| Label |
Class |
Class size |
Class degree |
Base field |
Field degree |
Field signature |
Conductor |
Conductor norm |
Discriminant norm |
Root analytic conductor |
Bad primes |
Rank |
Torsion |
CM |
CM |
Sato-Tate |
$\Q$-curve |
Base change |
Semistable |
Potentially good |
Nonmax $\ell$ |
mod-$\ell$ images |
$Ш_{\textrm{an}}$ |
Tamagawa |
Regulator |
Period |
Leading coeff |
j-invariant |
Weierstrass coefficients |
Weierstrass equation |
| 5.1-a1 |
5.1-a |
$2$ |
$5$ |
4.4.13525.1 |
$4$ |
$[4, 0]$ |
5.1 |
\( 5 \) |
\( 5^{5} \) |
$12.70804$ |
$(3/5a^3+a^2-16/5a-22/5)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.4.1[2] |
$1$ |
\( 5 \) |
$0.034210159$ |
$431.5969116$ |
2.539187619 |
\( \frac{12961}{125} a^{3} - \frac{49314}{125} a^{2} - \frac{11203}{25} a + \frac{275468}{125} \) |
\( \bigl[\frac{1}{5} a^{3} - \frac{7}{5} a + \frac{1}{5}\) , \( a + 1\) , \( \frac{1}{5} a^{3} + a^{2} - \frac{7}{5} a - \frac{24}{5}\) , \( \frac{24}{5} a^{3} - 12 a^{2} - \frac{203}{5} a + \frac{509}{5}\) , \( -\frac{1}{5} a^{3} - a^{2} + \frac{7}{5} a + \frac{29}{5}\bigr] \) |
${y}^2+\left(\frac{1}{5}a^{3}-\frac{7}{5}a+\frac{1}{5}\right){x}{y}+\left(\frac{1}{5}a^{3}+a^{2}-\frac{7}{5}a-\frac{24}{5}\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(\frac{24}{5}a^{3}-12a^{2}-\frac{203}{5}a+\frac{509}{5}\right){x}-\frac{1}{5}a^{3}-a^{2}+\frac{7}{5}a+\frac{29}{5}$ |
| 5.1-a2 |
5.1-a |
$2$ |
$5$ |
4.4.13525.1 |
$4$ |
$[4, 0]$ |
5.1 |
\( 5 \) |
\( 5 \) |
$12.70804$ |
$(3/5a^3+a^2-16/5a-22/5)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.4.1[2] |
$1$ |
\( 1 \) |
$0.171050799$ |
$431.5969116$ |
2.539187619 |
\( -\frac{1402799}{5} a^{3} + \frac{3494916}{5} a^{2} + 2377163 a - \frac{29139337}{5} \) |
\( \bigl[\frac{1}{5} a^{3} - \frac{2}{5} a + \frac{6}{5}\) , \( -\frac{1}{5} a^{3} + \frac{2}{5} a - \frac{1}{5}\) , \( a^{2} - 5\) , \( -\frac{12}{5} a^{3} + 6 a^{2} + \frac{84}{5} a - \frac{237}{5}\) , \( -7 a^{3} + 15 a^{2} + 59 a - 124\bigr] \) |
${y}^2+\left(\frac{1}{5}a^{3}-\frac{2}{5}a+\frac{6}{5}\right){x}{y}+\left(a^{2}-5\right){y}={x}^{3}+\left(-\frac{1}{5}a^{3}+\frac{2}{5}a-\frac{1}{5}\right){x}^{2}+\left(-\frac{12}{5}a^{3}+6a^{2}+\frac{84}{5}a-\frac{237}{5}\right){x}-7a^{3}+15a^{2}+59a-124$ |
| 5.2-a1 |
5.2-a |
$2$ |
$5$ |
4.4.13525.1 |
$4$ |
$[4, 0]$ |
5.2 |
\( 5 \) |
\( 5^{5} \) |
$12.70804$ |
$(2/5a^3-19/5a+2/5)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.4.1[2] |
$1$ |
\( 5 \) |
$0.034210159$ |
$431.5969116$ |
2.539187619 |
\( \frac{148831}{625} a^{3} + \frac{49314}{125} a^{2} - \frac{1215377}{625} a - \frac{1744044}{625} \) |
\( \bigl[1\) , \( \frac{1}{5} a^{3} + a^{2} - \frac{2}{5} a - \frac{24}{5}\) , \( a^{2} + a - 6\) , \( \frac{12}{5} a^{3} + 4 a^{2} - \frac{74}{5} a - \frac{88}{5}\) , \( \frac{16}{5} a^{3} + 8 a^{2} - \frac{87}{5} a - \frac{199}{5}\bigr] \) |
