| 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 |
| 324.1-a4 |
324.1-a |
$5$ |
$9$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
324.1 |
\( 2^{2} \cdot 3^{4} \) |
\( 2^{18} \cdot 3^{10} \) |
$0.65665$ |
$(-2a+1), (2)$ |
0 |
$\Z/9\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$3$ |
3B.1.1[2] |
$1$ |
\( 3^{3} \) |
$1$ |
$1.878378408$ |
0.722988186 |
\( -\frac{1167051}{512} \) |
\( \bigl[a + 1\) , \( 0\) , \( 1\) , \( -14 a + 13\) , \( 29\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(-14a+13\right){x}+29$ |
| 532.2-b1 |
532.2-b |
$5$ |
$9$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
532.2 |
\( 2^{2} \cdot 7 \cdot 19 \) |
\( 2^{18} \cdot 7^{9} \cdot 19 \) |
$0.74332$ |
$(-3a+1), (-5a+2), (2)$ |
0 |
$\Z/9\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1[2] |
$1$ |
\( 3^{4} \) |
$1$ |
$0.838099181$ |
0.967753576 |
\( -\frac{279029013952351}{98139972224} a + \frac{2198503800528025}{392559888896} \) |
\( \bigl[1\) , \( -a - 1\) , \( a + 1\) , \( 9 a - 90\) , \( 100 a - 261\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(9a-90\right){x}+100a-261$ |
| 532.3-b1 |
532.3-b |
$5$ |
$9$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
532.3 |
\( 2^{2} \cdot 7 \cdot 19 \) |
\( 2^{18} \cdot 7^{9} \cdot 19 \) |
$0.74332$ |
$(3a-2), (-5a+3), (2)$ |
0 |
$\Z/9\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1[2] |
$1$ |
\( 3^{4} \) |
$1$ |
$0.838099181$ |
0.967753576 |
\( \frac{279029013952351}{98139972224} a + \frac{1082387744718621}{392559888896} \) |
\( \bigl[1\) , \( a + 1\) , \( a + 1\) , \( -8 a - 81\) , \( -110 a - 241\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-8a-81\right){x}-110a-241$ |
| 876.1-a3 |
876.1-a |
$5$ |
$9$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
876.1 |
\( 2^{2} \cdot 3 \cdot 73 \) |
\( 2^{6} \cdot 3^{9} \cdot 73 \) |
$0.84203$ |
$(-2a+1), (-9a+1), (2)$ |
0 |
$\Z/9\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1[2] |
$1$ |
\( 3^{3} \) |
$1$ |
$2.961853922$ |
1.140018106 |
\( -\frac{172407319}{141912} a + \frac{108483835}{70956} \) |
\( \bigl[a + 1\) , \( a - 1\) , \( a + 1\) , \( -4 a + 5\) , \( 3 a + 3\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-4a+5\right){x}+3a+3$ |
| 876.2-a3 |
876.2-a |
$5$ |
$9$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
876.2 |
\( 2^{2} \cdot 3 \cdot 73 \) |
\( 2^{6} \cdot 3^{9} \cdot 73 \) |
$0.84203$ |
$(-2a+1), (9a-8), (2)$ |
0 |
$\Z/9\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1[2] |
$1$ |
\( 3^{3} \) |
$1$ |
$2.961853922$ |
1.140018106 |
\( \frac{172407319}{141912} a + \frac{44560351}{141912} \) |
\( \bigl[a + 1\) , \( 1\) , \( a\) , \( -6 a + 3\) , \( -4 a + 7\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+{x}^{2}+\left(-6a+3\right){x}-4a+7$ |
| 1036.2-a3 |
1036.2-a |
$5$ |
$9$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
1036.2 |
\( 2^{2} \cdot 7 \cdot 37 \) |
\( 2^{18} \cdot 7^{9} \cdot 37 \) |
$0.87809$ |
$(-3a+1), (-7a+3), (2)$ |
0 |
$\Z/9\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1[2] |
$1$ |
\( 3^{4} \) |
$1$ |
$0.694449686$ |
0.801881427 |
\( -\frac{7201542233586935}{382229365504} a - \frac{18769001765548989}{764458731008} \) |
\( \bigl[a\) , \( a + 1\) , \( 0\) , \( -176 a - 22\) , \( 1036 a - 352\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-176a-22\right){x}+1036a-352$ |
| 1036.3-a3 |
1036.3-a |
$5$ |
$9$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
1036.3 |
\( 2^{2} \cdot 7 \cdot 37 \) |
\( 2^{18} \cdot 7^{9} \cdot 37 \) |
$0.87809$ |
$(3a-2), (-7a+4), (2)$ |
0 |
$\Z/9\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1[2] |
$1$ |
\( 3^{4} \) |
$1$ |
$0.694449686$ |
0.801881427 |
