| 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 |
| 441.1-a1 |
441.1-a |
$6$ |
$8$ |
\(\Q(\sqrt{37}) \) |
$2$ |
$[2, 0]$ |
441.1 |
\( 3^{2} \cdot 7^{2} \) |
\( - 3^{5} \cdot 7^{10} \) |
$2.49086$ |
$(a-3), (a+2), (-a-1), (a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$16$ |
\( 2^{3} \) |
$1$ |
$0.203332557$ |
1.069685331 |
\( -\frac{1769911391246401339839916}{466948881} a + \frac{696436782436761985246235}{51883209} \) |
\( \bigl[a + 1\) , \( a\) , \( 0\) , \( -29975 a - 76229\) , \( -5612972 a - 14264814\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+a{x}^{2}+\left(-29975a-76229\right){x}-5612972a-14264814$ |
| 441.1-a2 |
441.1-a |
$6$ |
$8$ |
\(\Q(\sqrt{37}) \) |
$2$ |
$[2, 0]$ |
441.1 |
\( 3^{2} \cdot 7^{2} \) |
\( - 3^{4} \cdot 7^{17} \) |
$2.49086$ |
$(a-3), (a+2), (-a-1), (a-2)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{6} \) |
$1$ |
$1.626660463$ |
1.069685331 |
\( -\frac{242828989032670216}{299096375126409} a + \frac{926331648297720671}{299096375126409} \) |
\( \bigl[a + 1\) , \( a\) , \( 1\) , \( 2399 a - 8472\) , \( -92318 a + 326959\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+a{x}^{2}+\left(2399a-8472\right){x}-92318a+326959$ |
| 441.1-a3 |
441.1-a |
$6$ |
$8$ |
\(\Q(\sqrt{37}) \) |
$2$ |
$[2, 0]$ |
441.1 |
\( 3^{2} \cdot 7^{2} \) |
\( - 3^{10} \cdot 7^{5} \) |
$2.49086$ |
$(a-3), (a+2), (-a-1), (a-2)$ |
0 |
$\Z/8\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{6} \) |
$1$ |
$6.506641854$ |
1.069685331 |
\( \frac{19936139168}{15752961} a + \frac{52042580017}{15752961} \) |
\( \bigl[a + 1\) , \( a\) , \( 1\) , \( -41 a + 168\) , \( 1250 a - 4403\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+a{x}^{2}+\left(-41a+168\right){x}+1250a-4403$ |
| 441.1-a4 |
441.1-a |
$6$ |
$8$ |
\(\Q(\sqrt{37}) \) |
$2$ |
$[2, 0]$ |
441.1 |
\( 3^{2} \cdot 7^{2} \) |
\( 3^{8} \cdot 7^{10} \) |
$2.49086$ |
$(a-3), (a+2), (-a-1), (a-2)$ |
0 |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{7} \) |
$1$ |
$3.253320927$ |
1.069685331 |
\( -\frac{124375717136}{155649627} a + \frac{5160615684241}{466948881} \) |
\( \bigl[a + 1\) , \( a\) , \( 1\) , \( 734 a - 2577\) , \( 16996 a - 60167\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+a{x}^{2}+\left(734a-2577\right){x}+16996a-60167$ |
| 441.1-a5 |
441.1-a |
$6$ |
$8$ |
\(\Q(\sqrt{37}) \) |
$2$ |
$[2, 0]$ |
441.1 |
\( 3^{2} \cdot 7^{2} \) |
\( 3^{10} \cdot 7^{8} \) |
$2.49086$ |
$(a-3), (a+2), (-a-1), (a-2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$4$ |
\( 2^{5} \) |
$1$ |
$0.813330231$ |
1.069685331 |
\( -\frac{249452993404472}{15752961} a + \frac{195335055867937}{1750329} \) |
\( \bigl[a + 1\) , \( a\) , \( 1\) , \( 11469 a - 40602\) , \( 1158214 a - 4101689\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+a{x}^{2}+\left(11469a-40602\right){x}+1158214a-4101689$ |
| 441.1-a6 |
441.1-a |
$6$ |
$8$ |
\(\Q(\sqrt{37}) \) |
$2$ |
$[2, 0]$ |
441.1 |
\( 3^{2} \cdot 7^{2} \) |
\( - 3^{17} \cdot 7^{4} \) |
$2.49086$ |
$(a-3), (a+2), (-a-1), (a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$16$ |
\( 2^{3} \) |
$1$ |
$0.203332557$ |
1.069685331 |
\( \frac{1068871504372362777849388}{2109289329} a + \frac{301823335115467998237205}{234365481} \) |
