| 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 |
| 2.1-a1 |
2.1-a |
$2$ |
$5$ |
3.3.892.1 |
$3$ |
$[3, 0]$ |
2.1 |
\( 2 \) |
\( 2^{5} \) |
$2.99566$ |
$(a-2)$ |
0 |
$\Z/5\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.1.1 |
$1$ |
\( 5 \) |
$1$ |
$146.8894024$ |
0.983644193 |
\( -\frac{3083}{8} a^{2} - \frac{985}{8} a + \frac{11681}{4} \) |
\( \bigl[a^{2} + 2 a - 5\) , \( -a + 1\) , \( a^{2} + a - 5\) , \( 2 a^{2} - a - 10\) , \( -480 a^{2} - 769 a + 1847\bigr] \) |
${y}^2+\left(a^{2}+2a-5\right){x}{y}+\left(a^{2}+a-5\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(2a^{2}-a-10\right){x}-480a^{2}-769a+1847$ |
| 2.1-a2 |
2.1-a |
$2$ |
$5$ |
3.3.892.1 |
$3$ |
$[3, 0]$ |
2.1 |
\( 2 \) |
\( 2 \) |
$2.99566$ |
$(a-2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.1.2 |
$25$ |
\( 1 \) |
$1$ |
$1.175115219$ |
0.983644193 |
\( -\frac{761870922662501}{2} a^{2} - \frac{243853170706247}{2} a + 2886278452756999 \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( 1\) , \( 1518 a^{2} + 495 a - 11532\) , \( 52607 a^{2} + 16858 a - 398797\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(1518a^{2}+495a-11532\right){x}+52607a^{2}+16858a-398797$ |
| 2.1-b1 |
2.1-b |
$2$ |
$5$ |
3.3.892.1 |
$3$ |
$[3, 0]$ |
2.1 |
\( 2 \) |
\( 2^{5} \) |
$2.99566$ |
$(a-2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.4.1 |
$1$ |
\( 1 \) |
$0.018682772$ |
$290.9640609$ |
0.546033783 |
\( -\frac{3083}{8} a^{2} - \frac{985}{8} a + \frac{11681}{4} \) |
\( \bigl[a^{2} + 2 a - 5\) , \( -a^{2} - a + 5\) , \( a\) , \( -57765 a^{2} - 92292 a + 222367\) , \( 1337081588 a^{2} + 2136302303 a - 5147105041\bigr] \) |
${y}^2+\left(a^{2}+2a-5\right){x}{y}+a{y}={x}^{3}+\left(-a^{2}-a+5\right){x}^{2}+\left(-57765a^{2}-92292a+222367\right){x}+1337081588a^{2}+2136302303a-5147105041$ |
| 2.1-b2 |
2.1-b |
$2$ |
$5$ |
3.3.892.1 |
$3$ |
$[3, 0]$ |
2.1 |
\( 2 \) |
\( 2 \) |
$2.99566$ |
$(a-2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.4.2 |
$1$ |
\( 1 \) |
$0.093413864$ |
$58.19281218$ |
0.546033783 |
\( -\frac{761870922662501}{2} a^{2} - \frac{243853170706247}{2} a + 2886278452756999 \) |
\( \bigl[a + 1\) , \( a^{2} + 2 a - 7\) , \( a^{2} + 2 a - 6\) , \( -1564 a^{2} - 2503 a + 6008\) , \( 59225 a^{2} + 94637 a - 227958\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{2}+2a-6\right){y}={x}^{3}+\left(a^{2}+2a-7\right){x}^{2}+\left(-1564a^{2}-2503a+6008\right){x}+59225a^{2}+94637a-227958$ |
| 4.1-a1 |
4.1-a |
$2$ |
$2$ |
3.3.892.1 |
$3$ |
$[3, 0]$ |
4.1 |
\( 2^{2} \) |
\( 2^{8} \) |
$3.36252$ |
$(a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$226.8609389$ |
1.898966514 |
\( -2075 a^{2} - 7258 a + 13138 \) |
\( \bigl[a^{2} + 2 a - 6\) , \( 0\) , \( a^{2} + 2 a - 6\) , \( a^{2} + 6 a - 14\) , \( -2 a^{2} + 12 a - 1\bigr] \) |
${y}^2+\left(a^{2}+2a-6\right){x}{y}+\left(a^{2}+2a-6\right){y}={x}^{3}+\left(a^{2}+6a-14\right){x}-2a^{2}+12a-1$ |
| 4.1-a2 |
4.1-a |
$2$ |
$2$ |
3.3.892.1 |
$3$ |
$[3, 0]$ |
4.1 |
\( 2^{2} \) |
\( - 2^{4} \) |
$3.36252$ |
$(a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$226.8609389$ |
1.898966514 |
\( 59305979 a^{2} + 94806042 a - 228150562 \) |
\( \bigl[a\) , \( a - 1\) , \( a\) , \( 89 a^{2} + 29 a - 676\) , \( -727 a^{2} - 232 a + 5508\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(89a^{2}+29a-676\right){x}-727a^{2}-232a+5508$ |
| 4.1-b1 |
4.1-b |
$2$ |
$2$ |
3.3.892.1 |
$3$ |
$[3, 0]$ |
4.1 |
\( 2^{2} \) |
\( 2^{8} \) |
$3.36252$ |
$(a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 3 \) |
$1$ |
$36.75021483$ |
0.922866153 |
\( -2075 a^{2} - 7258 a + 13138 \) |
\( \bigl[a^{2} + 2 a - 6\) , \( -a^{2} - 2 a + 6\) , \( 0\) , \( -6 a^{2} - 12 a + 28\) , \( -24 a^{2} - 40 a + 95\bigr] \) |
${y}^2+\left(a^{2}+2a-6\right){x}{y}={x}^{3}+\left(-a^{2}-2a+6\right){x}^{2}+\left(-6a^{2}-12a+28\right){x}-24a^{2}-40a+95$ |
