| 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 |
| 11.1-a1 |
11.1-a |
$3$ |
$25$ |
\(\Q(\zeta_{11})^+\) |
$5$ |
$[5, 0]$ |
11.1 |
\( 11 \) |
\( - 11^{5} \) |
$13.74242$ |
$(a^2+a-2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$5$ |
5B.1.2 |
$15625$ |
\( 5 \) |
$1$ |
$0.001053940$ |
0.680488632 |
\( -\frac{52893159101157376}{11} \) |
\( \bigl[0\) , \( -1\) , \( 1\) , \( -7820\) , \( -263580\bigr] \) |
${y}^2+{y}={x}^{3}-{x}^{2}-7820{x}-263580$ |
| 11.1-a2 |
11.1-a |
$3$ |
$25$ |
\(\Q(\zeta_{11})^+\) |
$5$ |
$[5, 0]$ |
11.1 |
\( 11 \) |
\( - 11^{25} \) |
$13.74242$ |
$(a^2+a-2)$ |
0 |
$\Z/5\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$5$ |
5Cs.1.1 |
$25$ |
\( 5^{2} \) |
$1$ |
$3.293564976$ |
0.680488632 |
\( -\frac{122023936}{161051} \) |
\( \bigl[0\) , \( -1\) , \( 1\) , \( -10\) , \( -20\bigr] \) |
${y}^2+{y}={x}^{3}-{x}^{2}-10{x}-20$ |
| 11.1-a3 |
11.1-a |
$3$ |
$25$ |
\(\Q(\zeta_{11})^+\) |
$5$ |
$[5, 0]$ |
11.1 |
\( 11 \) |
\( - 11^{5} \) |
$13.74242$ |
$(a^2+a-2)$ |
0 |
$\Z/25\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$5$ |
5B.1.1 |
$1$ |
\( 5 \) |
$1$ |
$10292.39055$ |
0.680488632 |
\( -\frac{4096}{11} \) |
\( \bigl[0\) , \( -1\) , \( 1\) , \( 0\) , \( 0\bigr] \) |
${y}^2+{y}={x}^{3}-{x}^{2}$ |
| 23.1-a1 |
23.1-a |
$4$ |
$10$ |
\(\Q(\zeta_{11})^+\) |
$5$ |
$[5, 0]$ |
23.1 |
\( 23 \) |
\( - 23^{5} \) |
$14.79438$ |
$(a^4-3a^2-1)$ |
0 |
$\Z/10\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B.1.1 |
$1$ |
\( 5 \) |
$1$ |
$1986.252133$ |
0.820765345 |
\( -\frac{47053068568}{6436343} a^{4} + \frac{46268012320}{6436343} a^{3} + \frac{141240968488}{6436343} a^{2} - \frac{112796046627}{6436343} a + \frac{7676072842}{6436343} \) |
\( \bigl[a^{3} + a^{2} - 2 a - 2\) , \( -a^{4} - a^{3} + 5 a^{2} + 4 a - 4\) , \( a^{3} - 3 a + 1\) , \( 2 a^{3} + a^{2} - 3 a + 1\) , \( 2 a^{4} - 4 a^{2} + a\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-2a-2\right){x}{y}+\left(a^{3}-3a+1\right){y}={x}^{3}+\left(-a^{4}-a^{3}+5a^{2}+4a-4\right){x}^{2}+\left(2a^{3}+a^{2}-3a+1\right){x}+2a^{4}-4a^{2}+a$ |
| 23.1-a2 |
23.1-a |
$4$ |
$10$ |
\(\Q(\zeta_{11})^+\) |
$5$ |
$[5, 0]$ |
23.1 |
\( 23 \) |
\( - 23^{10} \) |
$14.79438$ |
$(a^4-3a^2-1)$ |
0 |
$\Z/10\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B.1.1 |
$1$ |
\( 2 \cdot 5 \) |
$1$ |
$993.1260669$ |
0.820765345 |
\( \frac{74868976618071917973}{41426511213649} a^{4} - \frac{54092178455960064989}{41426511213649} a^{3} - \frac{312961789930170680193}{41426511213649} a^{2} + \frac{134824139137681173208}{41426511213649} a + \frac{261494050662338262657}{41426511213649} \) |
\( \bigl[a^{3} + a^{2} - 2 a - 2\) , \( -a^{4} - a^{3} + 5 a^{2} + 4 a - 4\) , \( a^{3} - 3 a + 1\) , \( -5 a^{4} + 7 a^{3} + 11 a^{2} - 3 a - 4\) , \( -a^{4} - 13 a^{3} + 27 a^{2} + 14 a - 8\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-2a-2\right){x}{y}+\left(a^{3}-3a+1\right){y}={x}^{3}+\left(-a^{4}-a^{3}+5a^{2}+4a-4\right){x}^{2}+\left(-5a^{4}+7a^{3}+11a^{2}-3a-4\right){x}-a^{4}-13a^{3}+27a^{2}+14a-8$ |
| 23.1-a3 |
23.1-a |
$4$ |
$10$ |
\(\Q(\zeta_{11})^+\) |
$5$ |
$[5, 0]$ |
23.1 |
\( 23 \) |
\( -23 \) |
$14.79438$ |
$(a^4-3a^2-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B.1.2 |
$625$ |
\( 1 \) |
$1$ |
$0.635600682$ |
0.820765345 |
\( -\frac{23939398238252891600044}{23} a^{4} + \frac{43828185875438962615638}{23} a^{3} + \frac{59344380437326987721953}{23} a^{2} - \frac{121119995485666779459359}{23} a + \frac{28810521719920268473488}{23} \) |
\( \bigl[a^{3} - 3 a + 1\) , \( -a^{4} + a^{3} + 5 a^{2} - 4 a - 5\) , \( 0\) , \( -88 a^{4} + 205 a^{3} + 9 a^{2} - 233 a - 49\) , \( -1417 a^{4} + 3592 a^{3} - 564 a^{2} - 3064 a + 554\bigr] \) |
${y}^2+\left(a^{3}-3a+1\right){x}{y}={x}^{3}+\left(-a^{4}+a^{3}+5a^{2}-4a-5\right){x}^{2}+\left(-88a^{4}+205a^{3}+9a^{2}-233a-49\right){x}-1417a^{4}+3592a^{3}-564a^{2}-3064a+554$ |
| 23.1-a4 |
23.1-a |
$4$ |
$10$ |
\(\Q(\zeta_{11})^+\) |
$5$ |
$[5, 0]$ |
23.1 |
\( 23 \) |
\( - 23^{2} \) |
$14.79438$ |
$(a^4-3a^2-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B.1.2 |
$625$ |
\( 2 \) |
$1$ |
$0.317800341$ |
0.820765345 |
\( \frac{1812431798583025575975116650734948165}{529} a^{4} - \frac{1296559921989620389944481933388349849}{529} a^{3} - \frac{7618766625551254351602825393413091355}{529} a^{2} + \frac{3268768315434618465890517821484807321}{529} a + \frac{6367683864076909597378964320128797635}{529} \) |
\( \bigl[a^{4} - 3 a^{2} + a + 1\) , \( a^{4} + a^{3} - 4 a^{2} - 4 a + 2\) , \( a^{4} - 3 a^{2} + 1\) , \( -959 a^{4} - 683 a^{3} + 2238 a^{2} + 491 a - 1224\) , \( -40616 a^{4} - 34613 a^{3} + 92332 a^{2} + 42697 a - 29653\bigr] \) |
${y}^2+\left(a^{4}-3a^{2}+a+1\right){x}{y}+\left(a^{4}-3a^{2}+1\right){y}={x}^{3}+\left(a^{4}+a^{3}-4a^{2}-4a+2\right){x}^{2}+\left(-959a^{4}-683a^{3}+2238a^{2}+491a-1224\right){x}-40616a^{4}-34613a^{3}+92332a^{2}+42697a-29653$ |
| 23.2-a1 |
23.2-a |
$4$ |
$10$ |
\(\Q(\zeta_{11})^+\) |
$5$ |
$[5, 0]$ |
23.2 |
\( 23 \) |
\( - 23^{5} \) |
$14.79438$ |
$(-a^4+3a^2+a-2)$ |
0 |
$\Z/10\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B.1.1 |
$1$ |
\( 5 \) |
$1$ |
$1986.252133$ |
0.820765345 |
\( \frac{21045078235}{6436343} a^{4} - \frac{81762784}{6436343} a^{3} - \frac{37127244372}{6436343} a^{2} - \frac{539767896}{6436343} a + \frac{2876686312}{6436343} \) |
