| 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 |
| 81.1-CMa1 |
81.1-CMa |
$2$ |
$3$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
81.1 |
\( 3^{4} \) |
\( 3^{6} \) |
$0.46432$ |
$(-2a+1)$ |
0 |
$\Z/3\Z\oplus\Z/3\Z$ |
$\textsf{yes}$ |
$-3$ |
$\mathrm{U}(1)$ |
✓ |
✓ |
|
✓ |
$3$ |
3Cs.1.1[2] |
$1$ |
\( 3 \) |
$1$ |
$8.108628264$ |
0.346779163 |
\( 0 \) |
\( \bigl[0\) , \( 0\) , \( 1\) , \( 0\) , \( 0\bigr] \) |
${y}^2+{y}={x}^{3}$ |
| 324.1-a5 |
324.1-a |
$5$ |
$9$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
324.1 |
\( 2^{2} \cdot 3^{4} \) |
\( 2^{6} \cdot 3^{6} \) |
$0.65665$ |
$(-2a+1), (2)$ |
0 |
$\Z/3\Z\oplus\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$3$ |
3Cs.1.1[2] |
$1$ |
\( 3^{2} \) |
$1$ |
$5.635135226$ |
0.722988186 |
\( \frac{9261}{8} \) |
\( \bigl[a + 1\) , \( 0\) , \( 1\) , \( a - 2\) , \( -1\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(a-2\right){x}-1$ |
| 361.2-a4 |
361.2-a |
$5$ |
$9$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
361.2 |
\( 19^{2} \) |
\( 19^{6} \) |
$0.67465$ |
$(-5a+3), (-5a+2)$ |
$1$ |
$\Z/3\Z\oplus\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3$ |
3Cs.1.1[2] |
$1$ |
\( 3^{2} \) |
$0.677900606$ |
$2.805927025$ |
0.488089257 |
\( -\frac{89915392}{6859} \) |
\( \bigl[0\) , \( -a\) , \( 1\) , \( -9 a + 9\) , \( -15\bigr] \) |
${y}^2+{y}={x}^{3}-a{x}^{2}+\left(-9a+9\right){x}-15$ |
| 532.2-b3 |
532.2-b |
$5$ |
$9$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
532.2 |
\( 2^{2} \cdot 7 \cdot 19 \) |
\( 2^{6} \cdot 7^{3} \cdot 19^{3} \) |
$0.74332$ |
$(-3a+1), (-5a+2), (2)$ |
0 |
$\Z/3\Z\oplus\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3Cs.1.1[2] |
$1$ |
\( 3^{3} \) |
$1$ |
$2.514297545$ |
0.967753576 |
\( -\frac{27421842825}{4705274} a + \frac{371136361913}{18821096} \) |
\( \bigl[a + 1\) , \( a - 1\) , \( a + 1\) , \( 4 a - 15\) , \( 3 a - 17\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(4a-15\right){x}+3a-17$ |
| 532.3-b3 |
532.3-b |
$5$ |
$9$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
532.3 |
\( 2^{2} \cdot 7 \cdot 19 \) |
\( 2^{6} \cdot 7^{3} \cdot 19^{3} \) |
$0.74332$ |
$(3a-2), (-5a+3), (2)$ |
0 |
$\Z/3\Z\oplus\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3Cs.1.1[2] |
$1$ |
\( 3^{3} \) |
$1$ |
$2.514297545$ |
0.967753576 |
\( \frac{27421842825}{4705274} a + \frac{261448990613}{18821096} \) |
\( \bigl[a + 1\) , \( 1\) , \( a\) , \( 14 a - 5\) , \( -4 a - 13\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+{x}^{2}+\left(14a-5\right){x}-4a-13$ |
| 676.2-b2 |
676.2-b |
$5$ |
$9$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
676.2 |
\( 2^{2} \cdot 13^{2} \) |
\( 2^{6} \cdot 13^{6} \) |
$0.78920$ |
$(-4a+1), (4a-3), (2)$ |
0 |
$\Z/3\Z\oplus\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3$ |
3Cs.1.1[2] |
$1$ |
\( 3^{3} \) |
$1$ |
$2.690802392$ |
1.035690323 |
\( -\frac{10218313}{17576} \) |
\( \bigl[a + 1\) , \( -a\) , \( 1\) , \( -5 a + 4\) , \( -8\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}-a{x}^{2}+\left(-5a+4\right){x}-8$ |
| 756.1-a4 |
756.1-a |
$5$ |
$9$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
756.1 |
\( 2^{2} \cdot 3^{3} \cdot 7 \) |
\( 2^{6} \cdot 3^{9} \cdot 7^{3} \) |
$0.81158$ |
$(-2a+1), (-3a+1), (2)$ |
0 |
$\Z/3\Z\oplus\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3Cs.1.1[2] |
$1$ |
\( 3^{3} \) |
$1$ |
$2.554307252$ |
0.983153319 |
\( -\frac{1598955}{686} a + \frac{7343733}{2744} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( 9 a - 5\) , \( -6 a - 4\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}+\left(9a-5\right){x}-6a-4$ |