| 4.1-b2 |
4.1-b |
$2$ |
$2$ |
3.3.892.1 |
$3$ |
$[3, 0]$ |
4.1 |
\( 2^{2} \) |
\( - 2^{4} \) |
$3.36252$ |
$(a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 3 \) |
$1$ |
$36.75021483$ |
0.922866153 |
\( 59305979 a^{2} + 94806042 a - 228150562 \) |
\( \bigl[a\) , \( 1\) , \( a^{2} + a - 6\) , \( -836 a^{2} - 1336 a + 3220\) , \( -25431 a^{2} - 40633 a + 97895\bigr] \) |
${y}^2+a{x}{y}+\left(a^{2}+a-6\right){y}={x}^{3}+{x}^{2}+\left(-836a^{2}-1336a+3220\right){x}-25431a^{2}-40633a+97895$ |
| 5.1-a1 |
5.1-a |
$8$ |
$16$ |
3.3.892.1 |
$3$ |
$[3, 0]$ |
5.1 |
\( 5 \) |
\( 5^{2} \) |
$3.48992$ |
$(a^2+a-5)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2 \) |
$0.826660025$ |
$138.8373781$ |
1.441060391 |
\( \frac{4398708}{25} a^{2} - \frac{62624348}{25} a + \frac{133247801}{25} \) |
\( \bigl[a^{2} + a - 5\) , \( a^{2} + 2 a - 5\) , \( 0\) , \( -129798166664250 a^{2} - 207383098232791 a + 499658961613567\) , \( -1374335792494585709419 a^{2} - 2195824655959840595046 a + 5290515364230784327508\bigr] \) |
${y}^2+\left(a^{2}+a-5\right){x}{y}={x}^{3}+\left(a^{2}+2a-5\right){x}^{2}+\left(-129798166664250a^{2}-207383098232791a+499658961613567\right){x}-1374335792494585709419a^{2}-2195824655959840595046a+5290515364230784327508$ |
| 5.1-a2 |
5.1-a |
$8$ |
$16$ |
3.3.892.1 |
$3$ |
$[3, 0]$ |
5.1 |
\( 5 \) |
\( -5 \) |
$3.48992$ |
$(a^2+a-5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1.653320051$ |
$34.70934454$ |
1.441060391 |
\( \frac{42749498492312}{5} a^{2} - \frac{167461678612022}{5} a + \frac{146538153567389}{5} \) |
\( \bigl[a^{2} + a - 5\) , \( a^{2} + 2 a - 5\) , \( 0\) , \( -2024077354959430 a^{2} - 3233939613493261 a + 7791700109452442\) , \( -93058221449899116507021 a^{2} - 148682394954262530152214 a + 358228282372716828738153\bigr] \) |
${y}^2+\left(a^{2}+a-5\right){x}{y}={x}^{3}+\left(a^{2}+2a-5\right){x}^{2}+\left(-2024077354959430a^{2}-3233939613493261a+7791700109452442\right){x}-93058221449899116507021a^{2}-148682394954262530152214a+358228282372716828738153$ |
| 5.1-a3 |
5.1-a |
$8$ |
$16$ |
3.3.892.1 |
$3$ |
$[3, 0]$ |
5.1 |
\( 5 \) |
\( - 5^{2} \) |
$3.48992$ |
$(a^2+a-5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.206665006$ |
$138.8373781$ |
1.441060391 |
\( -\frac{3858}{25} a^{2} - \frac{2252}{25} a + \frac{40149}{25} \) |
\( \bigl[a^{2} + a - 5\) , \( a\) , \( 1\) , \( 2 a^{2} + 2 a - 3\) , \( 2 a^{2} + 3 a - 7\bigr] \) |
${y}^2+\left(a^{2}+a-5\right){x}{y}+{y}={x}^{3}+a{x}^{2}+\left(2a^{2}+2a-3\right){x}+2a^{2}+3a-7$ |
| 5.1-a4 |
5.1-a |
$8$ |
$16$ |
3.3.892.1 |
$3$ |
$[3, 0]$ |
5.1 |
\( 5 \) |
\( 5 \) |
$3.48992$ |
$(a^2+a-5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1.653320051$ |
$34.70934454$ |
1.441060391 |
\( -\frac{5012803179592}{5} a^{2} - \frac{1601845288298}{5} a + \frac{37988709186451}{5} \) |
\( \bigl[1\) , \( a - 1\) , \( a^{2} + a - 6\) , \( 9783986859018290079610 a^{2} + 15632220084746192480028 a - 37663526689582508074417\) , \( -3156073681547054786639749459260789 a^{2} - 5042569977303615210019300385785809 a + 12149327983783038214001365910381766\bigr] \) |
${y}^2+{x}{y}+\left(a^{2}+a-6\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(9783986859018290079610a^{2}+15632220084746192480028a-37663526689582508074417\right){x}-3156073681547054786639749459260789a^{2}-5042569977303615210019300385785809a+12149327983783038214001365910381766$ |
| 5.1-a5 |
5.1-a |
$8$ |
$16$ |
3.3.892.1 |
$3$ |
$[3, 0]$ |
5.1 |
\( 5 \) |
\( 5^{4} \) |
$3.48992$ |
$(a^2+a-5)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2 \) |
$0.413330012$ |
$277.6747563$ |
1.441060391 |
\( \frac{418328}{625} a^{2} + \frac{351432}{625} a + \frac{313441}{625} \) |
