| 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 |
| 5.1-a1 |
5.1-a |
$2$ |
$3$ |
5.5.101833.1 |
$5$ |
$[5, 0]$ |
5.1 |
\( 5 \) |
\( 5^{3} \) |
$33.49499$ |
$(a^2-a-2)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1 |
$1$ |
\( 1 \) |
$0.625212984$ |
$1813.124774$ |
1.97350807 |
\( -\frac{397312}{125} a^{4} + \frac{118784}{125} a^{3} + \frac{1478656}{125} a^{2} + \frac{200704}{125} a - \frac{258048}{125} \) |
\( \bigl[0\) , \( -a^{3} + 4 a - 1\) , \( a^{4} - 5 a^{2} + a + 2\) , \( a^{3} - 4 a + 1\) , \( -1\bigr] \) |
${y}^2+\left(a^{4}-5a^{2}+a+2\right){y}={x}^{3}+\left(-a^{3}+4a-1\right){x}^{2}+\left(a^{3}-4a+1\right){x}-1$ |
| 5.1-a2 |
5.1-a |
$2$ |
$3$ |
5.5.101833.1 |
$5$ |
$[5, 0]$ |
5.1 |
\( 5 \) |
\( 5^{9} \) |
$33.49499$ |
$(a^2-a-2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.2 |
$9$ |
\( 1 \) |
$1.875638952$ |
$7.461418823$ |
1.97350807 |
\( -\frac{836958877671886848}{1953125} a^{4} + \frac{2638484493361934336}{1953125} a^{3} - \frac{1496367277450776576}{1953125} a^{2} - \frac{958505246388137984}{1953125} a + \frac{387569019892625408}{1953125} \) |
\( \bigl[0\) , \( -a^{3} + 4 a - 1\) , \( a^{4} - 5 a^{2} + a + 2\) , \( 11 a^{3} - 44 a - 19\) , \( 16 a^{4} + 29 a^{3} - 72 a^{2} - 108 a - 35\bigr] \) |
${y}^2+\left(a^{4}-5a^{2}+a+2\right){y}={x}^{3}+\left(-a^{3}+4a-1\right){x}^{2}+\left(11a^{3}-44a-19\right){x}+16a^{4}+29a^{3}-72a^{2}-108a-35$ |
| 7.1-a1 |
7.1-a |
$4$ |
$6$ |
5.5.101833.1 |
$5$ |
$[5, 0]$ |
7.1 |
\( 7 \) |
\( - 7^{18} \) |
$34.64118$ |
$(a^3-4a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$9$ |
\( 2 \cdot 3^{2} \) |
$1$ |
$11.34142370$ |
1.43938950 |
\( -\frac{34935744732918356869916249373765}{1628413597910449} a^{4} - \frac{9913244538792403325921317576170}{1628413597910449} a^{3} + \frac{161952531583389814556375118193559}{1628413597910449} a^{2} + \frac{33228890929750486816905115590286}{1628413597910449} a - \frac{27213684853475936952493834323913}{1628413597910449} \) |
\( \bigl[a^{4} - 5 a^{2} + a + 2\) , \( -a^{2} + 3\) , \( a^{4} - 4 a^{2} + 2 a + 1\) , \( -20 a^{4} + 45 a^{3} + 12 a^{2} - 32 a - 42\) , \( -175 a^{4} + 431 a^{3} + 61 a^{2} - 387 a - 107\bigr] \) |
${y}^2+\left(a^{4}-5a^{2}+a+2\right){x}{y}+\left(a^{4}-4a^{2}+2a+1\right){y}={x}^{3}+\left(-a^{2}+3\right){x}^{2}+\left(-20a^{4}+45a^{3}+12a^{2}-32a-42\right){x}-175a^{4}+431a^{3}+61a^{2}-387a-107$ |
| 7.1-a2 |
7.1-a |
$4$ |
$6$ |
5.5.101833.1 |
$5$ |
$[5, 0]$ |
7.1 |
\( 7 \) |
\( - 7^{3} \) |
$34.64118$ |
$(a^3-4a)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 3 \) |
$1$ |
$5511.931918$ |
1.43938950 |
\( \frac{66024921}{343} a^{4} - \frac{100204585}{343} a^{3} - \frac{275255074}{343} a^{2} + \frac{474076146}{343} a - \frac{122356936}{343} \) |
\( \bigl[-a^{4} + a^{3} + 6 a^{2} - 4 a - 3\) , \( -a^{2} + a + 2\) , \( a^{3} - 3 a\) , \( 3 a^{4} - 2 a^{3} - 14 a^{2} + 9 a + 8\) , \( 4 a^{4} - a^{3} - 20 a^{2} + 8 a + 9\bigr] \) |
${y}^2+\left(-a^{4}+a^{3}+6a^{2}-4a-3\right){x}{y}+\left(a^{3}-3a\right){y}={x}^{3}+\left(-a^{2}+a+2\right){x}^{2}+\left(3a^{4}-2a^{3}-14a^{2}+9a+8\right){x}+4a^{4}-a^{3}-20a^{2}+8a+9$ |
| 7.1-a3 |
7.1-a |
$4$ |
$6$ |
5.5.101833.1 |
$5$ |
$[5, 0]$ |
7.1 |
\( 7 \) |
\( - 7^{9} \) |
$34.64118$ |
$(a^3-4a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$9$ |
\( 3^{2} \) |
$1$ |
$22.68284740$ |
1.43938950 |
\( \frac{16784310391671963764}{40353607} a^{4} + \frac{18111156800644108597}{40353607} a^{3} - \frac{46265469163472305991}{40353607} a^{2} - \frac{12263095868767053076}{40353607} a + \frac{8073330787842373203}{40353607} \) |
\( \bigl[a^{4} - 5 a^{2} + a + 2\) , \( -a^{2} + 3\) , \( a^{4} - 4 a^{2} + 2 a + 1\) , \( -15 a^{4} + 40 a^{3} - 18 a^{2} - 17 a + 8\) , \( -140 a^{4} + 425 a^{3} - 223 a^{2} - 165 a + 59\bigr] \) |
${y}^2+\left(a^{4}-5a^{2}+a+2\right){x}{y}+\left(a^{4}-4a^{2}+2a+1\right){y}={x}^{3}+\left(-a^{2}+3\right){x}^{2}+\left(-15a^{4}+40a^{3}-18a^{2}-17a+8\right){x}-140a^{4}+425a^{3}-223a^{2}-165a+59$ |
| 7.1-a4 |
7.1-a |
$4$ |
$6$ |
5.5.101833.1 |
$5$ |
$[5, 0]$ |
7.1 |
\( 7 \) |
\( - 7^{6} \) |
$34.64118$ |
$(a^3-4a)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$2755.965959$ |
1.43938950 |
\( -\frac{28483240131527841}{117649} a^{4} + \frac{43717350428981914}{117649} a^{3} + \frac{119034174838858816}{117649} a^{2} - \frac{206081010993208259}{117649} a + \frac{53255049874534180}{117649} \) |
\( \bigl[-a^{4} + a^{3} + 6 a^{2} - 4 a - 3\) , \( -a^{2} + a + 2\) , \( a^{3} - 3 a\) , \( 8 a^{4} + 3 a^{3} - 34 a^{2} - 11 a - 2\) , \( 32 a^{4} + 10 a^{3} - 148 a^{2} - 33 a + 26\bigr] \) |
${y}^2+\left(-a^{4}+a^{3}+6a^{2}-4a-3\right){x}{y}+\left(a^{3}-3a\right){y}={x}^{3}+\left(-a^{2}+a+2\right){x}^{2}+\left(8a^{4}+3a^{3}-34a^{2}-11a-2\right){x}+32a^{4}+10a^{3}-148a^{2}-33a+26$ |
| 7.2-a1 |
7.2-a |
$2$ |
$3$ |
5.5.101833.1 |
$5$ |
$[5, 0]$ |
7.2 |
\( 7 \) |
\( - 7^{18} \) |
$34.64118$ |
$(-a^4+5a^2-a-3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.2 |
$9$ |
\( 2 \cdot 3^{2} \) |
$1$ |
$4.293363963$ |
2.17955811 |