| 756.2-a4 |
756.2-a |
$5$ |
$9$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
756.2 |
\( 2^{2} \cdot 3^{3} \cdot 7 \) |
\( 2^{6} \cdot 3^{9} \cdot 7^{3} \) |
$0.81158$ |
$(-2a+1), (3a-2), (2)$ |
0 |
$\Z/3\Z\oplus\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3Cs.1.1[2] |
$1$ |
\( 3^{3} \) |
$1$ |
$2.554307252$ |
0.983153319 |
\( \frac{1598955}{686} a + \frac{947913}{2744} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -9 a + 4\) , \( 6 a - 10\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}+\left(-9a+4\right){x}+6a-10$ |
| 868.2-b3 |
868.2-b |
$5$ |
$9$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
868.2 |
\( 2^{2} \cdot 7 \cdot 31 \) |
\( 2^{6} \cdot 7^{6} \cdot 31^{3} \) |
$0.84010$ |
$(-3a+1), (6a-5), (2)$ |
0 |
$\Z/3\Z\oplus\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3Cs.1.1[2] |
$1$ |
\( 2 \cdot 3^{3} \) |
$1$ |
$1.491140745$ |
1.147880680 |
\( -\frac{27687863199645}{14019525436} a - \frac{39320031191761}{28039050872} \) |
\( \bigl[a + 1\) , \( 1\) , \( a\) , \( -9 a + 27\) , \( -49 a + 6\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+{x}^{2}+\left(-9a+27\right){x}-49a+6$ |
| 868.3-b3 |
868.3-b |
$5$ |
$9$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
868.3 |
\( 2^{2} \cdot 7 \cdot 31 \) |
\( 2^{6} \cdot 7^{6} \cdot 31^{3} \) |
$0.84010$ |
$(3a-2), (-6a+1), (2)$ |
0 |
$\Z/3\Z\oplus\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3Cs.1.1[2] |
$1$ |
\( 2 \cdot 3^{3} \) |
$1$ |
$1.491140745$ |
1.147880680 |
\( \frac{27687863199645}{14019525436} a - \frac{94695757591051}{28039050872} \) |
\( \bigl[a + 1\) , \( a - 1\) , \( a + 1\) , \( -28 a + 8\) , \( 48 a - 43\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-28a+8\right){x}+48a-43$ |
| 876.1-a5 |
876.1-a |
$5$ |
$9$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
876.1 |
\( 2^{2} \cdot 3 \cdot 73 \) |
\( 2^{18} \cdot 3^{3} \cdot 73^{3} \) |
$0.84203$ |
$(-2a+1), (-9a+1), (2)$ |
0 |
$\Z/3\Z\oplus\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3Cs.1.1[2] |
$1$ |
\( 3^{4} \) |
$1$ |
$0.987284640$ |
1.140018106 |
\( -\frac{88859939430115}{896295168} a + \frac{105897127856527}{1792590336} \) |
\( \bigl[a + 1\) , \( a - 1\) , \( a + 1\) , \( -19 a - 100\) , \( 36 a + 423\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-19a-100\right){x}+36a+423$ |
| 876.2-a5 |
876.2-a |
$5$ |
$9$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
876.2 |
\( 2^{2} \cdot 3 \cdot 73 \) |
\( 2^{18} \cdot 3^{3} \cdot 73^{3} \) |
$0.84203$ |
$(-2a+1), (9a-8), (2)$ |
0 |
$\Z/3\Z\oplus\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3Cs.1.1[2] |
$1$ |
\( 3^{4} \) |
$1$ |
$0.987284640$ |
1.140018106 |
\( \frac{88859939430115}{896295168} a - \frac{71822751003703}{1792590336} \) |
\( \bigl[a + 1\) , \( 1\) , \( a\) , \( 99 a + 18\) , \( -37 a + 460\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+{x}^{2}+\left(99a+18\right){x}-37a+460$ |
| 1036.2-a4 |
1036.2-a |
$5$ |
$9$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
1036.2 |
\( 2^{2} \cdot 7 \cdot 37 \) |
\( 2^{6} \cdot 7^{3} \cdot 37^{3} \) |
$0.87809$ |
$(-3a+1), (-7a+3), (2)$ |
0 |
$\Z/3\Z\oplus\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3Cs.1.1[2] |
$1$ |
\( 3^{3} \) |
$1$ |
$2.083349060$ |
0.801881427 |
\( \frac{506445552405}{69495916} a - \frac{3543562947041}{138991832} \) |
\( \bigl[a\) , \( a + 1\) , \( 0\) , \( 9 a - 22\) , \( 16 a - 47\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(9a-22\right){x}+16a-47$ |
| 1036.3-a4 |
1036.3-a |
$5$ |
$9$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
