| 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 |
| 14.1-a1 |
14.1-a |
$6$ |
$8$ |
5.5.186037.1 |
$5$ |
$[5, 0]$ |
14.1 |
\( 2 \cdot 7 \) |
\( - 2^{6} \cdot 7^{8} \) |
$50.18235$ |
$(a^4-a^3-5a^2+2), (-a^4+a^3+6a^2-a-5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$180.8470536$ |
1.67714945 |
\( -\frac{64477514513737305584321773}{368947264} a^{4} + \frac{10699491548325379494199235}{368947264} a^{3} + \frac{98947272401536641312835617}{92236816} a^{2} + \frac{100578124733041654403631191}{184473632} a - \frac{154611480625383330655439525}{368947264} \) |
\( \bigl[1\) , \( -a^{3} + a^{2} + 4 a - 2\) , \( a + 1\) , \( -10 a^{4} + 12 a^{3} - 38 a^{2} - 47 a + 25\) , \( 75 a^{4} + 363 a^{3} - 268 a^{2} - 469 a + 216\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a^{3}+a^{2}+4a-2\right){x}^{2}+\left(-10a^{4}+12a^{3}-38a^{2}-47a+25\right){x}+75a^{4}+363a^{3}-268a^{2}-469a+216$ |
| 14.1-a2 |
14.1-a |
$6$ |
$8$ |
5.5.186037.1 |
$5$ |
$[5, 0]$ |
14.1 |
\( 2 \cdot 7 \) |
\( 2^{12} \cdot 7^{4} \) |
$50.18235$ |
$(a^4-a^3-5a^2+2), (-a^4+a^3+6a^2-a-5)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1$ |
$1446.776429$ |
1.67714945 |
\( -\frac{2015179228898275}{9834496} a^{4} + \frac{369355527356077}{9834496} a^{3} + \frac{3114840854870799}{2458624} a^{2} + \frac{3157849651706553}{4917248} a - \frac{4862986220117483}{9834496} \) |
\( \bigl[-a^{4} + 7 a^{2} + 3 a - 5\) , \( 2 a^{4} - a^{3} - 13 a^{2} - a + 9\) , \( -a^{4} + 7 a^{2} + 4 a - 4\) , \( 8 a^{4} + 11 a^{3} - 79 a^{2} - 46 a + 49\) , \( 11 a^{4} + 23 a^{3} - 121 a^{2} - 89 a + 67\bigr] \) |
${y}^2+\left(-a^{4}+7a^{2}+3a-5\right){x}{y}+\left(-a^{4}+7a^{2}+4a-4\right){y}={x}^{3}+\left(2a^{4}-a^{3}-13a^{2}-a+9\right){x}^{2}+\left(8a^{4}+11a^{3}-79a^{2}-46a+49\right){x}+11a^{4}+23a^{3}-121a^{2}-89a+67$ |
| 14.1-a3 |
14.1-a |
$6$ |
$8$ |
5.5.186037.1 |
$5$ |
$[5, 0]$ |
14.1 |
\( 2 \cdot 7 \) |
\( - 2^{3} \cdot 7 \) |
$50.18235$ |
$(a^4-a^3-5a^2+2), (-a^4+a^3+6a^2-a-5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$2893.552859$ |
1.67714945 |
\( -\frac{69341}{56} a^{4} + \frac{29739}{56} a^{3} + \frac{112845}{14} a^{2} + \frac{76243}{28} a - \frac{256357}{56} \) |
\( \bigl[-2 a^{4} + a^{3} + 13 a^{2} + 3 a - 9\) , \( 2 a^{4} - a^{3} - 12 a^{2} - 3 a + 7\) , \( -a^{3} + 2 a^{2} + 4 a - 2\) , \( 12 a^{4} - 7 a^{3} - 74 a^{2} - 7 a + 55\) , \( 14 a^{4} - 8 a^{3} - 88 a^{2} - 9 a + 65\bigr] \) |
${y}^2+\left(-2a^{4}+a^{3}+13a^{2}+3a-9\right){x}{y}+\left(-a^{3}+2a^{2}+4a-2\right){y}={x}^{3}+\left(2a^{4}-a^{3}-12a^{2}-3a+7\right){x}^{2}+\left(12a^{4}-7a^{3}-74a^{2}-7a+55\right){x}+14a^{4}-8a^{3}-88a^{2}-9a+65$ |
| 14.1-a4 |
14.1-a |
$6$ |
$8$ |
5.5.186037.1 |
$5$ |
$[5, 0]$ |
14.1 |
\( 2 \cdot 7 \) |
\( 2^{6} \cdot 7^{2} \) |
$50.18235$ |
$(a^4-a^3-5a^2+2), (-a^4+a^3+6a^2-a-5)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$1$ |
$2893.552859$ |
1.67714945 |
\( \frac{6439246493}{3136} a^{4} - \frac{3437926419}{3136} a^{3} - \frac{10171320721}{784} a^{2} - \frac{2669466983}{1568} a + \frac{31727939541}{3136} \) |
\( \bigl[a^{2} - 1\) , \( -a^{4} + 7 a^{2} + 4 a - 5\) , \( -2 a^{4} + a^{3} + 13 a^{2} + 2 a - 8\) , \( -27 a^{4} + 78 a^{3} + 22 a^{2} - 87 a + 27\) , \( 223 a^{4} - 636 a^{3} - 145 a^{2} + 728 a - 247\bigr] \) |
${y}^2+\left(a^{2}-1\right){x}{y}+\left(-2a^{4}+a^{3}+13a^{2}+2a-8\right){y}={x}^{3}+\left(-a^{4}+7a^{2}+4a-5\right){x}^{2}+\left(-27a^{4}+78a^{3}+22a^{2}-87a+27\right){x}+223a^{4}-636a^{3}-145a^{2}+728a-247$ |
| 14.1-a5 |
14.1-a |
$6$ |
$8$ |
5.5.186037.1 |
$5$ |
$[5, 0]$ |
14.1 |
\( 2 \cdot 7 \) |
\( 2^{3} \cdot 7 \) |
$50.18235$ |
$(a^4-a^3-5a^2+2), (-a^4+a^3+6a^2-a-5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$16$ |
\( 1 \) |
$1$ |
$180.8470536$ |
1.67714945 |
\( \frac{836260903520797}{56} a^{4} - \frac{479828241285739}{56} a^{3} - \frac{1306585647550461}{14} a^{2} - \frac{273916339949587}{28} a + \frac{3966357864497381}{56} \) |
\( \bigl[a + 1\) , \( a^{4} - a^{3} - 5 a^{2} - a + 2\) , \( a + 1\) , \( -109 a^{4} + 35 a^{3} + 637 a^{2} + 295 a - 249\) , \( 13759 a^{4} - 2328 a^{3} - 84363 a^{2} - 42827 a + 32920\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a^{4}-a^{3}-5a^{2}-a+2\right){x}^{2}+\left(-109a^{4}+35a^{3}+637a^{2}+295a-249\right){x}+13759a^{4}-2328a^{3}-84363a^{2}-42827a+32920$ |
| 14.1-a6 |
14.1-a |
$6$ |
$8$ |
5.5.186037.1 |
$5$ |
$[5, 0]$ |
14.1 |
\( 2 \cdot 7 \) |
\( 2^{24} \cdot 7^{2} \) |
$50.18235$ |
$(a^4-a^3-5a^2+2), (-a^4+a^3+6a^2-a-5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 2^{2} \) |
$1$ |
$180.8470536$ |
1.67714945 |
\( \frac{222706542399852062965069}{822083584} a^{4} + \frac{383635863272989616232157}{822083584} a^{3} - \frac{72937385698581477092577}{205520896} a^{2} - \frac{174453140728195229962711}{411041792} a + \frac{163598005239275873913797}{822083584} \) |
\( \bigl[-a^{4} + 7 a^{2} + 4 a - 5\) , \( a^{4} - 6 a^{2} - 5 a + 3\) , \( 0\) , \( -a^{4} - 5 a^{3} - 7 a^{2} - 2 a + 8\) , \( 12 a^{4} + 24 a^{3} - 10 a^{2} - 23 a + 6\bigr] \) |
${y}^2+\left(-a^{4}+7a^{2}+4a-5\right){x}{y}={x}^{3}+\left(a^{4}-6a^{2}-5a+3\right){x}^{2}+\left(-a^{4}-5a^{3}-7a^{2}-2a+8\right){x}+12a^{4}+24a^{3}-10a^{2}-23a+6$ |
| 14.1-b1 |
14.1-b |
$6$ |
$8$ |
5.5.186037.1 |
$5$ |
$[5, 0]$ |
14.1 |
\( 2 \cdot 7 \) |
\( - 2^{6} \cdot 7^{8} \) |
$50.18235$ |
$(a^4-a^3-5a^2+2), (-a^4+a^3+6a^2-a-5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.221623924$ |
$955.3281208$ |
2.45436723 |
\( -\frac{64477514513737305584321773}{368947264} a^{4} + \frac{10699491548325379494199235}{368947264} a^{3} + \frac{98947272401536641312835617}{92236816} a^{2} + \frac{100578124733041654403631191}{184473632} a - \frac{154611480625383330655439525}{368947264} \) |
\( \bigl[-2 a^{4} + a^{3} + 13 a^{2} + 3 a - 9\) , \( a + 1\) , \( -a^{4} + 7 a^{2} + 3 a - 4\) , \( -101 a^{4} + 186 a^{3} + 38 a^{2} - 219 a + 96\) , \( 1811 a^{4} - 3337 a^{3} - 1547 a^{2} + 3988 a - 1192\bigr] \) |
${y}^2+\left(-2a^{4}+a^{3}+13a^{2}+3a-9\right){x}{y}+\left(-a^{4}+7a^{2}+3a-4\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-101a^{4}+186a^{3}+38a^{2}-219a+96\right){x}+1811a^{4}-3337a^{3}-1547a^{2}+3988a-1192$ |
| 14.1-b2 |
14.1-b |
$6$ |
$8$ |
5.5.186037.1 |