\( \bigl[1\) , \( -a^{2} - 2 a + 7\) , \( 0\) , \( -486309 a^{2} - 776994 a + 1872054\) , \( 297534897 a^{2} + 475381974 a - 1145362691\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(-a^{2}-2a+7\right){x}^{2}+\left(-486309a^{2}-776994a+1872054\right){x}+297534897a^{2}+475381974a-1145362691$ |
| 5.1-a6 |
5.1-a |
$8$ |
$16$ |
3.3.892.1 |
$3$ |
$[3, 0]$ |
5.1 |
\( 5 \) |
\( 5^{16} \) |
$3.48992$ |
$(a^2+a-5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1.653320051$ |
$17.35467227$ |
1.441060391 |
\( \frac{1399168804199214273}{152587890625} a^{2} - \frac{5481540016848311363}{152587890625} a + \frac{4796917779129304481}{152587890625} \) |
\( \bigl[1\) , \( -a^{2} - 2 a + 7\) , \( 0\) , \( -7152204 a^{2} - 11427329 a + 27532464\) , \( 22691674660 a^{2} + 36255287081 a - 87351762271\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(-a^{2}-2a+7\right){x}^{2}+\left(-7152204a^{2}-11427329a+27532464\right){x}+22691674660a^{2}+36255287081a-87351762271$ |
| 5.1-a7 |
5.1-a |
$8$ |
$16$ |
3.3.892.1 |
$3$ |
$[3, 0]$ |
5.1 |
\( 5 \) |
\( 5^{8} \) |
$3.48992$ |
$(a^2+a-5)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2 \) |
$0.826660025$ |
$138.8373781$ |
1.441060391 |
\( \frac{1797044704318}{390625} a^{2} + \frac{2874240159992}{390625} a - \frac{6902857908029}{390625} \) |
\( \bigl[1\) , \( -a^{2} - 2 a + 7\) , \( 0\) , \( -7466139 a^{2} - 11928914 a + 28740959\) , \( 20859042361 a^{2} + 33327225970 a - 80297031260\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(-a^{2}-2a+7\right){x}^{2}+\left(-7466139a^{2}-11928914a+28740959\right){x}+20859042361a^{2}+33327225970a-80297031260$ |
| 5.1-a8 |
5.1-a |
$8$ |
$16$ |
3.3.892.1 |
$3$ |
$[3, 0]$ |
5.1 |
\( 5 \) |
\( - 5^{4} \) |
$3.48992$ |
$(a^2+a-5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.413330012$ |
$69.41868909$ |
1.441060391 |
\( \frac{93574452060156047}{625} a^{2} + \frac{149507529072655443}{625} a - \frac{360214540492333441}{625} \) |
\( \bigl[1\) , \( -a^{2} - 2 a + 7\) , \( 0\) , \( -119457354 a^{2} - 190861219 a + 459851934\) , \( 1334438708278 a^{2} + 2132079680603 a - 5136931256045\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(-a^{2}-2a+7\right){x}^{2}+\left(-119457354a^{2}-190861219a+459851934\right){x}+1334438708278a^{2}+2132079680603a-5136931256045$ |
| 5.1-b1 |
5.1-b |
$8$ |
$16$ |
3.3.892.1 |
$3$ |
$[3, 0]$ |
5.1 |
\( 5 \) |
\( - 5^{2} \) |
$3.48992$ |
$(a^2+a-5)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$117.6868401$ |
0.492555857 |
\( -\frac{3858}{25} a^{2} - \frac{2252}{25} a + \frac{40149}{25} \) |
\( \bigl[a^{2} + a - 5\) , \( a^{2} - 6\) , \( a^{2} + 2 a - 6\) , \( 155895136906135 a^{2} + 249079145891543 a - 600119433340020\) , \( -4089790274014076705435 a^{2} - 6534401832818627786248 a + 15743676617691191434521\bigr] \) |
${y}^2+\left(a^{2}+a-5\right){x}{y}+\left(a^{2}+2a-6\right){y}={x}^{3}+\left(a^{2}-6\right){x}^{2}+\left(155895136906135a^{2}+249079145891543a-600119433340020\right){x}-4089790274014076705435a^{2}-6534401832818627786248a+15743676617691191434521$ |
| 5.1-b2 |
5.1-b |
$8$ |
$16$ |
3.3.892.1 |
$3$ |
$[3, 0]$ |
5.1 |
\( 5 \) |
\( 5^{2} \) |
$3.48992$ |
$(a^2+a-5)$ |
0 |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2 \) |
$1$ |
$470.7473605$ |
0.492555857 |
\( \frac{4398708}{25} a^{2} - \frac{62624348}{25} a + \frac{133247801}{25} \) |
\( \bigl[a^{2} + a - 5\) , \( -a^{2} - 2 a + 5\) , \( a + 1\) , \( -389317636341003297734 a^{2} - 622026486937288823086 a + 1498680997669065213653\) , \( 7139141291657151563394586623098 a^{2} + 11406457254633070112341076130734 a - 27482174951123063157492163719508\bigr] \) |
${y}^2+\left(a^{2}+a-5\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a^{2}-2a+5\right){x}^{2}+\left(-389317636341003297734a^{2}-622026486937288823086a+1498680997669065213653\right){x}+7139141291657151563394586623098a^{2}+11406457254633070112341076130734a-27482174951123063157492163719508$ |
| 5.1-b3 |