\( \bigl[a + 1\) , \( a\) , \( 1\) , \( 11224 a - 39867\) , \( 1205744 a - 4271033\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+a{x}^{2}+\left(11224a-39867\right){x}+1205744a-4271033$ |
| 441.1-b1 |
441.1-b |
$2$ |
$2$ |
\(\Q(\sqrt{37}) \) |
$2$ |
$[2, 0]$ |
441.1 |
\( 3^{2} \cdot 7^{2} \) |
\( 3^{2} \cdot 7^{4} \) |
$2.49086$ |
$(a-3), (a+2), (-a-1), (a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$19.20276704$ |
3.156915455 |
\( \frac{11246768}{49} a - \frac{119250013}{147} \) |
\( \bigl[1\) , \( a\) , \( 1\) , \( 2 a + 4\) , \( a + 5\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+a{x}^{2}+\left(2a+4\right){x}+a+5$ |
| 441.1-b2 |
441.1-b |
$2$ |
$2$ |
\(\Q(\sqrt{37}) \) |
$2$ |
$[2, 0]$ |
441.1 |
\( 3^{2} \cdot 7^{2} \) |
\( 3^{4} \cdot 7^{2} \) |
$2.49086$ |
$(a-3), (a+2), (-a-1), (a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$19.20276704$ |
3.156915455 |
\( -\frac{6721124171992}{21} a + \frac{71406189786769}{63} \) |
\( \bigl[1\) , \( a\) , \( 1\) , \( 2 a - 31\) , \( -27 a + 47\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+a{x}^{2}+\left(2a-31\right){x}-27a+47$ |
| 441.1-c1 |
441.1-c |
$6$ |
$8$ |
\(\Q(\sqrt{37}) \) |
$2$ |
$[2, 0]$ |
441.1 |
\( 3^{2} \cdot 7^{2} \) |
\( - 3^{10} \cdot 7^{9} \) |
$2.49086$ |
$(a-3), (a+2), (-a-1), (a-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$5.282598197$ |
$0.881304620$ |
3.061489365 |
\( -\frac{176648279942458577}{37822859361} a + \frac{69494988342762223}{4202539929} \) |
\( \bigl[a + 1\) , \( 1\) , \( a + 1\) , \( 25 a - 190\) , \( 160 a - 1279\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(25a-190\right){x}+160a-1279$ |
| 441.1-c2 |
441.1-c |
$6$ |
$8$ |
\(\Q(\sqrt{37}) \) |
$2$ |
$[2, 0]$ |
441.1 |
\( 3^{2} \cdot 7^{2} \) |
\( - 3^{2} \cdot 7^{9} \) |
$2.49086$ |
$(a-3), (a+2), (-a-1), (a-2)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$2.641299098$ |
$7.050436964$ |
3.061489365 |
\( -\frac{279233191322569}{17294403} a + \frac{988880210338610}{17294403} \) |
\( \bigl[a + 1\) , \( 1\) , \( a + 1\) , \( 15 a - 35\) , \( -33 a + 116\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(15a-35\right){x}-33a+116$ |
| 441.1-c3 |
441.1-c |
$6$ |
$8$ |
\(\Q(\sqrt{37}) \) |
$2$ |
$[2, 0]$ |
441.1 |
\( 3^{2} \cdot 7^{2} \) |
\( 3^{4} \cdot 7^{6} \) |
$2.49086$ |
$(a-3), (a+2), (-a-1), (a-2)$ |
$1$ |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$1.320649549$ |
$14.10087392$ |
3.061489365 |
\( -\frac{6992161}{7203} a + \frac{177350557}{21609} \) |
\( \bigl[a + 1\) , \( 1\) , \( a + 1\) , \( -5\) , \( -3 a - 7\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}-5{x}-3a-7$ |
| 441.1-c4 |
441.1-c |
$6$ |
$8$ |
\(\Q(\sqrt{37}) \) |
$2$ |
$[2, 0]$ |
441.1 |
\( 3^{2} \cdot 7^{2} \) |
\( - 3^{2} \cdot 7^{3} \) |
$2.49086$ |
$(a-3), (a+2), (-a-1), (a-2)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$2.641299098$ |
$28.20174785$ |
3.061489365 |
\( \frac{346753}{147} a + \frac{901150}{147} \) |
\( \bigl[a + 1\) , \( 1\) , \( a + 1\) , \( 0\) , \( 0\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}$ |
| 441.1-c5 |
441.1-c |
$6$ |
$8$ |
\(\Q(\sqrt{37}) \) |
$2$ |
$[2, 0]$ |
441.1 |