$5$ |
$[5, 0]$ |
14.1 |
\( 2 \cdot 7 \) |
\( 2^{12} \cdot 7^{4} \) |
$50.18235$ |
$(a^4-a^3-5a^2+2), (-a^4+a^3+6a^2-a-5)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$0.110811962$ |
$7642.624966$ |
2.45436723 |
\( -\frac{2015179228898275}{9834496} a^{4} + \frac{369355527356077}{9834496} a^{3} + \frac{3114840854870799}{2458624} a^{2} + \frac{3157849651706553}{4917248} a - \frac{4862986220117483}{9834496} \) |
\( \bigl[-a^{4} + 7 a^{2} + 4 a - 5\) , \( -a^{4} + 8 a^{2} + 3 a - 7\) , \( -a^{4} + 7 a^{2} + 4 a - 4\) , \( -43 a^{4} + 128 a^{3} + 19 a^{2} - 147 a + 52\) , \( 311 a^{4} - 887 a^{3} - 215 a^{2} + 1010 a - 332\bigr] \) |
${y}^2+\left(-a^{4}+7a^{2}+4a-5\right){x}{y}+\left(-a^{4}+7a^{2}+4a-4\right){y}={x}^{3}+\left(-a^{4}+8a^{2}+3a-7\right){x}^{2}+\left(-43a^{4}+128a^{3}+19a^{2}-147a+52\right){x}+311a^{4}-887a^{3}-215a^{2}+1010a-332$ |
| 14.1-b3 |
14.1-b |
$6$ |
$8$ |
5.5.186037.1 |
$5$ |
$[5, 0]$ |
14.1 |
\( 2 \cdot 7 \) |
\( - 2^{3} \cdot 7 \) |
$50.18235$ |
$(a^4-a^3-5a^2+2), (-a^4+a^3+6a^2-a-5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$0.110811962$ |
$7642.624966$ |
2.45436723 |
\( -\frac{69341}{56} a^{4} + \frac{29739}{56} a^{3} + \frac{112845}{14} a^{2} + \frac{76243}{28} a - \frac{256357}{56} \) |
\( \bigl[1\) , \( a^{3} - a^{2} - 4 a + 1\) , \( a^{2} - 2\) , \( -a^{4} + a^{3} + 5 a^{2} - a - 1\) , \( -a^{2} - a + 1\bigr] \) |
${y}^2+{x}{y}+\left(a^{2}-2\right){y}={x}^{3}+\left(a^{3}-a^{2}-4a+1\right){x}^{2}+\left(-a^{4}+a^{3}+5a^{2}-a-1\right){x}-a^{2}-a+1$ |
| 14.1-b4 |
14.1-b |
$6$ |
$8$ |
5.5.186037.1 |
$5$ |
$[5, 0]$ |
14.1 |
\( 2 \cdot 7 \) |
\( 2^{6} \cdot 7^{2} \) |
$50.18235$ |
$(a^4-a^3-5a^2+2), (-a^4+a^3+6a^2-a-5)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$0.055405981$ |
$15285.24993$ |
2.45436723 |
\( \frac{6439246493}{3136} a^{4} - \frac{3437926419}{3136} a^{3} - \frac{10171320721}{784} a^{2} - \frac{2669466983}{1568} a + \frac{31727939541}{3136} \) |
\( \bigl[-a^{4} + 8 a^{2} + 2 a - 7\) , \( a^{3} - 2 a^{2} - 2 a + 4\) , \( -a^{4} + a^{3} + 6 a^{2} - a - 3\) , \( 10 a^{4} + 6 a^{3} - 81 a^{2} - 42 a + 50\) , \( -18 a^{4} + 29 a^{3} + 52 a^{2} + 5 a + 8\bigr] \) |
${y}^2+\left(-a^{4}+8a^{2}+2a-7\right){x}{y}+\left(-a^{4}+a^{3}+6a^{2}-a-3\right){y}={x}^{3}+\left(a^{3}-2a^{2}-2a+4\right){x}^{2}+\left(10a^{4}+6a^{3}-81a^{2}-42a+50\right){x}-18a^{4}+29a^{3}+52a^{2}+5a+8$ |
| 14.1-b5 |
14.1-b |
$6$ |
$8$ |
5.5.186037.1 |
$5$ |
$[5, 0]$ |
14.1 |
\( 2 \cdot 7 \) |
\( 2^{3} \cdot 7 \) |
$50.18235$ |
$(a^4-a^3-5a^2+2), (-a^4+a^3+6a^2-a-5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 1 \) |
$0.110811962$ |
$1910.656241$ |
2.45436723 |
\( \frac{836260903520797}{56} a^{4} - \frac{479828241285739}{56} a^{3} - \frac{1306585647550461}{14} a^{2} - \frac{273916339949587}{28} a + \frac{3966357864497381}{56} \) |
\( \bigl[-a^{4} + 8 a^{2} + 2 a - 7\) , \( a^{3} - 2 a^{2} - 2 a + 4\) , \( -a^{4} + a^{3} + 6 a^{2} - a - 3\) , \( -50 a^{4} + 146 a^{3} + 24 a^{2} - 162 a + 70\) , \( -725 a^{4} + 1911 a^{3} + 819 a^{2} - 1976 a + 582\bigr] \) |
${y}^2+\left(-a^{4}+8a^{2}+2a-7\right){x}{y}+\left(-a^{4}+a^{3}+6a^{2}-a-3\right){y}={x}^{3}+\left(a^{3}-2a^{2}-2a+4\right){x}^{2}+\left(-50a^{4}+146a^{3}+24a^{2}-162a+70\right){x}-725a^{4}+1911a^{3}+819a^{2}-1976a+582$ |
| 14.1-b6 |
14.1-b |
$6$ |
$8$ |
5.5.186037.1 |
$5$ |
$[5, 0]$ |
14.1 |
\( 2 \cdot 7 \) |
\( 2^{24} \cdot 7^{2} \) |
$50.18235$ |
$(a^4-a^3-5a^2+2), (-a^4+a^3+6a^2-a-5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.221623924$ |
$955.3281208$ |
2.45436723 |
\( \frac{222706542399852062965069}{822083584} a^{4} + \frac{383635863272989616232157}{822083584} a^{3} - \frac{72937385698581477092577}{205520896} a^{2} - \frac{174453140728195229962711}{411041792} a + \frac{163598005239275873913797}{822083584} \) |
\( \bigl[-a^{3} + 2 a^{2} + 3 a - 3\) , \( -a^{2} + 2 a + 3\) , \( -a^{4} + 7 a^{2} + 3 a - 4\) , \( -7 a^{4} - 16 a^{3} + 8 a^{2} + 13 a + 1\) , \( 78 a^{4} + 117 a^{3} - 107 a^{2} - 108 a + 59\bigr] \) |
${y}^2+\left(-a^{3}+2a^{2}+3a-3\right){x}{y}+\left(-a^{4}+7a^{2}+3a-4\right){y}={x}^{3}+\left(-a^{2}+2a+3\right){x}^{2}+\left(-7a^{4}-16a^{3}+8a^{2}+13a+1\right){x}+78a^{4}+117a^{3}-107a^{2}-108a+59$ |
| 14.1-c1 |
14.1-c |
$4$ |
$4$ |
5.5.186037.1 |
$5$ |
$[5, 0]$ |
14.1 |
\( 2 \cdot 7 \) |
\( 2 \cdot 7^{6} \) |
$50.18235$ |
$(a^4-a^3-5a^2+2), (-a^4+a^3+6a^2-a-5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$16$ |
\( 2 \cdot 3 \) |
$1.503383728$ |
$13.02565410$ |
5.44817399 |
\( \frac{1835160407913915947}{235298} a^{4} - \frac{4818387286301378449}{235298} a^{3} - \frac{638760671491823421}{117649} a^{2} + \frac{2781427934882213802}{117649} a - \frac{1818373199977374297}{235298} \) |
\( \bigl[-a^{4} + 7 a^{2} + 3 a - 5\) , \( a^{4} - 7 a^{2} - 2 a + 6\) , \( -2 a^{4} + a^{3} + 13 a^{2} + 2 a - 8\) , \( 120 a^{4} - 263 a^{3} - 366 a^{2} + 715 a - 534\) , \( 1676 a^{4} - 3815 a^{3} - 5260 a^{2} + 10964 a - 6014\bigr] \) |
${y}^2+\left(-a^{4}+7a^{2}+3a-5\right){x}{y}+\left(-2a^{4}+a^{3}+13a^{2}+2a-8\right){y}={x}^{3}+\left(a^{4}-7a^{2}-2a+6\right){x}^{2}+\left(120a^{4}-263a^{3}-366a^{2}+715a-534\right){x}+1676a^{4}-3815a^{3}-5260a^{2}+10964a-6014$ |
| 14.1-c2 |
14.1-c |
$4$ |
$4$ |
5.5.186037.1 |
$5$ |
$[5, 0]$ |
14.1 |
\( 2 \cdot 7 \) |
\( 2^{2} \cdot 7^{12} \) |
$50.18235$ |
$(a^4-a^3-5a^2+2), (-a^4+a^3+6a^2-a-5)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \cdot 3 \) |
$0.751691864$ |
$416.8209312$ |
5.44817399 |
\( \frac{32740801508853265}{55365148804} a^{4} - \frac{86659054293916539}{55365148804} a^{3} - \frac{310725450709720}{13841287201} a^{2} + \frac{57533876947898993}{27682574402} a - \frac{42564809663720539}{55365148804} \) |
\( \bigl[-a^{4} + 7 a^{2} + 3 a - 5\) , \( a^{4} - 7 a^{2} - 2 a + 6\) , \( -2 a^{4} + a^{3} + 13 a^{2} + 2 a - 8\) , \( 5 a^{4} - 33 a^{3} + 24 a^{2} + 125 a - 124\) , \( -27 a^{4} + 108 a^{3} + 18 a^{2} - 390 a + 228\bigr] \) |
${y}^2+\left(-a^{4}+7a^{2}+3a-5\right){x}{y}+\left(-2a^{4}+a^{3}+13a^{2}+2a-8\right){y}={x}^{3}+\left(a^{4}-7a^{2}-2a+6\right){x}^{2}+\left(5a^{4}-33a^{3}+24a^{2}+125a-124\right){x}-27a^{4}+108a^{3}+18a^{2}-390a+228$ |
| 14.1-c3 |
14.1-c |
$4$ |
$4$ |
5.5.186037.1 |
$5$ |