5.1-b |
$8$ |
$16$ |
3.3.892.1 |
$3$ |
$[3, 0]$ |
5.1 |
\( 5 \) |
\( -5 \) |
$3.48992$ |
$(a^2+a-5)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$235.3736802$ |
0.492555857 |
\( \frac{42749498492312}{5} a^{2} - \frac{167461678612022}{5} a + \frac{146538153567389}{5} \) |
\( \bigl[a^{2} + a - 5\) , \( -a^{2} - 2 a + 5\) , \( a + 1\) , \( -6071033450283375466954 a^{2} - 9699903771764494043076 a + 23370486252987376836728\) , \( 483401496695624141075812337184719 a^{2} + 772347581259928958778422398634482 a - 1860857484267573175652313639731448\bigr] \) |
${y}^2+\left(a^{2}+a-5\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a^{2}-2a+5\right){x}^{2}+\left(-6071033450283375466954a^{2}-9699903771764494043076a+23370486252987376836728\right){x}+483401496695624141075812337184719a^{2}+772347581259928958778422398634482a-1860857484267573175652313639731448$ |
| 5.1-b4 |
5.1-b |
$8$ |
$16$ |
3.3.892.1 |
$3$ |
$[3, 0]$ |
5.1 |
\( 5 \) |
\( 5^{16} \) |
$3.48992$ |
$(a^2+a-5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$3.677713754$ |
0.492555857 |
\( \frac{1399168804199214273}{152587890625} a^{2} - \frac{5481540016848311363}{152587890625} a + \frac{4796917779129304481}{152587890625} \) |
\( \bigl[1\) , \( a - 1\) , \( a + 1\) , \( -359 a^{2} - 575 a + 1383\) , \( -8295 a^{2} - 13255 a + 31924\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-359a^{2}-575a+1383\right){x}-8295a^{2}-13255a+31924$ |
| 5.1-b5 |
5.1-b |
$8$ |
$16$ |
3.3.892.1 |
$3$ |
$[3, 0]$ |
5.1 |
\( 5 \) |
\( 5^{8} \) |
$3.48992$ |
$(a^2+a-5)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1$ |
$29.42171003$ |
0.492555857 |
\( \frac{1797044704318}{390625} a^{2} + \frac{2874240159992}{390625} a - \frac{6902857908029}{390625} \) |
\( \bigl[1\) , \( a - 1\) , \( a + 1\) , \( -374 a^{2} - 600 a + 1438\) , \( -7653 a^{2} - 12228 a + 29456\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-374a^{2}-600a+1438\right){x}-7653a^{2}-12228a+29456$ |
| 5.1-b6 |
5.1-b |
$8$ |
$16$ |
3.3.892.1 |
$3$ |
$[3, 0]$ |
5.1 |
\( 5 \) |
\( - 5^{4} \) |
$3.48992$ |
$(a^2+a-5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 2^{2} \) |
$1$ |
$3.677713754$ |
0.492555857 |
\( \frac{93574452060156047}{625} a^{2} + \frac{149507529072655443}{625} a - \frac{360214540492333441}{625} \) |
\( \bigl[1\) , \( a - 1\) , \( a + 1\) , \( -5989 a^{2} - 9585 a + 23013\) , \( -478699 a^{2} - 764881 a + 1842616\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-5989a^{2}-9585a+23013\right){x}-478699a^{2}-764881a+1842616$ |
| 5.1-b7 |
5.1-b |
$8$ |
$16$ |
3.3.892.1 |
$3$ |
$[3, 0]$ |
5.1 |
\( 5 \) |
\( 5^{4} \) |
$3.48992$ |
$(a^2+a-5)$ |
0 |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$1$ |
$235.3736802$ |
0.492555857 |
\( \frac{418328}{625} a^{2} + \frac{351432}{625} a + \frac{313441}{625} \) |
\( \bigl[1\) , \( -a\) , \( a\) , \( -1458641518599 a^{2} - 2330522881118 a + 5615050853800\) , \( -1541625400901361115 a^{2} - 2463109149917972896 a + 5934497896291400345\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}-a{x}^{2}+\left(-1458641518599a^{2}-2330522881118a+5615050853800\right){x}-1541625400901361115a^{2}-2463109149917972896a+5934497896291400345$ |
| 5.1-b8 |
5.1-b |
$8$ |
$16$ |
3.3.892.1 |
$3$ |
$[3, 0]$ |
5.1 |
\( 5 \) |
\( 5 \) |
$3.48992$ |
$(a^2+a-5)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$235.3736802$ |
0.492555857 |
\( -\frac{5012803179592}{5} a^{2} - \frac{1601845288298}{5} a + \frac{37988709186451}{5} \) |
\( \bigl[1\) , \( a\) , \( a\) , \( 29346166712795123540797378921 a^{2} + 46887403193435595820781052839 a - 112968276547256011963526055660\) , \( 16394584450421436435406416294990975532748117 a^{2} + 26194204471024883094100890431965395635911578 a - 63111068924209379891898546390017950437821265\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+a{x}^{2}+\left(29346166712795123540797378921a^{2}+46887403193435595820781052839a-112968276547256011963526055660\right){x}+16394584450421436435406416294990975532748117a^{2}+26194204471024883094100890431965395635911578a-63111068924209379891898546390017950437821265$ |