\( \bigl[a^{4} + a^{3} - 4 a^{2} - 3 a + 3\) , \( a^{4} - a^{3} - 3 a^{2} + 2 a\) , \( a^{4} - 3 a^{2}\) , \( -a^{3} - a^{2} + a\) , \( -2 a^{3} - a^{2} + 4 a\bigr] \) |
${y}^2+\left(a^{4}+a^{3}-4a^{2}-3a+3\right){x}{y}+\left(a^{4}-3a^{2}\right){y}={x}^{3}+\left(a^{4}-a^{3}-3a^{2}+2a\right){x}^{2}+\left(-a^{3}-a^{2}+a\right){x}-2a^{3}-a^{2}+4a$ |
| 23.2-a2 |
23.2-a |
$4$ |
$10$ |
\(\Q(\zeta_{11})^+\) |
$5$ |
$[5, 0]$ |
23.2 |
\( 23 \) |
\( - 23^{10} \) |
$14.79438$ |
$(-a^4+3a^2+a-2)$ |
0 |
$\Z/10\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B.1.1 |
$1$ |
\( 2 \cdot 5 \) |
$1$ |
$993.1260669$ |
0.820765345 |
\( -\frac{47416580387872896214}{41426511213649} a^{4} + \frac{88354860075954926274}{41426511213649} a^{3} + \frac{114797344933419666883}{41426511213649} a^{2} - \frac{244287782065752925838}{41426511213649} a + \frac{64820146352754535654}{41426511213649} \) |
\( \bigl[a^{4} + a^{3} - 3 a^{2} - 2 a + 1\) , \( a^{2} + a - 1\) , \( a^{4} + a^{3} - 4 a^{2} - 2 a + 2\) , \( 49 a^{4} - 67 a^{3} - 121 a^{2} + 192 a - 44\) , \( 233 a^{4} - 388 a^{3} - 573 a^{2} + 1088 a - 256\bigr] \) |
${y}^2+\left(a^{4}+a^{3}-3a^{2}-2a+1\right){x}{y}+\left(a^{4}+a^{3}-4a^{2}-2a+2\right){y}={x}^{3}+\left(a^{2}+a-1\right){x}^{2}+\left(49a^{4}-67a^{3}-121a^{2}+192a-44\right){x}+233a^{4}-388a^{3}-573a^{2}+1088a-256$ |
| 23.2-a3 |
23.2-a |
$4$ |
$10$ |
\(\Q(\zeta_{11})^+\) |
$5$ |
$[5, 0]$ |
23.2 |
\( 23 \) |
\( -23 \) |
$14.79438$ |
$(-a^4+3a^2+a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B.1.2 |
$625$ |
\( 1 \) |
$1$ |
$0.635600682$ |
0.820765345 |
\( \frac{13574836097602783212489}{23} a^{4} + \frac{12473814277431687078179}{23} a^{3} - \frac{30359946152158241249912}{23} a^{2} - \frac{17532655195108990218943}{23} a + \frac{7073167122009569142064}{23} \) |
\( \bigl[a^{3} - 2 a\) , \( a^{4} - a^{3} - 4 a^{2} + 2 a + 3\) , \( a^{3} + a^{2} - 2 a - 2\) , \( -187 a^{4} - 46 a^{3} + 506 a^{2} - 163 a - 437\) , \( -3375 a^{4} - 1423 a^{3} + 9018 a^{2} - 208 a - 5628\bigr] \) |
${y}^2+\left(a^{3}-2a\right){x}{y}+\left(a^{3}+a^{2}-2a-2\right){y}={x}^{3}+\left(a^{4}-a^{3}-4a^{2}+2a+3\right){x}^{2}+\left(-187a^{4}-46a^{3}+506a^{2}-163a-437\right){x}-3375a^{4}-1423a^{3}+9018a^{2}-208a-5628$ |
| 23.2-a4 |
23.2-a |
$4$ |
$10$ |
\(\Q(\zeta_{11})^+\) |
$5$ |
$[5, 0]$ |
23.2 |
\( 23 \) |
\( - 23^{2} \) |
$14.79438$ |
$(-a^4+3a^2+a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B.1.2 |
$625$ |
\( 2 \) |
$1$ |
$0.317800341$ |
0.820765345 |
\( -\frac{1191520348048782872032188672054705939}{529} a^{4} + \frac{2181471229802177623677475441208246860}{529} a^{3} + \frac{2953649593612105912153638037483875591}{529} a^{2} - \frac{6028541812813127685001791606278142264}{529} a + \frac{1434132506958014181934752744337840202}{529} \) |
\( \bigl[a^{3} + a^{2} - 3 a - 1\) , \( -a^{4} - a^{3} + 5 a^{2} + 2 a - 3\) , \( a^{4} - 4 a^{2} + a + 3\) , \( -4278 a^{4} + 3350 a^{3} + 17601 a^{2} - 8315 a - 15116\) , \( -209580 a^{4} + 154663 a^{3} + 874447 a^{2} - 386208 a - 735950\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-3a-1\right){x}{y}+\left(a^{4}-4a^{2}+a+3\right){y}={x}^{3}+\left(-a^{4}-a^{3}+5a^{2}+2a-3\right){x}^{2}+\left(-4278a^{4}+3350a^{3}+17601a^{2}-8315a-15116\right){x}-209580a^{4}+154663a^{3}+874447a^{2}-386208a-735950$ |
| 23.3-a1 |
23.3-a |
$4$ |
$10$ |
\(\Q(\zeta_{11})^+\) |
$5$ |
$[5, 0]$ |
23.3 |
\( 23 \) |
\( - 23^{2} \) |
$14.79438$ |
$(-a^4+a^3+3a^2-3a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B.1.2 |
$625$ |
\( 2 \) |
$1$ |
$0.317800341$ |
0.820765345 |
\( \frac{369039431219152047702358790473298695}{529} a^{4} - \frac{989950881753394751645286769153540921}{529} a^{3} + \frac{189441628332164246837405561968453764}{529} a^{2} + \frac{788381415458006631258384866252375903}{529} a - \frac{219339008287534382162591638591097088}{529} \) |
\( \bigl[a^{4} - 4 a^{2} + a + 3\) , \( a^{3} + a^{2} - 4 a - 1\) , \( a^{4} - 4 a^{2} + a + 3\) , \( -32 a^{4} + 731 a^{3} - 356 a^{2} - 1659 a - 761\) , \( -179 a^{4} + 13981 a^{3} - 10713 a^{2} - 28326 a - 8289\bigr] \) |
${y}^2+\left(a^{4}-4a^{2}+a+3\right){x}{y}+\left(a^{4}-4a^{2}+a+3\right){y}={x}^{3}+\left(a^{3}+a^{2}-4a-1\right){x}^{2}+\left(-32a^{4}+731a^{3}-356a^{2}-1659a-761\right){x}-179a^{4}+13981a^{3}-10713a^{2}-28326a-8289$ |
| 23.3-a2 |
23.3-a |
$4$ |
$10$ |
\(\Q(\zeta_{11})^+\) |
$5$ |
$[5, 0]$ |
23.3 |
\( 23 \) |
\( - 23^{10} \) |
$14.79438$ |
$(-a^4+a^3+3a^2-3a-2)$ |
0 |
$\Z/10\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B.1.1 |
$1$ |
\( 2 \cdot 5 \) |
$1$ |
$993.1260669$ |
0.820765345 |
\( \frac{13485883457883008301}{41426511213649} a^{4} - \frac{40938279688082030060}{41426511213649} a^{3} + \frac{13634528082311040086}{41426511213649} a^{2} + \frac{34459978988291163906}{41426511213649} a - \frac{9914142943608711568}{41426511213649} \) |
\( \bigl[a^{4} - 3 a^{2}\) , \( -a^{4} + a^{3} + 4 a^{2} - 4 a - 2\) , \( a^{4} - 3 a^{2} + a + 1\) , \( 18 a^{4} - 30 a^{3} - 46 a^{2} + 82 a - 17\) , \( -37 a^{4} + 76 a^{3} + 93 a^{2} - 205 a + 49\bigr] \) |
${y}^2+\left(a^{4}-3a^{2}\right){x}{y}+\left(a^{4}-3a^{2}+a+1\right){y}={x}^{3}+\left(-a^{4}+a^{3}+4a^{2}-4a-2\right){x}^{2}+\left(18a^{4}-30a^{3}-46a^{2}+82a-17\right){x}-37a^{4}+76a^{3}+93a^{2}-205a+49$ |