$[5, 0]$ |
14.1 |
\( 2 \cdot 7 \) |
\( 2^{4} \cdot 7^{6} \) |
$50.18235$ |
$(a^4-a^3-5a^2+2), (-a^4+a^3+6a^2-a-5)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \cdot 3 \) |
$0.375845932$ |
$833.6418624$ |
5.44817399 |
\( -\frac{176163971}{1882384} a^{4} + \frac{1240118861}{1882384} a^{3} - \frac{131663349}{470596} a^{2} - \frac{1307589391}{941192} a + \frac{1705329925}{1882384} \) |
\( \bigl[-a^{4} + 8 a^{2} + 3 a - 7\) , \( a^{4} - 2 a^{3} - 4 a^{2} + 4 a + 1\) , \( -a^{3} + 2 a^{2} + 3 a - 3\) , \( 46 a^{4} - 27 a^{3} - 285 a^{2} - 29 a + 216\) , \( 506 a^{4} - 293 a^{3} - 3157 a^{2} - 321 a + 2389\bigr] \) |
${y}^2+\left(-a^{4}+8a^{2}+3a-7\right){x}{y}+\left(-a^{3}+2a^{2}+3a-3\right){y}={x}^{3}+\left(a^{4}-2a^{3}-4a^{2}+4a+1\right){x}^{2}+\left(46a^{4}-27a^{3}-285a^{2}-29a+216\right){x}+506a^{4}-293a^{3}-3157a^{2}-321a+2389$ |
| 14.1-c4 |
14.1-c |
$4$ |
$4$ |
5.5.186037.1 |
$5$ |
$[5, 0]$ |
14.1 |
\( 2 \cdot 7 \) |
\( - 2 \cdot 7^{24} \) |
$50.18235$ |
$(a^4-a^3-5a^2+2), (-a^4+a^3+6a^2-a-5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \cdot 3 \) |
$0.375845932$ |
$208.4104656$ |
5.44817399 |
\( \frac{3837602039274568827309319493}{383162462761132828802} a^{4} - \frac{1960354647482444443082583999}{383162462761132828802} a^{3} - \frac{12196842101392711188322794963}{191581231380566414401} a^{2} - \frac{1781920177091150497277068938}{191581231380566414401} a + \frac{19222953586413072116443459625}{383162462761132828802} \) |
\( \bigl[-a^{4} + 7 a^{2} + 4 a - 5\) , \( a^{4} - 7 a^{2} - 3 a + 4\) , \( -a^{4} + 8 a^{2} + 3 a - 6\) , \( -3284 a^{4} + 9397 a^{3} + 2226 a^{2} - 10741 a + 3532\) , \( -253751 a^{4} + 725693 a^{3} + 172805 a^{2} - 828876 a + 272862\bigr] \) |
${y}^2+\left(-a^{4}+7a^{2}+4a-5\right){x}{y}+\left(-a^{4}+8a^{2}+3a-6\right){y}={x}^{3}+\left(a^{4}-7a^{2}-3a+4\right){x}^{2}+\left(-3284a^{4}+9397a^{3}+2226a^{2}-10741a+3532\right){x}-253751a^{4}+725693a^{3}+172805a^{2}-828876a+272862$ |
| 14.1-d1 |
14.1-d |
$4$ |
$14$ |
5.5.186037.1 |
$5$ |
$[5, 0]$ |
14.1 |
\( 2 \cdot 7 \) |
\( - 2^{2} \cdot 7^{2} \) |
$50.18235$ |
$(a^4-a^3-5a^2+2), (-a^4+a^3+6a^2-a-5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 7$ |
2B, 7B.6.3 |
$49$ |
\( 2^{2} \) |
$1$ |
$28.63763953$ |
3.25337133 |
\( -\frac{2067610835720863057955286798102431943}{196} a^{4} + \frac{343102317595962976613660641481178917}{196} a^{3} + \frac{3172958109894446647983359053556711974}{49} a^{2} + \frac{3225254914093937420670769269047735683}{98} a - \frac{4957951234289816952477391009636862963}{196} \) |
\( \bigl[a^{2} - a - 1\) , \( a^{4} - a^{3} - 6 a^{2} + a + 4\) , \( -2 a^{4} + a^{3} + 13 a^{2} + 3 a - 8\) , \( -54153 a^{4} + 31117 a^{3} + 338030 a^{2} + 35481 a - 256621\) , \( 8798881 a^{4} - 5076932 a^{3} - 54943929 a^{2} - 5650378 a + 41622383\bigr] \) |
${y}^2+\left(a^{2}-a-1\right){x}{y}+\left(-2a^{4}+a^{3}+13a^{2}+3a-8\right){y}={x}^{3}+\left(a^{4}-a^{3}-6a^{2}+a+4\right){x}^{2}+\left(-54153a^{4}+31117a^{3}+338030a^{2}+35481a-256621\right){x}+8798881a^{4}-5076932a^{3}-54943929a^{2}-5650378a+41622383$ |
| 14.1-d2 |
14.1-d |
$4$ |
$14$ |
5.5.186037.1 |
$5$ |
$[5, 0]$ |
14.1 |
\( 2 \cdot 7 \) |
\( - 2^{14} \cdot 7^{14} \) |
$50.18235$ |
$(a^4-a^3-5a^2+2), (-a^4+a^3+6a^2-a-5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 7$ |
2B, 7B.6.1 |
$1$ |
\( 2^{2} \cdot 7 \) |
$1$ |
$200.4634767$ |
3.25337133 |
\( -\frac{228005851807623232787}{11112006825558016} a^{4} + \frac{28893682402781220477}{11112006825558016} a^{3} + \frac{351233657882818767615}{2778001706389504} a^{2} + \frac{380160051242118750025}{5556003412779008} a - \frac{524281523912096022427}{11112006825558016} \) |
\( \bigl[-a^{4} + 8 a^{2} + 3 a - 7\) , \( -1\) , \( -a^{4} + 7 a^{2} + 3 a - 5\) , \( -584 a^{4} + 339 a^{3} + 3648 a^{2} + 365 a - 2773\) , \( -8215 a^{4} + 4738 a^{3} + 51295 a^{2} + 5282 a - 38833\bigr] \) |
${y}^2+\left(-a^{4}+8a^{2}+3a-7\right){x}{y}+\left(-a^{4}+7a^{2}+3a-5\right){y}={x}^{3}-{x}^{2}+\left(-584a^{4}+339a^{3}+3648a^{2}+365a-2773\right){x}-8215a^{4}+4738a^{3}+51295a^{2}+5282a-38833$ |
| 14.1-d3 |
14.1-d |
$4$ |
$14$ |
5.5.186037.1 |
$5$ |
$[5, 0]$ |
14.1 |
\( 2 \cdot 7 \) |
\( - 2^{7} \cdot 7^{7} \) |
$50.18235$ |
$(a^4-a^3-5a^2+2), (-a^4+a^3+6a^2-a-5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 7$ |
2B, 7B.6.1 |
$1$ |
\( 7 \) |
$1$ |
$801.8539070$ |
3.25337133 |
\( \frac{263471732268379}{105413504} a^{4} - \frac{88842995531317}{105413504} a^{3} - \frac{438077667237255}{26353376} a^{2} - \frac{221733421401441}{52706752} a + \frac{1512923564448547}{105413504} \) |
\( \bigl[-2 a^{4} + a^{3} + 13 a^{2} + 2 a - 9\) , \( -2 a^{4} + a^{3} + 12 a^{2} + 2 a - 8\) , \( a^{4} - a^{3} - 5 a^{2} + 2\) , \( -16 a^{4} + 9 a^{3} + 99 a^{2} + 12 a - 74\) , \( -71 a^{4} + 41 a^{3} + 443 a^{2} + 46 a - 336\bigr] \) |
${y}^2+\left(-2a^{4}+a^{3}+13a^{2}+2a-9\right){x}{y}+\left(a^{4}-a^{3}-5a^{2}+2\right){y}={x}^{3}+\left(-2a^{4}+a^{3}+12a^{2}+2a-8\right){x}^{2}+\left(-16a^{4}+9a^{3}+99a^{2}+12a-74\right){x}-71a^{4}+41a^{3}+443a^{2}+46a-336$ |
| 14.1-d4 |
14.1-d |
$4$ |
$14$ |
5.5.186037.1 |
$5$ |
$[5, 0]$ |
14.1 |
\( 2 \cdot 7 \) |
\( - 2 \cdot 7 \) |
$50.18235$ |
$(a^4-a^3-5a^2+2), (-a^4+a^3+6a^2-a-5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 7$ |
2B, 7B.6.3 |
$49$ |
\( 1 \) |
$1$ |
$114.5505581$ |
3.25337133 |
\( \frac{1063019781555591054781}{14} a^{4} + \frac{1829819778466395774605}{14} a^{3} - \frac{698004470600002452914}{7} a^{2} - \frac{833248460923316092660}{7} a + \frac{782065927131370532559}{14} \) |
\( \bigl[-2 a^{4} + a^{3} + 13 a^{2} + 2 a - 9\) , \( -2 a^{4} + a^{3} + 12 a^{2} + 2 a - 8\) , \( a^{4} - a^{3} - 5 a^{2} + 2\) , \( -836 a^{4} + 264 a^{3} + 4464 a^{2} - 13 a - 4034\) , \( 10455 a^{4} - 21984 a^{3} - 96108 a^{2} + 8179 a + 82776\bigr] \) |
${y}^2+\left(-2a^{4}+a^{3}+13a^{2}+2a-9\right){x}{y}+\left(a^{4}-a^{3}-5a^{2}+2\right){y}={x}^{3}+\left(-2a^{4}+a^{3}+12a^{2}+2a-8\right){x}^{2}+\left(-836a^{4}+264a^{3}+4464a^{2}-13a-4034\right){x}+10455a^{4}-21984a^{3}-96108a^{2}+8179a+82776$ |
| 14.1-e1 |
14.1-e |
$4$ |
$4$ |
5.5.186037.1 |
$5$ |
$[5, 0]$ |
14.1 |
\( 2 \cdot 7 \) |
\( 2 \cdot 7^{6} \) |
$50.18235$ |