| 8.1-a1 |
8.1-a |
$4$ |
$6$ |
3.3.892.1 |
$3$ |
$[3, 0]$ |
8.1 |
\( 2^{3} \) |
\( 2^{12} \) |
$3.77430$ |
$(a-2), (-a^2+7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$1$ |
$79.20837236$ |
1.326046233 |
\( \frac{37445}{16} a^{2} + \frac{2163}{8} a - \frac{137335}{8} \) |
\( \bigl[a^{2} + 2 a - 6\) , \( -a^{2} - a + 6\) , \( a^{2} + 2 a - 6\) , \( 31 a^{2} + 12 a - 248\) , \( 223 a^{2} + 76 a - 1705\bigr] \) |
${y}^2+\left(a^{2}+2a-6\right){x}{y}+\left(a^{2}+2a-6\right){y}={x}^{3}+\left(-a^{2}-a+6\right){x}^{2}+\left(31a^{2}+12a-248\right){x}+223a^{2}+76a-1705$ |
| 8.1-a2 |
8.1-a |
$4$ |
$6$ |
3.3.892.1 |
$3$ |
$[3, 0]$ |
8.1 |
\( 2^{3} \) |
\( 2^{20} \) |
$3.77430$ |
$(a-2), (-a^2+7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$26.40279078$ |
1.326046233 |
\( -\frac{1026781951835}{4096} a^{2} - \frac{1300707728621}{2048} a + \frac{2610277187945}{2048} \) |
\( \bigl[a^{2} + 2 a - 6\) , \( -a^{2} - a + 6\) , \( a^{2} + 2 a - 6\) , \( -244 a^{2} + 122 a + 1322\) , \( -811 a^{2} + 2528 a - 1097\bigr] \) |
${y}^2+\left(a^{2}+2a-6\right){x}{y}+\left(a^{2}+2a-6\right){y}={x}^{3}+\left(-a^{2}-a+6\right){x}^{2}+\left(-244a^{2}+122a+1322\right){x}-811a^{2}+2528a-1097$ |
| 8.1-a3 |
8.1-a |
$4$ |
$6$ |
3.3.892.1 |
$3$ |
$[3, 0]$ |
8.1 |
\( 2^{3} \) |
\( - 2^{10} \) |
$3.77430$ |
$(a-2), (-a^2+7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$26.40279078$ |
1.326046233 |
\( \frac{38787877956078973283}{64} a^{2} + \frac{30986378741444154789}{32} a - \frac{74657105415288647105}{32} \) |
\( \bigl[a\) , \( -a^{2} + 7\) , \( a^{2} + 2 a - 6\) , \( 3634 a^{2} + 1161 a - 27547\) , \( 13434 a^{2} + 4292 a - 101814\bigr] \) |
${y}^2+a{x}{y}+\left(a^{2}+2a-6\right){y}={x}^{3}+\left(-a^{2}+7\right){x}^{2}+\left(3634a^{2}+1161a-27547\right){x}+13434a^{2}+4292a-101814$ |
| 8.1-a4 |
8.1-a |
$4$ |
$6$ |
3.3.892.1 |
$3$ |
$[3, 0]$ |
8.1 |
\( 2^{3} \) |
\( - 2^{6} \) |
$3.77430$ |
$(a-2), (-a^2+7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$1$ |
$79.20837236$ |
1.326046233 |
\( -\frac{132988941}{4} a^{2} - \frac{20660203}{2} a + \frac{505636335}{2} \) |
\( \bigl[a\) , \( -a^{2} + 7\) , \( a^{2} + 2 a - 6\) , \( 2539 a^{2} + 811 a - 19247\) , \( 119640 a^{2} + 38230 a - 906678\bigr] \) |
${y}^2+a{x}{y}+\left(a^{2}+2a-6\right){y}={x}^{3}+\left(-a^{2}+7\right){x}^{2}+\left(2539a^{2}+811a-19247\right){x}+119640a^{2}+38230a-906678$ |
| 8.1-b1 |
8.1-b |
$4$ |
$6$ |
3.3.892.1 |
$3$ |
$[3, 0]$ |
8.1 |
\( 2^{3} \) |
\( 2^{12} \) |
$3.77430$ |
$(a-2), (-a^2+7)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$105.3317853$ |
0.587794837 |
\( \frac{37445}{16} a^{2} + \frac{2163}{8} a - \frac{137335}{8} \) |
\( \bigl[a^{2} + 2 a - 6\) , \( 0\) , \( a^{2} + 2 a - 6\) , \( a^{2} + 2 a - 6\) , \( a^{2} + 2 a - 5\bigr] \) |
${y}^2+\left(a^{2}+2a-6\right){x}{y}+\left(a^{2}+2a-6\right){y}={x}^{3}+\left(a^{2}+2a-6\right){x}+a^{2}+2a-5$ |
| 8.1-b2 |
8.1-b |
$4$ |
$6$ |
3.3.892.1 |
$3$ |
$[3, 0]$ |
8.1 |
\( 2^{3} \) |
\( 2^{20} \) |
$3.77430$ |
$(a-2), (-a^2+7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B.1.2 |
$9$ |
\( 2 \) |
$1$ |
$3.901177234$ |
0.587794837 |
\( -\frac{1026781951835}{4096} a^{2} - \frac{1300707728621}{2048} a + \frac{2610277187945}{2048} \) |
\( \bigl[a^{2} + 2 a - 6\) , \( 0\) , \( a^{2} + 2 a - 6\) , \( -34 a^{2} - 48 a + 124\) , \( -301 a^{2} - 466 a + 1139\bigr] \) |
${y}^2+\left(a^{2}+2a-6\right){x}{y}+\left(a^{2}+2a-6\right){y}={x}^{3}+\left(-34a^{2}-48a+124\right){x}-301a^{2}-466a+1139$ |
| 8.1-b3 |
8.1-b |
$4$ |
$6$ |
3.3.892.1 |
$3$ |