| 23.3-a3 |
23.3-a |
$4$ |
$10$ |
\(\Q(\zeta_{11})^+\) |
$5$ |
$[5, 0]$ |
23.3 |
\( 23 \) |
\( - 23^{5} \) |
$14.79438$ |
$(-a^4+a^3+3a^2-3a-2)$ |
0 |
$\Z/10\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B.1.1 |
$1$ |
\( 5 \) |
$1$ |
$1986.252133$ |
0.820765345 |
\( \frac{46971305784}{6436343} a^{4} - \frac{20963315451}{6436343} a^{3} - \frac{187181929672}{6436343} a^{2} + \frac{62971709137}{6436343} a + \frac{147346928834}{6436343} \) |
\( \bigl[a^{4} - 4 a^{2} + a + 3\) , \( a^{3} + a^{2} - 4 a - 1\) , \( a^{4} - 4 a^{2} + a + 3\) , \( -2 a^{4} + a^{3} + 9 a^{2} - 4 a - 6\) , \( -2 a^{4} + 8 a^{2} - 4\bigr] \) |
${y}^2+\left(a^{4}-4a^{2}+a+3\right){x}{y}+\left(a^{4}-4a^{2}+a+3\right){y}={x}^{3}+\left(a^{3}+a^{2}-4a-1\right){x}^{2}+\left(-2a^{4}+a^{3}+9a^{2}-4a-6\right){x}-2a^{4}+8a^{2}-4$ |
| 23.3-a4 |
23.3-a |
$4$ |
$10$ |
\(\Q(\zeta_{11})^+\) |
$5$ |
$[5, 0]$ |
23.3 |
\( 23 \) |
\( -23 \) |
$14.79438$ |
$(-a^4+a^3+3a^2-3a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B.1.2 |
$625$ |
\( 1 \) |
$1$ |
$0.635600682$ |
0.820765345 |
\( \frac{36413212515684578678223}{23} a^{4} - \frac{26048650375034470290668}{23} a^{3} - \frac{153067823422492698650307}{23} a^{2} + \frac{65672136847671723793825}{23} a + \frac{127932477431619398226629}{23} \) |
\( \bigl[a^{4} - 4 a^{2} + a + 3\) , \( a^{3} + a^{2} - 4 a - 1\) , \( a^{4} - 4 a^{2} + a + 3\) , \( -372 a^{4} + 226 a^{3} + 1434 a^{2} - 609 a - 1191\) , \( -5104 a^{4} + 2964 a^{3} + 20110 a^{2} - 7895 a - 16315\bigr] \) |
${y}^2+\left(a^{4}-4a^{2}+a+3\right){x}{y}+\left(a^{4}-4a^{2}+a+3\right){y}={x}^{3}+\left(a^{3}+a^{2}-4a-1\right){x}^{2}+\left(-372a^{4}+226a^{3}+1434a^{2}-609a-1191\right){x}-5104a^{4}+2964a^{3}+20110a^{2}-7895a-16315$ |
| 23.4-a1 |
23.4-a |
$4$ |
$10$ |
\(\Q(\zeta_{11})^+\) |
$5$ |
$[5, 0]$ |
23.4 |
\( 23 \) |
\( - 23^{2} \) |
$14.79438$ |
$(-a^4+2a^2+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B.1.2 |
$625$ |
\( 2 \) |
$1$ |
$0.317800341$ |
0.820765345 |
\( -\frac{1665599353208772437646840723861648544}{529} a^{4} - \frac{515871876593405186030634717346598316}{529} a^{3} + \frac{5986748941379712064585808940738486553}{529} a^{2} + \frac{2844175551769835948036386085428144797}{529} a - \frac{1271720281023855543211042033983127776}{529} \) |
\( \bigl[a^{4} + a^{3} - 3 a^{2} - 2 a\) , \( -a^{4} - a^{3} + 5 a^{2} + 3 a - 5\) , \( a^{4} + a^{3} - 4 a^{2} - 2 a + 3\) , \( -2681 a^{4} - 1331 a^{3} + 7125 a^{2} + 587 a - 4049\) , \( -146736 a^{4} - 108973 a^{3} + 354020 a^{2} + 126719 a - 132130\bigr] \) |
${y}^2+\left(a^{4}+a^{3}-3a^{2}-2a\right){x}{y}+\left(a^{4}+a^{3}-4a^{2}-2a+3\right){y}={x}^{3}+\left(-a^{4}-a^{3}+5a^{2}+3a-5\right){x}^{2}+\left(-2681a^{4}-1331a^{3}+7125a^{2}+587a-4049\right){x}-146736a^{4}-108973a^{3}+354020a^{2}+126719a-132130$ |
| 23.4-a2 |
23.4-a |
$4$ |
$10$ |
\(\Q(\zeta_{11})^+\) |
$5$ |
$[5, 0]$ |
23.4 |
\( 23 \) |
\( -23 \) |
$14.79438$ |
$(-a^4+2a^2+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B.1.2 |
$625$ |
\( 1 \) |
$1$ |
$0.635600682$ |
0.820765345 |
\( \frac{7414973359754383937415}{23} a^{4} - \frac{19888787637186071015594}{23} a^{3} + \frac{3803730295771318478423}{23} a^{2} + \frac{15838177036119250431144}{23} a - \frac{4406221709573083648568}{23} \) |
\( \bigl[a^{4} + a^{3} - 3 a^{2} - 2 a\) , \( -a^{4} - a^{3} + 5 a^{2} + 3 a - 5\) , \( a^{4} + a^{3} - 4 a^{2} - 2 a + 3\) , \( -136 a^{4} - 116 a^{3} + 365 a^{2} + 142 a - 269\) , \( -2624 a^{4} - 2311 a^{3} + 6124 a^{2} + 3032 a - 2236\bigr] \) |
${y}^2+\left(a^{4}+a^{3}-3a^{2}-2a\right){x}{y}+\left(a^{4}+a^{3}-4a^{2}-2a+3\right){y}={x}^{3}+\left(-a^{4}-a^{3}+5a^{2}+3a-5\right){x}^{2}+\left(-136a^{4}-116a^{3}+365a^{2}+142a-269\right){x}-2624a^{4}-2311a^{3}+6124a^{2}+3032a-2236$ |
| 23.4-a3 |
23.4-a |
$4$ |
$10$ |
\(\Q(\zeta_{11})^+\) |
$5$ |
$[5, 0]$ |
23.4 |
\( 23 \) |
\( - 23^{10} \) |
$14.79438$ |
$(-a^4+2a^2+1)$ |
0 |
$\Z/10\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B.1.1 |
$1$ |
\( 2 \cdot 5 \) |
$1$ |
$993.1260669$ |
0.820765345 |
\( -\frac{67578061913843073290}{41426511213649} a^{4} - \frac{20776798162111852984}{41426511213649} a^{3} + \frac{243672465429611249930}{41426511213649} a^{2} + \frac{116422572942295623941}{41426511213649} a - \frac{51184407321695715000}{41426511213649} \) |
\( \bigl[a^{4} + a^{3} - 3 a^{2} - 3 a\) , \( a^{4} + a^{3} - 3 a^{2} - 3 a + 1\) , \( a^{4} + a^{3} - 4 a^{2} - 3 a + 2\) , \( -7 a^{4} + 26 a^{3} + 4 a^{2} - 50 a + 12\) , \( -45 a^{4} + 84 a^{3} + 135 a^{2} - 274 a + 66\bigr] \) |
${y}^2+\left(a^{4}+a^{3}-3a^{2}-3a\right){x}{y}+\left(a^{4}+a^{3}-4a^{2}-3a+2\right){y}={x}^{3}+\left(a^{4}+a^{3}-3a^{2}-3a+1\right){x}^{2}+\left(-7a^{4}+26a^{3}+4a^{2}-50a+12\right){x}-45a^{4}+84a^{3}+135a^{2}-274a+66$ |
| 23.4-a4 |
23.4-a |
$4$ |
$10$ |
\(\Q(\zeta_{11})^+\) |
$5$ |
$[5, 0]$ |
23.4 |
\( 23 \) |
\( - 23^{5} \) |
$14.79438$ |
$(-a^4+2a^2+1)$ |
0 |
$\Z/10\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B.1.1 |
$1$ |
\( 5 \) |
$1$ |
$1986.252133$ |
0.820765345 |
\( -\frac{703293464}{6436343} a^{4} + \frac{785056248}{6436343} a^{3} + \frac{23073195843}{6436343} a^{2} - \frac{48623181064}{6436343} a + \frac{12180979828}{6436343} \) |