$(a^4-a^3-5a^2+2), (-a^4+a^3+6a^2-a-5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 2 \) |
$1$ |
$658.4548120$ |
3.05320741 |
\( \frac{1835160407913915947}{235298} a^{4} - \frac{4818387286301378449}{235298} a^{3} - \frac{638760671491823421}{117649} a^{2} + \frac{2781427934882213802}{117649} a - \frac{1818373199977374297}{235298} \) |
\( \bigl[-a^{4} + 7 a^{2} + 4 a - 5\) , \( -3 a^{4} + 2 a^{3} + 18 a^{2} + 3 a - 12\) , \( -a^{3} + 2 a^{2} + 3 a - 2\) , \( 621 a^{4} - 1360 a^{3} - 2182 a^{2} + 3948 a - 1289\) , \( -17759 a^{4} + 37905 a^{3} + 63929 a^{2} - 108799 a + 32873\bigr] \) |
${y}^2+\left(-a^{4}+7a^{2}+4a-5\right){x}{y}+\left(-a^{3}+2a^{2}+3a-2\right){y}={x}^{3}+\left(-3a^{4}+2a^{3}+18a^{2}+3a-12\right){x}^{2}+\left(621a^{4}-1360a^{3}-2182a^{2}+3948a-1289\right){x}-17759a^{4}+37905a^{3}+63929a^{2}-108799a+32873$ |
| 14.1-e2 |
14.1-e |
$4$ |
$4$ |
5.5.186037.1 |
$5$ |
$[5, 0]$ |
14.1 |
\( 2 \cdot 7 \) |
\( 2^{2} \cdot 7^{12} \) |
$50.18235$ |
$(a^4-a^3-5a^2+2), (-a^4+a^3+6a^2-a-5)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$4$ |
\( 2^{2} \) |
$1$ |
$1316.909624$ |
3.05320741 |
\( \frac{32740801508853265}{55365148804} a^{4} - \frac{86659054293916539}{55365148804} a^{3} - \frac{310725450709720}{13841287201} a^{2} + \frac{57533876947898993}{27682574402} a - \frac{42564809663720539}{55365148804} \) |
\( \bigl[a^{4} - a^{3} - 5 a^{2} + 3\) , \( a^{4} - a^{3} - 6 a^{2} + a + 3\) , \( a^{2} - 1\) , \( 98 a^{4} + 2 a^{3} - 584 a^{2} - 426 a + 66\) , \( -1960 a^{4} + 483 a^{3} + 12080 a^{2} + 5154 a - 5641\bigr] \) |
${y}^2+\left(a^{4}-a^{3}-5a^{2}+3\right){x}{y}+\left(a^{2}-1\right){y}={x}^{3}+\left(a^{4}-a^{3}-6a^{2}+a+3\right){x}^{2}+\left(98a^{4}+2a^{3}-584a^{2}-426a+66\right){x}-1960a^{4}+483a^{3}+12080a^{2}+5154a-5641$ |
| 14.1-e3 |
14.1-e |
$4$ |
$4$ |
5.5.186037.1 |
$5$ |
$[5, 0]$ |
14.1 |
\( 2 \cdot 7 \) |
\( 2^{4} \cdot 7^{6} \) |
$50.18235$ |
$(a^4-a^3-5a^2+2), (-a^4+a^3+6a^2-a-5)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$2633.819248$ |
3.05320741 |
\( -\frac{176163971}{1882384} a^{4} + \frac{1240118861}{1882384} a^{3} - \frac{131663349}{470596} a^{2} - \frac{1307589391}{941192} a + \frac{1705329925}{1882384} \) |
\( \bigl[-a^{3} + 2 a^{2} + 4 a - 3\) , \( a^{4} - a^{3} - 6 a^{2} + a + 5\) , \( a^{4} - a^{3} - 5 a^{2} + a + 3\) , \( 130 a^{4} - 75 a^{3} - 812 a^{2} - 84 a + 614\) , \( -1940 a^{4} + 1119 a^{3} + 12113 a^{2} + 1246 a - 9171\bigr] \) |
${y}^2+\left(-a^{3}+2a^{2}+4a-3\right){x}{y}+\left(a^{4}-a^{3}-5a^{2}+a+3\right){y}={x}^{3}+\left(a^{4}-a^{3}-6a^{2}+a+5\right){x}^{2}+\left(130a^{4}-75a^{3}-812a^{2}-84a+614\right){x}-1940a^{4}+1119a^{3}+12113a^{2}+1246a-9171$ |
| 14.1-e4 |
14.1-e |
$4$ |
$4$ |
5.5.186037.1 |
$5$ |
$[5, 0]$ |
14.1 |
\( 2 \cdot 7 \) |
\( - 2 \cdot 7^{24} \) |
$50.18235$ |
$(a^4-a^3-5a^2+2), (-a^4+a^3+6a^2-a-5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$64$ |
\( 2 \) |
$1$ |
$41.15342575$ |
3.05320741 |
\( \frac{3837602039274568827309319493}{383162462761132828802} a^{4} - \frac{1960354647482444443082583999}{383162462761132828802} a^{3} - \frac{12196842101392711188322794963}{191581231380566414401} a^{2} - \frac{1781920177091150497277068938}{191581231380566414401} a + \frac{19222953586413072116443459625}{383162462761132828802} \) |
\( \bigl[-a^{4} + 7 a^{2} + 3 a - 5\) , \( a^{3} - 2 a^{2} - 3 a + 3\) , \( a^{4} - a^{3} - 5 a^{2} + a + 3\) , \( -287 a^{4} + 1131 a^{3} - 430 a^{2} - 1678 a + 700\) , \( 11490 a^{4} - 32932 a^{3} - 7667 a^{2} + 37684 a - 12485\bigr] \) |
${y}^2+\left(-a^{4}+7a^{2}+3a-5\right){x}{y}+\left(a^{4}-a^{3}-5a^{2}+a+3\right){y}={x}^{3}+\left(a^{3}-2a^{2}-3a+3\right){x}^{2}+\left(-287a^{4}+1131a^{3}-430a^{2}-1678a+700\right){x}+11490a^{4}-32932a^{3}-7667a^{2}+37684a-12485$ |
| 14.1-f1 |
14.1-f |
$4$ |
$14$ |
5.5.186037.1 |
$5$ |
$[5, 0]$ |
14.1 |
\( 2 \cdot 7 \) |
\( - 2^{2} \cdot 7^{2} \) |
$50.18235$ |
$(a^4-a^3-5a^2+2), (-a^4+a^3+6a^2-a-5)$ |
$0 \le r \le 1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 7$ |
2B, 7B.1.3 |
|
\( 2^{2} \) |
$1$ |
$0.025837146$ |
5.43631864 |
\( -\frac{2067610835720863057955286798102431943}{196} a^{4} + \frac{343102317595962976613660641481178917}{196} a^{3} + \frac{3172958109894446647983359053556711974}{49} a^{2} + \frac{3225254914093937420670769269047735683}{98} a - \frac{4957951234289816952477391009636862963}{196} \) |
\( \bigl[-a^{4} + a^{3} + 6 a^{2} - a - 3\) , \( -a^{4} + a^{3} + 6 a^{2} - 2 a - 5\) , \( -a^{3} + 2 a^{2} + 4 a - 3\) , \( -162536 a^{4} + 93854 a^{3} + 1014912 a^{2} + 103687 a - 769392\) , \( -45954483 a^{4} + 26520125 a^{3} + 286942897 a^{2} + 29439055 a - 217328171\bigr] \) |
${y}^2+\left(-a^{4}+a^{3}+6a^{2}-a-3\right){x}{y}+\left(-a^{3}+2a^{2}+4a-3\right){y}={x}^{3}+\left(-a^{4}+a^{3}+6a^{2}-2a-5\right){x}^{2}+\left(-162536a^{4}+93854a^{3}+1014912a^{2}+103687a-769392\right){x}-45954483a^{4}+26520125a^{3}+286942897a^{2}+29439055a-217328171$ |
| 14.1-f2 |
14.1-f |
$4$ |
$14$ |
5.5.186037.1 |
$5$ |
$[5, 0]$ |
14.1 |
\( 2 \cdot 7 \) |
\( - 2^{14} \cdot 7^{14} \) |
$50.18235$ |
$(a^4-a^3-5a^2+2), (-a^4+a^3+6a^2-a-5)$ |
$0 \le r \le 1$ |
$\Z/14\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 7$ |
2B, 7B.1.1 |
|
\( 2^{2} \cdot 7^{2} \) |
$1$ |
$434.2449246$ |
5.43631864 |
\( -\frac{228005851807623232787}{11112006825558016} a^{4} + \frac{28893682402781220477}{11112006825558016} a^{3} + \frac{351233657882818767615}{2778001706389504} a^{2} + \frac{380160051242118750025}{5556003412779008} a - \frac{524281523912096022427}{11112006825558016} \) |
\( \bigl[-a^{4} + a^{3} + 6 a^{2} - a - 3\) , \( -a^{4} + a^{3} + 6 a^{2} - 2 a - 5\) , \( -a^{3} + 2 a^{2} + 4 a - 3\) , \( -196 a^{4} + 114 a^{3} + 1222 a^{2} + 122 a - 922\) , \( 1660 a^{4} - 958 a^{3} - 10365 a^{2} - 1063 a + 7849\bigr] \) |
${y}^2+\left(-a^{4}+a^{3}+6a^{2}-a-3\right){x}{y}+\left(-a^{3}+2a^{2}+4a-3\right){y}={x}^{3}+\left(-a^{4}+a^{3}+6a^{2}-2a-5\right){x}^{2}+\left(-196a^{4}+114a^{3}+1222a^{2}+122a-922\right){x}+1660a^{4}-958a^{3}-10365a^{2}-1063a+7849$ |
| 14.1-f3 |
14.1-f |
$4$ |
$14$ |
5.5.186037.1 |
$5$ |
$[5, 0]$ |
14.1 |
\( 2 \cdot 7 \) |
\( - 2^{7} \cdot 7^{7} \) |
$50.18235$ |
$(a^4-a^3-5a^2+2), (-a^4+a^3+6a^2-a-5)$ |
$0 \le r \le 1$ |