\( -\frac{8299662076855549170261286086588}{1628413597910449} a^{4} - \frac{8956875689405632622076555588090}{1628413597910449} a^{3} + \frac{22875303550996342235969307745418}{1628413597910449} a^{2} + \frac{6063691056732384627706845863407}{1628413597910449} a - \frac{3991785116498736470982228805450}{1628413597910449} \) |
\( \bigl[a + 1\) , \( a^{4} - 6 a^{2} + 2 a + 4\) , \( a^{2} + a - 1\) , \( 107 a^{4} - 184 a^{3} - 447 a^{2} + 861 a - 216\) , \( 1394 a^{4} - 1959 a^{3} - 5869 a^{2} + 9253 a - 2333\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{2}+a-1\right){y}={x}^{3}+\left(a^{4}-6a^{2}+2a+4\right){x}^{2}+\left(107a^{4}-184a^{3}-447a^{2}+861a-216\right){x}+1394a^{4}-1959a^{3}-5869a^{2}+9253a-2333$ |
| 7.2-a2 |
7.2-a |
$2$ |
$3$ |
5.5.101833.1 |
$5$ |
$[5, 0]$ |
7.2 |
\( 7 \) |
\( - 7^{6} \) |
$34.64118$ |
$(-a^4+5a^2-a-3)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1 |
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$1043.287443$ |
2.17955811 |
\( -\frac{10979115211801161}{117649} a^{4} + \frac{34621401561515437}{117649} a^{3} - \frac{19657765977069155}{117649} a^{2} - \frac{12564731083519550}{117649} a + \frac{5098526600665186}{117649} \) |
\( \bigl[a + 1\) , \( a^{4} - 6 a^{2} + 2 a + 4\) , \( a^{2} + a - 1\) , \( 2 a^{4} + a^{3} - 12 a^{2} - 4 a + 9\) , \( 4 a^{4} - 15 a^{3} - 10 a^{2} + 53 a - 13\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{2}+a-1\right){y}={x}^{3}+\left(a^{4}-6a^{2}+2a+4\right){x}^{2}+\left(2a^{4}+a^{3}-12a^{2}-4a+9\right){x}+4a^{4}-15a^{3}-10a^{2}+53a-13$ |
| 7.2-b1 |
7.2-b |
$4$ |
$6$ |
5.5.101833.1 |
$5$ |
$[5, 0]$ |
7.2 |
\( 7 \) |
\( - 7^{9} \) |
$34.64118$ |
$(-a^4+5a^2-a-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$9$ |
\( 3^{2} \) |
$1$ |
$15.63014046$ |
0.991844614 |
\( -\frac{129905211929111696759}{40353607} a^{4} - \frac{36847878589687577110}{40353607} a^{3} + \frac{602201291343435387454}{40353607} a^{2} + \frac{123496923865332601875}{40353607} a - \frac{101171544475898817040}{40353607} \) |
\( \bigl[a^{3} - 3 a + 1\) , \( a^{4} - 4 a^{2} + 1\) , \( a^{3} - 4 a + 1\) , \( 38 a^{4} - 61 a^{3} - 155 a^{2} + 285 a - 88\) , \( 312 a^{4} - 452 a^{3} - 1346 a^{2} + 2127 a - 405\bigr] \) |
${y}^2+\left(a^{3}-3a+1\right){x}{y}+\left(a^{3}-4a+1\right){y}={x}^{3}+\left(a^{4}-4a^{2}+1\right){x}^{2}+\left(38a^{4}-61a^{3}-155a^{2}+285a-88\right){x}+312a^{4}-452a^{3}-1346a^{2}+2127a-405$ |
| 7.2-b2 |
7.2-b |
$4$ |
$6$ |
5.5.101833.1 |
$5$ |
$[5, 0]$ |
7.2 |
\( 7 \) |
\( - 7^{3} \) |
$34.64118$ |
$(-a^4+5a^2-a-3)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 3 \) |
$1$ |
$3798.124133$ |
0.991844614 |
\( -\frac{7248523749}{343} a^{4} + \frac{4888935720}{343} a^{3} + \frac{37832389751}{343} a^{2} - \frac{23928280283}{343} a - \frac{22278421960}{343} \) |
\( \bigl[a^{4} - 5 a^{2} + a + 2\) , \( a^{3} + a^{2} - 3 a - 2\) , \( 0\) , \( a^{4} - 3 a^{2} + a + 1\) , \( 0\bigr] \) |
${y}^2+\left(a^{4}-5a^{2}+a+2\right){x}{y}={x}^{3}+\left(a^{3}+a^{2}-3a-2\right){x}^{2}+\left(a^{4}-3a^{2}+a+1\right){x}$ |
| 7.2-b3 |
7.2-b |
$4$ |
$6$ |
5.5.101833.1 |
$5$ |
$[5, 0]$ |
7.2 |
\( 7 \) |
\( - 7^{18} \) |
$34.64118$ |
$(-a^4+5a^2-a-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$9$ |
\( 2 \cdot 3^{2} \) |
$1$ |
$7.815070232$ |
0.991844614 |
\( \frac{202244099233249301987463016784}{1628413597910449} a^{4} + \frac{218258900994709298179800644103}{1628413597910449} a^{3} - \frac{557419681646490388575999100179}{1628413597910449} a^{2} - \frac{147758505836585744175799501677}{1628413597910449} a + \frac{97270821948072542864023504891}{1628413597910449} \) |
\( \bigl[a^{3} - 3 a + 1\) , \( a^{4} - 4 a^{2} + 1\) , \( a^{3} - 4 a + 1\) , \( -107 a^{4} + 19 a^{3} + 565 a^{2} - 145 a - 498\) , \( 1302 a^{4} - 1267 a^{3} - 6769 a^{2} + 5784 a + 2873\bigr] \) |
${y}^2+\left(a^{3}-3a+1\right){x}{y}+\left(a^{3}-4a+1\right){y}={x}^{3}+\left(a^{4}-4a^{2}+1\right){x}^{2}+\left(-107a^{4}+19a^{3}+565a^{2}-145a-498\right){x}+1302a^{4}-1267a^{3}-6769a^{2}+5784a+2873$ |
| 7.2-b4 |
7.2-b |
$4$ |
$6$ |
5.5.101833.1 |
$5$ |
$[5, 0]$ |
7.2 |
\( 7 \) |
\( - 7^{6} \) |
$34.64118$ |
$(-a^4+5a^2-a-3)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$1899.062066$ |
0.991844614 |
\( \frac{188210228389311551660}{117649} a^{4} - \frac{126986956452006245093}{117649} a^{3} - \frac{982358976453471058583}{117649} a^{2} + \frac{621497676285282124964}{117649} a + \frac{578588646935243724999}{117649} \) |
\( \bigl[a^{4} - 5 a^{2} + a + 2\) , \( a^{3} + a^{2} - 3 a - 2\) , \( 0\) , \( -4 a^{4} + 12 a^{2} - 4 a - 4\) , \( -10 a^{4} - 15 a^{3} + 22 a^{2} + 17 a + 1\bigr] \) |
${y}^2+\left(a^{4}-5a^{2}+a+2\right){x}{y}={x}^{3}+\left(a^{3}+a^{2}-3a-2\right){x}^{2}+\left(-4a^{4}+12a^{2}-4a-4\right){x}-10a^{4}-15a^{3}+22a^{2}+17a+1$ |
| 7.2-c1 |
7.2-c |
$1$ |
$1$ |
5.5.101833.1 |
$5$ |
$[5, 0]$ |
7.2 |
\( 7 \) |
\( - 7^{2} \) |
$34.64118$ |
$(-a^4+5a^2-a-3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \) |
$0.042782853$ |
$1608.086267$ |
2.15593082 |
\( -\frac{208344}{49} a^{4} + \frac{176415}{49} a^{3} + \frac{1078676}{49} a^{2} - \frac{800173}{49} a - \frac{692364}{49} \) |