\( \bigl[a^{3} - 2 a + 1\) , \( a^{4} - 4 a^{2} + 2\) , \( a^{3} + a^{2} - 3 a - 1\) , \( a^{4} - 2 a^{3} - 3 a^{2} + 6 a\) , \( a^{3} - 2 a\bigr] \) |
${y}^2+\left(a^{3}-2a+1\right){x}{y}+\left(a^{3}+a^{2}-3a-1\right){y}={x}^{3}+\left(a^{4}-4a^{2}+2\right){x}^{2}+\left(a^{4}-2a^{3}-3a^{2}+6a\right){x}+a^{3}-2a$ |
| 23.5-a1 |
23.5-a |
$4$ |
$10$ |
\(\Q(\zeta_{11})^+\) |
$5$ |
$[5, 0]$ |
23.5 |
\( 23 \) |
\( -23 \) |
$14.79438$ |
$(a^2-a-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B.1.2 |
$625$ |
\( 1 \) |
$1$ |
$0.635600682$ |
0.820765345 |
\( -\frac{33463623734788854228083}{23} a^{4} - \frac{10364562140650108387555}{23} a^{3} + \frac{120279658841552633699843}{23} a^{2} + \frac{57142336796984795453333}{23} a - \frac{25550119968665139326503}{23} \) |
\( \bigl[a^{4} + a^{3} - 4 a^{2} - 3 a + 2\) , \( -a^{4} + 3 a^{2} + a + 1\) , \( a\) , \( -308 a^{4} + 310 a^{3} + 1145 a^{2} - 661 a - 1021\) , \( -4125 a^{4} + 3861 a^{3} + 15898 a^{2} - 8465 a - 13846\bigr] \) |
${y}^2+\left(a^{4}+a^{3}-4a^{2}-3a+2\right){x}{y}+a{y}={x}^{3}+\left(-a^{4}+3a^{2}+a+1\right){x}^{2}+\left(-308a^{4}+310a^{3}+1145a^{2}-661a-1021\right){x}-4125a^{4}+3861a^{3}+15898a^{2}-8465a-13846$ |
| 23.5-a2 |
23.5-a |
$4$ |
$10$ |
\(\Q(\zeta_{11})^+\) |
$5$ |
$[5, 0]$ |
23.5 |
\( 23 \) |
\( - 23^{5} \) |
$14.79438$ |
$(a^2-a-3)$ |
0 |
$\Z/10\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B.1.1 |
$1$ |
\( 5 \) |
$1$ |
$1986.252133$ |
0.820765345 |
\( -\frac{20260021987}{6436343} a^{4} - \frac{26007990333}{6436343} a^{3} + \frac{59995009713}{6436343} a^{2} + \frac{98987286450}{6436343} a + \frac{35417701239}{6436343} \) |
\( \bigl[a^{3} + a^{2} - 3 a - 1\) , \( -a^{4} + a^{3} + 5 a^{2} - 4 a - 5\) , \( a^{4} - 4 a^{2} + a + 3\) , \( 2 a^{4} - 3 a^{3} - 7 a^{2} + 5 a + 6\) , \( -a^{2} - a + 3\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-3a-1\right){x}{y}+\left(a^{4}-4a^{2}+a+3\right){y}={x}^{3}+\left(-a^{4}+a^{3}+5a^{2}-4a-5\right){x}^{2}+\left(2a^{4}-3a^{3}-7a^{2}+5a+6\right){x}-a^{2}-a+3$ |
| 23.5-a3 |
23.5-a |
$4$ |
$10$ |
\(\Q(\zeta_{11})^+\) |
$5$ |
$[5, 0]$ |
23.5 |
\( 23 \) |
\( - 23^{10} \) |
$14.79438$ |
$(a^2-a-3)$ |
0 |
$\Z/10\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B.1.1 |
$1$ |
\( 2 \cdot 5 \) |
$1$ |
$993.1260669$ |
0.820765345 |
\( \frac{26639782225761043230}{41426511213649} a^{4} + \frac{27452396230199021759}{41426511213649} a^{3} - \frac{59142548515171276706}{41426511213649} a^{2} - \frac{41418909002515035217}{41426511213649} a + \frac{15778337956005682382}{41426511213649} \) |
\( \bigl[a^{3} + a^{2} - 3 a - 1\) , \( -a^{4} + a^{3} + 5 a^{2} - 4 a - 5\) , \( a^{4} - 4 a^{2} + a + 3\) , \( 12 a^{4} - 18 a^{3} - 37 a^{2} + 45 a + 6\) , \( -18 a^{4} + 26 a^{3} + 47 a^{2} - 72 a + 15\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-3a-1\right){x}{y}+\left(a^{4}-4a^{2}+a+3\right){y}={x}^{3}+\left(-a^{4}+a^{3}+5a^{2}-4a-5\right){x}^{2}+\left(12a^{4}-18a^{3}-37a^{2}+45a+6\right){x}-18a^{4}+26a^{3}+47a^{2}-72a+15$ |
| 23.5-a4 |
23.5-a |
$4$ |
$10$ |
\(\Q(\zeta_{11})^+\) |
$5$ |
$[5, 0]$ |
23.5 |
\( 23 \) |
\( - 23^{2} \) |
$14.79438$ |
$(a^2-a-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B.1.2 |
$625$ |
\( 2 \) |
$1$ |
$0.317800341$ |
0.820765345 |
\( \frac{675648471455377686001553954708107623}{529} a^{4} + \frac{620911450534242703942927978680242226}{529} a^{3} - \frac{1511073537772727871974027146777724553}{529} a^{2} - \frac{872783469849333360183497166887185757}{529} a + \frac{352086200751501274019816024338865057}{529} \) |
\( \bigl[a^{3} + a^{2} - 3 a - 1\) , \( -a^{4} + a^{3} + 5 a^{2} - 4 a - 5\) , \( a^{4} - 4 a^{2} + a + 3\) , \( 247 a^{4} - 703 a^{3} - 792 a^{2} + 1375 a - 829\) , \( 3387 a^{4} - 14884 a^{3} - 12485 a^{2} + 30720 a - 11294\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-3a-1\right){x}{y}+\left(a^{4}-4a^{2}+a+3\right){y}={x}^{3}+\left(-a^{4}+a^{3}+5a^{2}-4a-5\right){x}^{2}+\left(247a^{4}-703a^{3}-792a^{2}+1375a-829\right){x}+3387a^{4}-14884a^{3}-12485a^{2}+30720a-11294$ |
| 43.1-a1 |
43.1-a |
$2$ |
$7$ |
\(\Q(\zeta_{11})^+\) |
$5$ |
$[5, 0]$ |
43.1 |
\( 43 \) |
\( -43 \) |
$15.74965$ |
$(-a^3-a^2+2a+3)$ |
0 |
$\Z/7\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$7$ |
7B.1.1 |
$1$ |
\( 1 \) |
$1$ |
$5702.693977$ |
0.961830659 |
\( -\frac{166996603}{43} a^{4} - \frac{153441602}{43} a^{3} + \frac{373478096}{43} a^{2} + \frac{215672423}{43} a - \frac{87008899}{43} \) |
\( \bigl[a^{3} + a^{2} - 3 a - 1\) , \( -a^{3} + a^{2} + 2 a - 2\) , \( a^{2} - 2\) , \( -a^{4} + 3 a^{2} - 2 a - 1\) , \( a^{4} - 3 a^{2} - a\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-3a-1\right){x}{y}+\left(a^{2}-2\right){y}={x}^{3}+\left(-a^{3}+a^{2}+2a-2\right){x}^{2}+\left(-a^{4}+3a^{2}-2a-1\right){x}+a^{4}-3a^{2}-a$ |
| 43.1-a2 |
43.1-a |
$2$ |
$7$ |
\(\Q(\zeta_{11})^+\) |
$5$ |
$[5, 0]$ |
43.1 |
\( 43 \) |
\( - 43^{7} \) |
$15.74965$ |
$(-a^3-a^2+2a+3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$7$ |
7B.1.3 |
$49$ |
\( 7 \) |
$1$ |
$0.339304693$ |
0.961830659 |
\( \frac{318410900614494023095122767009}{271818611107} a^{4} + \frac{98618610535417258075069052493}{271818611107} a^{3} - \frac{1144480542817566448101585501712}{271818611107} a^{2} - \frac{543717833889392347185233669478}{271818611107} a + \frac{243113372524798476732529529704}{271818611107} \) |