\( \frac{7201542233586935}{382229365504} a - \frac{33172086232722859}{764458731008} \) |
\( \bigl[1\) , \( -a - 1\) , \( a\) , \( 22 a + 177\) , \( -1235 a + 706\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(22a+177\right){x}-1235a+706$ |
| 6916.1-b4 |
6916.1-b |
$5$ |
$9$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
6916.1 |
\( 2^{2} \cdot 7 \cdot 13 \cdot 19 \) |
\( 2^{6} \cdot 7^{9} \cdot 13^{9} \cdot 19 \) |
$1.41144$ |
$(-3a+1), (-4a+1), (-5a+3), (2)$ |
$1$ |
$\Z/9\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1[2] |
$1$ |
\( 3^{5} \) |
$0.996930295$ |
$0.252222755$ |
1.742086354 |
\( \frac{67901057295884009394205}{65045329619727838472} a - \frac{14955764288876698082267}{8130666202465979809} \) |
\( \bigl[a + 1\) , \( 1\) , \( a + 1\) , \( 688 a + 4\) , \( 2093 a + 8727\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(688a+4\right){x}+2093a+8727$ |
| 6916.8-b4 |
6916.8-b |
$5$ |
$9$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
6916.8 |
\( 2^{2} \cdot 7 \cdot 13 \cdot 19 \) |
\( 2^{6} \cdot 7^{9} \cdot 13^{9} \cdot 19 \) |
$1.41144$ |
$(3a-2), (4a-3), (-5a+2), (2)$ |
$1$ |
$\Z/9\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1[2] |
$1$ |
\( 3^{5} \) |
$0.996930295$ |
$0.252222755$ |
1.742086354 |
\( -\frac{67901057295884009394205}{65045329619727838472} a - \frac{51745057015129575263931}{65045329619727838472} \) |
\( \bigl[a + 1\) , \( a - 1\) , \( a\) , \( -5 a - 689\) , \( -2094 a + 10821\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-5a-689\right){x}-2094a+10821$ |
| 25788.2-d2 |
25788.2-d |
$5$ |
$9$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
25788.2 |
\( 2^{2} \cdot 3 \cdot 7 \cdot 307 \) |
\( 2^{18} \cdot 3^{9} \cdot 7^{3} \cdot 307 \) |
$1.96134$ |
$(-2a+1), (-3a+1), (18a-17), (2)$ |
$1$ |
$\Z/9\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1[2] |
$1$ |
\( 3^{5} \) |
$0.705189072$ |
$0.791355632$ |
3.866320841 |
\( -\frac{8542611944677}{6550564608} a - \frac{10759542163145}{13101129216} \) |
\( \bigl[a\) , \( 0\) , \( 0\) , \( -28 a + 83\) , \( 303 a + 48\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-28a+83\right){x}+303a+48$ |
| 25788.3-d2 |
25788.3-d |
$5$ |
$9$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
25788.3 |
\( 2^{2} \cdot 3 \cdot 7 \cdot 307 \) |
\( 2^{18} \cdot 3^{9} \cdot 7^{3} \cdot 307 \) |
$1.96134$ |
$(-2a+1), (3a-2), (-18a+1), (2)$ |
$1$ |
$\Z/9\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1[2] |
$1$ |
\( 3^{5} \) |
$0.705189072$ |
$0.791355632$ |
3.866320841 |
\( \frac{8542611944677}{6550564608} a - \frac{27844766052499}{13101129216} \) |
\( \bigl[a + 1\) , \( -a\) , \( 0\) , \( 28 a + 55\) , \( -303 a + 351\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}-a{x}^{2}+\left(28a+55\right){x}-303a+351$ |
| 30324.2-d4 |
30324.2-d |
$5$ |
$9$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
30324.2 |
\( 2^{2} \cdot 3 \cdot 7 \cdot 19^{2} \) |
\( 2^{18} \cdot 3^{9} \cdot 7^{3} \cdot 19^{2} \) |
$2.04242$ |
$(-2a+1), (-3a+1), (-5a+3), (-5a+2), (2)$ |
0 |
$\Z/9\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1[2] |
$1$ |
\( 3^{5} \) |
$1$ |
$0.754208388$ |
2.612654495 |
\( -\frac{967375366015}{202704768} a + \frac{4969541824649}{810819072} \) |
\( \bigl[a\) , \( 0\) , \( 1\) , \( 56 a - 125\) , \( 330 a - 427\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+\left(56a-125\right){x}+330a-427$ |
| 30324.5-d4 |
30324.5-d |
$5$ |
$9$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
30324.5 |
\( 2^{2} \cdot 3 \cdot 7 \cdot 19^{2} \) |
\( 2^{18} \cdot 3^{9} \cdot 7^{3} \cdot 19^{2} \) |
$2.04242$ |
$(-2a+1), (3a-2), (-5a+3), (-5a+2), (2)$ |
0 |
$\Z/9\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1[2] |
$1$ |
\( 3^{5} \) |
$1$ |