1036.3 |
\( 2^{2} \cdot 7 \cdot 37 \) |
\( 2^{6} \cdot 7^{3} \cdot 37^{3} \) |
$0.87809$ |
$(3a-2), (-7a+4), (2)$ |
0 |
$\Z/3\Z\oplus\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3Cs.1.1[2] |
$1$ |
\( 3^{3} \) |
$1$ |
$2.083349060$ |
0.801881427 |
\( -\frac{506445552405}{69495916} a - \frac{2530671842231}{138991832} \) |
\( \bigl[1\) , \( -a - 1\) , \( a\) , \( 22 a - 8\) , \( -30 a - 9\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(22a-8\right){x}-30a-9$ |
| 1204.1-b3 |
1204.1-b |
$5$ |
$9$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
1204.1 |
\( 2^{2} \cdot 7 \cdot 43 \) |
\( 2^{12} \cdot 7^{3} \cdot 43^{3} \) |
$0.91171$ |
$(-3a+1), (-7a+1), (2)$ |
0 |
$\Z/3\Z\oplus\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3Cs.1.1[2] |
$1$ |
\( 2 \cdot 3^{3} \) |
$1$ |
$1.648651125$ |
1.269132228 |
\( -\frac{405076613535}{436334416} a + \frac{1385286605803}{1745337664} \) |
\( \bigl[a\) , \( -a - 1\) , \( 0\) , \( 14 a - 14\) , \( 20 a + 12\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(14a-14\right){x}+20a+12$ |
| 1204.4-b3 |
1204.4-b |
$5$ |
$9$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
1204.4 |
\( 2^{2} \cdot 7 \cdot 43 \) |
\( 2^{12} \cdot 7^{3} \cdot 43^{3} \) |
$0.91171$ |
$(3a-2), (7a-6), (2)$ |
0 |
$\Z/3\Z\oplus\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3Cs.1.1[2] |
$1$ |
\( 2 \cdot 3^{3} \) |
$1$ |
$1.648651125$ |
1.269132228 |
\( \frac{405076613535}{436334416} a - \frac{235019848337}{1745337664} \) |
\( \bigl[1\) , \( a + 1\) , \( a\) , \( 15 a - 13\) , \( -19 a + 18\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(15a-13\right){x}-19a+18$ |
| 1225.2-a3 |
1225.2-a |
$5$ |
$9$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
1225.2 |
\( 5^{2} \cdot 7^{2} \) |
\( 5^{6} \cdot 7^{6} \) |
$0.91566$ |
$(-3a+1), (3a-2), (5)$ |
0 |
$\Z/3\Z\oplus\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3$ |
3Cs.1.1[2] |
$1$ |
\( 3^{3} \) |
$1$ |
$2.324925606$ |
0.894864283 |
\( \frac{71991296}{42875} \) |
\( \bigl[0\) , \( -a\) , \( 1\) , \( 9 a - 9\) , \( 1\bigr] \) |
${y}^2+{y}={x}^{3}-a{x}^{2}+\left(9a-9\right){x}+1$ |
| 1369.2-b3 |
1369.2-b |
$5$ |
$9$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
1369.2 |
\( 37^{2} \) |
\( 37^{6} \) |
$0.94146$ |
$(-7a+4), (-7a+3)$ |
$1$ |
$\Z/3\Z\oplus\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3$ |
3Cs.1.1[2] |
$1$ |
\( 3^{2} \) |
$2.174309583$ |
$1.924082382$ |
1.073499626 |
\( \frac{1404928000}{50653} \) |
\( \bigl[0\) , \( a - 1\) , \( 1\) , \( 23 a\) , \( -50\bigr] \) |
${y}^2+{y}={x}^{3}+\left(a-1\right){x}^{2}+23a{x}-50$ |
| 1404.1-b3 |
1404.1-b |
$5$ |
$9$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
1404.1 |
\( 2^{2} \cdot 3^{3} \cdot 13 \) |
\( 2^{12} \cdot 3^{9} \cdot 13^{3} \) |
$0.94742$ |
$(-2a+1), (-4a+1), (2)$ |
0 |
$\Z/3\Z\oplus\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3Cs.1.1[2] |
$1$ |
\( 2 \cdot 3^{3} \) |
$1$ |
$1.480078951$ |
1.139365308 |
\( -\frac{475773585}{70304} a + \frac{788110071}{140608} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -21 a + 33\) , \( -21 a - 48\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}+\left(-21a+33\right){x}-21a-48$ |
| 1404.2-b3 |
1404.2-b |
$5$ |
$9$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
1404.2 |
\( 2^{2} \cdot 3^{3} \cdot 13 \) |
\( 2^{12} \cdot 3^{9} \cdot 13^{3} \) |
$0.94742$ |
$(-2a+1), (4a-3), (2)$ |
0 |
$\Z/3\Z\oplus\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3Cs.1.1[2] |
$1$ |
\( 2 \cdot 3^{3} \) |
$1$ |
$1.480078951$ |
1.139365308 |