$\Z/14\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 7$ |
2B, 7B.1.1 |
|
\( 7^{2} \) |
$1$ |
$3473.959397$ |
5.43631864 |
\( \frac{263471732268379}{105413504} a^{4} - \frac{88842995531317}{105413504} a^{3} - \frac{438077667237255}{26353376} a^{2} - \frac{221733421401441}{52706752} a + \frac{1512923564448547}{105413504} \) |
\( \bigl[-a^{3} + 2 a^{2} + 3 a - 3\) , \( a^{4} - 2 a^{3} - 4 a^{2} + 4 a + 1\) , \( -2 a^{4} + a^{3} + 13 a^{2} + 2 a - 9\) , \( -51 a^{4} + 27 a^{3} + 326 a^{2} + 34 a - 250\) , \( 243 a^{4} - 137 a^{3} - 1505 a^{2} - 194 a + 1095\bigr] \) |
${y}^2+\left(-a^{3}+2a^{2}+3a-3\right){x}{y}+\left(-2a^{4}+a^{3}+13a^{2}+2a-9\right){y}={x}^{3}+\left(a^{4}-2a^{3}-4a^{2}+4a+1\right){x}^{2}+\left(-51a^{4}+27a^{3}+326a^{2}+34a-250\right){x}+243a^{4}-137a^{3}-1505a^{2}-194a+1095$ |
| 14.1-f4 |
14.1-f |
$4$ |
$14$ |
5.5.186037.1 |
$5$ |
$[5, 0]$ |
14.1 |
\( 2 \cdot 7 \) |
\( - 2 \cdot 7 \) |
$50.18235$ |
$(a^4-a^3-5a^2+2), (-a^4+a^3+6a^2-a-5)$ |
$0 \le r \le 1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 7$ |
2B, 7B.1.3 |
|
\( 1 \) |
$1$ |
$0.206697173$ |
5.43631864 |
\( \frac{1063019781555591054781}{14} a^{4} + \frac{1829819778466395774605}{14} a^{3} - \frac{698004470600002452914}{7} a^{2} - \frac{833248460923316092660}{7} a + \frac{782065927131370532559}{14} \) |
\( \bigl[a^{4} - a^{3} - 5 a^{2} + 3\) , \( -a^{4} + a^{3} + 5 a^{2} - 1\) , \( a^{2} - a - 1\) , \( -816 a^{4} - 407 a^{3} + 2440 a^{2} + 887 a - 1837\) , \( -37951 a^{4} - 48719 a^{3} + 68047 a^{2} + 50018 a - 42523\bigr] \) |
${y}^2+\left(a^{4}-a^{3}-5a^{2}+3\right){x}{y}+\left(a^{2}-a-1\right){y}={x}^{3}+\left(-a^{4}+a^{3}+5a^{2}-1\right){x}^{2}+\left(-816a^{4}-407a^{3}+2440a^{2}+887a-1837\right){x}-37951a^{4}-48719a^{3}+68047a^{2}+50018a-42523$ |
| 14.1-g1 |
14.1-g |
$12$ |
$24$ |
5.5.186037.1 |
$5$ |
$[5, 0]$ |
14.1 |
\( 2 \cdot 7 \) |
\( - 2^{8} \cdot 7 \) |
$50.18235$ |
$(a^4-a^3-5a^2+2), (-a^4+a^3+6a^2-a-5)$ |
$0 \le r \le 1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
|
\( 2 \) |
$1$ |
$142.9870352$ |
2.52418817 |
\( \frac{5335044957544711087381}{1792} a^{4} - \frac{15257583149480334781403}{1792} a^{3} - \frac{908252699740037573641}{448} a^{2} + \frac{8713525087037414546641}{896} a - \frac{5736980454376339246003}{1792} \) |
\( \bigl[a^{2} - 1\) , \( 2 a^{4} - a^{3} - 12 a^{2} - 2 a + 8\) , \( a^{2} - 1\) , \( 93 a^{4} - 91 a^{3} - 474 a^{2} + 81 a + 47\) , \( 62 a^{4} + 466 a^{3} - 1003 a^{2} - 2383 a + 1152\bigr] \) |
${y}^2+\left(a^{2}-1\right){x}{y}+\left(a^{2}-1\right){y}={x}^{3}+\left(2a^{4}-a^{3}-12a^{2}-2a+8\right){x}^{2}+\left(93a^{4}-91a^{3}-474a^{2}+81a+47\right){x}+62a^{4}+466a^{3}-1003a^{2}-2383a+1152$ |
| 14.1-g2 |
14.1-g |
$12$ |
$24$ |
5.5.186037.1 |
$5$ |
$[5, 0]$ |
14.1 |
\( 2 \cdot 7 \) |
\( 2^{32} \cdot 7 \) |
$50.18235$ |
$(a^4-a^3-5a^2+2), (-a^4+a^3+6a^2-a-5)$ |
$0 \le r \le 1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
|
\( 2 \) |
$1$ |
$35.74675880$ |
2.52418817 |
\( -\frac{726386420776840914221244725}{30064771072} a^{4} + \frac{120537608012963835840463035}{30064771072} a^{3} + \frac{1114713487133164269444744041}{7516192768} a^{2} + \frac{1133086232992183408798274831}{15032385536} a - \frac{1741811558172349827602065261}{30064771072} \) |
\( \bigl[a^{4} - a^{3} - 5 a^{2} + 3\) , \( a^{3} - a^{2} - 5 a + 1\) , \( 0\) , \( 12 a^{4} - 76 a^{2} - 49 a + 27\) , \( 45 a^{4} - 7 a^{3} - 276 a^{2} - 115 a + 139\bigr] \) |
${y}^2+\left(a^{4}-a^{3}-5a^{2}+3\right){x}{y}={x}^{3}+\left(a^{3}-a^{2}-5a+1\right){x}^{2}+\left(12a^{4}-76a^{2}-49a+27\right){x}+45a^{4}-7a^{3}-276a^{2}-115a+139$ |
| 14.1-g3 |
14.1-g |
$12$ |
$24$ |
5.5.186037.1 |
$5$ |
$[5, 0]$ |
14.1 |
\( 2 \cdot 7 \) |
\( - 2^{12} \cdot 7^{24} \) |
$50.18235$ |
$(a^4-a^3-5a^2+2), (-a^4+a^3+6a^2-a-5)$ |
$0 \le r \le 1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
|
\( 2^{2} \) |
$1$ |
$47.66234506$ |
2.52418817 |
\( -\frac{6253140508119409583220510794036973}{784716723734800033386496} a^{4} + \frac{929470606281116007439940708826499}{784716723734800033386496} a^{3} + \frac{9650883648349436994727682052294913}{196179180933700008346624} a^{2} + \frac{9882366558548123868586700148128951}{392358361867400016693248} a - \frac{15133882175405211652739029888443493}{784716723734800033386496} \) |
\( \bigl[-a^{4} + 7 a^{2} + 3 a - 5\) , \( 3 a^{4} - 2 a^{3} - 18 a^{2} - a + 12\) , \( a^{2} - 1\) , \( -3332 a^{4} + 1904 a^{3} + 20831 a^{2} + 2203 a - 15855\) , \( 114229 a^{4} - 66017 a^{3} - 713151 a^{2} - 72807 a + 539936\bigr] \) |
${y}^2+\left(-a^{4}+7a^{2}+3a-5\right){x}{y}+\left(a^{2}-1\right){y}={x}^{3}+\left(3a^{4}-2a^{3}-18a^{2}-a+12\right){x}^{2}+\left(-3332a^{4}+1904a^{3}+20831a^{2}+2203a-15855\right){x}+114229a^{4}-66017a^{3}-713151a^{2}-72807a+539936$ |
| 14.1-g4 |
14.1-g |
$12$ |
$24$ |
5.5.186037.1 |
$5$ |
$[5, 0]$ |
14.1 |
\( 2 \cdot 7 \) |
\( 2^{16} \cdot 7^{2} \) |
$50.18235$ |
$(a^4-a^3-5a^2+2), (-a^4+a^3+6a^2-a-5)$ |
$0 \le r \le 1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2Cs, 3B |
|
\( 2^{2} \) |
$1$ |
$571.9481408$ |
2.52418817 |
\( \frac{966488813284045}{3211264} a^{4} - \frac{3428717490176931}{3211264} a^{3} + \frac{172059539464095}{802816} a^{2} + \frac{2366534825074089}{1605632} a - \frac{1895686830744251}{3211264} \) |
\( \bigl[-2 a^{4} + a^{3} + 13 a^{2} + 2 a - 9\) , \( -a^{3} + 2 a^{2} + 2 a - 3\) , \( -2 a^{4} + a^{3} + 13 a^{2} + 2 a - 8\) , \( -35 a^{4} + 105 a^{3} + 18 a^{2} - 134 a + 29\) , \( -476 a^{4} + 1389 a^{3} + 269 a^{2} - 1623 a + 543\bigr] \) |
${y}^2+\left(-2a^{4}+a^{3}+13a^{2}+2a-9\right){x}{y}+\left(-2a^{4}+a^{3}+13a^{2}+2a-8\right){y}={x}^{3}+\left(-a^{3}+2a^{2}+2a-3\right){x}^{2}+\left(-35a^{4}+105a^{3}+18a^{2}-134a+29\right){x}-476a^{4}+1389a^{3}+269a^{2}-1623a+543$ |
| 14.1-g5 |
14.1-g |
$12$ |
$24$ |
5.5.186037.1 |
$5$ |
$[5, 0]$ |
14.1 |
\( 2 \cdot 7 \) |
\( 2^{96} \cdot 7^{3} \) |
$50.18235$ |
$(a^4-a^3-5a^2+2), (-a^4+a^3+6a^2-a-5)$ |
$0 \le r \le 1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
|
\( 2 \) |
$1$ |
$11.91558626$ |
2.52418817 |