\( 3^{2} \cdot 7^{2} \) |
\( 3^{8} \cdot 7^{6} \) |
$2.49086$ |
$(a-3), (a+2), (-a-1), (a-2)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$2.641299098$ |
$3.525218482$ |
3.061489365 |
\( \frac{168305915569}{64827} a + \frac{1284377040586}{194481} \) |
\( \bigl[a + 1\) , \( 1\) , \( a + 1\) , \( -15 a - 55\) , \( -105 a - 298\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(-15a-55\right){x}-105a-298$ |
| 441.1-c6 |
441.1-c |
$6$ |
$8$ |
\(\Q(\sqrt{37}) \) |
$2$ |
$[2, 0]$ |
441.1 |
\( 3^{2} \cdot 7^{2} \) |
\( - 3^{10} \cdot 7^{3} \) |
$2.49086$ |
$(a-3), (a+2), (-a-1), (a-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$5.282598197$ |
$0.881304620$ |
3.061489365 |
\( \frac{13190129224514444609}{321489} a + \frac{33521147296193211481}{321489} \) |
\( \bigl[a + 1\) , \( 1\) , \( a + 1\) , \( -295 a - 720\) , \( -5278 a - 13521\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(-295a-720\right){x}-5278a-13521$ |
| 441.1-d1 |
441.1-d |
$6$ |
$8$ |
\(\Q(\sqrt{37}) \) |
$2$ |
$[2, 0]$ |
441.1 |
\( 3^{2} \cdot 7^{2} \) |
\( - 3^{17} \cdot 7^{4} \) |
$2.49086$ |
$(a-3), (a+2), (-a-1), (a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$16$ |
\( 2^{3} \) |
$1$ |
$0.203332557$ |
1.069685331 |
\( -\frac{1068871504372362777849388}{2109289329} a + \frac{3785281520411574761984233}{2109289329} \) |
\( \bigl[a\) , \( a - 1\) , \( 0\) , \( -11219 a - 28652\) , \( -1234396 a - 3137628\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-11219a-28652\right){x}-1234396a-3137628$ |
| 441.1-d2 |
441.1-d |
$6$ |
$8$ |
\(\Q(\sqrt{37}) \) |
$2$ |
$[2, 0]$ |
441.1 |
\( 3^{2} \cdot 7^{2} \) |
\( - 3^{10} \cdot 7^{5} \) |
$2.49086$ |
$(a-3), (a+2), (-a-1), (a-2)$ |
0 |
$\Z/8\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{6} \) |
$1$ |
$6.506641854$ |
1.069685331 |
\( -\frac{19936139168}{15752961} a + \frac{7997635465}{1750329} \) |
\( \bigl[a\) , \( a - 1\) , \( 0\) , \( 46 a + 118\) , \( -1132 a - 2877\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(46a+118\right){x}-1132a-2877$ |
| 441.1-d3 |
441.1-d |
$6$ |
$8$ |
\(\Q(\sqrt{37}) \) |
$2$ |
$[2, 0]$ |
441.1 |
\( 3^{2} \cdot 7^{2} \) |
\( - 3^{4} \cdot 7^{17} \) |
$2.49086$ |
$(a-3), (a+2), (-a-1), (a-2)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{6} \) |
$1$ |
$1.626660463$ |
1.069685331 |
\( \frac{242828989032670216}{299096375126409} a + \frac{683502659265050455}{299096375126409} \) |
\( \bigl[a\) , \( a - 1\) , \( 0\) , \( -2394 a - 6082\) , \( 86236 a + 219157\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-2394a-6082\right){x}+86236a+219157$ |
| 441.1-d4 |
441.1-d |
$6$ |
$8$ |
\(\Q(\sqrt{37}) \) |
$2$ |
$[2, 0]$ |
441.1 |
\( 3^{2} \cdot 7^{2} \) |
\( 3^{8} \cdot 7^{10} \) |
$2.49086$ |
$(a-3), (a+2), (-a-1), (a-2)$ |
0 |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{7} \) |
$1$ |
$3.253320927$ |
1.069685331 |
\( \frac{124375717136}{155649627} a + \frac{4787488532833}{466948881} \) |
\( \bigl[a\) , \( a - 1\) , \( 0\) , \( -729 a - 1852\) , \( -18848 a - 47900\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-729a-1852\right){x}-18848a-47900$ |
| 441.1-d5 |
441.1-d |
$6$ |
$8$ |
\(\Q(\sqrt{37}) \) |
$2$ |
$[2, 0]$ |
441.1 |
\( 3^{2} \cdot 7^{2} \) |