\( \frac{475773585}{70304} a - \frac{163437099}{140608} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( 21 a + 12\) , \( 21 a - 69\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}+\left(21a+12\right){x}+21a-69$ |
| 1444.2-b5 |
1444.2-b |
$5$ |
$9$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
1444.2 |
\( 2^{2} \cdot 19^{2} \) |
\( 2^{18} \cdot 19^{6} \) |
$0.95409$ |
$(-5a+3), (-5a+2), (2)$ |
0 |
$\Z/3\Z\oplus\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3$ |
3Cs.1.1[2] |
$1$ |
\( 3^{4} \) |
$1$ |
$1.136863399$ |
1.312736779 |
\( \frac{94196375}{3511808} \) |
\( \bigl[a\) , \( 0\) , \( 1\) , \( -10 a\) , \( 90\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}-10a{x}+90$ |
| 1612.1-a3 |
1612.1-a |
$5$ |
$9$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
1612.1 |
\( 2^{2} \cdot 13 \cdot 31 \) |
\( 2^{6} \cdot 13^{3} \cdot 31^{3} \) |
$0.98071$ |
$(-4a+1), (-6a+1), (2)$ |
0 |
$\Z/3\Z\oplus\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3Cs.1.1[2] |
$1$ |
\( 3^{3} \) |
$1$ |
$2.125838984$ |
0.818235806 |
\( -\frac{312668878725}{261803308} a + \frac{1517634305173}{523606616} \) |
\( \bigl[1\) , \( a + 1\) , \( a + 1\) , \( 10 a - 13\) , \( 14 a - 15\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(10a-13\right){x}+14a-15$ |
| 1612.4-a3 |
1612.4-a |
$5$ |
$9$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
1612.4 |
\( 2^{2} \cdot 13 \cdot 31 \) |
\( 2^{6} \cdot 13^{3} \cdot 31^{3} \) |
$0.98071$ |
$(4a-3), (6a-5), (2)$ |
0 |
$\Z/3\Z\oplus\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3Cs.1.1[2] |
$1$ |
\( 3^{3} \) |
$1$ |
$2.125838984$ |
0.818235806 |
\( \frac{312668878725}{261803308} a + \frac{892296547723}{523606616} \) |
\( \bigl[a\) , \( -a - 1\) , \( 1\) , \( 13 a - 9\) , \( -18 a + 12\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(13a-9\right){x}-18a+12$ |
| 2268.1-a1 |
2268.1-a |
$5$ |
$9$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
2268.1 |
\( 2^{2} \cdot 3^{4} \cdot 7 \) |
\( 2^{6} \cdot 3^{6} \cdot 7^{3} \) |
$1.06810$ |
$(-2a+1), (-3a+1), (2)$ |
0 |
$\Z/3\Z\oplus\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3Cs.1.1[2] |
$1$ |
\( 3^{3} \) |
$1$ |
$3.432415362$ |
1.321137289 |
\( \frac{1192725}{1372} a - \frac{2098143}{2744} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -3 a\) , \( -3 a + 3\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}-3a{x}-3a+3$ |
| 2268.2-a1 |
2268.2-a |
$5$ |
$9$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
2268.2 |
\( 2^{2} \cdot 3^{4} \cdot 7 \) |
\( 2^{6} \cdot 3^{6} \cdot 7^{3} \) |
$1.06810$ |
$(-2a+1), (3a-2), (2)$ |
0 |
$\Z/3\Z\oplus\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3Cs.1.1[2] |
$1$ |
\( 3^{3} \) |
$1$ |
$3.432415362$ |
1.321137289 |
\( -\frac{1192725}{1372} a + \frac{287307}{2744} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( 3 a - 3\) , \( 3 a\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}+\left(3a-3\right){x}+3a$ |
| 2457.1-a2 |
2457.1-a |
$5$ |
$9$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
2457.1 |
\( 3^{3} \cdot 7 \cdot 13 \) |
\( 3^{9} \cdot 7^{3} \cdot 13^{3} \) |
$1.08968$ |
$(-2a+1), (-3a+1), (-4a+1)$ |
0 |
$\Z/3\Z\oplus\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3Cs.1.1[2] |
$1$ |
\( 3^{3} \) |
$1$ |
$1.858636986$ |
0.715389709 |
\( \frac{2895052800}{753571} a - \frac{2546368512}{753571} \) |
\( \bigl[0\) , \( 0\) , \( 1\) , \( 18 a - 12\) , \( -30 a + 6\bigr] \) |
${y}^2+{y}={x}^{3}+\left(18a-12\right){x}-30a+6$ |
| 2457.4-a2 |
2457.4-a |
$5$ |
$9$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