\( \bigl[a^{4} - 4 a^{2} + 3\) , \( -a^{4} + a^{3} + 3 a^{2} - 2 a - 1\) , \( a^{3} - 2 a\) , \( 294 a^{4} - 510 a^{3} - 733 a^{2} + 1419 a - 379\) , \( 4714 a^{4} - 8577 a^{3} - 11707 a^{2} + 23701 a - 5755\bigr] \) |
${y}^2+\left(a^{4}-4a^{2}+3\right){x}{y}+\left(a^{3}-2a\right){y}={x}^{3}+\left(-a^{4}+a^{3}+3a^{2}-2a-1\right){x}^{2}+\left(294a^{4}-510a^{3}-733a^{2}+1419a-379\right){x}+4714a^{4}-8577a^{3}-11707a^{2}+23701a-5755$ |
| 43.1-b1 |
43.1-b |
$2$ |
$5$ |
\(\Q(\zeta_{11})^+\) |
$5$ |
$[5, 0]$ |
43.1 |
\( 43 \) |
\( -43 \) |
$15.74965$ |
$(-a^3-a^2+2a+3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.1.2 |
$625$ |
\( 1 \) |
$1$ |
$0.172110778$ |
0.889001954 |
\( -\frac{1952398804851696160384169}{43} a^{4} - \frac{1794012696727694534309545}{43} a^{3} + \frac{4366335020709066338090051}{43} a^{2} + \frac{2521849174288181955441002}{43} a - \frac{1017345331588181941808577}{43} \) |
\( \bigl[a^{3} - 2 a\) , \( a^{4} + a^{3} - 4 a^{2} - 2 a + 2\) , \( a^{2} + a - 1\) , \( -273 a^{4} + 380 a^{3} + 846 a^{2} - 1091 a - 235\) , \( 2716 a^{4} - 6086 a^{3} - 5200 a^{2} + 16501 a - 8269\bigr] \) |
${y}^2+\left(a^{3}-2a\right){x}{y}+\left(a^{2}+a-1\right){y}={x}^{3}+\left(a^{4}+a^{3}-4a^{2}-2a+2\right){x}^{2}+\left(-273a^{4}+380a^{3}+846a^{2}-1091a-235\right){x}+2716a^{4}-6086a^{3}-5200a^{2}+16501a-8269$ |
| 43.1-b2 |
43.1-b |
$2$ |
$5$ |
\(\Q(\zeta_{11})^+\) |
$5$ |
$[5, 0]$ |
43.1 |
\( 43 \) |
\( - 43^{5} \) |
$15.74965$ |
$(-a^3-a^2+2a+3)$ |
0 |
$\Z/5\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.1.1 |
$1$ |
\( 5 \) |
$1$ |
$537.8461822$ |
0.889001954 |
\( \frac{1668625015062}{147008443} a^{4} - \frac{5087619914002}{147008443} a^{3} - \frac{4613121597415}{147008443} a^{2} + \frac{13348817253799}{147008443} a - \frac{3093462765934}{147008443} \) |
\( \bigl[a^{4} + a^{3} - 3 a^{2} - 3 a + 1\) , \( -a^{4} - a^{3} + 4 a^{2} + 2 a - 2\) , \( a^{4} + a^{3} - 4 a^{2} - 3 a + 2\) , \( -a^{4} - 4 a^{3} + a^{2} + 7 a + 1\) , \( -5 a^{4} - 4 a^{3} + 12 a^{2} + 5 a - 4\bigr] \) |
${y}^2+\left(a^{4}+a^{3}-3a^{2}-3a+1\right){x}{y}+\left(a^{4}+a^{3}-4a^{2}-3a+2\right){y}={x}^{3}+\left(-a^{4}-a^{3}+4a^{2}+2a-2\right){x}^{2}+\left(-a^{4}-4a^{3}+a^{2}+7a+1\right){x}-5a^{4}-4a^{3}+12a^{2}+5a-4$ |
| 43.2-a1 |
43.2-a |
$2$ |
$7$ |
\(\Q(\zeta_{11})^+\) |
$5$ |
$[5, 0]$ |
43.2 |
\( 43 \) |
\( -43 \) |
$15.74965$ |
$(-a^4+2a^2+a+1)$ |
0 |
$\Z/7\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$7$ |
7B.1.1 |
$1$ |
\( 1 \) |
$1$ |
$5702.693977$ |
0.961830659 |
\( \frac{411648986}{43} a^{4} + \frac{127511713}{43} a^{3} - 34409287 a^{2} - \frac{702973344}{43} a + \frac{314269044}{43} \) |
\( \bigl[a^{3} + a^{2} - 2 a - 1\) , \( -a^{4} + a^{3} + 3 a^{2} - 2 a - 1\) , \( a^{4} - 4 a^{2} + 3\) , \( 2 a^{4} + 2 a^{3} - 5 a^{2} - 3 a + 2\) , \( 2 a^{4} + 3 a^{3} - 5 a^{2} - 4 a + 1\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-2a-1\right){x}{y}+\left(a^{4}-4a^{2}+3\right){y}={x}^{3}+\left(-a^{4}+a^{3}+3a^{2}-2a-1\right){x}^{2}+\left(2a^{4}+2a^{3}-5a^{2}-3a+2\right){x}+2a^{4}+3a^{3}-5a^{2}-4a+1$ |
| 43.2-a2 |
43.2-a |
$2$ |
$7$ |
\(\Q(\zeta_{11})^+\) |
$5$ |
$[5, 0]$ |
43.2 |
\( 43 \) |
\( - 43^{7} \) |
$15.74965$ |
$(-a^4+2a^2+a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$7$ |
7B.1.3 |
$49$ |
\( 7 \) |
$1$ |
$0.339304693$ |
0.961830659 |
\( -\frac{70548898331353450135096255010}{271818611107} a^{4} + \frac{189247840974084378816217200685}{271818611107} a^{3} - \frac{842216448583260989645063883}{6321363049} a^{2} - \frac{150714011772341855278459782553}{271818611107} a + \frac{41930794528416841925025385323}{271818611107} \) |
\( \bigl[a^{4} + a^{3} - 3 a^{2} - 3 a + 1\) , \( -a^{4} + 4 a^{2} + a - 3\) , \( a^{4} + a^{3} - 3 a^{2} - 3 a + 1\) , \( -30 a^{4} + 30 a^{3} + 25 a^{2} + 160 a - 215\) , \( -226 a^{4} + 563 a^{3} - 458 a^{2} + 913 a - 1012\bigr] \) |
${y}^2+\left(a^{4}+a^{3}-3a^{2}-3a+1\right){x}{y}+\left(a^{4}+a^{3}-3a^{2}-3a+1\right){y}={x}^{3}+\left(-a^{4}+4a^{2}+a-3\right){x}^{2}+\left(-30a^{4}+30a^{3}+25a^{2}+160a-215\right){x}-226a^{4}+563a^{3}-458a^{2}+913a-1012$ |
| 43.2-b1 |
43.2-b |
$2$ |
$5$ |
\(\Q(\zeta_{11})^+\) |
$5$ |
$[5, 0]$ |
43.2 |
\( 43 \) |
\( - 43^{5} \) |
$15.74965$ |
$(-a^4+2a^2+a+1)$ |
0 |
$\Z/5\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.1.1 |
$1$ |
\( 5 \) |
$1$ |
$537.8461822$ |
0.889001954 |
\( \frac{245417473145}{147008443} a^{4} - \frac{392753447771}{147008443} a^{3} - \frac{61634765294}{3418801} a^{2} - \frac{2240734555627}{147008443} a - \frac{148495909040}{147008443} \) |
\( \bigl[a^{4} - 3 a^{2} + 1\) , \( -a^{4} - a^{3} + 3 a^{2} + 4 a + 1\) , \( a^{4} + a^{3} - 3 a^{2} - 2 a + 1\) , \( -6 a^{4} - a^{3} + 20 a^{2} + 4 a - 8\) , \( -6 a^{4} + a^{3} + 23 a^{2} - 3 a - 15\bigr] \) |
${y}^2+\left(a^{4}-3a^{2}+1\right){x}{y}+\left(a^{4}+a^{3}-3a^{2}-2a+1\right){y}={x}^{3}+\left(-a^{4}-a^{3}+3a^{2}+4a+1\right){x}^{2}+\left(-6a^{4}-a^{3}+20a^{2}+4a-8\right){x}-6a^{4}+a^{3}+23a^{2}-3a-15$ |
| 43.2-b2 |
43.2-b |
$2$ |
$5$ |
\(\Q(\zeta_{11})^+\) |
$5$ |
$[5, 0]$ |
43.2 |
\( 43 \) |
\( -43 \) |
$15.74965$ |
$(-a^4+2a^2+a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.1.2 |
$625$ |
\( 1 \) |
$1$ |
$0.172110778$ |
0.889001954 |