$0.754208388$ |
2.612654495 |
\( \frac{967375366015}{202704768} a + \frac{1100040360589}{810819072} \) |
\( \bigl[a + 1\) , \( -a\) , \( 1\) , \( -57 a - 69\) , \( -330 a - 97\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}-a{x}^{2}+\left(-57a-69\right){x}-330a-97$ |
| 59332.1-b3 |
59332.1-b |
$5$ |
$9$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
59332.1 |
\( 2^{2} \cdot 7 \cdot 13 \cdot 163 \) |
\( 2^{6} \cdot 7^{9} \cdot 13^{9} \cdot 163 \) |
$2.41558$ |
$(-3a+1), (-4a+1), (-14a+3), (2)$ |
$1$ |
$\Z/9\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1[2] |
$1$ |
\( 3^{5} \) |
$4.624425573$ |
$0.147107446$ |
4.713169617 |
\( -\frac{255287897377375285148635811}{558020459369244087944} a + \frac{228708785052139599772688715}{558020459369244087944} \) |
\( \bigl[a + 1\) , \( a - 1\) , \( a\) , \( 143 a + 6335\) , \( 231466 a - 121471\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(143a+6335\right){x}+231466a-121471$ |
| 59332.8-b1 |
59332.8-b |
$5$ |
$9$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
59332.8 |
\( 2^{2} \cdot 7 \cdot 13 \cdot 163 \) |
\( 2^{6} \cdot 7^{9} \cdot 13^{9} \cdot 163 \) |
$2.41558$ |
$(3a-2), (4a-3), (-14a+11), (2)$ |
$1$ |
$\Z/9\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1[2] |
$1$ |
\( 3^{5} \) |
$4.624425573$ |
$0.147107446$ |
4.713169617 |
\( \frac{255287897377375285148635811}{558020459369244087944} a - \frac{3322389040654460671993387}{69752557421155510993} \) |
\( \bigl[a + 1\) , \( 1\) , \( a + 1\) , \( -6336 a - 144\) , \( -231467 a + 109995\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(-6336a-144\right){x}-231467a+109995$ |
| 70756.5-e4 |
70756.5-e |
$5$ |
$9$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
70756.5 |
\( 2^{2} \cdot 7^{2} \cdot 19^{2} \) |
\( 2^{18} \cdot 7^{12} \cdot 19^{11} \) |
$2.52429$ |
$(-3a+1), (3a-2), (-5a+3), (-5a+2), (2)$ |
0 |
$\Z/9\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1[2] |
$1$ |
\( 2 \cdot 3^{7} \) |
$1$ |
$0.046707178$ |
2.912371455 |
\( -\frac{246906770413118172153949}{3333532810216585946368} a + \frac{11553400855801868504987373}{6667065620433171892736} \) |
\( \bigl[a + 1\) , \( 1\) , \( a\) , \( 24234 a - 16908\) , \( -25622 a - 241987\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+{x}^{2}+\left(24234a-16908\right){x}-25622a-241987$ |
| 70756.5-f5 |
70756.5-f |
$5$ |
$9$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
70756.5 |
\( 2^{2} \cdot 7^{2} \cdot 19^{2} \) |
\( 2^{18} \cdot 7^{12} \cdot 19^{11} \) |
$2.52429$ |
$(-3a+1), (3a-2), (-5a+3), (-5a+2), (2)$ |
0 |
$\Z/9\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1[2] |
$1$ |
\( 2 \cdot 3^{7} \) |
$1$ |
$0.046707178$ |
2.912371455 |
\( \frac{246906770413118172153949}{3333532810216585946368} a + \frac{11059587314975632160679475}{6667065620433171892736} \) |
\( \bigl[1\) , \( -a - 1\) , \( a + 1\) , \( 7326 a + 16908\) , \( 25621 a - 267609\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(7326a+16908\right){x}+25621a-267609$ |
| 72436.4-c5 |
72436.4-c |
$5$ |
$9$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
72436.4 |
\( 2^{2} \cdot 7 \cdot 13 \cdot 199 \) |
\( 2^{36} \cdot 7^{3} \cdot 13^{9} \cdot 199 \) |
$2.53915$ |
$(-3a+1), (4a-3), (15a-2), (2)$ |
$1$ |
$\Z/9\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1[2] |
$1$ |
\( 2 \cdot 3^{5} \) |
$5.321423898$ |
$0.071306996$ |
5.257879305 |
\( -\frac{12670215427084219535088157}{47437008974830698496} a + \frac{37466331181904304071659425}{189748035899322793984} \) |
\( \bigl[1\) , \( a + 1\) , \( a\) , \( 7378 a + 20303\) , \( -1596327 a + 1377942\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(7378a+20303\right){x}-1596327a+1377942$ |
| 72436.5-c2 |