\( \bigl[-a^{4} + a^{3} + 6 a^{2} - 5 a - 3\) , \( a^{4} - 4 a^{2} + a - 1\) , \( a^{3} + a^{2} - 3 a - 2\) , \( -a^{4} + a^{3} + 5 a^{2} - 5 a - 2\) , \( -a - 1\bigr] \) |
${y}^2+\left(-a^{4}+a^{3}+6a^{2}-5a-3\right){x}{y}+\left(a^{3}+a^{2}-3a-2\right){y}={x}^{3}+\left(a^{4}-4a^{2}+a-1\right){x}^{2}+\left(-a^{4}+a^{3}+5a^{2}-5a-2\right){x}-a-1$ |
| 25.1-a1 |
25.1-a |
$2$ |
$3$ |
5.5.101833.1 |
$5$ |
$[5, 0]$ |
25.1 |
\( 5^{2} \) |
\( 5^{9} \) |
$39.34385$ |
$(a^2-a-2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B |
$1$ |
\( 2 \) |
$0.019926828$ |
$4043.214277$ |
2.52476335 |
\( -\frac{397312}{125} a^{4} + \frac{118784}{125} a^{3} + \frac{1478656}{125} a^{2} + \frac{200704}{125} a - \frac{258048}{125} \) |
\( \bigl[0\) , \( a^{4} - 6 a^{2} + 2 a + 3\) , \( a^{2} + a - 1\) , \( 2 a^{4} - a^{3} - 7 a^{2} + 2 a + 3\) , \( -a^{4} + 2 a^{2} + 2 a\bigr] \) |
${y}^2+\left(a^{2}+a-1\right){y}={x}^{3}+\left(a^{4}-6a^{2}+2a+3\right){x}^{2}+\left(2a^{4}-a^{3}-7a^{2}+2a+3\right){x}-a^{4}+2a^{2}+2a$ |
| 25.1-a2 |
25.1-a |
$2$ |
$3$ |
5.5.101833.1 |
$5$ |
$[5, 0]$ |
25.1 |
\( 5^{2} \) |
\( 5^{15} \) |
$39.34385$ |
$(a^2-a-2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B |
$1$ |
\( 2 \) |
$0.059780486$ |
$1347.738092$ |
2.52476335 |
\( -\frac{836958877671886848}{1953125} a^{4} + \frac{2638484493361934336}{1953125} a^{3} - \frac{1496367277450776576}{1953125} a^{2} - \frac{958505246388137984}{1953125} a + \frac{387569019892625408}{1953125} \) |
\( \bigl[0\) , \( a^{4} - 6 a^{2} + 2 a + 3\) , \( a^{2} + a - 1\) , \( 2 a^{4} - a^{3} - 17 a^{2} - 18 a - 7\) , \( 52 a^{4} + 28 a^{3} - 199 a^{2} - 36 a + 43\bigr] \) |
${y}^2+\left(a^{2}+a-1\right){y}={x}^{3}+\left(a^{4}-6a^{2}+2a+3\right){x}^{2}+\left(2a^{4}-a^{3}-17a^{2}-18a-7\right){x}+52a^{4}+28a^{3}-199a^{2}-36a+43$ |
| 25.1-b1 |
25.1-b |
$2$ |
$5$ |
5.5.101833.1 |
$5$ |
$[5, 0]$ |
25.1 |
\( 5^{2} \) |
\( 5^{3} \) |
$39.34385$ |
$(a^2-a-2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$5$ |
5B.1.2 |
$25$ |
\( 2 \) |
$1$ |
$10.18824902$ |
1.59633960 |
\( -507978499956736 a^{4} - 157070633910272 a^{3} + 2358095202992128 a^{2} + 541356688142336 a - 414526257295360 \) |
\( \bigl[0\) , \( 2 a^{4} - a^{3} - 10 a^{2} + 5 a + 4\) , \( a + 1\) , \( 37 a^{4} - 39 a^{3} - 156 a^{2} + 177 a - 35\) , \( 135 a^{4} - 177 a^{3} - 559 a^{2} + 809 a - 200\bigr] \) |
${y}^2+\left(a+1\right){y}={x}^{3}+\left(2a^{4}-a^{3}-10a^{2}+5a+4\right){x}^{2}+\left(37a^{4}-39a^{3}-156a^{2}+177a-35\right){x}+135a^{4}-177a^{3}-559a^{2}+809a-200$ |
| 25.1-b2 |
25.1-b |
$2$ |
$5$ |
5.5.101833.1 |
$5$ |
$[5, 0]$ |
25.1 |
\( 5^{2} \) |
\( 5^{3} \) |
$39.34385$ |
$(a^2-a-2)$ |
0 |
$\Z/5\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$5$ |
5B.1.1 |
$1$ |
\( 2 \) |
$1$ |
$6367.655640$ |
1.59633960 |
\( -7806976 a^{4} + 24616960 a^{3} - 13975552 a^{2} - 8933376 a + 3624960 \) |
\( \bigl[0\) , \( -a^{4} + a^{3} + 4 a^{2} - 6 a\) , \( -a^{4} + a^{3} + 6 a^{2} - 5 a - 3\) , \( a^{4} + a^{3} - 5 a^{2} - 2 a + 6\) , \( a^{4} - a^{3} - 7 a^{2} + 4 a + 6\bigr] \) |
${y}^2+\left(-a^{4}+a^{3}+6a^{2}-5a-3\right){y}={x}^{3}+\left(-a^{4}+a^{3}+4a^{2}-6a\right){x}^{2}+\left(a^{4}+a^{3}-5a^{2}-2a+6\right){x}+a^{4}-a^{3}-7a^{2}+4a+6$ |
| 25.1-c1 |
25.1-c |
$1$ |
$1$ |
5.5.101833.1 |
$5$ |
$[5, 0]$ |
25.1 |
\( 5^{2} \) |
\( - 5^{9} \) |
$39.34385$ |
$(a^2-a-2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
|
|
$1$ |
\( 2 \) |
$1$ |
$228.3338322$ |
1.43105390 |
\( -14500766162 a^{4} + 46166045392 a^{3} - 27584159917 a^{2} - 14941115720 a + 6352331879 \) |
\( \bigl[-a^{4} + a^{3} + 6 a^{2} - 5 a - 3\) , \( -a^{4} + 6 a^{2} - 3\) , \( -a^{4} + a^{3} + 5 a^{2} - 4 a - 1\) , \( -5 a^{4} - 2 a^{3} + 24 a^{2} - 2 a - 9\) , \( 37 a^{4} - 88 a^{3} - 278 a^{2} + 268 a + 205\bigr] \) |
${y}^2+\left(-a^{4}+a^{3}+6a^{2}-5a-3\right){x}{y}+\left(-a^{4}+a^{3}+5a^{2}-4a-1\right){y}={x}^{3}+\left(-a^{4}+6a^{2}-3\right){x}^{2}+\left(-5a^{4}-2a^{3}+24a^{2}-2a-9\right){x}+37a^{4}-88a^{3}-278a^{2}+268a+205$ |
| 25.1-d1 |
25.1-d |
$1$ |
$1$ |
5.5.101833.1 |
$5$ |
$[5, 0]$ |
25.1 |
\( 5^{2} \) |
\( - 5^{3} \) |
$39.34385$ |
$(a^2-a-2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
|
|
$1$ |
\( 2 \) |
$1$ |
$428.1037187$ |
2.68308683 |
\( -14500766162 a^{4} + 46166045392 a^{3} - 27584159917 a^{2} - 14941115720 a + 6352331879 \) |
\( \bigl[a^{4} - 5 a^{2} + a + 3\) , \( a^{2} - 3\) , \( a^{4} - 5 a^{2} + 2 a + 3\) , \( -4 a^{4} - 3 a^{3} + 13 a^{2} + 2 a - 6\) , \( 52 a^{4} + 61 a^{3} - 141 a^{2} - 50 a + 26\bigr] \) |
${y}^2+\left(a^{4}-5a^{2}+a+3\right){x}{y}+\left(a^{4}-5a^{2}+2a+3\right){y}={x}^{3}+\left(a^{2}-3\right){x}^{2}+\left(-4a^{4}-3a^{3}+13a^{2}+2a-6\right){x}+52a^{4}+61a^{3}-141a^{2}-50a+26$ |
| 25.1-e1 |
25.1-e |
$2$ |
$5$ |
5.5.101833.1 |
$5$ |
$[5, 0]$ |
25.1 |
\( 5^{2} \) |
\( 5^{9} \) |
$39.34385$ |
$(a^2-a-2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$5$ |
5B.4.2 |
$1$ |
\( 2 \) |
$1$ |
$298.0173658$ |
1.86778678 |
\( -507978499956736 a^{4} - 157070633910272 a^{3} + 2358095202992128 a^{2} + 541356688142336 a - 414526257295360 \) |