\( 3^{10} \cdot 7^{8} \) |
$2.49086$ |
$(a-3), (a+2), (-a-1), (a-2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$4$ |
\( 2^{5} \) |
$1$ |
$0.813330231$ |
1.069685331 |
\( \frac{249452993404472}{15752961} a + \frac{1508562509406961}{15752961} \) |
\( \bigl[a\) , \( a - 1\) , \( 0\) , \( -11464 a - 29142\) , \( -1187356 a - 3017529\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-11464a-29142\right){x}-1187356a-3017529$ |
| 441.1-d6 |
441.1-d |
$6$ |
$8$ |
\(\Q(\sqrt{37}) \) |
$2$ |
$[2, 0]$ |
441.1 |
\( 3^{2} \cdot 7^{2} \) |
\( - 3^{5} \cdot 7^{10} \) |
$2.49086$ |
$(a-3), (a+2), (-a-1), (a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$16$ |
\( 2^{3} \) |
$1$ |
$0.203332557$ |
1.069685331 |
\( \frac{1769911391246401339839916}{466948881} a + \frac{4498019650684456527376199}{466948881} \) |
\( \bigl[a\) , \( a - 1\) , \( 1\) , \( 29980 a - 106214\) , \( 5506758 a - 19501768\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(29980a-106214\right){x}+5506758a-19501768$ |
| 441.1-e1 |
441.1-e |
$4$ |
$4$ |
\(\Q(\sqrt{37}) \) |
$2$ |
$[2, 0]$ |
441.1 |
\( 3^{2} \cdot 7^{2} \) |
\( 3^{16} \cdot 7^{5} \) |
$2.49086$ |
$(a-3), (a+2), (-a-1), (a-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$0.895675112$ |
$1.935568190$ |
4.560139241 |
\( \frac{395722393357}{1275989841} a + \frac{85075672216}{141776649} \) |
\( \bigl[a + 1\) , \( a\) , \( 0\) , \( 90 a - 293\) , \( 2364 a - 8346\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+a{x}^{2}+\left(90a-293\right){x}+2364a-8346$ |
| 441.1-e2 |
441.1-e |
$4$ |
$4$ |
\(\Q(\sqrt{37}) \) |
$2$ |
$[2, 0]$ |
441.1 |
\( 3^{2} \cdot 7^{2} \) |
\( 3^{8} \cdot 7^{4} \) |
$2.49086$ |
$(a-3), (a+2), (-a-1), (a-2)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$1.791350225$ |
$7.742272761$ |
4.560139241 |
\( -\frac{2782512335}{35721} a + \frac{1101859729}{3969} \) |
\( \bigl[a + 1\) , \( a\) , \( 0\) , \( 135 a - 453\) , \( 1341 a - 4725\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+a{x}^{2}+\left(135a-453\right){x}+1341a-4725$ |
| 441.1-e3 |
441.1-e |
$4$ |
$4$ |
\(\Q(\sqrt{37}) \) |
$2$ |
$[2, 0]$ |
441.1 |
\( 3^{2} \cdot 7^{2} \) |
\( 3^{4} \cdot 7^{5} \) |
$2.49086$ |
$(a-3), (a+2), (-a-1), (a-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$3.582700450$ |
$3.871136380$ |
4.560139241 |
\( -\frac{2402921797082959}{64827} a + \frac{945519377112808}{7203} \) |
\( \bigl[a + 1\) , \( a\) , \( 0\) , \( 2100 a - 7413\) , \( 89754 a - 317832\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+a{x}^{2}+\left(2100a-7413\right){x}+89754a-317832$ |
| 441.1-e4 |
441.1-e |
$4$ |
$4$ |
\(\Q(\sqrt{37}) \) |
$2$ |
$[2, 0]$ |
441.1 |
\( 3^{2} \cdot 7^{2} \) |
\( 3^{4} \cdot 7^{2} \) |
$2.49086$ |
$(a-3), (a+2), (-a-1), (a-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$3.582700450$ |
$15.48454552$ |
4.560139241 |
\( \frac{13851175}{189} a + \frac{3948338}{21} \) |
\( \bigl[a + 1\) , \( a\) , \( 0\) , \( 15 a - 28\) , \( 2 a + 17\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+a{x}^{2}+\left(15a-28\right){x}+2a+17$ |
| 441.1-f1 |
441.1-f |
$1$ |
$1$ |
\(\Q(\sqrt{37}) \) |
$2$ |
$[2, 0]$ |
441.1 |
\( 3^{2} \cdot 7^{2} \) |
\( 3^{34} \cdot 7^{8} \) |