$[3, 0]$ |
8.1 |
\( 2^{3} \) |
\( - 2^{6} \) |
$3.77430$ |
$(a-2), (-a^2+7)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$105.3317853$ |
0.587794837 |
\( -\frac{132988941}{4} a^{2} - \frac{20660203}{2} a + \frac{505636335}{2} \) |
\( \bigl[a\) , \( a - 1\) , \( a^{2} + 2 a - 6\) , \( -47 a^{2} - 82 a + 157\) , \( -458 a^{2} - 715 a + 1809\bigr] \) |
${y}^2+a{x}{y}+\left(a^{2}+2a-6\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-47a^{2}-82a+157\right){x}-458a^{2}-715a+1809$ |
| 8.1-b4 |
8.1-b |
$4$ |
$6$ |
3.3.892.1 |
$3$ |
$[3, 0]$ |
8.1 |
\( 2^{3} \) |
\( - 2^{10} \) |
$3.77430$ |
$(a-2), (-a^2+7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B.1.2 |
$9$ |
\( 2 \) |
$1$ |
$3.901177234$ |
0.587794837 |
\( \frac{38787877956078973283}{64} a^{2} + \frac{30986378741444154789}{32} a - \frac{74657105415288647105}{32} \) |
\( \bigl[a\) , \( a - 1\) , \( a^{2} + 2 a - 6\) , \( -4232 a^{2} - 6772 a + 16257\) , \( -286792 a^{2} - 458219 a + 1104001\bigr] \) |
${y}^2+a{x}{y}+\left(a^{2}+2a-6\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-4232a^{2}-6772a+16257\right){x}-286792a^{2}-458219a+1104001$ |
| 8.2-a1 |
8.2-a |
$6$ |
$8$ |
3.3.892.1 |
$3$ |
$[3, 0]$ |
8.2 |
\( 2^{3} \) |
\( 2^{8} \) |
$3.77430$ |
$(a-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.202315656$ |
$78.30653355$ |
1.591352238 |
\( 338029 a^{2} - 1322986 a + 1157026 \) |
\( \bigl[a^{2} + 2 a - 6\) , \( a^{2} + a - 7\) , \( a^{2} + 2 a - 6\) , \( 392 a^{2} + 628 a - 1509\) , \( -2657 a^{2} - 4245 a + 10226\bigr] \) |
${y}^2+\left(a^{2}+2a-6\right){x}{y}+\left(a^{2}+2a-6\right){y}={x}^{3}+\left(a^{2}+a-7\right){x}^{2}+\left(392a^{2}+628a-1509\right){x}-2657a^{2}-4245a+10226$ |
| 8.2-a2 |
8.2-a |
$6$ |
$8$ |
3.3.892.1 |
$3$ |
$[3, 0]$ |
8.2 |
\( 2^{3} \) |
\( 2^{10} \) |
$3.77430$ |
$(a-2)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$1.618525252$ |
$78.30653355$ |
1.591352238 |
\( 18536569 a^{2} - 72614908 a + 63544636 \) |
\( \bigl[a\) , \( a^{2} - 6\) , \( a^{2} + 2 a - 6\) , \( -573021156714232361 a^{2} - 915536065618909618 a + 2205849000063705668\) , \( -838726079605326167583958550 a^{2} - 1340062170578422662607539110 a + 3228681982064082059133266274\bigr] \) |
${y}^2+a{x}{y}+\left(a^{2}+2a-6\right){y}={x}^{3}+\left(a^{2}-6\right){x}^{2}+\left(-573021156714232361a^{2}-915536065618909618a+2205849000063705668\right){x}-838726079605326167583958550a^{2}-1340062170578422662607539110a+3228681982064082059133266274$ |
| 8.2-a3 |
8.2-a |
$6$ |
$8$ |
3.3.892.1 |
$3$ |
$[3, 0]$ |
8.2 |
\( 2^{3} \) |
\( 2^{4} \) |
$3.77430$ |
$(a-2)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2 \) |
$0.404631313$ |
$313.2261342$ |
1.591352238 |
\( -70363 a^{2} - 22746 a + 536098 \) |
\( \bigl[a\) , \( -a^{2} + 5\) , \( a^{2} + a - 6\) , \( -16 a^{2} - 24 a + 66\) , \( -25 a^{2} - 40 a + 96\bigr] \) |
${y}^2+a{x}{y}+\left(a^{2}+a-6\right){y}={x}^{3}+\left(-a^{2}+5\right){x}^{2}+\left(-16a^{2}-24a+66\right){x}-25a^{2}-40a+96$ |
| 8.2-a4 |
8.2-a |
$6$ |
$8$ |
3.3.892.1 |
$3$ |
$[3, 0]$ |
8.2 |
\( 2^{3} \) |
\( - 2^{8} \) |
$3.77430$ |
$(a-2)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$0.809262626$ |
$156.6130671$ |
1.591352238 |
\( -27061895169 a^{2} - 8647639022 a + 205084181226 \) |
\( \bigl[a\) , \( -a^{2} + 5\) , \( a^{2} + a - 6\) , \( -116 a^{2} - 184 a + 451\) , \( 1233 a^{2} + 1970 a - 4747\bigr] \) |
${y}^2+a{x}{y}+\left(a^{2}+a-6\right){y}={x}^{3}+\left(-a^{2}+5\right){x}^{2}+\left(-116a^{2}-184a+451\right){x}+1233a^{2}+1970a-4747$ |
| 8.2-a5 |
8.2-a |
$6$ |
$8$ |
3.3.892.1 |
$3$ |
$[3, 0]$ |
8.2 |
\( 2^{3} \) |
\( 2^{8} \) |
$3.77430$ |
$(a-2)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2 \) |
$0.809262626$ |
$156.6130671$ |
1.591352238 |
\( 230169 a^{2} + 363070 a - 878122 \) |