\( \frac{4812587720746597807871802}{43} a^{4} + \frac{1490861393846022143062456}{43} a^{3} - 402277955305458024909373 a^{2} - \frac{8218995683117457123881082}{43} a + \frac{3673708517361273227425946}{43} \) |
\( \bigl[a^{3} - 2 a + 1\) , \( -a^{3} + 3 a\) , \( a^{4} - 4 a^{2} + 2\) , \( 42 a^{4} - 193 a^{3} + 148 a^{2} + 559 a - 755\) , \( 589 a^{4} - 2716 a^{3} + 1086 a^{2} + 7676 a - 7875\bigr] \) |
${y}^2+\left(a^{3}-2a+1\right){x}{y}+\left(a^{4}-4a^{2}+2\right){y}={x}^{3}+\left(-a^{3}+3a\right){x}^{2}+\left(42a^{4}-193a^{3}+148a^{2}+559a-755\right){x}+589a^{4}-2716a^{3}+1086a^{2}+7676a-7875$ |
| 43.3-a1 |
43.3-a |
$2$ |
$7$ |
\(\Q(\zeta_{11})^+\) |
$5$ |
$[5, 0]$ |
43.3 |
\( 43 \) |
\( - 43^{7} \) |
$15.74965$ |
$(a^3+a^2-4a-2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$7$ |
7B.1.3 |
$49$ |
\( 7 \) |
$1$ |
$0.339304693$ |
0.961830659 |
\( -\frac{346480612818557831035095564492}{271818611107} a^{4} + \frac{247862002283140572960026511999}{271818611107} a^{3} + \frac{1456471349605584774275478512978}{271818611107} a^{2} - \frac{14532257307132343958115316054}{6321363049} a - \frac{1217303334006333416200315022669}{271818611107} \) |
\( \bigl[a^{3} + a^{2} - 3 a - 1\) , \( a^{4} - 5 a^{2} + a + 4\) , \( a^{3} + a^{2} - 3 a - 1\) , \( 201 a^{4} - 446 a^{3} - 237 a^{2} + 764 a - 199\) , \( -340 a^{4} + 1924 a^{3} - 3845 a^{2} + 2952 a - 615\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-3a-1\right){x}{y}+\left(a^{3}+a^{2}-3a-1\right){y}={x}^{3}+\left(a^{4}-5a^{2}+a+4\right){x}^{2}+\left(201a^{4}-446a^{3}-237a^{2}+764a-199\right){x}-340a^{4}+1924a^{3}-3845a^{2}+2952a-615$ |
| 43.3-a2 |
43.3-a |
$2$ |
$7$ |
\(\Q(\zeta_{11})^+\) |
$5$ |
$[5, 0]$ |
43.3 |
\( 43 \) |
\( -43 \) |
$15.74965$ |
$(a^3+a^2-4a-2)$ |
0 |
$\Z/7\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$7$ |
7B.1.1 |
$1$ |
\( 1 \) |
$1$ |
$5702.693977$ |
0.961830659 |
\( -\frac{91210781}{43} a^{4} + \frac{244652383}{43} a^{3} - \frac{46805862}{43} a^{2} - 4530150 a + \frac{54191702}{43} \) |
\( \bigl[a^{3} + a^{2} - 2 a - 2\) , \( a^{4} + a^{3} - 5 a^{2} - 4 a + 5\) , \( a^{4} + a^{3} - 3 a^{2} - 2 a + 1\) , \( -a^{4} + 8\) , \( a^{4} + a^{3} - 5 a^{2} - 4 a + 4\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-2a-2\right){x}{y}+\left(a^{4}+a^{3}-3a^{2}-2a+1\right){y}={x}^{3}+\left(a^{4}+a^{3}-5a^{2}-4a+5\right){x}^{2}+\left(-a^{4}+8\right){x}+a^{4}+a^{3}-5a^{2}-4a+4$ |
| 43.3-b1 |
43.3-b |
$2$ |
$5$ |
\(\Q(\zeta_{11})^+\) |
$5$ |
$[5, 0]$ |
43.3 |
\( 43 \) |
\( - 43^{5} \) |
$15.74965$ |
$(a^3+a^2-4a-2)$ |
0 |
$\Z/5\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.1.1 |
$1$ |
\( 5 \) |
$1$ |
$537.8461822$ |
0.889001954 |
\( \frac{3173577425795}{147008443} a^{4} + \frac{1914042488207}{147008443} a^{3} - \frac{12939727176325}{147008443} a^{2} - \frac{136964266029}{3418801} a + \frac{2615991439281}{147008443} \) |
\( \bigl[a^{4} - 3 a^{2} + a + 1\) , \( -a^{3} + a^{2} + 4 a - 2\) , \( a^{3} - 2 a\) , \( 7 a^{3} - 2 a^{2} - 10 a + 2\) , \( 3 a^{4} + 7 a^{3} - 12 a^{2} - 6 a + 4\bigr] \) |
${y}^2+\left(a^{4}-3a^{2}+a+1\right){x}{y}+\left(a^{3}-2a\right){y}={x}^{3}+\left(-a^{3}+a^{2}+4a-2\right){x}^{2}+\left(7a^{3}-2a^{2}-10a+2\right){x}+3a^{4}+7a^{3}-12a^{2}-6a+4$ |
| 43.3-b2 |
43.3-b |
$2$ |
$5$ |
\(\Q(\zeta_{11})^+\) |
$5$ |
$[5, 0]$ |
43.3 |
\( 43 \) |
\( -43 \) |
$15.74965$ |
$(a^3+a^2-4a-2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.1.2 |
$625$ |
\( 1 \) |
$1$ |
$0.172110778$ |
0.889001954 |
\( -\frac{1066176219167207113178088}{43} a^{4} + \frac{2860188915894901647487633}{43} a^{3} - \frac{547882844077769355159450}{43} a^{2} - 52956224025397325384387 a + \frac{633565967983653513966306}{43} \) |
\( \bigl[a^{4} - 4 a^{2} + a + 3\) , \( a^{4} - 5 a^{2} + 3\) , \( a^{4} - 4 a^{2} + 2\) , \( -21 a^{4} - 275 a^{3} + 41 a^{2} + 674 a - 204\) , \( -200 a^{4} - 2874 a^{3} + 60 a^{2} + 6329 a - 1829\bigr] \) |
${y}^2+\left(a^{4}-4a^{2}+a+3\right){x}{y}+\left(a^{4}-4a^{2}+2\right){y}={x}^{3}+\left(a^{4}-5a^{2}+3\right){x}^{2}+\left(-21a^{4}-275a^{3}+41a^{2}+674a-204\right){x}-200a^{4}-2874a^{3}+60a^{2}+6329a-1829$ |
| 43.4-a1 |
43.4-a |
$2$ |
$7$ |
\(\Q(\zeta_{11})^+\) |
$5$ |
$[5, 0]$ |
43.4 |
\( 43 \) |
\( - 43^{7} \) |
$15.74965$ |
$(a^4+a^3-3a^2-3a+2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$7$ |
7B.1.3 |
$49$ |
\( 7 \) |
$1$ |
$0.339304693$ |
0.961830659 |
\( -\frac{129163059640409644278905566324}{271818611107} a^{4} - \frac{118698942642730928681120945675}{271818611107} a^{3} + \frac{288870568385811674761647646479}{271818611107} a^{2} + \frac{166848986954108407227145636340}{271818611107} a - \frac{67308147992945409028672333004}{271818611107} \) |
\( \bigl[a^{4} - 3 a^{2} + a + 1\) , \( -a^{3} + 3 a\) , \( a^{3} - 3 a\) , \( -281 a^{4} + 780 a^{3} - 124 a^{2} - 737 a + 173\) , \( -7165 a^{4} + 19524 a^{3} - 4247 a^{2} - 15318 a + 4221\bigr] \) |
${y}^2+\left(a^{4}-3a^{2}+a+1\right){x}{y}+\left(a^{3}-3a\right){y}={x}^{3}+\left(-a^{3}+3a\right){x}^{2}+\left(-281a^{4}+780a^{3}-124a^{2}-737a+173\right){x}-7165a^{4}+19524a^{3}-4247a^{2}-15318a+4221$ |
| 43.4-a2 |
43.4-a |
$2$ |
$7$ |
\(\Q(\zeta_{11})^+\) |
$5$ |
$[5, 0]$ |
43.4 |
\( 43 \) |
\( -43 \) |
$15.74965$ |
$(a^4+a^3-3a^2-3a+2)$ |
0 |
$\Z/7\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$7$ |