$2.49086$ |
$(a-3), (a+2), (-a-1), (a-2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2^{3} \cdot 5 \) |
$1$ |
$0.251579910$ |
1.654379299 |
\( \frac{1022949143384768512}{2871516885952743} a - \frac{3140868186815008768}{2871516885952743} \) |
\( \bigl[0\) , \( a + 1\) , \( 1\) , \( 5350 a - 18897\) , \( 503403 a - 1782349\bigr] \) |
${y}^2+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(5350a-18897\right){x}+503403a-1782349$ |
| 441.1-g1 |
441.1-g |
$2$ |
$2$ |
\(\Q(\sqrt{37}) \) |
$2$ |
$[2, 0]$ |
441.1 |
\( 3^{2} \cdot 7^{2} \) |
\( 3^{12} \cdot 7^{12} \) |
$2.49086$ |
$(a-3), (a+2), (-a-1), (a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \cdot 11 \) |
$1$ |
$1.372894099$ |
2.482726395 |
\( \frac{15696337148069215}{50039642934603} a - \frac{83509196232149617}{50039642934603} \) |
\( \bigl[a + 1\) , \( a\) , \( 0\) , \( -242 a - 620\) , \( -8171 a - 20754\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+a{x}^{2}+\left(-242a-620\right){x}-8171a-20754$ |
| 441.1-g2 |
441.1-g |
$2$ |
$2$ |
\(\Q(\sqrt{37}) \) |
$2$ |
$[2, 0]$ |
441.1 |
\( 3^{2} \cdot 7^{2} \) |
\( 3^{24} \cdot 7^{6} \) |
$2.49086$ |
$(a-3), (a+2), (-a-1), (a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \cdot 11 \) |
$1$ |
$1.372894099$ |
2.482726395 |
\( -\frac{746296655485226290225}{527421468848463} a + \frac{3335997623498205653914}{527421468848463} \) |
\( \bigl[a + 1\) , \( a\) , \( 0\) , \( -4967 a - 12730\) , \( -348812 a - 885961\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+a{x}^{2}+\left(-4967a-12730\right){x}-348812a-885961$ |
| 441.1-h1 |
441.1-h |
$6$ |
$8$ |
\(\Q(\sqrt{37}) \) |
$2$ |
$[2, 0]$ |
441.1 |
\( 3^{2} \cdot 7^{2} \) |
\( 3^{33} \cdot 7^{3} \) |
$2.49086$ |
$(a-3), (a+2), (-a-1), (a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$16$ |
\( 2^{2} \) |
$1$ |
$0.512088511$ |
1.346989323 |
\( \frac{1180491997524001055}{90797989253740209} a + \frac{2924895833867635219}{90797989253740209} \) |
\( \bigl[a + 1\) , \( -a + 1\) , \( a\) , \( 69 a + 174\) , \( -2443 a - 6417\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(69a+174\right){x}-2443a-6417$ |
| 441.1-h2 |
441.1-h |
$6$ |
$8$ |
\(\Q(\sqrt{37}) \) |
$2$ |
$[2, 0]$ |
441.1 |
\( 3^{2} \cdot 7^{2} \) |
\( - 3^{12} \cdot 7^{9} \) |
$2.49086$ |
$(a-3), (a+2), (-a-1), (a-2)$ |
0 |
$\Z/8\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{7} \) |
$1$ |
$4.096708093$ |
1.346989323 |
\( -\frac{8078421083818283}{37822859361} a + \frac{3180818998237726}{4202539929} \) |
\( \bigl[a + 1\) , \( -a + 1\) , \( a\) , \( 39 a + 49\) , \( 283 a + 798\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(39a+49\right){x}+283a+798$ |
| 441.1-h3 |
441.1-h |
$6$ |
$8$ |
\(\Q(\sqrt{37}) \) |
$2$ |
$[2, 0]$ |
441.1 |
\( 3^{2} \cdot 7^{2} \) |
\( 3^{12} \cdot 7^{6} \) |
$2.49086$ |
$(a-3), (a+2), (-a-1), (a-2)$ |
0 |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{6} \) |
$1$ |
$8.193416186$ |
1.346989323 |
\( \frac{7504801205}{15752961} a + \frac{51737937061}{15752961} \) |
\( \bigl[a + 1\) , \( -a + 1\) , \( a\) , \( -16 a - 41\) , \( 32 a + 78\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-16a-41\right){x}+32a+78$ |
| 441.1-h4 |
441.1-h |
$6$ |
$8$ |