\( -\frac{799446816805818795467805496748415850021}{27175259742392667794585574965248} a^{4} + \frac{460075243697438365626926720888068274379}{27175259742392667794585574965248} a^{3} + \frac{1247868826719145735373104518438683455001}{6793814935598166948646393741312} a^{2} + \frac{259938685343951649842094949734532401375}{13587629871196333897292787482624} a - \frac{3773429204149288618033727858586916818653}{27175259742392667794585574965248} \) |
\( \bigl[a^{4} - a^{3} - 5 a^{2} + 3\) , \( a^{3} - a^{2} - 5 a + 1\) , \( 0\) , \( -328 a^{4} + 195 a^{3} + 2064 a^{2} + 176 a - 1598\) , \( 4519 a^{4} - 2683 a^{3} - 28409 a^{2} - 2945 a + 21458\bigr] \) |
${y}^2+\left(a^{4}-a^{3}-5a^{2}+3\right){x}{y}={x}^{3}+\left(a^{3}-a^{2}-5a+1\right){x}^{2}+\left(-328a^{4}+195a^{3}+2064a^{2}+176a-1598\right){x}+4519a^{4}-2683a^{3}-28409a^{2}-2945a+21458$ |
| 14.1-g6 |
14.1-g |
$12$ |
$24$ |
5.5.186037.1 |
$5$ |
$[5, 0]$ |
14.1 |
\( 2 \cdot 7 \) |
\( 2^{4} \cdot 7^{2} \) |
$50.18235$ |
$(a^4-a^3-5a^2+2), (-a^4+a^3+6a^2-a-5)$ |
$0 \le r \le 1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
|
\( 2^{2} \) |
$1$ |
$571.9481408$ |
2.52418817 |
\( \frac{7813069}{784} a^{4} + \frac{6062029}{784} a^{3} - \frac{4025297}{196} a^{2} + \frac{505689}{392} a + \frac{3086901}{784} \) |
\( \bigl[a^{4} - a^{3} - 5 a^{2} + 3\) , \( -3 a^{4} + 2 a^{3} + 18 a^{2} + 2 a - 11\) , \( a^{4} - a^{3} - 5 a^{2} + a + 2\) , \( 22 a^{4} - 13 a^{3} - 137 a^{2} - 12 a + 105\) , \( -46 a^{4} + 26 a^{3} + 288 a^{2} + 32 a - 219\bigr] \) |
${y}^2+\left(a^{4}-a^{3}-5a^{2}+3\right){x}{y}+\left(a^{4}-a^{3}-5a^{2}+a+2\right){y}={x}^{3}+\left(-3a^{4}+2a^{3}+18a^{2}+2a-11\right){x}^{2}+\left(22a^{4}-13a^{3}-137a^{2}-12a+105\right){x}-46a^{4}+26a^{3}+288a^{2}+32a-219$ |
| 14.1-g7 |
14.1-g |
$12$ |
$24$ |
5.5.186037.1 |
$5$ |
$[5, 0]$ |
14.1 |
\( 2 \cdot 7 \) |
\( 2^{8} \cdot 7^{4} \) |
$50.18235$ |
$(a^4-a^3-5a^2+2), (-a^4+a^3+6a^2-a-5)$ |
$0 \le r \le 1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2Cs, 3B |
|
\( 2^{2} \) |
$1$ |
$1143.896281$ |
2.52418817 |
\( -\frac{26377361048867}{614656} a^{4} + \frac{55905459300717}{614656} a^{3} + \frac{23918174144143}{153664} a^{2} - \frac{79924333102471}{307328} a + \frac{47107110736597}{614656} \) |
\( \bigl[-a^{4} + 7 a^{2} + 3 a - 5\) , \( 3 a^{4} - 2 a^{3} - 18 a^{2} - a + 12\) , \( a^{2} - 1\) , \( -52 a^{4} + 29 a^{3} + 326 a^{2} + 38 a - 250\) , \( -225 a^{4} + 129 a^{3} + 1405 a^{2} + 147 a - 1066\bigr] \) |
${y}^2+\left(-a^{4}+7a^{2}+3a-5\right){x}{y}+\left(a^{2}-1\right){y}={x}^{3}+\left(3a^{4}-2a^{3}-18a^{2}-a+12\right){x}^{2}+\left(-52a^{4}+29a^{3}+326a^{2}+38a-250\right){x}-225a^{4}+129a^{3}+1405a^{2}+147a-1066$ |
| 14.1-g8 |
14.1-g |
$12$ |
$24$ |
5.5.186037.1 |
$5$ |
$[5, 0]$ |
14.1 |
\( 2 \cdot 7 \) |
\( 2^{24} \cdot 7^{12} \) |
$50.18235$ |
$(a^4-a^3-5a^2+2), (-a^4+a^3+6a^2-a-5)$ |
$0 \le r \le 1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2Cs, 3B |
|
\( 2^{2} \) |
$1$ |
$381.2987605$ |
2.52418817 |
\( \frac{8061349964616130414179165}{232218265089212416} a^{4} - \frac{1745413918020479621518867}{232218265089212416} a^{3} - \frac{11021918803504032488077617}{58054566272303104} a^{2} - \frac{3155414882749832831233799}{116109132544606208} a + \frac{33087123829064169050511189}{232218265089212416} \) |
\( \bigl[a + 1\) , \( a^{4} - 2 a^{3} - 4 a^{2} + 3 a + 2\) , \( -a^{4} + 8 a^{2} + 3 a - 7\) , \( -205 a^{4} + 590 a^{3} + 122 a^{2} - 683 a + 232\) , \( 4614 a^{4} - 13215 a^{3} - 3124 a^{2} + 15100 a - 4980\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(-a^{4}+8a^{2}+3a-7\right){y}={x}^{3}+\left(a^{4}-2a^{3}-4a^{2}+3a+2\right){x}^{2}+\left(-205a^{4}+590a^{3}+122a^{2}-683a+232\right){x}+4614a^{4}-13215a^{3}-3124a^{2}+15100a-4980$ |
| 14.1-g9 |
14.1-g |
$12$ |
$24$ |
5.5.186037.1 |
$5$ |
$[5, 0]$ |
14.1 |
\( 2 \cdot 7 \) |
\( 2^{12} \cdot 7^{6} \) |
$50.18235$ |
$(a^4-a^3-5a^2+2), (-a^4+a^3+6a^2-a-5)$ |
$0 \le r \le 1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
|
\( 2^{2} \) |
$1$ |
$190.6493802$ |
2.52418817 |
\( \frac{1095429029481480424228861}{481890304} a^{4} + \frac{1886993785020689365262477}{481890304} a^{3} - \frac{358757891706639381351505}{120472576} a^{2} - \frac{858084511453953093237479}{240945152} a + \frac{804691241489768307413749}{481890304} \) |
\( \bigl[a^{4} - a^{3} - 5 a^{2} + 3\) , \( -3 a^{4} + 2 a^{3} + 18 a^{2} + 2 a - 11\) , \( a^{4} - a^{3} - 5 a^{2} + a + 2\) , \( -253 a^{4} + 147 a^{3} + 1578 a^{2} + 158 a - 1190\) , \( 3602 a^{4} - 2080 a^{3} - 22488 a^{2} - 2306 a + 17032\bigr] \) |
${y}^2+\left(a^{4}-a^{3}-5a^{2}+3\right){x}{y}+\left(a^{4}-a^{3}-5a^{2}+a+2\right){y}={x}^{3}+\left(-3a^{4}+2a^{3}+18a^{2}+2a-11\right){x}^{2}+\left(-253a^{4}+147a^{3}+1578a^{2}+158a-1190\right){x}+3602a^{4}-2080a^{3}-22488a^{2}-2306a+17032$ |
| 14.1-g10 |
14.1-g |
$12$ |
$24$ |
5.5.186037.1 |
$5$ |
$[5, 0]$ |
14.1 |
\( 2 \cdot 7 \) |
\( 2^{48} \cdot 7^{6} \) |
$50.18235$ |
$(a^4-a^3-5a^2+2), (-a^4+a^3+6a^2-a-5)$ |
$0 \le r \le 1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2Cs, 3B |
|
\( 2^{2} \) |
$1$ |
$190.6493802$ |
2.52418817 |
\( \frac{94689501464059464642805327242667565}{33115249535031967744} a^{4} - \frac{54643328707821420414455422266092099}{33115249535031967744} a^{3} - \frac{147811704151459971726377363330080065}{8278812383757991936} a^{2} - \frac{30335827601127171936473814075819639}{16557624767515983872} a + \frac{447788194012596481367067420891283877}{33115249535031967744} \) |
\( \bigl[-2 a^{4} + a^{3} + 13 a^{2} + 2 a - 9\) , \( -a^{3} + 2 a^{2} + 2 a - 3\) , \( -2 a^{4} + a^{3} + 13 a^{2} + 2 a - 8\) , \( -470 a^{4} + 365 a^{3} + 2713 a^{2} + 131 a - 2016\) , \( 5111 a^{4} - 2041 a^{3} - 34122 a^{2} - 4845 a + 26478\bigr] \) |
${y}^2+\left(-2a^{4}+a^{3}+13a^{2}+2a-9\right){x}{y}+\left(-2a^{4}+a^{3}+13a^{2}+2a-8\right){y}={x}^{3}+\left(-a^{3}+2a^{2}+2a-3\right){x}^{2}+\left(-470a^{4}+365a^{3}+2713a^{2}+131a-2016\right){x}+5111a^{4}-2041a^{3}-34122a^{2}-4845a+26478$ |
| 14.1-g11 |
14.1-g |
$12$ |
$24$ |
5.5.186037.1 |
$5$ |
$[5, 0]$ |
14.1 |
\( 2 \cdot 7 \) |
\( - 2^{4} \cdot 7^{8} \) |
$50.18235$ |
$(a^4-a^3-5a^2+2), (-a^4+a^3+6a^2-a-5)$ |
$0 \le r \le 1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
|
\( 2^{2} \) |
$1$ |
$142.9870352$ |
2.52418817 |