72436.5-c |
$5$ |
$9$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
72436.5 |
\( 2^{2} \cdot 7 \cdot 13 \cdot 199 \) |
\( 2^{36} \cdot 7^{3} \cdot 13^{9} \cdot 199 \) |
$2.53915$ |
$(3a-2), (-4a+1), (15a-13), (2)$ |
$1$ |
$\Z/9\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1[2] |
$1$ |
\( 2 \cdot 3^{5} \) |
$5.321423898$ |
$0.071306996$ |
5.257879305 |
\( \frac{12670215427084219535088157}{47437008974830698496} a - \frac{13214530526432574068693203}{189748035899322793984} \) |
\( \bigl[a\) , \( -a - 1\) , \( 0\) , \( -20302 a - 7377\) , \( 1624007 a - 238688\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-20302a-7377\right){x}+1624007a-238688$ |
| 137956.3-b4 |
137956.3-b |
$5$ |
$9$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
137956.3 |
\( 2^{2} \cdot 7 \cdot 13 \cdot 379 \) |
\( 2^{36} \cdot 7^{3} \cdot 13^{9} \cdot 379 \) |
$2.98287$ |
$(-3a+1), (4a-3), (22a-15), (2)$ |
$1$ |
$\Z/9\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1[2] |
$1$ |
\( 2 \cdot 3^{5} \) |
$4.024981177$ |
$0.059662609$ |
3.327489652 |
\( \frac{41190401540033094612818731}{45172428144373956608} a + \frac{29855183119266456999502207}{361379425154991652864} \) |
\( \bigl[a + 1\) , \( a - 1\) , \( a\) , \( -50596 a + 25247\) , \( 2885839 a - 3913340\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-50596a+25247\right){x}+2885839a-3913340$ |
| 137956.6-b5 |
137956.6-b |
$5$ |
$9$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
137956.6 |
\( 2^{2} \cdot 7 \cdot 13 \cdot 379 \) |
\( 2^{36} \cdot 7^{3} \cdot 13^{9} \cdot 379 \) |
$2.98287$ |
$(3a-2), (-4a+1), (22a-7), (2)$ |
$1$ |
$\Z/9\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1[2] |
$1$ |
\( 2 \cdot 3^{5} \) |
$4.024981177$ |
$0.059662609$ |
3.327489652 |
\( -\frac{41190401540033094612818731}{45172428144373956608} a + \frac{359378395439531213902052055}{361379425154991652864} \) |
\( \bigl[1\) , \( a + 1\) , \( a\) , \( -25347 a - 25247\) , \( -2911187 a - 1052748\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-25347a-25247\right){x}-2911187a-1052748$ |
| 106.1-a1 |
106.1-a |
$3$ |
$9$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
106.1 |
\( 2 \cdot 53 \) |
\( 2^{9} \cdot 53 \) |
$0.57345$ |
$(a+1), (-2a+7)$ |
0 |
$\Z/9\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1 |
$1$ |
\( 3^{2} \) |
$1$ |
$5.985343332$ |
0.665038148 |
\( -\frac{24565}{1696} a + \frac{44217}{1696} \) |
\( \bigl[1\) , \( i - 1\) , \( i + 1\) , \( -i - 1\) , \( 0\bigr] \) |
${y}^2+{x}{y}+\left(i+1\right){y}={x}^{3}+\left(i-1\right){x}^{2}+\left(-i-1\right){x}$ |
| 106.2-a1 |
106.2-a |
$3$ |
$9$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
106.2 |
\( 2 \cdot 53 \) |
\( 2^{9} \cdot 53 \) |
$0.57345$ |
$(a+1), (2a+7)$ |
0 |
$\Z/9\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1 |
$1$ |
\( 3^{2} \) |
$1$ |
$5.985343332$ |
0.665038148 |
\( \frac{24565}{1696} a + \frac{44217}{1696} \) |
\( \bigl[1\) , \( -i - 1\) , \( i + 1\) , \( -1\) , \( -i\bigr] \) |
${y}^2+{x}{y}+\left(i+1\right){y}={x}^{3}+\left(-i-1\right){x}^{2}-{x}-i$ |
| 1458.1-d2 |
1458.1-d |
$3$ |
$9$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
1458.1 |
\( 2 \cdot 3^{6} \) |
\( 2^{18} \cdot 3^{10} \) |
$1.10435$ |
$(a+1), (3)$ |
$1$ |
$\Z/9\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$3$ |
3B.1.1 |
$1$ |
\( 2 \cdot 3^{3} \) |
$0.693964260$ |
$1.878378408$ |
1.738036644 |
\( -\frac{1167051}{512} \) |
\( \bigl[i\) , \( 1\) , \( i\) , \( -13\) , \( -29\bigr] \) |
${y}^2+i{x}{y}+i{y}={x}^{3}+{x}^{2}-13{x}-29$ |
| 23530.1-d3 |
23530.1-d |
$3$ |
$9$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
23530.1 |
\( 2 \cdot 5 \cdot 13 \cdot 181 \) |
\( 2^{9} \cdot 5^{9} \cdot 13^{3} \cdot 181 \) |