\(\Q(\sqrt{37}) \) |
$2$ |
$[2, 0]$ |
441.1 |
\( 3^{2} \cdot 7^{2} \) |
\( 3^{18} \cdot 7^{6} \) |
$2.49086$ |
$(a-3), (a+2), (-a-1), (a-2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$4$ |
\( 2^{4} \) |
$1$ |
$2.048354046$ |
1.346989323 |
\( -\frac{1044477270651925}{103355177121} a + \frac{5116935617366338}{103355177121} \) |
\( \bigl[a + 1\) , \( -a + 1\) , \( a\) , \( -71 a - 211\) , \( -623 a - 1706\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-71a-211\right){x}-623a-1706$ |
| 441.1-h5 |
441.1-h |
$6$ |
$8$ |
\(\Q(\sqrt{37}) \) |
$2$ |
$[2, 0]$ |
441.1 |
\( 3^{2} \cdot 7^{2} \) |
\( - 3^{6} \cdot 7^{3} \) |
$2.49086$ |
$(a-3), (a+2), (-a-1), (a-2)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$16.38683237$ |
1.346989323 |
\( \frac{11395436987}{3969} a + \frac{28965836554}{3969} \) |
\( \bigl[a + 1\) , \( -a + 1\) , \( a\) , \( -16 a - 36\) , \( 38 a + 99\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-16a-36\right){x}+38a+99$ |
| 441.1-h6 |
441.1-h |
$6$ |
$8$ |
\(\Q(\sqrt{37}) \) |
$2$ |
$[2, 0]$ |
441.1 |
\( 3^{2} \cdot 7^{2} \) |
\( 3^{9} \cdot 7^{9} \) |
$2.49086$ |
$(a-3), (a+2), (-a-1), (a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$16$ |
\( 2^{2} \) |
$1$ |
$0.512088511$ |
1.346989323 |
\( -\frac{33415363342536318575}{37822859361} a + \frac{124690123544497013933}{37822859361} \) |
\( \bigl[a + 1\) , \( -a + 1\) , \( a\) , \( -1091 a - 3316\) , \( -38543 a - 103631\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-1091a-3316\right){x}-38543a-103631$ |
| 441.1-i1 |
441.1-i |
$6$ |
$8$ |
\(\Q(\sqrt{37}) \) |
$2$ |
$[2, 0]$ |
441.1 |
\( 3^{2} \cdot 7^{2} \) |
\( 3^{2} \cdot 7^{16} \) |
$2.49086$ |
$(a-3), (a+2), (-a-1), (a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$16$ |
\( 2^{2} \) |
$1$ |
$0.814020435$ |
2.141186164 |
\( -\frac{4354703137}{17294403} \) |
\( \bigl[1\) , \( 0\) , \( 0\) , \( -34\) , \( -217\bigr] \) |
${y}^2+{x}{y}={x}^{3}-34{x}-217$ |
| 441.1-i2 |
441.1-i |
$6$ |
$8$ |
\(\Q(\sqrt{37}) \) |
$2$ |
$[2, 0]$ |
441.1 |
\( 3^{2} \cdot 7^{2} \) |
\( 3^{4} \cdot 7^{2} \) |
$2.49086$ |
$(a-3), (a+2), (-a-1), (a-2)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$4$ |
\( 2^{2} \) |
$1$ |
$13.02432697$ |
2.141186164 |
\( \frac{103823}{63} \) |
\( \bigl[1\) , \( 0\) , \( 0\) , \( 1\) , \( 0\bigr] \) |
${y}^2+{x}{y}={x}^{3}+{x}$ |
| 441.1-i3 |
441.1-i |
$6$ |
$8$ |
\(\Q(\sqrt{37}) \) |
$2$ |
$[2, 0]$ |
441.1 |
\( 3^{2} \cdot 7^{2} \) |
\( 3^{8} \cdot 7^{4} \) |
$2.49086$ |
$(a-3), (a+2), (-a-1), (a-2)$ |
0 |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{6} \) |
$1$ |
$13.02432697$ |
2.141186164 |
\( \frac{7189057}{3969} \) |
\( \bigl[1\) , \( 0\) , \( 0\) , \( -4\) , \( -1\bigr] \) |
${y}^2+{x}{y}={x}^{3}-4{x}-1$ |
| 441.1-i4 |
441.1-i |
$6$ |
$8$ |
\(\Q(\sqrt{37}) \) |
$2$ |
$[2, 0]$ |
441.1 |
\( 3^{2} \cdot 7^{2} \) |
\( 3^{16} \cdot 7^{2} \) |
$2.49086$ |
$(a-3), (a+2), (-a-1), (a-2)$ |
0 |
$\Z/8\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{6} \) |
$1$ |
$13.02432697$ |
2.141186164 |
\( \frac{6570725617}{45927} \) |
\( \bigl[1\) , \( 0\) , \( 0\) , \( -39\) , \( 90\bigr] \) |
${y}^2+{x}{y}={x}^{3}-39{x}+90$ |
| 441.1-i5 |
441.1-i |
$6$ |