7B.1.1 |
$1$ |
\( 1 \) |
$1$ |
$5702.693977$ |
0.961830659 |
\( \frac{294508316}{43} a^{4} - \frac{539160699}{43} a^{3} - \frac{730083346}{43} a^{2} + \frac{1489970384}{43} a - \frac{354407213}{43} \) |
\( \bigl[a^{3} - 2 a\) , \( -a^{4} + a^{3} + 3 a^{2} - 2 a - 1\) , \( a^{4} + a^{3} - 3 a^{2} - 3 a + 1\) , \( -a^{3} - a^{2} + a + 1\) , \( -a^{4} - a^{3} + 2 a^{2} + a - 1\bigr] \) |
${y}^2+\left(a^{3}-2a\right){x}{y}+\left(a^{4}+a^{3}-3a^{2}-3a+1\right){y}={x}^{3}+\left(-a^{4}+a^{3}+3a^{2}-2a-1\right){x}^{2}+\left(-a^{3}-a^{2}+a+1\right){x}-a^{4}-a^{3}+2a^{2}+a-1$ |
| 43.4-b1 |
43.4-b |
$2$ |
$5$ |
\(\Q(\zeta_{11})^+\) |
$5$ |
$[5, 0]$ |
43.4 |
\( 43 \) |
\( -43 \) |
$15.74965$ |
$(a^4+a^3-3a^2-3a+2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.1.2 |
$625$ |
\( 1 \) |
$1$ |
$0.172110778$ |
0.889001954 |
\( \frac{3443260198697718303446625}{43} a^{4} - \frac{6303449114592619950934258}{43} a^{3} - \frac{8535767899365460376030330}{43} a^{2} + \frac{17419485949931837709740318}{43} a - \frac{4143833314037896993105954}{43} \) |
\( \bigl[a^{4} + a^{3} - 4 a^{2} - 2 a + 2\) , \( a^{2} - 3\) , \( a^{2} - 2\) , \( 124 a^{4} + 151 a^{3} - 668 a^{2} - 260 a + 194\) , \( 581 a^{4} + 2293 a^{3} - 4817 a^{2} - 3846 a + 946\bigr] \) |
${y}^2+\left(a^{4}+a^{3}-4a^{2}-2a+2\right){x}{y}+\left(a^{2}-2\right){y}={x}^{3}+\left(a^{2}-3\right){x}^{2}+\left(124a^{4}+151a^{3}-668a^{2}-260a+194\right){x}+581a^{4}+2293a^{3}-4817a^{2}-3846a+946$ |
| 43.4-b2 |
43.4-b |
$2$ |
$5$ |
\(\Q(\zeta_{11})^+\) |
$5$ |
$[5, 0]$ |
43.4 |
\( 43 \) |
\( - 43^{5} \) |
$15.74965$ |
$(a^4+a^3-3a^2-3a+2)$ |
0 |
$\Z/5\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.1.1 |
$1$ |
\( 5 \) |
$1$ |
$537.8461822$ |
0.889001954 |
\( -\frac{2061378462833}{147008443} a^{4} + \frac{147335974626}{147008443} a^{3} + \frac{11271755302501}{147008443} a^{2} - \frac{49254476107}{147008443} a - \frac{14544574161229}{147008443} \) |
\( \bigl[a^{4} + a^{3} - 4 a^{2} - 2 a + 2\) , \( a^{2} - 3\) , \( a^{2} - 2\) , \( -a^{4} + a^{3} + 7 a^{2} - 5 a - 6\) , \( 6 a^{4} - 4 a^{3} - 24 a^{2} + 10 a + 19\bigr] \) |
${y}^2+\left(a^{4}+a^{3}-4a^{2}-2a+2\right){x}{y}+\left(a^{2}-2\right){y}={x}^{3}+\left(a^{2}-3\right){x}^{2}+\left(-a^{4}+a^{3}+7a^{2}-5a-6\right){x}+6a^{4}-4a^{3}-24a^{2}+10a+19$ |
| 43.5-a1 |
43.5-a |
$2$ |
$7$ |
\(\Q(\zeta_{11})^+\) |
$5$ |
$[5, 0]$ |
43.5 |
\( 43 \) |
\( - 43^{7} \) |
$15.74965$ |
$(a^4+a^3-4a^2-2a+3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$7$ |
7B.1.3 |
$49$ |
\( 7 \) |
$1$ |
$0.339304693$ |
0.961830659 |
\( \frac{227781670175826902353974618817}{271818611107} a^{4} - \frac{417029511149911281170191819502}{271818611107} a^{3} - \frac{564646067884749778380802910776}{271818611107} a^{2} + \frac{1152469922914316585435506406013}{271818611107} a - \frac{274161584173414880187077710523}{271818611107} \) |
\( \bigl[a^{3} - 3 a + 1\) , \( -a^{3} + 2 a\) , \( a^{4} + a^{3} - 4 a^{2} - 2 a + 3\) , \( -66 a^{4} + 214 a^{3} - 135 a^{2} - 134 a + 75\) , \( -1428 a^{4} + 3862 a^{3} - 836 a^{2} - 3010 a + 777\bigr] \) |
${y}^2+\left(a^{3}-3a+1\right){x}{y}+\left(a^{4}+a^{3}-4a^{2}-2a+3\right){y}={x}^{3}+\left(-a^{3}+2a\right){x}^{2}+\left(-66a^{4}+214a^{3}-135a^{2}-134a+75\right){x}-1428a^{4}+3862a^{3}-836a^{2}-3010a+777$ |
| 43.5-a2 |
43.5-a |
$2$ |
$7$ |
\(\Q(\zeta_{11})^+\) |
$5$ |
$[5, 0]$ |
43.5 |
\( 43 \) |
\( -43 \) |
$15.74965$ |
$(a^4+a^3-4a^2-2a+3)$ |
0 |
$\Z/7\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$7$ |
7B.1.1 |
$1$ |
\( 1 \) |
$1$ |
$5702.693977$ |
0.961830659 |
\( -\frac{447949918}{43} a^{4} + \frac{320438205}{43} a^{3} + \frac{1883010453}{43} a^{2} - \frac{807873013}{43} a - \frac{1573795325}{43} \) |
\( \bigl[a^{4} - 3 a^{2} + a + 1\) , \( a^{4} - 4 a^{2} - a + 3\) , \( a^{4} + a^{3} - 3 a^{2} - 2 a + 1\) , \( -a^{4} + 3 a^{2}\) , \( 0\bigr] \) |
${y}^2+\left(a^{4}-3a^{2}+a+1\right){x}{y}+\left(a^{4}+a^{3}-3a^{2}-2a+1\right){y}={x}^{3}+\left(a^{4}-4a^{2}-a+3\right){x}^{2}+\left(-a^{4}+3a^{2}\right){x}$ |
| 43.5-b1 |
43.5-b |
$2$ |
$5$ |
\(\Q(\zeta_{11})^+\) |
$5$ |
$[5, 0]$ |
43.5 |
\( 43 \) |
\( -43 \) |
$15.74965$ |
$(a^4+a^3-4a^2-2a+3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.1.2 |
$625$ |
\( 1 \) |
$1$ |
$0.172110778$ |
0.889001954 |
\( -\frac{5237272895425412837756170}{43} a^{4} + \frac{3746411501579390694693714}{43} a^{3} + \frac{22015267800868858464202768}{43} a^{2} - \frac{9445221808010477549771597}{43} a - \frac{18399979045193160664111550}{43} \) |
\( \bigl[a^{3} + a^{2} - 2 a - 2\) , \( -a^{3} + 4 a\) , \( a^{4} + a^{3} - 3 a^{2} - 2 a\) , \( 172 a^{4} + 21 a^{3} - 667 a^{2} - 358 a + 75\) , \( 2438 a^{4} + 494 a^{3} - 9737 a^{2} - 4830 a + 1787\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-2a-2\right){x}{y}+\left(a^{4}+a^{3}-3a^{2}-2a\right){y}={x}^{3}+\left(-a^{3}+4a\right){x}^{2}+\left(172a^{4}+21a^{3}-667a^{2}-358a+75\right){x}+2438a^{4}+494a^{3}-9737a^{2}-4830a+1787$ |
| 43.5-b2 |
43.5-b |
$2$ |
$5$ |
\(\Q(\zeta_{11})^+\) |
$5$ |
$[5, 0]$ |
43.5 |
\( 43 \) |
\( - 43^{5} \) |
$15.74965$ |
$(a^4+a^3-4a^2-2a+3)$ |
0 |
$\Z/5\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.1.1 |
$1$ |
\( 5 \) |
$1$ |
$537.8461822$ |
0.889001954 |