$2.21347$ |
$(a+1), (-a-2), (-3a-2), (-10a-9)$ |
$1$ |
$\Z/9\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1 |
$1$ |
\( 3^{5} \) |
$0.926835476$ |
$0.834723109$ |
4.641905944 |
\( -\frac{466833875519731}{24853562500000} a + \frac{43148287121224167}{24853562500000} \) |
\( \bigl[i\) , \( 0\) , \( i + 1\) , \( 49 i + 47\) , \( 14 i - 18\bigr] \) |
${y}^2+i{x}{y}+\left(i+1\right){y}={x}^{3}+\left(49i+47\right){x}+14i-18$ |
| 23530.8-b3 |
23530.8-b |
$3$ |
$9$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
23530.8 |
\( 2 \cdot 5 \cdot 13 \cdot 181 \) |
\( 2^{9} \cdot 5^{9} \cdot 13^{3} \cdot 181 \) |
$2.21347$ |
$(a+1), (2a+1), (2a+3), (9a+10)$ |
$1$ |
$\Z/9\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1 |
$1$ |
\( 3^{5} \) |
$0.926835476$ |
$0.834723109$ |
4.641905944 |
\( \frac{466833875519731}{24853562500000} a + \frac{43148287121224167}{24853562500000} \) |
\( \bigl[1\) , \( 0\) , \( i + 1\) , \( -50 i + 46\) , \( 14 i + 18\bigr] \) |
${y}^2+{x}{y}+\left(i+1\right){y}={x}^{3}+\left(-50i+46\right){x}+14i+18$ |
| 37570.11-e2 |
37570.11-e |
$3$ |
$9$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
37570.11 |
\( 2 \cdot 5 \cdot 13 \cdot 17^{2} \) |
\( 2^{9} \cdot 5^{9} \cdot 13^{3} \cdot 17^{2} \) |
$2.48816$ |
$(a+1), (2a+1), (2a+3), (a+4), (a-4)$ |
0 |
$\Z/9\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1 |
$1$ |
\( 3^{5} \) |
$1$ |
$0.731648805$ |
2.194946417 |
\( -\frac{14861228276049287}{2334312500000} a + \frac{17091695749685391}{2334312500000} \) |
\( \bigl[i\) , \( -1\) , \( i\) , \( 33 i - 125\) , \( -247 i + 534\bigr] \) |
${y}^2+i{x}{y}+i{y}={x}^{3}-{x}^{2}+\left(33i-125\right){x}-247i+534$ |
| 37570.2-f2 |
37570.2-f |
$3$ |
$9$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
37570.2 |
\( 2 \cdot 5 \cdot 13 \cdot 17^{2} \) |
\( 2^{9} \cdot 5^{9} \cdot 13^{3} \cdot 17^{2} \) |
$2.48816$ |
$(a+1), (-a-2), (-3a-2), (a+4), (a-4)$ |
0 |
$\Z/9\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1 |
$1$ |
\( 3^{5} \) |
$1$ |
$0.731648805$ |
2.194946417 |
\( \frac{14861228276049287}{2334312500000} a + \frac{17091695749685391}{2334312500000} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -33 i - 126\) , \( -247 i - 534\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}+\left(-33i-126\right){x}-247i-534$ |
| 67730.3-b2 |
67730.3-b |
$3$ |
$9$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
67730.3 |
\( 2 \cdot 5 \cdot 13 \cdot 521 \) |
\( 2^{18} \cdot 5^{9} \cdot 13^{3} \cdot 521 \) |
$2.88313$ |
$(a+1), (-a-2), (2a+3), (11a-20)$ |
0 |
$\Z/9\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1 |
$1$ |
\( 2 \cdot 3^{5} \) |
$1$ |
$0.424506046$ |
2.547036281 |
\( \frac{3297286972031996087}{1144637000000000} a - \frac{1272295307112576021}{286159250000000} \) |
\( \bigl[i\) , \( i + 1\) , \( 0\) , \( -295 i - 152\) , \( 2492 i - 315\bigr] \) |
${y}^2+i{x}{y}={x}^{3}+\left(i+1\right){x}^{2}+\left(-295i-152\right){x}+2492i-315$ |
| 67730.6-a2 |
67730.6-a |
$3$ |
$9$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
67730.6 |
\( 2 \cdot 5 \cdot 13 \cdot 521 \) |
\( 2^{18} \cdot 5^{9} \cdot 13^{3} \cdot 521 \) |
$2.88313$ |
$(a+1), (2a+1), (-3a-2), (11a+20)$ |
0 |
$\Z/9\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1 |
$1$ |
\( 2 \cdot 3^{5} \) |
$1$ |
$0.424506046$ |
2.547036281 |
\( -\frac{3297286972031996087}{1144637000000000} a - \frac{1272295307112576021}{286159250000000} \) |
\( \bigl[i\) , \( -i + 1\) , \( 0\) , \( 295 i - 152\) , \( -2492 i - 315\bigr] \) |
${y}^2+i{x}{y}={x}^{3}+\left(-i+1\right){x}^{2}+\left(295i-152\right){x}-2492i-315$ |
| 81770.10-d2 |
81770.10-d |
$3$ |
$9$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
81770.10 |