$8$ |
\(\Q(\sqrt{37}) \) |
$2$ |
$[2, 0]$ |
441.1 |
\( 3^{2} \cdot 7^{2} \) |
\( 3^{4} \cdot 7^{8} \) |
$2.49086$ |
$(a-3), (a+2), (-a-1), (a-2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$4$ |
\( 2^{4} \) |
$1$ |
$3.256081743$ |
2.141186164 |
\( \frac{13027640977}{21609} \) |
\( \bigl[1\) , \( 0\) , \( 0\) , \( -49\) , \( -136\bigr] \) |
${y}^2+{x}{y}={x}^{3}-49{x}-136$ |
| 441.1-i6 |
441.1-i |
$6$ |
$8$ |
\(\Q(\sqrt{37}) \) |
$2$ |
$[2, 0]$ |
441.1 |
\( 3^{2} \cdot 7^{2} \) |
\( 3^{2} \cdot 7^{4} \) |
$2.49086$ |
$(a-3), (a+2), (-a-1), (a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$16$ |
\( 2^{2} \) |
$1$ |
$0.814020435$ |
2.141186164 |
\( \frac{53297461115137}{147} \) |
\( \bigl[1\) , \( 0\) , \( 0\) , \( -784\) , \( -8515\bigr] \) |
${y}^2+{x}{y}={x}^{3}-784{x}-8515$ |
| 441.1-j1 |
441.1-j |
$2$ |
$2$ |
\(\Q(\sqrt{37}) \) |
$2$ |
$[2, 0]$ |
441.1 |
\( 3^{2} \cdot 7^{2} \) |
\( 3^{12} \cdot 7^{12} \) |
$2.49086$ |
$(a-3), (a+2), (-a-1), (a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \cdot 11 \) |
$1$ |
$1.372894099$ |
2.482726395 |
\( -\frac{15696337148069215}{50039642934603} a - \frac{7534762120453378}{5559960326067} \) |
\( \bigl[a\) , \( a - 1\) , \( 1\) , \( 247 a - 872\) , \( 7299 a - 25846\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(247a-872\right){x}+7299a-25846$ |
| 441.1-j2 |
441.1-j |
$2$ |
$2$ |
\(\Q(\sqrt{37}) \) |
$2$ |
$[2, 0]$ |
441.1 |
\( 3^{2} \cdot 7^{2} \) |
\( 3^{24} \cdot 7^{6} \) |
$2.49086$ |
$(a-3), (a+2), (-a-1), (a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \cdot 11 \) |
$1$ |
$1.372894099$ |
2.482726395 |
\( \frac{746296655485226290225}{527421468848463} a + \frac{287744552001442151521}{58602385427607} \) |
\( \bigl[a\) , \( a - 1\) , \( 1\) , \( 4972 a - 17707\) , \( 331105 a - 1172334\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(4972a-17707\right){x}+331105a-1172334$ |
| 441.1-k1 |
441.1-k |
$1$ |
$1$ |
\(\Q(\sqrt{37}) \) |
$2$ |
$[2, 0]$ |
441.1 |
\( 3^{2} \cdot 7^{2} \) |
\( 3^{10} \cdot 7^{4} \) |
$2.49086$ |
$(a-3), (a+2), (-a-1), (a-2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2^{3} \cdot 3 \) |
$0.085767569$ |
$7.948031304$ |
5.379266313 |
\( -\frac{467492864}{250047} a - \frac{1136496640}{250047} \) |
\( \bigl[0\) , \( 1\) , \( 1\) , \( -82 a - 208\) , \( 730 a + 1855\bigr] \) |
${y}^2+{y}={x}^{3}+{x}^{2}+\left(-82a-208\right){x}+730a+1855$ |
| 441.1-l1 |
441.1-l |
$4$ |
$4$ |
\(\Q(\sqrt{37}) \) |
$2$ |
$[2, 0]$ |
441.1 |
\( 3^{2} \cdot 7^{2} \) |
\( 3^{16} \cdot 7^{5} \) |
$2.49086$ |
$(a-3), (a+2), (-a-1), (a-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$0.895675112$ |
$1.935568190$ |
4.560139241 |
\( -\frac{395722393357}{1275989841} a + \frac{1161403443301}{1275989841} \) |
\( \bigl[a\) , \( a - 1\) , \( 1\) , \( -85 a - 213\) , \( -2577 a - 6550\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-85a-213\right){x}-2577a-6550$ |
| 441.1-l2 |
441.1-l |
$4$ |
$4$ |
\(\Q(\sqrt{37}) \) |
$2$ |
$[2, 0]$ |
441.1 |
\( 3^{2} \cdot 7^{2} \) |
\( 3^{4} \cdot 7^{2} \) |
$2.49086$ |
$(a-3), (a+2), (-a-1), (a-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$3.582700450$ |
$15.48454552$ |
4.560139241 |