\( -\frac{1456017422050110613788813}{92236816} a^{4} + \frac{3086331095718964274967043}{92236816} a^{3} + \frac{1320079089828575062187785}{23059204} a^{2} - \frac{4412222420555377541968577}{46118408} a + \frac{2600710240774080546787803}{92236816} \) |
\( \bigl[a + 1\) , \( a^{4} - 2 a^{3} - 4 a^{2} + 3 a + 2\) , \( -a^{4} + 8 a^{2} + 3 a - 7\) , \( -45 a^{4} + 135 a^{3} + 12 a^{2} - 148 a + 57\) , \( 100 a^{4} - 287 a^{3} - 71 a^{2} + 342 a - 118\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(-a^{4}+8a^{2}+3a-7\right){y}={x}^{3}+\left(a^{4}-2a^{3}-4a^{2}+3a+2\right){x}^{2}+\left(-45a^{4}+135a^{3}+12a^{2}-148a+57\right){x}+100a^{4}-287a^{3}-71a^{2}+342a-118$ |
| 14.1-g12 |
14.1-g |
$12$ |
$24$ |
5.5.186037.1 |
$5$ |
$[5, 0]$ |
14.1 |
\( 2 \cdot 7 \) |
\( - 2^{24} \cdot 7^{3} \) |
$50.18235$ |
$(a^4-a^3-5a^2+2), (-a^4+a^3+6a^2-a-5)$ |
$0 \le r \le 1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
|
\( 2 \) |
$1$ |
$47.66234506$ |
2.52418817 |
\( \frac{156655843128556057595253161048181625179589}{5754585088} a^{4} - \frac{90402807046973766791273783632678096416555}{5754585088} a^{3} - \frac{244542074675954792847272063096051541725241}{1438646272} a^{2} - \frac{50188083959123703866898286025038375243199}{2877292544} a + \frac{740828032577995072481323190148700493997437}{5754585088} \) |
\( \bigl[-a^{4} + 8 a^{2} + 2 a - 7\) , \( a^{4} - 6 a^{2} - 4 a + 2\) , \( -2 a^{4} + a^{3} + 13 a^{2} + 3 a - 9\) , \( -571 a^{4} - 270 a^{3} + 1572 a^{2} + 473 a - 1036\) , \( 13985 a^{4} + 27298 a^{3} - 25789 a^{2} - 27537 a + 18276\bigr] \) |
${y}^2+\left(-a^{4}+8a^{2}+2a-7\right){x}{y}+\left(-2a^{4}+a^{3}+13a^{2}+3a-9\right){y}={x}^{3}+\left(a^{4}-6a^{2}-4a+2\right){x}^{2}+\left(-571a^{4}-270a^{3}+1572a^{2}+473a-1036\right){x}+13985a^{4}+27298a^{3}-25789a^{2}-27537a+18276$ |
| 14.1-h1 |
14.1-h |
$12$ |
$24$ |
5.5.186037.1 |
$5$ |
$[5, 0]$ |
14.1 |
\( 2 \cdot 7 \) |
\( - 2^{8} \cdot 7 \) |
$50.18235$ |
$(a^4-a^3-5a^2+2), (-a^4+a^3+6a^2-a-5)$ |
$0 \le r \le 2$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$16$ |
\( 2 \) |
$1$ |
$649.2496325$ |
1.33801051 |
\( \frac{5335044957544711087381}{1792} a^{4} - \frac{15257583149480334781403}{1792} a^{3} - \frac{908252699740037573641}{448} a^{2} + \frac{8713525087037414546641}{896} a - \frac{5736980454376339246003}{1792} \) |
\( \bigl[-a^{4} + 8 a^{2} + 2 a - 7\) , \( -a^{4} + a^{3} + 6 a^{2} - 5\) , \( -a^{4} + a^{3} + 6 a^{2} - 4\) , \( 1982 a^{4} - 341 a^{3} - 12140 a^{2} - 6136 a + 4675\) , \( -72923 a^{4} + 12075 a^{3} + 447694 a^{2} + 227600 a - 175071\bigr] \) |
${y}^2+\left(-a^{4}+8a^{2}+2a-7\right){x}{y}+\left(-a^{4}+a^{3}+6a^{2}-4\right){y}={x}^{3}+\left(-a^{4}+a^{3}+6a^{2}-5\right){x}^{2}+\left(1982a^{4}-341a^{3}-12140a^{2}-6136a+4675\right){x}-72923a^{4}+12075a^{3}+447694a^{2}+227600a-175071$ |
| 14.1-h2 |
14.1-h |
$12$ |
$24$ |
5.5.186037.1 |
$5$ |
$[5, 0]$ |
14.1 |
\( 2 \cdot 7 \) |
\( 2^{32} \cdot 7 \) |
$50.18235$ |
$(a^4-a^3-5a^2+2), (-a^4+a^3+6a^2-a-5)$ |
$0 \le r \le 2$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$16$ |
\( 2 \) |
$1$ |
$649.2496325$ |
1.33801051 |
\( -\frac{726386420776840914221244725}{30064771072} a^{4} + \frac{120537608012963835840463035}{30064771072} a^{3} + \frac{1114713487133164269444744041}{7516192768} a^{2} + \frac{1133086232992183408798274831}{15032385536} a - \frac{1741811558172349827602065261}{30064771072} \) |
\( \bigl[-a^{4} + 7 a^{2} + 3 a - 5\) , \( -a^{2} + a + 3\) , \( a^{4} - a^{3} - 5 a^{2} + 2\) , \( -3 a^{4} + 8 a^{3} - 2 a^{2} - 8 a + 10\) , \( 17 a^{4} - 19 a^{3} - 2 a^{2} + 27 a - 18\bigr] \) |
${y}^2+\left(-a^{4}+7a^{2}+3a-5\right){x}{y}+\left(a^{4}-a^{3}-5a^{2}+2\right){y}={x}^{3}+\left(-a^{2}+a+3\right){x}^{2}+\left(-3a^{4}+8a^{3}-2a^{2}-8a+10\right){x}+17a^{4}-19a^{3}-2a^{2}+27a-18$ |
| 14.1-h3 |
14.1-h |
$12$ |
$24$ |
5.5.186037.1 |
$5$ |
$[5, 0]$ |
14.1 |
\( 2 \cdot 7 \) |
\( - 2^{12} \cdot 7^{24} \) |
$50.18235$ |
$(a^4-a^3-5a^2+2), (-a^4+a^3+6a^2-a-5)$ |
$0 \le r \le 2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$9$ |
\( 2^{4} \cdot 3 \) |
$1$ |
$5.343618374$ |
1.33801051 |
\( -\frac{6253140508119409583220510794036973}{784716723734800033386496} a^{4} + \frac{929470606281116007439940708826499}{784716723734800033386496} a^{3} + \frac{9650883648349436994727682052294913}{196179180933700008346624} a^{2} + \frac{9882366558548123868586700148128951}{392358361867400016693248} a - \frac{15133882175405211652739029888443493}{784716723734800033386496} \) |
\( \bigl[a^{4} - a^{3} - 5 a^{2} + 3\) , \( 3 a^{4} - 2 a^{3} - 18 a^{2} - 3 a + 10\) , \( -a^{4} + a^{3} + 6 a^{2} - 3\) , \( -9781 a^{4} + 5763 a^{3} + 61115 a^{2} + 5535 a - 46985\) , \( -670046 a^{4} + 388198 a^{3} + 4184177 a^{2} + 420124 a - 3177218\bigr] \) |
${y}^2+\left(a^{4}-a^{3}-5a^{2}+3\right){x}{y}+\left(-a^{4}+a^{3}+6a^{2}-3\right){y}={x}^{3}+\left(3a^{4}-2a^{3}-18a^{2}-3a+10\right){x}^{2}+\left(-9781a^{4}+5763a^{3}+61115a^{2}+5535a-46985\right){x}-670046a^{4}+388198a^{3}+4184177a^{2}+420124a-3177218$ |
| 14.1-h4 |
14.1-h |
$12$ |
$24$ |
5.5.186037.1 |
$5$ |
$[5, 0]$ |
14.1 |
\( 2 \cdot 7 \) |
\( 2^{16} \cdot 7^{2} \) |
$50.18235$ |
$(a^4-a^3-5a^2+2), (-a^4+a^3+6a^2-a-5)$ |
$0 \le r \le 2$ |
$\Z/2\Z\oplus\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2Cs, 3B.1.1 |
$4$ |
\( 2^{2} \) |
$1$ |
$5193.997060$ |
1.33801051 |
\( \frac{966488813284045}{3211264} a^{4} - \frac{3428717490176931}{3211264} a^{3} + \frac{172059539464095}{802816} a^{2} + \frac{2366534825074089}{1605632} a - \frac{1895686830744251}{3211264} \) |
\( \bigl[a^{4} - a^{3} - 5 a^{2} + 3\) , \( -a^{3} + 2 a^{2} + 4 a - 2\) , \( -a^{4} + 7 a^{2} + 3 a - 5\) , \( -302 a^{4} + 861 a^{3} + 212 a^{2} - 980 a + 318\) , \( 8402 a^{4} - 24035 a^{3} - 5705 a^{2} + 27453 a - 9050\bigr] \) |
${y}^2+\left(a^{4}-a^{3}-5a^{2}+3\right){x}{y}+\left(-a^{4}+7a^{2}+3a-5\right){y}={x}^{3}+\left(-a^{3}+2a^{2}+4a-2\right){x}^{2}+\left(-302a^{4}+861a^{3}+212a^{2}-980a+318\right){x}+8402a^{4}-24035a^{3}-5705a^{2}+27453a-9050$ |
| 14.1-h5 |
14.1-h |
$12$ |
$24$ |
5.5.186037.1 |
$5$ |
$[5, 0]$ |
14.1 |
\( 2 \cdot 7 \) |
\( 2^{96} \cdot 7^{3} \) |
$50.18235$ |
$(a^4-a^3-5a^2+2), (-a^4+a^3+6a^2-a-5)$ |
$0 \le r \le 2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$144$ |
\( 2 \cdot 3 \) |
$1$ |
$2.671809187$ |
1.33801051 |