\( 2 \cdot 5 \cdot 13 \cdot 17 \cdot 37 \) |
\( 2^{18} \cdot 5^{9} \cdot 13^{3} \cdot 17 \cdot 37 \) |
$3.02216$ |
$(a+1), (2a+1), (-3a-2), (a+4), (a-6)$ |
$1$ |
$\Z/9\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1 |
$1$ |
\( 2 \cdot 3^{5} \) |
$1.368971915$ |
$0.401664617$ |
6.598410977 |
\( -\frac{8568716914402669477}{1381913000000000} a + \frac{7484969002618578843}{690956500000000} \) |
\( \bigl[1\) , \( i - 1\) , \( i + 1\) , \( -403 i + 215\) , \( 474 i - 3430\bigr] \) |
${y}^2+{x}{y}+\left(i+1\right){y}={x}^{3}+\left(i-1\right){x}^{2}+\left(-403i+215\right){x}+474i-3430$ |
| 81770.7-d2 |
81770.7-d |
$3$ |
$9$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
81770.7 |
\( 2 \cdot 5 \cdot 13 \cdot 17 \cdot 37 \) |
\( 2^{18} \cdot 5^{9} \cdot 13^{3} \cdot 17 \cdot 37 \) |
$3.02216$ |
$(a+1), (-a-2), (2a+3), (a-4), (a+6)$ |
$1$ |
$\Z/9\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1 |
$1$ |
\( 2 \cdot 3^{5} \) |
$1.368971915$ |
$0.401664617$ |
6.598410977 |
\( \frac{8568716914402669477}{1381913000000000} a + \frac{7484969002618578843}{690956500000000} \) |
\( \bigl[i\) , \( i + 1\) , \( i + 1\) , \( 402 i + 216\) , \( 474 i + 3430\bigr] \) |
${y}^2+i{x}{y}+\left(i+1\right){y}={x}^{3}+\left(i+1\right){x}^{2}+\left(402i+216\right){x}+474i+3430$ |
| 436.3-a2 |
436.3-a |
$3$ |
$9$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
436.3 |
\( 2^{2} \cdot 109 \) |
\( 2^{18} \cdot 109 \) |
$1.08034$ |
$(a), (-a+1), (-4a-7)$ |
0 |
$\Z/9\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1 |
$1$ |
\( 3^{4} \) |
$1$ |
$3.291296508$ |
2.487986300 |
\( -\frac{513973}{13952} a + \frac{88705163}{55808} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( 3 a\) , \( 2 a - 1\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}+3a{x}+2a-1$ |
| 436.4-a2 |
436.4-a |
$3$ |
$9$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
436.4 |
\( 2^{2} \cdot 109 \) |
\( 2^{18} \cdot 109 \) |
$1.08034$ |
$(a), (-a+1), (4a-11)$ |
0 |
$\Z/9\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1 |
$1$ |
\( 3^{4} \) |
$1$ |
$3.291296508$ |
2.487986300 |
\( \frac{513973}{13952} a + \frac{86649271}{55808} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -3 a + 3\) , \( -2 a + 1\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}+\left(-3a+3\right){x}-2a+1$ |
| 2916.2-l2 |
2916.2-l |
$3$ |
$9$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
2916.2 |
\( 2^{2} \cdot 3^{6} \) |
\( 2^{18} \cdot 3^{10} \) |
$1.73734$ |
$(a), (-a+1), (3)$ |
0 |
$\Z/9\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$3$ |
3B.1.1 |
$1$ |
\( 3^{5} \) |
$1$ |
$1.878378408$ |
4.259761832 |
\( -\frac{1167051}{512} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -14\) , \( 29\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}-14{x}+29$ |
| 5012.3-d2 |
5012.3-d |
$3$ |
$9$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
5012.3 |
\( 2^{2} \cdot 7 \cdot 179 \) |
\( 2^{27} \cdot 7^{3} \cdot 179 \) |
$1.98925$ |
$(a), (-a+1), (-2a+1), (10a-7)$ |
0 |
$\Z/9\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1 |
$1$ |
\( 2 \cdot 3^{5} \) |
$1$ |
$1.155708882$ |
5.241802783 |
\( -\frac{1086757026275}{2299265024} a + \frac{1874366024113}{2299265024} \) |
\( \bigl[1\) , \( -a + 1\) , \( a + 1\) , \( 14 a - 28\) , \( -37 a - 13\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(14a-28\right){x}-37a-13$ |
| 5012.4-d2 |
5012.4-d |
$3$ |
$9$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
5012.4 |
\( 2^{2} \cdot 7 \cdot 179 \) |
\( 2^{27} \cdot 7^{3} \cdot 179 \) |
$1.98925$ |
$(a), (-a+1), (-2a+1), (10a-3)$ |
0 |
$\Z/9\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1 |
$1$ |
\( 2 \cdot 3^{5} \) |
$1$ |
$1.155708882$ |
5.241802783 |