\( \bigl[0\) , \( -a^{4} + 5 a^{2} - 2 a - 1\) , \( a^{3} + a^{2} - 4 a - 1\) , \( -31 a^{4} - 23 a^{3} + 281 a^{2} - 120 a - 178\) , \( 101 a^{4} + 425 a^{3} - 1908 a^{2} + 718 a + 1044\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-4a-1\right){y}={x}^{3}+\left(-a^{4}+5a^{2}-2a-1\right){x}^{2}+\left(-31a^{4}-23a^{3}+281a^{2}-120a-178\right){x}+101a^{4}+425a^{3}-1908a^{2}+718a+1044$ |
| 25.1-e2 |
25.1-e |
$2$ |
$5$ |
5.5.101833.1 |
$5$ |
$[5, 0]$ |
25.1 |
\( 5^{2} \) |
\( 5^{9} \) |
$39.34385$ |
$(a^2-a-2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$5$ |
5B.4.1 |
$1$ |
\( 2 \) |
$1$ |
$298.0173658$ |
1.86778678 |
\( -7806976 a^{4} + 24616960 a^{3} - 13975552 a^{2} - 8933376 a + 3624960 \) |
\( \bigl[0\) , \( a^{4} - 4 a^{2}\) , \( a^{4} - 4 a^{2} + 2 a\) , \( -a^{3} + 4 a + 1\) , \( -2 a^{4} + a^{3} + 9 a^{2} - 7 a - 4\bigr] \) |
${y}^2+\left(a^{4}-4a^{2}+2a\right){y}={x}^{3}+\left(a^{4}-4a^{2}\right){x}^{2}+\left(-a^{3}+4a+1\right){x}-2a^{4}+a^{3}+9a^{2}-7a-4$ |
| 32.1-a1 |
32.1-a |
$2$ |
$3$ |
5.5.101833.1 |
$5$ |
$[5, 0]$ |
32.1 |
\( 2^{5} \) |
\( - 2^{45} \) |
$40.32718$ |
$(2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.2 |
$9$ |
\( 1 \) |
$2.436021787$ |
$8.655040613$ |
2.97316165 |
\( \frac{11533582024659}{256} a^{4} - \frac{35404549440767}{512} a^{3} - \frac{96399870422913}{512} a^{2} + \frac{20861863150351}{64} a - \frac{10782164784821}{128} \) |
\( \bigl[a^{4} - 4 a^{2} + a + 1\) , \( -a^{4} + 4 a^{2} - a\) , \( a^{4} - 5 a^{2} + 2 a + 2\) , \( -14 a^{4} - 5 a^{3} + 65 a^{2} + 13 a - 19\) , \( -21 a^{4} - 6 a^{3} + 98 a^{2} + 16 a - 33\bigr] \) |
${y}^2+\left(a^{4}-4a^{2}+a+1\right){x}{y}+\left(a^{4}-5a^{2}+2a+2\right){y}={x}^{3}+\left(-a^{4}+4a^{2}-a\right){x}^{2}+\left(-14a^{4}-5a^{3}+65a^{2}+13a-19\right){x}-21a^{4}-6a^{3}+98a^{2}+16a-33$ |
| 32.1-a2 |
32.1-a |
$2$ |
$3$ |
5.5.101833.1 |
$5$ |
$[5, 0]$ |
32.1 |
\( 2^{5} \) |
\( - 2^{15} \) |
$40.32718$ |
$(2)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1 |
$1$ |
\( 1 \) |
$0.812007262$ |
$2103.174868$ |
2.97316165 |
\( \frac{36691}{8} a^{4} - \frac{3305}{8} a^{3} - \frac{83327}{4} a^{2} + 3514 a + \frac{11475}{8} \) |
\( \bigl[a^{3} - 4 a\) , \( a^{3} - 4 a + 1\) , \( a^{2} - 1\) , \( -a^{4} + a^{3} + 5 a^{2} - 6 a + 1\) , \( -a^{3} + 2 a^{2} - a\bigr] \) |
${y}^2+\left(a^{3}-4a\right){x}{y}+\left(a^{2}-1\right){y}={x}^{3}+\left(a^{3}-4a+1\right){x}^{2}+\left(-a^{4}+a^{3}+5a^{2}-6a+1\right){x}-a^{3}+2a^{2}-a$ |
| 35.2-a1 |
35.2-a |
$1$ |
$1$ |
5.5.101833.1 |
$5$ |
$[5, 0]$ |
35.2 |
\( 5 \cdot 7 \) |
\( 5 \cdot 7^{5} \) |
$40.69018$ |
$(a^2-a-2), (a^3-4a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$0.060838928$ |
$3552.658847$ |
3.38657575 |
\( -\frac{7965413821839}{84035} a^{4} + \frac{5374459831973}{84035} a^{3} + \frac{41576219993947}{84035} a^{2} - \frac{26302620386757}{84035} a - \frac{24489206321511}{84035} \) |
\( \bigl[a^{4} - 4 a^{2} + a + 1\) , \( -a^{4} + a^{3} + 5 a^{2} - 5 a - 3\) , \( a^{4} - 5 a^{2} + a + 3\) , \( -a^{4} + 7 a^{2} - 4 a - 4\) , \( 6 a^{4} - 7 a^{3} - 22 a^{2} + 16 a + 13\bigr] \) |
${y}^2+\left(a^{4}-4a^{2}+a+1\right){x}{y}+\left(a^{4}-5a^{2}+a+3\right){y}={x}^{3}+\left(-a^{4}+a^{3}+5a^{2}-5a-3\right){x}^{2}+\left(-a^{4}+7a^{2}-4a-4\right){x}+6a^{4}-7a^{3}-22a^{2}+16a+13$ |
| 35.2-b1 |
35.2-b |
$1$ |
$1$ |
5.5.101833.1 |
$5$ |
$[5, 0]$ |
35.2 |
\( 5 \cdot 7 \) |
\( 5 \cdot 7^{4} \) |
$40.69018$ |
$(a^2-a-2), (a^3-4a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2^{2} \) |
$0.040138740$ |
$1312.877857$ |
3.30273549 |
\( -\frac{1930575872}{12005} a^{4} - \frac{541515776}{12005} a^{3} + \frac{8948125696}{12005} a^{2} + \frac{1812230144}{12005} a - \frac{1496690688}{12005} \) |
\( \bigl[0\) , \( a^{3} - 3 a\) , \( -a^{4} + a^{3} + 5 a^{2} - 4 a - 2\) , \( -a^{4} + a^{3} + 6 a^{2} - 5 a - 3\) , \( -6 a^{4} + 4 a^{3} + 31 a^{2} - 19 a - 18\bigr] \) |
${y}^2+\left(-a^{4}+a^{3}+5a^{2}-4a-2\right){y}={x}^{3}+\left(a^{3}-3a\right){x}^{2}+\left(-a^{4}+a^{3}+6a^{2}-5a-3\right){x}-6a^{4}+4a^{3}+31a^{2}-19a-18$ |
| 41.1-a1 |
41.1-a |
$1$ |
$1$ |
5.5.101833.1 |
$5$ |
$[5, 0]$ |
41.1 |
\( 41 \) |
\( 41 \) |
$41.33912$ |
$(2a^4-2a^3-9a^2+9a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$0.171064409$ |
$1427.972605$ |
3.82741253 |
\( -\frac{566838}{41} a^{4} + \frac{420567}{41} a^{3} + \frac{2930075}{41} a^{2} - \frac{1910000}{41} a - \frac{1749530}{41} \) |
\( \bigl[a^{3} - 4 a\) , \( a^{2} + a - 1\) , \( -a^{4} + a^{3} + 6 a^{2} - 4 a - 4\) , \( -3 a^{4} + 14 a^{2} - 3 a - 5\) , \( -5 a^{4} - 2 a^{3} + 19 a^{2} - 3 a - 7\bigr] \) |
${y}^2+\left(a^{3}-4a\right){x}{y}+\left(-a^{4}+a^{3}+6a^{2}-4a-4\right){y}={x}^{3}+\left(a^{2}+a-1\right){x}^{2}+\left(-3a^{4}+14a^{2}-3a-5\right){x}-5a^{4}-2a^{3}+19a^{2}-3a-7$ |
| 41.1-b1 |
41.1-b |
$4$ |
$6$ |
5.5.101833.1 |
$5$ |
$[5, 0]$ |
41.1 |
\( 41 \) |
\( 41^{9} \) |
$41.33912$ |
$(2a^4-2a^3-9a^2+9a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$9$ |
\( 1 \) |
$3.133722564$ |
$30.22783309$ |
3.33945668 |