\( -\frac{799446816805818795467805496748415850021}{27175259742392667794585574965248} a^{4} + \frac{460075243697438365626926720888068274379}{27175259742392667794585574965248} a^{3} + \frac{1247868826719145735373104518438683455001}{6793814935598166948646393741312} a^{2} + \frac{259938685343951649842094949734532401375}{13587629871196333897292787482624} a - \frac{3773429204149288618033727858586916818653}{27175259742392667794585574965248} \) |
\( \bigl[-a^{4} + 7 a^{2} + 3 a - 5\) , \( -a^{2} + a + 3\) , \( a^{4} - a^{3} - 5 a^{2} + 2\) , \( -98 a^{4} + 38 a^{3} + 693 a^{2} + 112 a - 545\) , \( -1196 a^{4} + 102 a^{3} + 6758 a^{2} + 1201 a - 5183\bigr] \) |
${y}^2+\left(-a^{4}+7a^{2}+3a-5\right){x}{y}+\left(a^{4}-a^{3}-5a^{2}+2\right){y}={x}^{3}+\left(-a^{2}+a+3\right){x}^{2}+\left(-98a^{4}+38a^{3}+693a^{2}+112a-545\right){x}-1196a^{4}+102a^{3}+6758a^{2}+1201a-5183$ |
| 14.1-h6 |
14.1-h |
$12$ |
$24$ |
5.5.186037.1 |
$5$ |
$[5, 0]$ |
14.1 |
\( 2 \cdot 7 \) |
\( 2^{4} \cdot 7^{2} \) |
$50.18235$ |
$(a^4-a^3-5a^2+2), (-a^4+a^3+6a^2-a-5)$ |
$0 \le r \le 2$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{2} \) |
$1$ |
$5193.997060$ |
1.33801051 |
\( \frac{7813069}{784} a^{4} + \frac{6062029}{784} a^{3} - \frac{4025297}{196} a^{2} + \frac{505689}{392} a + \frac{3086901}{784} \) |
\( \bigl[-2 a^{4} + a^{3} + 13 a^{2} + 2 a - 9\) , \( 2 a^{4} - a^{3} - 13 a^{2} - 2 a + 10\) , \( a^{2} - 1\) , \( 81 a^{4} - 47 a^{3} - 507 a^{2} - 51 a + 385\) , \( 368 a^{4} - 213 a^{3} - 2299 a^{2} - 233 a + 1744\bigr] \) |
${y}^2+\left(-2a^{4}+a^{3}+13a^{2}+2a-9\right){x}{y}+\left(a^{2}-1\right){y}={x}^{3}+\left(2a^{4}-a^{3}-13a^{2}-2a+10\right){x}^{2}+\left(81a^{4}-47a^{3}-507a^{2}-51a+385\right){x}+368a^{4}-213a^{3}-2299a^{2}-233a+1744$ |
| 14.1-h7 |
14.1-h |
$12$ |
$24$ |
5.5.186037.1 |
$5$ |
$[5, 0]$ |
14.1 |
\( 2 \cdot 7 \) |
\( 2^{8} \cdot 7^{4} \) |
$50.18235$ |
$(a^4-a^3-5a^2+2), (-a^4+a^3+6a^2-a-5)$ |
$0 \le r \le 2$ |
$\Z/2\Z\oplus\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2Cs, 3B.1.1 |
$1$ |
\( 2^{3} \) |
$1$ |
$10387.99412$ |
1.33801051 |
\( -\frac{26377361048867}{614656} a^{4} + \frac{55905459300717}{614656} a^{3} + \frac{23918174144143}{153664} a^{2} - \frac{79924333102471}{307328} a + \frac{47107110736597}{614656} \) |
\( \bigl[a^{4} - a^{3} - 5 a^{2} + 3\) , \( 3 a^{4} - 2 a^{3} - 18 a^{2} - 3 a + 10\) , \( -a^{4} + a^{3} + 6 a^{2} - 3\) , \( -181 a^{4} + 103 a^{3} + 1135 a^{2} + 120 a - 860\) , \( -240 a^{4} + 136 a^{3} + 1499 a^{2} + 161 a - 1130\bigr] \) |
${y}^2+\left(a^{4}-a^{3}-5a^{2}+3\right){x}{y}+\left(-a^{4}+a^{3}+6a^{2}-3\right){y}={x}^{3}+\left(3a^{4}-2a^{3}-18a^{2}-3a+10\right){x}^{2}+\left(-181a^{4}+103a^{3}+1135a^{2}+120a-860\right){x}-240a^{4}+136a^{3}+1499a^{2}+161a-1130$ |
| 14.1-h8 |
14.1-h |
$12$ |
$24$ |
5.5.186037.1 |
$5$ |
$[5, 0]$ |
14.1 |
\( 2 \cdot 7 \) |
\( 2^{24} \cdot 7^{12} \) |
$50.18235$ |
$(a^4-a^3-5a^2+2), (-a^4+a^3+6a^2-a-5)$ |
$0 \le r \le 2$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2Cs, 3B.1.2 |
$9$ |
\( 2^{3} \cdot 3 \) |
$1$ |
$42.74894699$ |
1.33801051 |
\( \frac{8061349964616130414179165}{232218265089212416} a^{4} - \frac{1745413918020479621518867}{232218265089212416} a^{3} - \frac{11021918803504032488077617}{58054566272303104} a^{2} - \frac{3155414882749832831233799}{116109132544606208} a + \frac{33087123829064169050511189}{232218265089212416} \) |
\( \bigl[-a^{4} + 8 a^{2} + 2 a - 7\) , \( -a^{4} + 7 a^{2} + 3 a - 5\) , \( -a^{4} + 8 a^{2} + 3 a - 6\) , \( -1707 a^{4} + 4865 a^{3} + 1172 a^{2} - 5551 a + 1819\) , \( -124884 a^{4} + 357072 a^{3} + 85059 a^{2} - 407852 a + 134257\bigr] \) |
${y}^2+\left(-a^{4}+8a^{2}+2a-7\right){x}{y}+\left(-a^{4}+8a^{2}+3a-6\right){y}={x}^{3}+\left(-a^{4}+7a^{2}+3a-5\right){x}^{2}+\left(-1707a^{4}+4865a^{3}+1172a^{2}-5551a+1819\right){x}-124884a^{4}+357072a^{3}+85059a^{2}-407852a+134257$ |
| 14.1-h9 |
14.1-h |
$12$ |
$24$ |
5.5.186037.1 |
$5$ |
$[5, 0]$ |
14.1 |
\( 2 \cdot 7 \) |
\( 2^{12} \cdot 7^{6} \) |
$50.18235$ |
$(a^4-a^3-5a^2+2), (-a^4+a^3+6a^2-a-5)$ |
$0 \le r \le 2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$9$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$21.37447349$ |
1.33801051 |
\( \frac{1095429029481480424228861}{481890304} a^{4} + \frac{1886993785020689365262477}{481890304} a^{3} - \frac{358757891706639381351505}{120472576} a^{2} - \frac{858084511453953093237479}{240945152} a + \frac{804691241489768307413749}{481890304} \) |
\( \bigl[-2 a^{4} + a^{3} + 13 a^{2} + 2 a - 9\) , \( 2 a^{4} - a^{3} - 13 a^{2} - 2 a + 10\) , \( a^{2} - 1\) , \( -739 a^{4} + 428 a^{3} + 4613 a^{2} + 464 a - 3500\) , \( -20007 a^{4} + 11559 a^{3} + 124927 a^{2} + 12738 a - 94688\bigr] \) |
${y}^2+\left(-2a^{4}+a^{3}+13a^{2}+2a-9\right){x}{y}+\left(a^{2}-1\right){y}={x}^{3}+\left(2a^{4}-a^{3}-13a^{2}-2a+10\right){x}^{2}+\left(-739a^{4}+428a^{3}+4613a^{2}+464a-3500\right){x}-20007a^{4}+11559a^{3}+124927a^{2}+12738a-94688$ |
| 14.1-h10 |
14.1-h |
$12$ |
$24$ |
5.5.186037.1 |
$5$ |
$[5, 0]$ |
14.1 |
\( 2 \cdot 7 \) |
\( 2^{48} \cdot 7^{6} \) |
$50.18235$ |
$(a^4-a^3-5a^2+2), (-a^4+a^3+6a^2-a-5)$ |
$0 \le r \le 2$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2Cs, 3B.1.2 |
$36$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$21.37447349$ |
1.33801051 |
\( \frac{94689501464059464642805327242667565}{33115249535031967744} a^{4} - \frac{54643328707821420414455422266092099}{33115249535031967744} a^{3} - \frac{147811704151459971726377363330080065}{8278812383757991936} a^{2} - \frac{30335827601127171936473814075819639}{16557624767515983872} a + \frac{447788194012596481367067420891283877}{33115249535031967744} \) |
\( \bigl[-a^{3} + 2 a^{2} + 3 a - 3\) , \( -a^{4} + 8 a^{2} + 2 a - 8\) , \( -a^{4} + 8 a^{2} + 3 a - 7\) , \( -1023 a^{4} + 721 a^{3} + 6399 a^{2} - 95 a - 5514\) , \( -32058 a^{4} + 18223 a^{3} + 200087 a^{2} + 22232 a - 149994\bigr] \) |
${y}^2+\left(-a^{3}+2a^{2}+3a-3\right){x}{y}+\left(-a^{4}+8a^{2}+3a-7\right){y}={x}^{3}+\left(-a^{4}+8a^{2}+2a-8\right){x}^{2}+\left(-1023a^{4}+721a^{3}+6399a^{2}-95a-5514\right){x}-32058a^{4}+18223a^{3}+200087a^{2}+22232a-149994$ |
*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.