\( \frac{1086757026275}{2299265024} a + \frac{393804498919}{1149632512} \) |
\( \bigl[1\) , \( a\) , \( a\) , \( -15 a - 13\) , \( 36 a - 49\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+a{x}^{2}+\left(-15a-13\right){x}+36a-49$ |
| 6524.3-d1 |
6524.3-d |
$3$ |
$9$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
6524.3 |
\( 2^{2} \cdot 7 \cdot 233 \) |
\( 2^{27} \cdot 7^{3} \cdot 233 \) |
$2.12479$ |
$(a), (-a+1), (-2a+1), (-8a-7)$ |
0 |
$\Z/9\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1 |
$1$ |
\( 2 \cdot 3^{5} \) |
$1$ |
$1.070081174$ |
4.853432005 |
\( -\frac{2481805210219}{2992898048} a - \frac{9249827004919}{2992898048} \) |
\( \bigl[1\) , \( -a + 1\) , \( a + 1\) , \( -25 a + 47\) , \( -67 a - 111\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-25a+47\right){x}-67a-111$ |
| 6524.4-d1 |
6524.4-d |
$3$ |
$9$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
6524.4 |
\( 2^{2} \cdot 7 \cdot 233 \) |
\( 2^{27} \cdot 7^{3} \cdot 233 \) |
$2.12479$ |
$(a), (-a+1), (-2a+1), (8a-15)$ |
0 |
$\Z/9\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1 |
$1$ |
\( 2 \cdot 3^{5} \) |
$1$ |
$1.070081174$ |
4.853432005 |
\( \frac{2481805210219}{2992898048} a - \frac{5865816107569}{1496449024} \) |
\( \bigl[1\) , \( a\) , \( a\) , \( 24 a + 23\) , \( 66 a - 177\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+a{x}^{2}+\left(24a+23\right){x}+66a-177$ |
| 1458.4-e2 |
1458.4-e |
$3$ |
$9$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
1458.4 |
\( 2 \cdot 3^{6} \) |
\( 2^{18} \cdot 3^{10} \) |
$1.56179$ |
$(a), (-a-1), (a-1)$ |
0 |
$\Z/9\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$3$ |
3B.1.1 |
$1$ |
\( 2 \cdot 3^{4} \) |
$1$ |
$1.878378408$ |
2.656428221 |
\( -\frac{1167051}{512} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -14\) , \( 29\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}-14{x}+29$ |
| 2754.3-g1 |
2754.3-g |
$3$ |
$9$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
2754.3 |
\( 2 \cdot 3^{4} \cdot 17 \) |
\( 2^{9} \cdot 3^{14} \cdot 17 \) |
$1.83094$ |
$(a), (-a-1), (a-1), (-2a+3)$ |
$1$ |
$\Z/9\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.1 |
$1$ |
\( 3^{5} \) |
$0.592435964$ |
$1.807051096$ |
4.542010151 |
\( \frac{1601023325}{10707552} a - \frac{461700499}{2676888} \) |
\( \bigl[a + 1\) , \( 0\) , \( a\) , \( -6 a + 3\) , \( a + 25\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(-6a+3\right){x}+a+25$ |
| 2754.8-g1 |
2754.8-g |
$3$ |
$9$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
2754.8 |
\( 2 \cdot 3^{4} \cdot 17 \) |
\( 2^{9} \cdot 3^{14} \cdot 17 \) |
$1.83094$ |
$(a), (-a-1), (a-1), (2a+3)$ |
$1$ |
$\Z/9\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.1 |
$1$ |
\( 3^{5} \) |
$0.592435964$ |
$1.807051096$ |
4.542010151 |
\( -\frac{1601023325}{10707552} a - \frac{461700499}{2676888} \) |
\( \bigl[a + 1\) , \( -a\) , \( a\) , \( 5 a + 3\) , \( -a + 25\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}-a{x}^{2}+\left(5a+3\right){x}-a+25$ |
| 3078.4-b3 |
3078.4-b |
$3$ |
$9$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
3078.4 |
\( 2 \cdot 3^{4} \cdot 19 \) |
\( 2^{9} \cdot 3^{14} \cdot 19 \) |
$1.88257$ |
$(a), (-a-1), (a-1), (3a+1)$ |
0 |
$\Z/9\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.1 |
$1$ |
\( 3^{5} \) |
$1$ |
$1.747642786$ |
3.707310197 |
\( \frac{13180875521}{11967264} a + \frac{4642263991}{5983632} \) |
\( \bigl[1\) , \( -a + 1\) , \( 1\) , \( 8 a - 9\) , \( -7 a + 15\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(8a-9\right){x}-7a+15$ |
| 3078.7-b3 |
3078.7-b |
$3$ |
$9$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
3078.7 |
\( 2 \cdot 3^{4} \cdot 19 \) |