2457.4 |
\( 3^{3} \cdot 7 \cdot 13 \) |
\( 3^{9} \cdot 7^{3} \cdot 13^{3} \) |
$1.08968$ |
$(-2a+1), (3a-2), (4a-3)$ |
0 |
$\Z/3\Z\oplus\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3Cs.1.1[2] |
$1$ |
\( 3^{3} \) |
$1$ |
$1.858636986$ |
0.715389709 |
\( -\frac{2895052800}{753571} a + \frac{348684288}{753571} \) |
\( \bigl[0\) , \( 0\) , \( 1\) , \( -18 a + 6\) , \( 30 a - 24\bigr] \) |
${y}^2+{y}={x}^{3}+\left(-18a+6\right){x}+30a-24$ |
| 3969.2-a3 |
3969.2-a |
$5$ |
$9$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
3969.2 |
\( 3^{4} \cdot 7^{2} \) |
\( 3^{6} \cdot 7^{6} \) |
$1.22848$ |
$(-2a+1), (-3a+1), (3a-2)$ |
$1$ |
$\Z/3\Z\oplus\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$3$ |
3Cs.1.1[2] |
$1$ |
\( 3^{3} \) |
$0.621081184$ |
$2.944550565$ |
1.407814708 |
\( \frac{884736}{343} \) |
\( \bigl[0\) , \( 0\) , \( 1\) , \( -6\) , \( 3\bigr] \) |
${y}^2+{y}={x}^{3}-6{x}+3$ |
| 5929.2-b2 |
5929.2-b |
$5$ |
$9$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
5929.2 |
\( 7^{2} \cdot 11^{2} \) |
\( 7^{12} \cdot 11^{6} \) |
$1.35814$ |
$(-3a+1), (3a-2), (11)$ |
0 |
$\Z/3\Z\oplus\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3$ |
3Cs.1.1[2] |
$1$ |
\( 2^{2} \cdot 3^{3} \) |
$1$ |
$0.601329074$ |
0.925806674 |
\( -\frac{13278380032}{156590819} \) |
\( \bigl[0\) , \( a - 1\) , \( 1\) , \( 49 a\) , \( 600\bigr] \) |
${y}^2+{y}={x}^{3}+\left(a-1\right){x}^{2}+49a{x}+600$ |
| 6916.1-b5 |
6916.1-b |
$5$ |
$9$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
6916.1 |
\( 2^{2} \cdot 7 \cdot 13 \cdot 19 \) |
\( 2^{18} \cdot 7^{3} \cdot 13^{3} \cdot 19^{3} \) |
$1.41144$ |
$(-3a+1), (-4a+1), (-5a+3), (2)$ |
$1$ |
$\Z/3\Z\oplus\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3Cs.1.1[2] |
$1$ |
\( 3^{5} \) |
$0.332310098$ |
$0.756668267$ |
1.742086354 |
\( -\frac{133973299354905}{330799583296} a + \frac{3018911930774371}{2646396666368} \) |
\( \bigl[a + 1\) , \( 1\) , \( a + 1\) , \( -72 a + 4\) , \( -147 a - 113\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(-72a+4\right){x}-147a-113$ |
| 6916.8-b5 |
6916.8-b |
$5$ |
$9$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
6916.8 |
\( 2^{2} \cdot 7 \cdot 13 \cdot 19 \) |
\( 2^{18} \cdot 7^{3} \cdot 13^{3} \cdot 19^{3} \) |
$1.41144$ |
$(3a-2), (4a-3), (-5a+2), (2)$ |
$1$ |
$\Z/3\Z\oplus\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3Cs.1.1[2] |
$1$ |
\( 3^{5} \) |
$0.332310098$ |
$0.756668267$ |
1.742086354 |
\( \frac{133973299354905}{330799583296} a + \frac{1947125535935131}{2646396666368} \) |
\( \bigl[a + 1\) , \( a - 1\) , \( a\) , \( -5 a + 71\) , \( 146 a - 259\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-5a+71\right){x}+146a-259$ |
| 8281.5-a3 |
8281.5-a |
$5$ |
$9$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
8281.5 |
\( 7^{2} \cdot 13^{2} \) |
\( 7^{6} \cdot 13^{6} \) |
$1.47645$ |
$(-3a+1), (3a-2), (-4a+1), (4a-3)$ |
$1$ |
$\Z/3\Z\oplus\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3$ |
3Cs.1.1[2] |
$1$ |
\( 3^{4} \) |
$0.353081695$ |
$1.459953528$ |
1.190456688 |
\( \frac{224755712}{753571} \) |
\( \bigl[0\) , \( -a\) , \( 1\) , \( 13 a - 13\) , \( 42\bigr] \) |
${y}^2+{y}={x}^{3}-a{x}^{2}+\left(13a-13\right){x}+42$ |
| 8463.3-b3 |
8463.3-b |
$5$ |
$9$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
8463.3 |
\( 3 \cdot 7 \cdot 13 \cdot 31 \) |
\( 3^{3} \cdot 7^{6} \cdot 13^{3} \cdot 31^{3} \) |
$1.48450$ |
$(-2a+1), (-3a+1), (4a-3), (-6a+1)$ |
$1$ |
$\Z/3\Z\oplus\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3Cs.1.1[2] |
$1$ |
\( 2 \cdot 3^{4} \) |
$0.476468865$ |