\( \frac{565501320122673519474997688469487}{327381934393961} a^{4} - \frac{1783245346673583753510012166226979}{327381934393961} a^{3} + \frac{1012513380799579655069501638372518}{327381934393961} a^{2} + \frac{647171953465078336451644774104711}{327381934393961} a - \frac{262609987064562784432907323059873}{327381934393961} \) |
\( \bigl[a^{4} - 4 a^{2} + 2 a + 1\) , \( 2 a^{4} - a^{3} - 11 a^{2} + 7 a + 5\) , \( a^{4} - 5 a^{2} + a + 3\) , \( -4 a^{4} - a^{3} + 36 a^{2} + 11 a - 49\) , \( -481 a^{4} - 70 a^{3} + 2283 a^{2} + 194 a - 538\bigr] \) |
${y}^2+\left(a^{4}-4a^{2}+2a+1\right){x}{y}+\left(a^{4}-5a^{2}+a+3\right){y}={x}^{3}+\left(2a^{4}-a^{3}-11a^{2}+7a+5\right){x}^{2}+\left(-4a^{4}-a^{3}+36a^{2}+11a-49\right){x}-481a^{4}-70a^{3}+2283a^{2}+194a-538$ |
| 41.1-b2 |
41.1-b |
$4$ |
$6$ |
5.5.101833.1 |
$5$ |
$[5, 0]$ |
41.1 |
\( 41 \) |
\( - 41^{6} \) |
$41.33912$ |
$(2a^4-2a^3-9a^2+9a)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2 \) |
$2.089148376$ |
$1836.340860$ |
3.33945668 |
\( -\frac{93529057695815465290510}{4750104241} a^{4} - \frac{26521605333714022012803}{4750104241} a^{3} + \frac{433617293017427228726186}{4750104241} a^{2} + \frac{88964469069633175974446}{4750104241} a - \frac{72862457808974877253508}{4750104241} \) |
\( \bigl[a^{3} + a^{2} - 3 a - 2\) , \( a^{3} + a^{2} - 4 a - 2\) , \( a^{4} - 5 a^{2} + 2 a + 3\) , \( 18 a^{4} - 38 a^{3} - 86 a^{2} + 155 a - 39\) , \( -107 a^{4} + 174 a^{3} + 462 a^{2} - 784 a + 201\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-3a-2\right){x}{y}+\left(a^{4}-5a^{2}+2a+3\right){y}={x}^{3}+\left(a^{3}+a^{2}-4a-2\right){x}^{2}+\left(18a^{4}-38a^{3}-86a^{2}+155a-39\right){x}-107a^{4}+174a^{3}+462a^{2}-784a+201$ |
| 41.1-b3 |
41.1-b |
$4$ |
$6$ |
5.5.101833.1 |
$5$ |
$[5, 0]$ |
41.1 |
\( 41 \) |
\( - 41^{18} \) |
$41.33912$ |
$(2a^4-2a^3-9a^2+9a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$9$ |
\( 2 \) |
$6.267445128$ |
$7.556958272$ |
3.33945668 |
\( \frac{19614009157341759127851293527570694685}{107178930967531784356353269521} a^{4} - \frac{58937764329408142624000993463638328329}{107178930967531784356353269521} a^{3} + \frac{26877418632289460695144966692089670344}{107178930967531784356353269521} a^{2} + \frac{24987325567962449009341332998805618494}{107178930967531784356353269521} a - \frac{4946386114556014711705594273916691044}{107178930967531784356353269521} \) |
\( \bigl[a^{3} + a^{2} - 3 a - 2\) , \( a^{3} + a^{2} - 4 a - 2\) , \( a^{4} - 5 a^{2} + 2 a + 3\) , \( -202 a^{4} + 267 a^{3} + 849 a^{2} - 1215 a + 131\) , \( 273 a^{4} - 549 a^{3} - 1145 a^{2} + 3141 a - 1692\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-3a-2\right){x}{y}+\left(a^{4}-5a^{2}+2a+3\right){y}={x}^{3}+\left(a^{3}+a^{2}-4a-2\right){x}^{2}+\left(-202a^{4}+267a^{3}+849a^{2}-1215a+131\right){x}+273a^{4}-549a^{3}-1145a^{2}+3141a-1692$ |
| 41.1-b4 |
41.1-b |
$4$ |
$6$ |
5.5.101833.1 |
$5$ |
$[5, 0]$ |
41.1 |
\( 41 \) |
\( 41^{3} \) |
$41.33912$ |
$(2a^4-2a^3-9a^2+9a)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 1 \) |
$1.044574188$ |
$7345.363440$ |
3.33945668 |
\( -\frac{204440949698}{68921} a^{4} + \frac{569159061812}{68921} a^{3} + \frac{806228180249}{68921} a^{2} - \frac{2707713557093}{68921} a + \frac{830816272453}{68921} \) |
\( \bigl[a^{3} + a^{2} - 3 a - 2\) , \( a^{3} + a^{2} - 4 a - 2\) , \( a^{4} - 5 a^{2} + 2 a + 3\) , \( 23 a^{4} - 33 a^{3} - 96 a^{2} + 160 a - 39\) , \( -99 a^{4} + 154 a^{3} + 414 a^{2} - 721 a + 187\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-3a-2\right){x}{y}+\left(a^{4}-5a^{2}+2a+3\right){y}={x}^{3}+\left(a^{3}+a^{2}-4a-2\right){x}^{2}+\left(23a^{4}-33a^{3}-96a^{2}+160a-39\right){x}-99a^{4}+154a^{3}+414a^{2}-721a+187$ |
| 47.1-a1 |
47.1-a |
$2$ |
$3$ |
5.5.101833.1 |
$5$ |
$[5, 0]$ |
47.1 |
\( 47 \) |
\( 47^{9} \) |
$41.90758$ |
$(-2a^4+a^3+10a^2-6a-4)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.2 |
$9$ |
\( 1 \) |
$2.703692702$ |
$10.01071569$ |
3.81672352 |
\( \frac{411480251133078258292009}{1119130473102767} a^{4} - \frac{631912550193977746031962}{1119130473102767} a^{3} - \frac{1719175847951640835620131}{1119130473102767} a^{2} + \frac{2978755937111923304953368}{1119130473102767} a - \frac{771410168780062283610507}{1119130473102767} \) |
\( \bigl[a^{4} - 4 a^{2} + 2 a + 1\) , \( -a^{3} + 4 a + 1\) , \( a^{4} - 5 a^{2} + a + 2\) , \( 5 a^{4} - 24 a^{3} + 30 a^{2} + 4 a - 13\) , \( -6 a^{4} - 38 a^{3} + 77 a^{2} - a - 29\bigr] \) |
${y}^2+\left(a^{4}-4a^{2}+2a+1\right){x}{y}+\left(a^{4}-5a^{2}+a+2\right){y}={x}^{3}+\left(-a^{3}+4a+1\right){x}^{2}+\left(5a^{4}-24a^{3}+30a^{2}+4a-13\right){x}-6a^{4}-38a^{3}+77a^{2}-a-29$ |
| 47.1-a2 |
47.1-a |
$2$ |
$3$ |
5.5.101833.1 |
$5$ |
$[5, 0]$ |
47.1 |
\( 47 \) |
\( 47^{3} \) |
$41.90758$ |
$(-2a^4+a^3+10a^2-6a-4)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1 |
$1$ |
\( 1 \) |
$0.901230900$ |
$2432.603914$ |
3.81672352 |
\( \frac{673229541}{103823} a^{4} + \frac{816421116}{103823} a^{3} - \frac{1932765100}{103823} a^{2} - \frac{427923599}{103823} a + \frac{317388426}{103823} \) |