\( -\frac{13851175}{189} a + \frac{49386217}{189} \) |
\( \bigl[a\) , \( a - 1\) , \( 1\) , \( -10 a - 23\) , \( -25 a - 64\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-10a-23\right){x}-25a-64$ |
| 441.1-l3 |
441.1-l |
$4$ |
$4$ |
\(\Q(\sqrt{37}) \) |
$2$ |
$[2, 0]$ |
441.1 |
\( 3^{2} \cdot 7^{2} \) |
\( 3^{8} \cdot 7^{4} \) |
$2.49086$ |
$(a-3), (a+2), (-a-1), (a-2)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$1.791350225$ |
$7.742272761$ |
4.560139241 |
\( \frac{2782512335}{35721} a + \frac{7134225226}{35721} \) |
\( \bigl[a\) , \( a - 1\) , \( 1\) , \( -130 a - 328\) , \( -1669 a - 4242\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-130a-328\right){x}-1669a-4242$ |
| 441.1-l4 |
441.1-l |
$4$ |
$4$ |
\(\Q(\sqrt{37}) \) |
$2$ |
$[2, 0]$ |
441.1 |
\( 3^{2} \cdot 7^{2} \) |
\( 3^{4} \cdot 7^{5} \) |
$2.49086$ |
$(a-3), (a+2), (-a-1), (a-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$3.582700450$ |
$3.871136380$ |
4.560139241 |
\( \frac{2402921797082959}{64827} a + \frac{6106752596932313}{64827} \) |
\( \bigl[a\) , \( a - 1\) , \( 1\) , \( -2095 a - 5323\) , \( -95077 a - 241626\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-2095a-5323\right){x}-95077a-241626$ |
| 441.1-m1 |
441.1-m |
$2$ |
$2$ |
\(\Q(\sqrt{37}) \) |
$2$ |
$[2, 0]$ |
441.1 |
\( 3^{2} \cdot 7^{2} \) |
\( 3^{2} \cdot 7^{4} \) |
$2.49086$ |
$(a-3), (a+2), (-a-1), (a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$19.20276704$ |
3.156915455 |
\( -\frac{11246768}{49} a - \frac{85509709}{147} \) |
\( \bigl[1\) , \( -a + 1\) , \( 1\) , \( -2 a + 6\) , \( -a + 6\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-2a+6\right){x}-a+6$ |
| 441.1-m2 |
441.1-m |
$2$ |
$2$ |
\(\Q(\sqrt{37}) \) |
$2$ |
$[2, 0]$ |
441.1 |
\( 3^{2} \cdot 7^{2} \) |
\( 3^{4} \cdot 7^{2} \) |
$2.49086$ |
$(a-3), (a+2), (-a-1), (a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$19.20276704$ |
3.156915455 |
\( \frac{6721124171992}{21} a + \frac{51242817270793}{63} \) |
\( \bigl[1\) , \( -a + 1\) , \( 1\) , \( -2 a - 29\) , \( 27 a + 20\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-2a-29\right){x}+27a+20$ |
| 441.1-n1 |
441.1-n |
$6$ |
$8$ |
\(\Q(\sqrt{37}) \) |
$2$ |
$[2, 0]$ |
441.1 |
\( 3^{2} \cdot 7^{2} \) |
\( 3^{33} \cdot 7^{3} \) |
$2.49086$ |
$(a-3), (a+2), (-a-1), (a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$16$ |
\( 2^{2} \) |
$1$ |
$0.512088511$ |
1.346989323 |
\( -\frac{1180491997524001055}{90797989253740209} a + \frac{456154203487959586}{10088665472637801} \) |
\( \bigl[a\) , \( 1\) , \( a + 1\) , \( -71 a + 244\) , \( 2442 a - 8860\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(-71a+244\right){x}+2442a-8860$ |
| 441.1-n2 |
441.1-n |
$6$ |
$8$ |
\(\Q(\sqrt{37}) \) |
$2$ |
$[2, 0]$ |
441.1 |
\( 3^{2} \cdot 7^{2} \) |
\( - 3^{6} \cdot 7^{3} \) |
$2.49086$ |
$(a-3), (a+2), (-a-1), (a-2)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$16.38683237$ |
1.346989323 |
\( -\frac{11395436987}{3969} a + \frac{1494861983}{147} \) |
\( \bigl[a\) , \( 1\) , \( a + 1\) , \( 14 a - 51\) , \( -39 a + 137\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(14a-51\right){x}-39a+137$ |
*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.