\( \bigl[a\) , \( -a^{2} - 2 a + 6\) , \( a\) , \( -11597191637 a^{2} - 18529241163 a + 44643471323\) , \( -1275587082327300 a^{2} - 2038050366944217 a + 4910381505248825\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a^{2}-2a+6\right){x}^{2}+\left(-11597191637a^{2}-18529241163a+44643471323\right){x}-1275587082327300a^{2}-2038050366944217a+4910381505248825$ |
| 8.2-a6 |
8.2-a |
$6$ |
$8$ |
3.3.892.1 |
$3$ |
$[3, 0]$ |
8.2 |
\( 2^{3} \) |
\( - 2^{10} \) |
$3.77430$ |
$(a-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$1.618525252$ |
$19.57663338$ |
1.591352238 |
\( 371160776695 a^{2} + 593016684572 a - 1428785888524 \) |
\( \bigl[a\) , \( -a^{2} - 2 a + 6\) , \( a\) , \( -185527538472 a^{2} - 296423876583 a + 714189572983\) , \( -81663809104384714 a^{2} - 130477141401898041 a + 314365411370205003\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a^{2}-2a+6\right){x}^{2}+\left(-185527538472a^{2}-296423876583a+714189572983\right){x}-81663809104384714a^{2}-130477141401898041a+314365411370205003$ |
| 8.2-b1 |
8.2-b |
$1$ |
$1$ |
3.3.892.1 |
$3$ |
$[3, 0]$ |
8.2 |
\( 2^{3} \) |
\( 2^{11} \) |
$3.77430$ |
$(a-2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
|
|
$1$ |
\( 1 \) |
$1$ |
$103.1005708$ |
3.452062440 |
\( -1007069 a^{2} - 322089 a + 7632644 \) |
\( \bigl[a^{2} + a - 6\) , \( -a^{2} + 7\) , \( a\) , \( 4 a + 15\) , \( -94 a^{2} - 146 a + 371\bigr] \) |
${y}^2+\left(a^{2}+a-6\right){x}{y}+a{y}={x}^{3}+\left(-a^{2}+7\right){x}^{2}+\left(4a+15\right){x}-94a^{2}-146a+371$ |
| 8.2-c1 |
8.2-c |
$1$ |
$1$ |
3.3.892.1 |
$3$ |
$[3, 0]$ |
8.2 |
\( 2^{3} \) |
\( 2^{11} \) |
$3.77430$ |
$(a-2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
|
|
$1$ |
\( 1 \) |
$0.529971091$ |
$67.35488776$ |
3.585585847 |
\( -1007069 a^{2} - 322089 a + 7632644 \) |
\( \bigl[a^{2} + a - 6\) , \( a - 1\) , \( a\) , \( 7 a^{2} - 27 a + 25\) , \( 3 a^{2} - 8 a + 2\bigr] \) |
${y}^2+\left(a^{2}+a-6\right){x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(7a^{2}-27a+25\right){x}+3a^{2}-8a+2$ |
| 8.2-d1 |
8.2-d |
$6$ |
$8$ |
3.3.892.1 |
$3$ |
$[3, 0]$ |
8.2 |
\( 2^{3} \) |
\( 2^{8} \) |
$3.77430$ |
$(a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$43.54235267$ |
0.728952900 |
\( 338029 a^{2} - 1322986 a + 1157026 \) |
\( \bigl[a^{2} + 2 a - 6\) , \( -a^{2} - a + 7\) , \( a^{2} + 2 a - 6\) , \( 2 a^{2} - 17\) , \( 27 a^{2} + 9 a - 204\bigr] \) |
${y}^2+\left(a^{2}+2a-6\right){x}{y}+\left(a^{2}+2a-6\right){y}={x}^{3}+\left(-a^{2}-a+7\right){x}^{2}+\left(2a^{2}-17\right){x}+27a^{2}+9a-204$ |
| 8.2-d2 |
8.2-d |
$6$ |
$8$ |
3.3.892.1 |
$3$ |
$[3, 0]$ |
8.2 |
\( 2^{3} \) |
\( - 2^{8} \) |
$3.77430$ |
$(a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$21.77117633$ |
0.728952900 |
\( -27061895169 a^{2} - 8647639022 a + 205084181226 \) |
\( \bigl[a\) , \( a^{2} - 6\) , \( a^{2} + 2 a - 6\) , \( 19 a^{2} - 134\) , \( 52 a^{2} + 18 a - 406\bigr] \) |
${y}^2+a{x}{y}+\left(a^{2}+2a-6\right){y}={x}^{3}+\left(a^{2}-6\right){x}^{2}+\left(19a^{2}-134\right){x}+52a^{2}+18a-406$ |
| 8.2-d3 |
8.2-d |
$6$ |
$8$ |
3.3.892.1 |
$3$ |
$[3, 0]$ |
8.2 |
\( 2^{3} \) |
\( 2^{4} \) |
$3.77430$ |
$(a-2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2 \) |
$1$ |
$174.1694107$ |
0.728952900 |
\( -70363 a^{2} - 22746 a + 536098 \) |
\( \bigl[a\) , \( a^{2} - 6\) , \( a^{2} + 2 a - 6\) , \( -a^{2} + 1\) , \( -2 a^{2} + 2 a\bigr] \) |
${y}^2+a{x}{y}+\left(a^{2}+2a-6\right){y}={x}^{3}+\left(a^{2}-6\right){x}^{2}+\left(-a^{2}+1\right){x}-2a^{2}+2a$ |
| 8.2-d4 |
8.2-d |
$6$ |
$8$ |
3.3.892.1 |
$3$ |
$[3, 0]$ |
8.2 |
\( 2^{3} \) |
\( 2^{8} \) |
$3.77430$ |
$(a-2)$ |
0 |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$1$ |
$348.3388214$ |
0.728952900 |
\( 230169 a^{2} + 363070 a - 878122 \) |