$0.880502832$ |
1.937736163 |
\( \frac{61621848119705600}{69302019111507} a - \frac{20422185105719296}{69302019111507} \) |
\( \bigl[0\) , \( -a\) , \( 1\) , \( 27 a + 27\) , \( -48 a + 206\bigr] \) |
${y}^2+{y}={x}^{3}-a{x}^{2}+\left(27a+27\right){x}-48a+206$ |
| 8463.6-b3 |
8463.6-b |
$5$ |
$9$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
8463.6 |
\( 3 \cdot 7 \cdot 13 \cdot 31 \) |
\( 3^{3} \cdot 7^{6} \cdot 13^{3} \cdot 31^{3} \) |
$1.48450$ |
$(-2a+1), (3a-2), (-4a+1), (6a-5)$ |
$1$ |
$\Z/3\Z\oplus\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3Cs.1.1[2] |
$1$ |
\( 2 \cdot 3^{4} \) |
$0.476468865$ |
$0.880502832$ |
1.937736163 |
\( -\frac{61621848119705600}{69302019111507} a + \frac{41199663013986304}{69302019111507} \) |
\( \bigl[0\) , \( -a\) , \( 1\) , \( -27 a - 27\) , \( 48 a + 158\bigr] \) |
${y}^2+{y}={x}^{3}-a{x}^{2}+\left(-27a-27\right){x}+48a+158$ |
| 9100.2-b2 |
9100.2-b |
$5$ |
$9$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
9100.2 |
\( 2^{2} \cdot 5^{2} \cdot 7 \cdot 13 \) |
\( 2^{6} \cdot 5^{6} \cdot 7^{3} \cdot 13^{3} \) |
$1.51168$ |
$(-3a+1), (4a-3), (2), (5)$ |
$1$ |
$\Z/3\Z\oplus\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3Cs.1.1[2] |
$1$ |
\( 3^{4} \) |
$0.580444204$ |
$1.397012090$ |
1.872664632 |
\( \frac{21985425981}{75357100} a - \frac{685267624981}{753571000} \) |
\( \bigl[a\) , \( -a - 1\) , \( 1\) , \( -18 a\) , \( -50 a + 31\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+\left(-a-1\right){x}^{2}-18a{x}-50a+31$ |
| 9100.3-b2 |
9100.3-b |
$5$ |
$9$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
9100.3 |
\( 2^{2} \cdot 5^{2} \cdot 7 \cdot 13 \) |
\( 2^{6} \cdot 5^{6} \cdot 7^{3} \cdot 13^{3} \) |
$1.51168$ |
$(3a-2), (-4a+1), (2), (5)$ |
$1$ |
$\Z/3\Z\oplus\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3Cs.1.1[2] |
$1$ |
\( 3^{4} \) |
$0.580444204$ |
$1.397012090$ |
1.872664632 |
\( -\frac{21985425981}{75357100} a - \frac{465413365171}{753571000} \) |
\( \bigl[1\) , \( a + 1\) , \( a + 1\) , \( a + 18\) , \( 68 a - 19\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(a+18\right){x}+68a-19$ |
| 13588.1-b2 |
13588.1-b |
$5$ |
$9$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
13588.1 |
\( 2^{2} \cdot 43 \cdot 79 \) |
\( 2^{12} \cdot 43^{3} \cdot 79^{3} \) |
$1.67104$ |
$(-7a+1), (10a-7), (2)$ |
0 |
$\Z/3\Z\oplus\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3Cs.1.1[2] |
$1$ |
\( 2 \cdot 3^{3} \) |
$1$ |
$0.908927007$ |
0.699692336 |
\( -\frac{235980861541425}{627200828368} a + \frac{820884881398841}{2508803313472} \) |
\( \bigl[a + 1\) , \( 1\) , \( a + 1\) , \( 18 a + 21\) , \( -174 a + 73\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(18a+21\right){x}-174a+73$ |
| 13588.4-b2 |
13588.4-b |
$5$ |
$9$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
13588.4 |
\( 2^{2} \cdot 43 \cdot 79 \) |
\( 2^{12} \cdot 43^{3} \cdot 79^{3} \) |
$1.67104$ |
$(7a-6), (10a-3), (2)$ |
0 |
$\Z/3\Z\oplus\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3Cs.1.1[2] |
$1$ |
\( 2 \cdot 3^{3} \) |
$1$ |
$0.908927007$ |
0.699692336 |
\( \frac{235980861541425}{627200828368} a - \frac{123038564766859}{2508803313472} \) |
\( \bigl[a\) , \( -a - 1\) , \( 0\) , \( -18 a + 40\) , \( 192 a - 140\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-18a+40\right){x}+192a-140$ |
| 14364.1-c2 |
14364.1-c |
$5$ |
$9$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
14364.1 |
\( 2^{2} \cdot 3^{3} \cdot 7 \cdot 19 \) |
\( 2^{6} \cdot 3^{9} \cdot 7^{3} \cdot 19^{3} \) |
$1.69441$ |
$(-2a+1), (-3a+1), (-5a+3), (2)$ |