\( -\frac{3026241451169}{147008443} a^{4} + \frac{3418994898940}{147008443} a^{3} + \frac{8931388378881}{147008443} a^{2} - \frac{5169364782818}{147008443} a - \frac{7100903835142}{147008443} \) |
\( \bigl[a^{4} - 4 a^{2} + 2\) , \( a^{4} + a^{3} - 4 a^{2} - 4 a + 3\) , \( a^{4} + a^{3} - 4 a^{2} - 3 a + 3\) , \( -5 a^{4} + a^{3} + 17 a^{2} - 3 a - 7\) , \( -3 a^{4} + a^{3} + 10 a^{2} - 7 a - 11\bigr] \) |
${y}^2+\left(a^{4}-4a^{2}+2\right){x}{y}+\left(a^{4}+a^{3}-4a^{2}-3a+3\right){y}={x}^{3}+\left(a^{4}+a^{3}-4a^{2}-4a+3\right){x}^{2}+\left(-5a^{4}+a^{3}+17a^{2}-3a-7\right){x}-3a^{4}+a^{3}+10a^{2}-7a-11$ |
| 121.1-a1 |
121.1-a |
$2$ |
$11$ |
\(\Q(\zeta_{11})^+\) |
$5$ |
$[5, 0]$ |
121.1 |
\( 11^{2} \) |
\( - 11^{4} \) |
$17.46636$ |
$(a^2+a-2)$ |
0 |
$\Z/11\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
✓ |
$11$ |
11B.1.1[5] |
$1$ |
\( 1 \) |
$1$ |
$17090.60992$ |
1.16731165 |
\( -24729001 \) |
\( \bigl[a^{4} - 3 a^{2} + 1\) , \( a^{4} - a^{3} - 3 a^{2} + 2 a\) , \( a^{2} + a - 1\) , \( -15 a^{4} + 38 a^{3} - 10 a^{2} - 19 a\) , \( 94 a^{4} - 262 a^{3} + 77 a^{2} + 174 a - 46\bigr] \) |
${y}^2+\left(a^{4}-3a^{2}+1\right){x}{y}+\left(a^{2}+a-1\right){y}={x}^{3}+\left(a^{4}-a^{3}-3a^{2}+2a\right){x}^{2}+\left(-15a^{4}+38a^{3}-10a^{2}-19a\right){x}+94a^{4}-262a^{3}+77a^{2}+174a-46$ |
| 121.1-a2 |
121.1-a |
$2$ |
$11$ |
\(\Q(\zeta_{11})^+\) |
$5$ |
$[5, 0]$ |
121.1 |
\( 11^{2} \) |
\( - 11^{8} \) |
$17.46636$ |
$(a^2+a-2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
✓ |
$11$ |
11B.1.10[5] |
$1$ |
\( 1 \) |
$1$ |
$141.2447101$ |
1.16731165 |
\( -121 \) |
\( \bigl[a^{2} - 1\) , \( -a^{3} + a^{2} + 3 a - 3\) , \( a^{4} + a^{3} - 4 a^{2} - 2 a + 3\) , \( 2 a^{4} - 5 a^{3} - 6 a^{2} + 13 a - 1\) , \( 16 a^{4} - 31 a^{3} - 40 a^{2} + 86 a - 22\bigr] \) |
${y}^2+\left(a^{2}-1\right){x}{y}+\left(a^{4}+a^{3}-4a^{2}-2a+3\right){y}={x}^{3}+\left(-a^{3}+a^{2}+3a-3\right){x}^{2}+\left(2a^{4}-5a^{3}-6a^{2}+13a-1\right){x}+16a^{4}-31a^{3}-40a^{2}+86a-22$ |
| 121.1-b1 |
121.1-b |
$2$ |
$11$ |
\(\Q(\zeta_{11})^+\) |
$5$ |
$[5, 0]$ |
121.1 |
\( 11^{2} \) |
\( - 11^{3} \) |
$17.46636$ |
$(a^2+a-2)$ |
$1$ |
$\Z/11\Z$ |
$\textsf{potential}$ |
$-11$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$11$ |
11B.1.1[5] |
$1$ |
\( 2 \) |
$0.089785156$ |
$28099.20145$ |
1.72316863 |
\( -32768 \) |
\( \bigl[0\) , \( a^{4} - a^{3} - 4 a^{2} + 3 a + 1\) , \( a^{3} + a^{2} - 2 a - 2\) , \( 9 a^{4} - 16 a^{3} - 23 a^{2} + 45 a - 10\) , \( -38 a^{4} + 67 a^{3} + 96 a^{2} - 188 a + 43\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-2a-2\right){y}={x}^{3}+\left(a^{4}-a^{3}-4a^{2}+3a+1\right){x}^{2}+\left(9a^{4}-16a^{3}-23a^{2}+45a-10\right){x}-38a^{4}+67a^{3}+96a^{2}-188a+43$ |
| 121.1-b2 |
121.1-b |
$2$ |
$11$ |
\(\Q(\zeta_{11})^+\) |
$5$ |
$[5, 0]$ |
121.1 |
\( 11^{2} \) |
\( - 11^{9} \) |
$17.46636$ |
$(a^2+a-2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{potential}$ |
$-11$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$11$ |
11B.1.10[5] |
$1$ |
\( 2 \) |
$0.987636717$ |
$21.11134594$ |
1.72316863 |
\( -32768 \) |
\( \bigl[0\) , \( -a^{4} + 4 a^{2} + a - 2\) , \( a^{4} - 4 a^{2} + 3\) , \( -4 a^{4} + 9 a^{3} - a^{2} - 3 a\) , \( -13 a^{4} + 34 a^{3} - 6 a^{2} - 25 a + 5\bigr] \) |
${y}^2+\left(a^{4}-4a^{2}+3\right){y}={x}^{3}+\left(-a^{4}+4a^{2}+a-2\right){x}^{2}+\left(-4a^{4}+9a^{3}-a^{2}-3a\right){x}-13a^{4}+34a^{3}-6a^{2}-25a+5$ |
| 121.1-c1 |
121.1-c |
$3$ |
$25$ |
\(\Q(\zeta_{11})^+\) |
$5$ |
$[5, 0]$ |
121.1 |
\( 11^{2} \) |
\( - 11^{11} \) |
$17.46636$ |
$(a^2+a-2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$5$ |
5B.4.2 |
$1$ |
\( 2 \) |
$1$ |
$63.74661725$ |
1.05366309 |
\( -\frac{52893159101157376}{11} \) |
\( \bigl[0\) , \( a - 1\) , \( a^{3} + a^{2} - 2 a - 1\) , \( -7820 a^{2} - 31282 a - 31281\) , \( -a^{4} + 263579 a^{3} + 1589301 a^{2} + 3194239 a + 2139918\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-2a-1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-7820a^{2}-31282a-31281\right){x}-a^{4}+263579a^{3}+1589301a^{2}+3194239a+2139918$ |
| 121.1-c2 |
121.1-c |
$3$ |
$25$ |
\(\Q(\zeta_{11})^+\) |
$5$ |
$[5, 0]$ |
121.1 |
\( 11^{2} \) |
\( - 11^{31} \) |
$17.46636$ |
$(a^2+a-2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$5$ |
5Cs.4.1 |
$1$ |
\( 2 \) |
$1$ |
$63.74661725$ |
1.05366309 |
\( -\frac{122023936}{161051} \) |
\( \bigl[0\) , \( a - 1\) , \( a^{3} + a^{2} - 2 a - 1\) , \( -10 a^{2} - 42 a - 41\) , \( -a^{4} + 19 a^{3} + 131 a^{2} + 279 a + 198\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-2a-1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-10a^{2}-42a-41\right){x}-a^{4}+19a^{3}+131a^{2}+279a+198$ |
| 121.1-c3 |
121.1-c |
$3$ |
$25$ |
\(\Q(\zeta_{11})^+\) |
$5$ |
$[5, 0]$ |
121.1 |
\( 11^{2} \) |
\( - 11^{11} \) |
$17.46636$ |
$(a^2+a-2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$5$ |
5B.4.1 |
$1$ |
\( 2 \) |
$1$ |
$63.74661725$ |
1.05366309 |
\( -\frac{4096}{11} \) |
\( \bigl[0\) , \( a - 1\) , \( a^{3} + a^{2} - 2 a - 1\) , \( -2 a - 1\) , \( -a^{4} - a^{3} + a^{2} - a - 2\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-2a-1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-2a-1\right){x}-a^{4}-a^{3}+a^{2}-a-2$ |
*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.