\( 2^{9} \cdot 3^{14} \cdot 19 \) |
$1.88257$ |
$(a), (-a-1), (a-1), (-3a+1)$ |
0 |
$\Z/9\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.1 |
$1$ |
\( 3^{5} \) |
$1$ |
$1.747642786$ |
3.707310197 |
\( -\frac{13180875521}{11967264} a + \frac{4642263991}{5983632} \) |
\( \bigl[1\) , \( a + 1\) , \( 1\) , \( -8 a - 9\) , \( 7 a + 15\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-8a-9\right){x}+7a+15$ |
| 17478.3-b1 |
17478.3-b |
$3$ |
$9$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
17478.3 |
\( 2 \cdot 3^{2} \cdot 971 \) |
\( 2^{18} \cdot 3^{18} \cdot 971 \) |
$2.90607$ |
$(a), (-a-1), (a-1), (11a+27)$ |
0 |
$\Z/9\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1 |
$1$ |
\( 2 \cdot 3^{6} \) |
$1$ |
$0.496517968$ |
6.319642007 |
\( \frac{17325531933743}{9785442816} a - \frac{441659180651}{120807936} \) |
\( \bigl[a + 1\) , \( a - 1\) , \( a + 1\) , \( 138 a + 121\) , \( -47 a - 1769\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(138a+121\right){x}-47a-1769$ |
| 17478.4-b1 |
17478.4-b |
$3$ |
$9$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
17478.4 |
\( 2 \cdot 3^{2} \cdot 971 \) |
\( 2^{18} \cdot 3^{18} \cdot 971 \) |
$2.90607$ |
$(a), (-a-1), (a-1), (11a-27)$ |
0 |
$\Z/9\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1 |
$1$ |
\( 2 \cdot 3^{6} \) |
$1$ |
$0.496517968$ |
6.319642007 |
\( -\frac{17325531933743}{9785442816} a - \frac{441659180651}{120807936} \) |
\( \bigl[a + 1\) , \( a - 1\) , \( 1\) , \( -142 a + 120\) , \( 168 a - 1489\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-142a+120\right){x}+168a-1489$ |
| 2916.4-a2 |
2916.4-a |
$3$ |
$9$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
2916.4 |
\( 2^{2} \cdot 3^{6} \) |
\( 2^{18} \cdot 3^{10} \) |
$2.17787$ |
$(-a), (a-1), (2)$ |
0 |
$\Z/9\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$3$ |
3B.1.1 |
$1$ |
\( 3^{4} \) |
$1$ |
$1.878378408$ |
1.132704799 |
\( -\frac{1167051}{512} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -14\) , \( 29\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}-14{x}+29$ |
| 9036.3-c2 |
9036.3-c |
$3$ |
$9$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
9036.3 |
\( 2^{2} \cdot 3^{2} \cdot 251 \) |
\( 2^{6} \cdot 3^{18} \cdot 251 \) |
$2.88954$ |
$(-a), (a-1), (-5a+16), (2)$ |
0 |
$\Z/9\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1 |
$1$ |
\( 3^{5} \) |
$1$ |
$1.151738623$ |
2.083573566 |
\( -\frac{33192777235}{39523464} a + \frac{108236242883}{39523464} \) |
\( \bigl[a + 1\) , \( 0\) , \( 1\) , \( -24 a + 17\) , \( -30 a + 77\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(-24a+17\right){x}-30a+77$ |
| 9036.4-c2 |
9036.4-c |
$3$ |
$9$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
9036.4 |
\( 2^{2} \cdot 3^{2} \cdot 251 \) |
\( 2^{6} \cdot 3^{18} \cdot 251 \) |
$2.88954$ |
$(-a), (a-1), (5a+11), (2)$ |
0 |
$\Z/9\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1 |
$1$ |
\( 3^{5} \) |
$1$ |
$1.151738623$ |
2.083573566 |
\( \frac{33192777235}{39523464} a + \frac{9380433206}{4940433} \) |
\( \bigl[a\) , \( -a + 1\) , \( 1\) , \( 23 a - 6\) , \( 30 a + 47\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(23a-6\right){x}+30a+47$ |
| 324.2-d2 |
324.2-d |
$3$ |
$9$ |
\(\Q(\sqrt{-15}) \) |
$2$ |
$[0, 1]$ |
324.2 |
\( 2^{2} \cdot 3^{4} \) |
\( 2^{18} \cdot 3^{10} \) |
$1.46832$ |
$(2,a), (2,a+1), (3,a+1)$ |
0 |
$\Z/9\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$3$ |
3B.1.2 |
$1$ |
\( 3^{5} \) |
$1$ |
$1.878378408$ |
2.909971318 |
\( -\frac{1167051}{512} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -14\) , \( 29\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3-{x}^2-14{x}+29$ |
*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.