\( \bigl[a^{4} - 5 a^{2} + a + 2\) , \( -2 a^{4} + a^{3} + 9 a^{2} - 5 a - 1\) , \( -a^{4} + a^{3} + 5 a^{2} - 4 a - 2\) , \( a^{4} - 2 a^{3} - 8 a^{2} + 10 a + 12\) , \( -21 a^{4} + 13 a^{3} + 109 a^{2} - 65 a - 61\bigr] \) |
${y}^2+\left(a^{4}-5a^{2}+a+2\right){x}{y}+\left(-a^{4}+a^{3}+5a^{2}-4a-2\right){y}={x}^{3}+\left(-2a^{4}+a^{3}+9a^{2}-5a-1\right){x}^{2}+\left(a^{4}-2a^{3}-8a^{2}+10a+12\right){x}-21a^{4}+13a^{3}+109a^{2}-65a-61$ |
| 49.1-a1 |
49.1-a |
$4$ |
$4$ |
5.5.101833.1 |
$5$ |
$[5, 0]$ |
49.1 |
\( 7^{2} \) |
\( - 7^{5} \) |
$42.08259$ |
$(a^3-4a), (-a^4+5a^2-a-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 2 \) |
$1$ |
$421.2041337$ |
2.63984453 |
\( \frac{38751418709522459}{2401} a^{4} - \frac{122339380606804286}{2401} a^{3} + \frac{69902593913992472}{2401} a^{2} + \frac{43819613297271730}{2401} a - \frac{17873782114898526}{2401} \) |
\( \bigl[a^{4} - 4 a^{2} + 2 a\) , \( -a^{4} + a^{3} + 5 a^{2} - 6 a - 2\) , \( a^{4} - 4 a^{2} + a + 1\) , \( -192 a^{4} + 133 a^{3} + 992 a^{2} - 621 a - 609\) , \( 2280 a^{4} - 1570 a^{3} - 11828 a^{2} + 7569 a + 6896\bigr] \) |
${y}^2+\left(a^{4}-4a^{2}+2a\right){x}{y}+\left(a^{4}-4a^{2}+a+1\right){y}={x}^{3}+\left(-a^{4}+a^{3}+5a^{2}-6a-2\right){x}^{2}+\left(-192a^{4}+133a^{3}+992a^{2}-621a-609\right){x}+2280a^{4}-1570a^{3}-11828a^{2}+7569a+6896$ |
| 49.1-a2 |
49.1-a |
$4$ |
$4$ |
5.5.101833.1 |
$5$ |
$[5, 0]$ |
49.1 |
\( 7^{2} \) |
\( 7^{2} \) |
$42.08259$ |
$(a^3-4a), (-a^4+5a^2-a-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$3369.633070$ |
2.63984453 |
\( \frac{299862}{7} a^{4} - 28729 a^{3} - \frac{1568998}{7} a^{2} + \frac{992443}{7} a + 131851 \) |
\( \bigl[-a^{4} + a^{3} + 5 a^{2} - 4 a - 1\) , \( -a^{4} + a^{3} + 4 a^{2} - 5 a\) , \( -a^{4} + a^{3} + 6 a^{2} - 5 a - 4\) , \( -3 a^{4} + 3 a^{3} + 13 a^{2} - 13 a - 2\) , \( -2 a^{4} + a^{3} + 12 a^{2} - 10 a - 4\bigr] \) |
${y}^2+\left(-a^{4}+a^{3}+5a^{2}-4a-1\right){x}{y}+\left(-a^{4}+a^{3}+6a^{2}-5a-4\right){y}={x}^{3}+\left(-a^{4}+a^{3}+4a^{2}-5a\right){x}^{2}+\left(-3a^{4}+3a^{3}+13a^{2}-13a-2\right){x}-2a^{4}+a^{3}+12a^{2}-10a-4$ |
| 49.1-a3 |
49.1-a |
$4$ |
$4$ |
5.5.101833.1 |
$5$ |
$[5, 0]$ |
49.1 |
\( 7^{2} \) |
\( 7^{4} \) |
$42.08259$ |
$(a^3-4a), (-a^4+5a^2-a-3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$1$ |
$3369.633070$ |
2.63984453 |
\( \frac{320058753269}{49} a^{4} - \frac{216006983729}{49} a^{3} - \frac{1670362039497}{49} a^{2} + \frac{1056811122786}{49} a + \frac{983839052642}{49} \) |
\( \bigl[1\) , \( -a^{4} + a^{3} + 5 a^{2} - 6 a - 3\) , \( a + 1\) , \( 6 a^{4} - 6 a^{3} - 35 a^{2} + 15 a + 4\) , \( 4 a^{4} - 11 a^{3} - 30 a^{2} + 23 a - 7\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a^{4}+a^{3}+5a^{2}-6a-3\right){x}^{2}+\left(6a^{4}-6a^{3}-35a^{2}+15a+4\right){x}+4a^{4}-11a^{3}-30a^{2}+23a-7$ |
| 49.1-a4 |
49.1-a |
$4$ |
$4$ |
5.5.101833.1 |
$5$ |
$[5, 0]$ |
49.1 |
\( 7^{2} \) |
\( 7^{5} \) |
$42.08259$ |
$(a^3-4a), (-a^4+5a^2-a-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$842.4082675$ |
2.63984453 |
\( \frac{367085398231746795395045}{2401} a^{4} - \frac{247675473744662250483394}{2401} a^{3} - \frac{1915993828628377966351640}{2401} a^{2} + \frac{1212169625172946768411726}{2401} a + \frac{1128479815846732538107438}{2401} \) |
\( \bigl[-a^{4} + a^{3} + 5 a^{2} - 5 a - 2\) , \( -a^{2} + a + 2\) , \( a^{4} - 4 a^{2} + 2 a + 1\) , \( 23 a^{4} - 43 a^{3} - 89 a^{2} + 188 a - 99\) , \( 58 a^{4} - 108 a^{3} - 277 a^{2} + 468 a - 37\bigr] \) |
${y}^2+\left(-a^{4}+a^{3}+5a^{2}-5a-2\right){x}{y}+\left(a^{4}-4a^{2}+2a+1\right){y}={x}^{3}+\left(-a^{2}+a+2\right){x}^{2}+\left(23a^{4}-43a^{3}-89a^{2}+188a-99\right){x}+58a^{4}-108a^{3}-277a^{2}+468a-37$ |
| 49.1-b1 |
49.1-b |
$2$ |
$2$ |
5.5.101833.1 |
$5$ |
$[5, 0]$ |
49.1 |
\( 7^{2} \) |
\( - 7^{11} \) |
$42.08259$ |
$(a^3-4a), (-a^4+5a^2-a-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 2 \cdot 3 \) |
$1$ |
$23.89726103$ |
0.449319336 |
\( \frac{8870393888706462600}{117649} a^{4} - \frac{27970011438306732435}{117649} a^{3} + \frac{15877125457545800054}{117649} a^{2} + \frac{10153026094053639655}{117649} a - \frac{4116722048733472027}{117649} \) |
\( \bigl[a^{4} - 5 a^{2} + a + 3\) , \( -2 a^{4} + a^{3} + 9 a^{2} - 6 a - 3\) , \( a^{3} + a^{2} - 4 a - 1\) , \( -278 a^{4} + 193 a^{3} + 1436 a^{2} - 948 a - 806\) , \( -3036 a^{4} + 2053 a^{3} + 15838 a^{2} - 10046 a - 9306\bigr] \) |
${y}^2+\left(a^{4}-5a^{2}+a+3\right){x}{y}+\left(a^{3}+a^{2}-4a-1\right){y}={x}^{3}+\left(-2a^{4}+a^{3}+9a^{2}-6a-3\right){x}^{2}+\left(-278a^{4}+193a^{3}+1436a^{2}-948a-806\right){x}-3036a^{4}+2053a^{3}+15838a^{2}-10046a-9306$ |
| 49.1-b2 |
49.1-b |
$2$ |
$2$ |
5.5.101833.1 |
$5$ |
$[5, 0]$ |
49.1 |
\( 7^{2} \) |
\( - 7^{13} \) |
$42.08259$ |
$(a^3-4a), (-a^4+5a^2-a-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$95.58904415$ |
0.449319336 |
\( -\frac{332844701011348}{282475249} a^{4} + \frac{1020307048346386}{282475249} a^{3} - \frac{513320755400510}{282475249} a^{2} - \frac{406213121605483}{282475249} a + \frac{113414705556030}{282475249} \) |
