\( - 2^{7} \cdot 3^{3} \cdot 5^{4} \) |
$2.13637$ |
$(-a-2), (-a+3), (-2a+7), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2^{2} \cdot 3 \cdot 5 \) |
$1$ |
$2.283677502$ |
5.963058399 |
\( -\frac{208640806561}{1440} a + \frac{3517970171029}{7200} \) |
\( \bigl[1\) , \( 0\) , \( 0\) , \( 69 a - 234\) , \( 537 a - 1812\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(69a-234\right){x}+537a-1812$ |
| 300.1-k2 |
300.1-k |
$4$ |
$6$ |
\(\Q(\sqrt{33}) \) |
$2$ |
$[2, 0]$ |
300.1 |
\( 2^{2} \cdot 3 \cdot 5^{2} \) |
\( - 2^{21} \cdot 3 \cdot 5^{12} \) |
$2.13637$ |
$(-a-2), (-a+3), (-2a+7), (5)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{2} \cdot 3^{3} \cdot 5 \) |
$1$ |
$2.283677502$ |
5.963058399 |
\( -\frac{64550919851}{307200000} a + \frac{2182406508623}{1536000000} \) |
\( \bigl[1\) , \( 0\) , \( 0\) , \( 89 a - 289\) , \( 247 a - 815\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(89a-289\right){x}+247a-815$ |
| 300.1-k3 |
300.1-k |
$4$ |
$6$ |
\(\Q(\sqrt{33}) \) |
$2$ |
$[2, 0]$ |
300.1 |
\( 2^{2} \cdot 3 \cdot 5^{2} \) |
\( - 2^{33} \cdot 3^{2} \cdot 5^{6} \) |
$2.13637$ |
$(-a-2), (-a+3), (-2a+7), (5)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{2} \cdot 3^{3} \cdot 5 \) |
$1$ |
$2.283677502$ |
5.963058399 |
\( \frac{52022105302299}{134217728000} a + \frac{995623501641319}{402653184000} \) |
\( \bigl[1\) , \( a + 1\) , \( a + 1\) , \( -17095 a + 57654\) , \( 698224 a - 2354609\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-17095a+57654\right){x}+698224a-2354609$ |
| 300.1-k4 |
300.1-k |
$4$ |
$6$ |
\(\Q(\sqrt{33}) \) |
$2$ |
$[2, 0]$ |
300.1 |
\( 2^{2} \cdot 3 \cdot 5^{2} \) |
\( - 2^{11} \cdot 3^{6} \cdot 5^{2} \) |
$2.13637$ |
$(-a-2), (-a+3), (-2a+7), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2^{2} \cdot 3 \cdot 5 \) |
$1$ |
$2.283677502$ |
5.963058399 |
\( \frac{2442771683}{5120} a + \frac{152577105607}{138240} \) |
\( \bigl[1\) , \( a + 1\) , \( a + 1\) , \( 3575 a - 12051\) , \( 201769 a - 680423\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(3575a-12051\right){x}+201769a-680423$ |
| 300.1-l1 |
300.1-l |
$2$ |
$2$ |
\(\Q(\sqrt{33}) \) |
$2$ |
$[2, 0]$ |
300.1 |
\( 2^{2} \cdot 3 \cdot 5^{2} \) |
\( - 2^{9} \cdot 3^{10} \cdot 5^{2} \) |
$2.13637$ |
$(-a-2), (-a+3), (-2a+7), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \cdot 7 \) |
$1$ |
$3.143096606$ |
3.830000228 |
\( -\frac{87232522733081}{155520} a + \frac{98057127270187}{51840} \) |
\( \bigl[1\) , \( -a\) , \( a\) , \( -11887 a - 28196\) , \( 1332527 a + 3161128\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}-a{x}^{2}+\left(-11887a-28196\right){x}+1332527a+3161128$ |
| 300.1-l2 |
300.1-l |
$2$ |
$2$ |
\(\Q(\sqrt{33}) \) |
$2$ |
$[2, 0]$ |
300.1 |
\( 2^{2} \cdot 3 \cdot 5^{2} \) |
\( - 2^{15} \cdot 3^{5} \cdot 5^{4} \) |
$2.13637$ |
$(-a-2), (-a+3), (-2a+7), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \cdot 7 \) |
$1$ |
$3.143096606$ |
3.830000228 |
\( \frac{142516147786397}{11059200} a + \frac{337468819536827}{11059200} \) |
\( \bigl[1\) , \( a - 1\) , \( a + 1\) , \( -234 a - 560\) , \( 3115 a + 7387\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-234a-560\right){x}+3115a+7387$ |
*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.