$1$ |
$\Z/3\Z\oplus\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3Cs.1.1[2] |
$1$ |
\( 3^{4} \) |
$0.974358103$ |
$1.271889024$ |
2.861983890 |
\( -\frac{1753015875}{9410548} a + \frac{792457125}{18821096} \) |
\( \bigl[a\) , \( -a + 1\) , \( 0\) , \( -3 a + 15\) , \( 45 a + 27\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-3a+15\right){x}+45a+27$ |
| 14364.4-c3 |
14364.4-c |
$5$ |
$9$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
14364.4 |
\( 2^{2} \cdot 3^{3} \cdot 7 \cdot 19 \) |
\( 2^{6} \cdot 3^{9} \cdot 7^{3} \cdot 19^{3} \) |
$1.69441$ |
$(-2a+1), (3a-2), (-5a+2), (2)$ |
$1$ |
$\Z/3\Z\oplus\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3Cs.1.1[2] |
$1$ |
\( 3^{4} \) |
$0.974358103$ |
$1.271889024$ |
2.861983890 |
\( \frac{1753015875}{9410548} a - \frac{2713574625}{18821096} \) |
\( \bigl[a\) , \( -a + 1\) , \( 0\) , \( 12 a - 15\) , \( -45 a + 72\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(12a-15\right){x}-45a+72$ |
| 15876.2-c2 |
15876.2-c |
$5$ |
$9$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
15876.2 |
\( 2^{2} \cdot 3^{4} \cdot 7^{2} \) |
\( 2^{12} \cdot 3^{6} \cdot 7^{6} \) |
$1.73734$ |
$(-2a+1), (-3a+1), (3a-2), (2)$ |
$1$ |
$\Z/3\Z\oplus\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$3$ |
3Cs.1.1[2] |
$1$ |
\( 2 \cdot 3^{4} \) |
$0.434324480$ |
$1.513949445$ |
3.037071679 |
\( -\frac{5000211}{21952} \) |
\( \bigl[a\) , \( -a + 1\) , \( 1\) , \( 10 a\) , \( -37\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+\left(-a+1\right){x}^{2}+10a{x}-37$ |
| 15876.2-d3 |
15876.2-d |
$5$ |
$9$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
15876.2 |
\( 2^{2} \cdot 3^{4} \cdot 7^{2} \) |
\( 2^{6} \cdot 3^{6} \cdot 7^{6} \) |
$1.73734$ |
$(-2a+1), (-3a+1), (3a-2), (2)$ |
0 |
$\Z/3\Z\oplus\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$3$ |
3Cs.1.1[2] |
$1$ |
\( 3^{4} \) |
$1$ |
$2.035709838$ |
2.350635247 |
\( -\frac{7414875}{2744} \) |
\( \bigl[a\) , \( -a + 1\) , \( 0\) , \( 12 a\) , \( 24\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+12a{x}+24$ |
| 18300.1-b5 |
18300.1-b |
$5$ |
$9$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
18300.1 |
\( 2^{2} \cdot 3 \cdot 5^{2} \cdot 61 \) |
\( 2^{12} \cdot 3^{3} \cdot 5^{6} \cdot 61^{3} \) |
$1.80016$ |
$(-2a+1), (-9a+5), (2), (5)$ |
$1$ |
$\Z/3\Z\oplus\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3Cs.1.1[2] |
$1$ |
\( 2 \cdot 3^{4} \) |
$0.876154868$ |
$0.836535135$ |
3.385278671 |
\( \frac{4114651446451}{8171316000} a + \frac{15343684459019}{16342632000} \) |
\( \bigl[1\) , \( -a - 1\) , \( a + 1\) , \( 54 a - 67\) , \( -48 a + 185\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(54a-67\right){x}-48a+185$ |
| 18300.2-b5 |
18300.2-b |
$5$ |
$9$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
18300.2 |
\( 2^{2} \cdot 3 \cdot 5^{2} \cdot 61 \) |
\( 2^{12} \cdot 3^{3} \cdot 5^{6} \cdot 61^{3} \) |
$1.80016$ |
$(-2a+1), (-9a+4), (2), (5)$ |
$1$ |
$\Z/3\Z\oplus\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3Cs.1.1[2] |
$1$ |
\( 2 \cdot 3^{4} \) |
$0.876154868$ |
$0.836535135$ |
3.385278671 |
\( -\frac{4114651446451}{8171316000} a + \frac{23572987351921}{16342632000} \) |
\( \bigl[a + 1\) , \( 1\) , \( a\) , \( -13 a + 67\) , \( 47 a + 138\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+{x}^{2}+\left(-13a+67\right){x}+47a+138$ |
| 18361.2-a2 |
18361.2-a |
$5$ |
$9$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
18361.2 |
\( 7 \cdot 43 \cdot 61 \) |
\( 7^{3} \cdot 43^{3} \cdot 61^{3} \) |
$1.80166$ |
$(-3a+1), (-7a+1), (-9a+4)$ |
0 |