\( \bigl[a^{4} - 5 a^{2} + a + 3\) , \( -2 a^{4} + a^{3} + 9 a^{2} - 6 a - 3\) , \( a^{3} + a^{2} - 4 a - 1\) , \( -13 a^{4} + 8 a^{3} + 71 a^{2} - 38 a - 51\) , \( -38 a^{4} + 22 a^{3} + 198 a^{2} - 113 a - 126\bigr] \) |
${y}^2+\left(a^{4}-5a^{2}+a+3\right){x}{y}+\left(a^{3}+a^{2}-4a-1\right){y}={x}^{3}+\left(-2a^{4}+a^{3}+9a^{2}-6a-3\right){x}^{2}+\left(-13a^{4}+8a^{3}+71a^{2}-38a-51\right){x}-38a^{4}+22a^{3}+198a^{2}-113a-126$ |
| 49.1-c1 |
49.1-c |
$2$ |
$2$ |
5.5.101833.1 |
$5$ |
$[5, 0]$ |
49.1 |
\( 7^{2} \) |
\( - 7^{3} \) |
$42.08259$ |
$(a^3-4a), (-a^4+5a^2-a-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$847.1428247$ |
1.32734058 |
\( -\frac{15123228}{49} a^{4} - \frac{15631760}{49} a^{3} + \frac{41223524}{49} a^{2} + \frac{10786920}{49} a - \frac{7090191}{49} \) |
\( \bigl[a^{3} + a^{2} - 4 a - 1\) , \( -a^{4} + a^{3} + 5 a^{2} - 6 a - 1\) , \( 0\) , \( 2 a^{4} - a^{3} - 10 a^{2} + 4 a + 8\) , \( 0\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-4a-1\right){x}{y}={x}^{3}+\left(-a^{4}+a^{3}+5a^{2}-6a-1\right){x}^{2}+\left(2a^{4}-a^{3}-10a^{2}+4a+8\right){x}$ |
| 49.1-c2 |
49.1-c |
$2$ |
$2$ |
5.5.101833.1 |
$5$ |
$[5, 0]$ |
49.1 |
\( 7^{2} \) |
\( - 7^{3} \) |
$42.08259$ |
$(a^3-4a), (-a^4+5a^2-a-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 2 \) |
$1$ |
$211.7857061$ |
1.32734058 |
\( \frac{69736595718592}{49} a^{4} + \frac{75156884030448}{49} a^{3} - \frac{192096696403530}{49} a^{2} - \frac{50904111517940}{49} a + \frac{33517601656151}{49} \) |
\( \bigl[a^{4} - 4 a^{2} + 2 a\) , \( a^{4} - 6 a^{2} + a + 3\) , \( a^{2} + a - 2\) , \( -47 a^{4} + 27 a^{3} + 244 a^{2} - 138 a - 140\) , \( 29 a^{4} - 31 a^{3} - 159 a^{2} + 144 a + 110\bigr] \) |
${y}^2+\left(a^{4}-4a^{2}+2a\right){x}{y}+\left(a^{2}+a-2\right){y}={x}^{3}+\left(a^{4}-6a^{2}+a+3\right){x}^{2}+\left(-47a^{4}+27a^{3}+244a^{2}-138a-140\right){x}+29a^{4}-31a^{3}-159a^{2}+144a+110$ |
| 49.2-a1 |
49.2-a |
$2$ |
$2$ |
5.5.101833.1 |
$5$ |
$[5, 0]$ |
49.2 |
\( 7^{2} \) |
\( - 7^{3} \) |
$42.08259$ |
$(-a^4+5a^2-a-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$1866.596074$ |
2.92466470 |
\( -9743459 a^{4} + 11218540 a^{3} + 41658182 a^{2} - 53680928 a + 12763545 \) |
\( \bigl[a^{4} - 5 a^{2} + 2 a + 3\) , \( a^{3} + a^{2} - 5 a - 1\) , \( a^{4} - 5 a^{2} + 2 a + 3\) , \( a^{4} + a^{3} - a^{2} - 8 a - 3\) , \( a^{4} - 2 a^{2} - 3 a - 1\bigr] \) |
${y}^2+\left(a^{4}-5a^{2}+2a+3\right){x}{y}+\left(a^{4}-5a^{2}+2a+3\right){y}={x}^{3}+\left(a^{3}+a^{2}-5a-1\right){x}^{2}+\left(a^{4}+a^{3}-a^{2}-8a-3\right){x}+a^{4}-2a^{2}-3a-1$ |
| 49.2-a2 |
49.2-a |
$2$ |
$2$ |
5.5.101833.1 |
$5$ |
$[5, 0]$ |
49.2 |
\( 7^{2} \) |
\( 7^{3} \) |
$42.08259$ |
$(-a^4+5a^2-a-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$1866.596074$ |
2.92466470 |
\( -391110274974348 a^{4} + 600293951864650 a^{3} + 1634486831483849 a^{2} - 2829749741813142 a + 731258650231045 \) |
\( \bigl[a^{4} - 5 a^{2} + 2 a + 3\) , \( a^{3} + a^{2} - 5 a - 1\) , \( a^{4} - 5 a^{2} + 2 a + 3\) , \( -4 a^{4} + 6 a^{3} + 14 a^{2} - 18 a - 13\) , \( -4 a^{4} + 9 a^{3} - 21 a^{2} + 10 a + 13\bigr] \) |
${y}^2+\left(a^{4}-5a^{2}+2a+3\right){x}{y}+\left(a^{4}-5a^{2}+2a+3\right){y}={x}^{3}+\left(a^{3}+a^{2}-5a-1\right){x}^{2}+\left(-4a^{4}+6a^{3}+14a^{2}-18a-13\right){x}-4a^{4}+9a^{3}-21a^{2}+10a+13$ |
| 49.2-b1 |
49.2-b |
$1$ |
$1$ |
5.5.101833.1 |
$5$ |
$[5, 0]$ |
49.2 |
\( 7^{2} \) |
\( - 7^{8} \) |
$42.08259$ |
$(-a^4+5a^2-a-3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2 \) |
$1$ |
$370.6853921$ |
2.32322460 |
\( -\frac{208344}{49} a^{4} + \frac{176415}{49} a^{3} + \frac{1078676}{49} a^{2} - \frac{800173}{49} a - \frac{692364}{49} \) |
\( \bigl[a^{2} + a - 2\) , \( a^{2} + a - 2\) , \( a^{4} - 4 a^{2} + 2 a + 1\) , \( -a^{4} + 3 a^{3} + 8 a^{2} - 10 a - 8\) , \( 8 a^{4} - 2 a^{3} - 38 a^{2} + 16 a + 18\bigr] \) |
${y}^2+\left(a^{2}+a-2\right){x}{y}+\left(a^{4}-4a^{2}+2a+1\right){y}={x}^{3}+\left(a^{2}+a-2\right){x}^{2}+\left(-a^{4}+3a^{3}+8a^{2}-10a-8\right){x}+8a^{4}-2a^{3}-38a^{2}+16a+18$ |
| 49.2-c1 |
49.2-c |
$2$ |
$2$ |
5.5.101833.1 |
$5$ |
$[5, 0]$ |
49.2 |
\( 7^{2} \) |
\( - 7^{9} \) |
$42.08259$ |
$(-a^4+5a^2-a-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$891.2884758$ |
1.39650993 |
\( -9743459 a^{4} + 11218540 a^{3} + 41658182 a^{2} - 53680928 a + 12763545 \) |
\( \bigl[a^{4} - 4 a^{2} + 2 a + 1\) , \( -a^{4} + 5 a^{2} - a - 2\) , \( a^{4} - 4 a^{2} + a + 1\) , \( -12 a^{4} + 12 a^{3} + 67 a^{2} - 54 a - 46\) , \( -33 a^{4} + 31 a^{3} + 180 a^{2} - 142 a - 120\bigr] \) |
${y}^2+\left(a^{4}-4a^{2}+2a+1\right){x}{y}+\left(a^{4}-4a^{2}+a+1\right){y}={x}^{3}+\left(-a^{4}+5a^{2}-a-2\right){x}^{2}+\left(-12a^{4}+12a^{3}+67a^{2}-54a-46\right){x}-33a^{4}+31a^{3}+180a^{2}-142a-120$ |
| 49.2-c2 |
49.2-c |
$2$ |
$2$ |
5.5.101833.1 |
$5$ |
$[5, 0]$ |
49.2 |
\( 7^{2} \) |
\( 7^{9} \) |
$42.08259$ |
$(-a^4+5a^2-a-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$891.2884758$ |
1.39650993 |
\( -391110274974348 a^{4} + 600293951864650 a^{3} + 1634486831483849 a^{2} - 2829749741813142 a + 731258650231045 \) |