\( \bigl[a\) , \( -a - 1\) , \( 0\) , \( -582569 a^{2} - 930792 a + 2242606\) , \( 454529832 a^{2} + 726218306 a - 1749715806\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-582569a^{2}-930792a+2242606\right){x}+454529832a^{2}+726218306a-1749715806$ |
| 8.2-d5 |
8.2-d |
$6$ |
$8$ |
3.3.892.1 |
$3$ |
$[3, 0]$ |
8.2 |
\( 2^{3} \) |
\( - 2^{10} \) |
$3.77430$ |
$(a-2)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$174.1694107$ |
0.728952900 |
\( 371160776695 a^{2} + 593016684572 a - 1428785888524 \) |
\( \bigl[a\) , \( -a - 1\) , \( 0\) , \( -9319724 a^{2} - 14890452 a + 35876346\) , \( 29081158361 a^{2} + 46463990024 a - 111948125020\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-9319724a^{2}-14890452a+35876346\right){x}+29081158361a^{2}+46463990024a-111948125020$ |
| 8.2-d6 |
8.2-d |
$6$ |
$8$ |
3.3.892.1 |
$3$ |
$[3, 0]$ |
8.2 |
\( 2^{3} \) |
\( 2^{10} \) |
$3.77430$ |
$(a-2)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$174.1694107$ |
0.728952900 |
\( 18536569 a^{2} - 72614908 a + 63544636 \) |
\( \bigl[a\) , \( -a^{2} - a + 7\) , \( a\) , \( -28784940415319 a^{2} - 45990712189459 a + 110807831941347\) , \( 298615380645155711998 a^{2} + 477108301370277443568 a - 1149522022148050926614\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a^{2}-a+7\right){x}^{2}+\left(-28784940415319a^{2}-45990712189459a+110807831941347\right){x}+298615380645155711998a^{2}+477108301370277443568a-1149522022148050926614$ |
| 8.3-a1 |
8.3-a |
$2$ |
$3$ |
3.3.892.1 |
$3$ |
$[3, 0]$ |
8.3 |
\( 2^{3} \) |
\( 2^{21} \) |
$3.77430$ |
$(a-2), (-a^2+7)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.1 |
$1$ |
\( 3 \) |
$1$ |
$122.8024940$ |
1.370577207 |
\( -\frac{227083}{128} a^{2} - \frac{56793}{128} a + \frac{857633}{64} \) |
\( \bigl[a + 1\) , \( a - 1\) , \( a^{2} + a - 6\) , \( -37 a^{2} + 143 a - 120\) , \( 983 a^{2} - 3848 a + 3364\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{2}+a-6\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-37a^{2}+143a-120\right){x}+983a^{2}-3848a+3364$ |
| 8.3-a2 |
8.3-a |
$2$ |
$3$ |
3.3.892.1 |
$3$ |
$[3, 0]$ |
8.3 |
\( 2^{3} \) |
\( 2^{47} \) |
$3.77430$ |
$(a-2), (-a^2+7)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.2 |
$9$ |
\( 1 \) |
$1$ |
$4.548240521$ |
1.370577207 |
\( -\frac{87059088253}{1048576} a^{2} - \frac{27944772857}{1048576} a + \frac{164940192053}{262144} \) |
\( \bigl[a + 1\) , \( a - 1\) , \( a^{2} + a - 6\) , \( 318 a^{2} - 1247 a + 1095\) , \( -21449 a^{2} + 84025 a - 73531\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{2}+a-6\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(318a^{2}-1247a+1095\right){x}-21449a^{2}+84025a-73531$ |
| 8.3-b1 |
8.3-b |
$2$ |
$3$ |
3.3.892.1 |
$3$ |
$[3, 0]$ |
8.3 |
\( 2^{3} \) |
\( 2^{47} \) |
$3.77430$ |
$(a-2), (-a^2+7)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B |
$1$ |
\( 3 \cdot 13 \) |
$0.034761670$ |
$20.23807344$ |
2.755962112 |
\( -\frac{87059088253}{1048576} a^{2} - \frac{27944772857}{1048576} a + \frac{164940192053}{262144} \) |
\( \bigl[a^{2} + 2 a - 5\) , \( a - 1\) , \( a + 1\) , \( 44 a^{2} + 22 a - 307\) , \( -187 a^{2} - 43 a + 1457\bigr] \) |
${y}^2+\left(a^{2}+2a-5\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(44a^{2}+22a-307\right){x}-187a^{2}-43a+1457$ |
| 8.3-b2 |
8.3-b |
$2$ |
$3$ |
3.3.892.1 |
$3$ |
$[3, 0]$ |
8.3 |
\( 2^{3} \) |
\( 2^{21} \) |
$3.77430$ |
$(a-2), (-a^2+7)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B |
$1$ |
\( 3 \cdot 13 \) |
$0.011587223$ |
$60.71422034$ |
2.755962112 |
\( -\frac{227083}{128} a^{2} - \frac{56793}{128} a + \frac{857633}{64} \) |
\( \bigl[a^{2} + 2 a - 5\) , \( a - 1\) , \( a + 1\) , \( 9 a^{2} + 12 a - 42\) , \( 16 a^{2} + 22 a - 73\bigr] \) |
${y}^2+\left(a^{2}+2a-5\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(9a^{2}+12a-42\right){x}+16a^{2}+22a-73$ |
*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.