$\Z/3\Z\oplus\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3Cs.1.1[2] |
$1$ |
\( 3^{3} \) |
$1$ |
$1.155799752$ |
0.444867532 |
\( \frac{13628440248975360}{6189976379881} a - \frac{3666319632990208}{6189976379881} \) |
\( \bigl[0\) , \( 1\) , \( 1\) , \( -40 a + 13\) , \( 50 a - 95\bigr] \) |
${y}^2+{y}={x}^{3}+{x}^{2}+\left(-40a+13\right){x}+50a-95$ |
| 18361.7-a4 |
18361.7-a |
$5$ |
$9$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
18361.7 |
\( 7 \cdot 43 \cdot 61 \) |
\( 7^{3} \cdot 43^{3} \cdot 61^{3} \) |
$1.80166$ |
$(3a-2), (7a-6), (-9a+5)$ |
0 |
$\Z/3\Z\oplus\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3Cs.1.1[2] |
$1$ |
\( 3^{3} \) |
$1$ |
$1.155799752$ |
0.444867532 |
\( -\frac{13628440248975360}{6189976379881} a + \frac{9962120615985152}{6189976379881} \) |
\( \bigl[0\) , \( -a\) , \( 1\) , \( -27 a - 13\) , \( -50 a - 45\bigr] \) |
${y}^2+{y}={x}^{3}-a{x}^{2}+\left(-27a-13\right){x}-50a-45$ |
| 18900.1-b4 |
18900.1-b |
$5$ |
$9$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
18900.1 |
\( 2^{2} \cdot 3^{3} \cdot 5^{2} \cdot 7 \) |
\( 2^{18} \cdot 3^{9} \cdot 5^{6} \cdot 7^{6} \) |
$1.81474$ |
$(-2a+1), (-3a+1), (2), (5)$ |
$1$ |
$\Z/3\Z\oplus\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3Cs.1.1[2] |
$1$ |
\( 2 \cdot 3^{5} \) |
$0.619900916$ |
$0.355978607$ |
3.057713517 |
\( \frac{5300081186829}{3764768000} a + \frac{4786104045711}{7529536000} \) |
\( \bigl[a\) , \( -a + 1\) , \( 0\) , \( -423 a + 162\) , \( 1032 a - 2703\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-423a+162\right){x}+1032a-2703$ |
| 18900.2-b4 |
18900.2-b |
$5$ |
$9$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
18900.2 |
\( 2^{2} \cdot 3^{3} \cdot 5^{2} \cdot 7 \) |
\( 2^{18} \cdot 3^{9} \cdot 5^{6} \cdot 7^{6} \) |
$1.81474$ |
$(-2a+1), (3a-2), (2), (5)$ |
$1$ |
$\Z/3\Z\oplus\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3Cs.1.1[2] |
$1$ |
\( 2 \cdot 3^{5} \) |
$0.619900916$ |
$0.355978607$ |
3.057713517 |
\( -\frac{5300081186829}{3764768000} a + \frac{15386266419369}{7529536000} \) |
\( \bigl[a\) , \( -a + 1\) , \( 0\) , \( -261 a - 162\) , \( -1032 a - 1671\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-261a-162\right){x}-1032a-1671$ |
| 19929.3-b1 |
19929.3-b |
$5$ |
$9$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
19929.3 |
\( 3 \cdot 7 \cdot 13 \cdot 73 \) |
\( 3^{3} \cdot 7^{3} \cdot 13^{3} \cdot 73^{3} \) |
$1.83895$ |
$(-2a+1), (-3a+1), (4a-3), (-9a+1)$ |
$1$ |
$\Z/3\Z\oplus\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3Cs.1.1[2] |
$1$ |
\( 3^{4} \) |
$1.151421976$ |
$0.891596343$ |
2.370839514 |
\( \frac{307733452619776000}{2638367367363} a - \frac{203804074999808000}{2638367367363} \) |
\( \bigl[0\) , \( -a\) , \( 1\) , \( -113 a + 153\) , \( 260 a + 402\bigr] \) |
${y}^2+{y}={x}^{3}-a{x}^{2}+\left(-113a+153\right){x}+260a+402$ |
| 19929.6-b4 |
19929.6-b |
$5$ |
$9$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
19929.6 |
\( 3 \cdot 7 \cdot 13 \cdot 73 \) |
\( 3^{3} \cdot 7^{3} \cdot 13^{3} \cdot 73^{3} \) |
$1.83895$ |
$(-2a+1), (3a-2), (-4a+1), (9a-8)$ |
$1$ |
$\Z/3\Z\oplus\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3Cs.1.1[2] |
$1$ |
\( 3^{4} \) |
$1.151421976$ |
$0.891596343$ |
2.370839514 |
\( -\frac{307733452619776000}{2638367367363} a + \frac{103929377619968000}{2638367367363} \) |
\( \bigl[0\) , \( a - 1\) , \( 1\) , \( 113 a + 40\) , \( -260 a + 662\bigr] \) |
${y}^2+{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(113a+40\right){x}-260a+662$ |
*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.