\( \bigl[a^{4} - 4 a^{2} + 2 a + 1\) , \( -a^{4} + 5 a^{2} - a - 2\) , \( a^{4} - 4 a^{2} + a + 1\) , \( -252 a^{4} + 172 a^{3} + 1317 a^{2} - 839 a - 786\) , \( -2854 a^{4} + 1932 a^{3} + 14899 a^{2} - 9453 a - 8782\bigr] \) |
${y}^2+\left(a^{4}-4a^{2}+2a+1\right){x}{y}+\left(a^{4}-4a^{2}+a+1\right){y}={x}^{3}+\left(-a^{4}+5a^{2}-a-2\right){x}^{2}+\left(-252a^{4}+172a^{3}+1317a^{2}-839a-786\right){x}-2854a^{4}+1932a^{3}+14899a^{2}-9453a-8782$ |
| 49.2-d1 |
49.2-d |
$2$ |
$3$ |
5.5.101833.1 |
$5$ |
$[5, 0]$ |
49.2 |
\( 7^{2} \) |
\( - 7^{24} \) |
$42.08259$ |
$(-a^4+5a^2-a-3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B |
$9$ |
\( 2 \) |
$1$ |
$8.561975344$ |
0.482950043 |
\( -\frac{8299662076855549170261286086588}{1628413597910449} a^{4} - \frac{8956875689405632622076555588090}{1628413597910449} a^{3} + \frac{22875303550996342235969307745418}{1628413597910449} a^{2} + \frac{6063691056732384627706845863407}{1628413597910449} a - \frac{3991785116498736470982228805450}{1628413597910449} \) |
\( \bigl[a^{4} - 4 a^{2} + a\) , \( a^{4} - a^{3} - 6 a^{2} + 6 a + 5\) , \( a^{4} - 5 a^{2} + a + 3\) , \( 4 a^{4} - 83 a^{3} - 27 a^{2} + 350 a - 91\) , \( 684 a^{4} - 282 a^{3} - 2997 a^{2} + 1645 a - 196\bigr] \) |
${y}^2+\left(a^{4}-4a^{2}+a\right){x}{y}+\left(a^{4}-5a^{2}+a+3\right){y}={x}^{3}+\left(a^{4}-a^{3}-6a^{2}+6a+5\right){x}^{2}+\left(4a^{4}-83a^{3}-27a^{2}+350a-91\right){x}+684a^{4}-282a^{3}-2997a^{2}+1645a-196$ |
| 49.2-d2 |
49.2-d |
$2$ |
$3$ |
5.5.101833.1 |
$5$ |
$[5, 0]$ |
49.2 |
\( 7^{2} \) |
\( - 7^{12} \) |
$42.08259$ |
$(-a^4+5a^2-a-3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B |
$1$ |
\( 2 \) |
$1$ |
$77.05777810$ |
0.482950043 |
\( -\frac{10979115211801161}{117649} a^{4} + \frac{34621401561515437}{117649} a^{3} - \frac{19657765977069155}{117649} a^{2} - \frac{12564731083519550}{117649} a + \frac{5098526600665186}{117649} \) |
\( \bigl[a^{4} - 4 a^{2} + a\) , \( a^{4} - a^{3} - 6 a^{2} + 6 a + 5\) , \( a^{4} - 5 a^{2} + a + 3\) , \( 4 a^{4} + 2 a^{3} - 27 a^{2} + 5 a + 14\) , \( -11 a^{4} - a^{3} + 39 a^{2} + 25 a - 6\bigr] \) |
${y}^2+\left(a^{4}-4a^{2}+a\right){x}{y}+\left(a^{4}-5a^{2}+a+3\right){y}={x}^{3}+\left(a^{4}-a^{3}-6a^{2}+6a+5\right){x}^{2}+\left(4a^{4}+2a^{3}-27a^{2}+5a+14\right){x}-11a^{4}-a^{3}+39a^{2}+25a-6$ |
| 49.2-e1 |
49.2-e |
$4$ |
$6$ |
5.5.101833.1 |
$5$ |
$[5, 0]$ |
49.2 |
\( 7^{2} \) |
\( - 7^{15} \) |
$42.08259$ |
$(-a^4+5a^2-a-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$9$ |
\( 2 \) |
$1$ |
$51.35388679$ |
0.724171725 |
\( -\frac{129905211929111696759}{40353607} a^{4} - \frac{36847878589687577110}{40353607} a^{3} + \frac{602201291343435387454}{40353607} a^{2} + \frac{123496923865332601875}{40353607} a - \frac{101171544475898817040}{40353607} \) |
\( \bigl[-a^{4} + a^{3} + 6 a^{2} - 4 a - 4\) , \( a^{2} - 2\) , \( -a^{4} + a^{3} + 6 a^{2} - 5 a - 3\) , \( -3 a^{4} - 34 a^{3} - 7 a^{2} + 97 a - 46\) , \( 80 a^{4} + 19 a^{3} - 212 a^{2} + 180 a - 156\bigr] \) |
${y}^2+\left(-a^{4}+a^{3}+6a^{2}-4a-4\right){x}{y}+\left(-a^{4}+a^{3}+6a^{2}-5a-3\right){y}={x}^{3}+\left(a^{2}-2\right){x}^{2}+\left(-3a^{4}-34a^{3}-7a^{2}+97a-46\right){x}+80a^{4}+19a^{3}-212a^{2}+180a-156$ |
| 49.2-e2 |
49.2-e |
$4$ |
$6$ |
5.5.101833.1 |
$5$ |
$[5, 0]$ |
49.2 |
\( 7^{2} \) |
\( - 7^{9} \) |
$42.08259$ |
$(-a^4+5a^2-a-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$1$ |
$462.1849811$ |
0.724171725 |
\( -\frac{7248523749}{343} a^{4} + \frac{4888935720}{343} a^{3} + \frac{37832389751}{343} a^{2} - \frac{23928280283}{343} a - \frac{22278421960}{343} \) |
\( \bigl[-a^{4} + a^{3} + 6 a^{2} - 4 a - 4\) , \( a^{2} - 2\) , \( -a^{4} + a^{3} + 6 a^{2} - 5 a - 3\) , \( -8 a^{4} + 6 a^{3} + 43 a^{2} - 28 a - 26\) , \( -22 a^{4} + 16 a^{3} + 116 a^{2} - 75 a - 69\bigr] \) |
${y}^2+\left(-a^{4}+a^{3}+6a^{2}-4a-4\right){x}{y}+\left(-a^{4}+a^{3}+6a^{2}-5a-3\right){y}={x}^{3}+\left(a^{2}-2\right){x}^{2}+\left(-8a^{4}+6a^{3}+43a^{2}-28a-26\right){x}-22a^{4}+16a^{3}+116a^{2}-75a-69$ |
| 49.2-e3 |
49.2-e |
$4$ |
$6$ |
5.5.101833.1 |
$5$ |
$[5, 0]$ |
49.2 |
\( 7^{2} \) |
\( - 7^{24} \) |
$42.08259$ |
$(-a^4+5a^2-a-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$9$ |
\( 2^{2} \) |
$1$ |
$25.67694339$ |
0.724171725 |
\( \frac{202244099233249301987463016784}{1628413597910449} a^{4} + \frac{218258900994709298179800644103}{1628413597910449} a^{3} - \frac{557419681646490388575999100179}{1628413597910449} a^{2} - \frac{147758505836585744175799501677}{1628413597910449} a + \frac{97270821948072542864023504891}{1628413597910449} \) |
\( \bigl[-a^{4} + a^{3} + 6 a^{2} - 4 a - 4\) , \( a^{2} - 2\) , \( -a^{4} + a^{3} + 6 a^{2} - 5 a - 3\) , \( -353 a^{4} - 204 a^{3} + 1213 a^{2} - 98 a - 496\) , \( 4604 a^{4} + 6531 a^{3} - 10211 a^{2} - 7005 a - 518\bigr] \) |
${y}^2+\left(-a^{4}+a^{3}+6a^{2}-4a-4\right){x}{y}+\left(-a^{4}+a^{3}+6a^{2}-5a-3\right){y}={x}^{3}+\left(a^{2}-2\right){x}^{2}+\left(-353a^{4}-204a^{3}+1213a^{2}-98a-496\right){x}+4604a^{4}+6531a^{3}-10211a^{2}-7005a-518$ |
*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.