${y}^2+{x}{y}+\left(a^{2}+a-6\right){y}={x}^{3}+\left(\frac{1}{5}a^{3}+a^{2}-\frac{2}{5}a-\frac{24}{5}\right){x}^{2}+\left(\frac{12}{5}a^{3}+4a^{2}-\frac{74}{5}a-\frac{88}{5}\right){x}+\frac{16}{5}a^{3}+8a^{2}-\frac{87}{5}a-\frac{199}{5}$ |
| 5.2-a2 |
5.2-a |
$2$ |
$5$ |
4.4.13525.1 |
$4$ |
$[4, 0]$ |
5.2 |
\( 5 \) |
\( 5 \) |
$12.70804$ |
$(2/5a^3-19/5a+2/5)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.4.1[2] |
$1$ |
\( 1 \) |
$0.171050799$ |
$431.5969116$ |
2.539187619 |
\( -\frac{8442689}{25} a^{3} - \frac{3494916}{5} a^{2} + \frac{48767713}{25} a + \frac{80044161}{25} \) |
\( \bigl[a + 1\) , \( -\frac{1}{5} a^{3} - a^{2} + \frac{7}{5} a + \frac{34}{5}\) , \( \frac{1}{5} a^{3} + a^{2} - \frac{7}{5} a - \frac{29}{5}\) , \( -\frac{18}{5} a^{3} - 8 a^{2} + \frac{116}{5} a + \frac{212}{5}\) , \( -\frac{41}{5} a^{3} - 16 a^{2} + \frac{237}{5} a + \frac{384}{5}\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(\frac{1}{5}a^{3}+a^{2}-\frac{7}{5}a-\frac{29}{5}\right){y}={x}^{3}+\left(-\frac{1}{5}a^{3}-a^{2}+\frac{7}{5}a+\frac{34}{5}\right){x}^{2}+\left(-\frac{18}{5}a^{3}-8a^{2}+\frac{116}{5}a+\frac{212}{5}\right){x}-\frac{41}{5}a^{3}-16a^{2}+\frac{237}{5}a+\frac{384}{5}$ |
| 9.1-a1 |
9.1-a |
$1$ |
$1$ |
4.4.13525.1 |
$4$ |
$[4, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{12} \) |
$13.67689$ |
$(-2/5a^3-a^2+19/5a+43/5)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \cdot 3 \) |
$0.054586874$ |
$270.1214392$ |
3.042915445 |
\( -\frac{283299683}{3645} a^{3} + \frac{93901877}{729} a^{2} + \frac{754548142}{1215} a - \frac{4288943888}{3645} \) |
\( \bigl[a + 1\) , \( -\frac{1}{5} a^{3} - a^{2} + \frac{7}{5} a + \frac{24}{5}\) , \( \frac{1}{5} a^{3} + a^{2} - \frac{7}{5} a - \frac{24}{5}\) , \( \frac{212}{5} a^{3} + 54 a^{2} - \frac{1944}{5} a - \frac{2718}{5}\) , \( -\frac{2068}{5} a^{3} - 531 a^{2} + \frac{18756}{5} a + \frac{26272}{5}\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(\frac{1}{5}a^{3}+a^{2}-\frac{7}{5}a-\frac{24}{5}\right){y}={x}^{3}+\left(-\frac{1}{5}a^{3}-a^{2}+\frac{7}{5}a+\frac{24}{5}\right){x}^{2}+\left(\frac{212}{5}a^{3}+54a^{2}-\frac{1944}{5}a-\frac{2718}{5}\right){x}-\frac{2068}{5}a^{3}-531a^{2}+\frac{18756}{5}a+\frac{26272}{5}$ |
| 9.1-b1 |
9.1-b |
$1$ |
$1$ |
4.4.13525.1 |
$4$ |
$[4, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{4} \) |
$13.67689$ |
$(-2/5a^3-a^2+19/5a+43/5)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \) |
$0.028735632$ |
$1196.561040$ |
2.365249524 |
\( -\frac{1141}{45} a^{3} + \frac{970}{9} a^{2} + \frac{28}{5} a - \frac{13276}{45} \) |
\( \bigl[\frac{1}{5} a^{3} + a^{2} - \frac{7}{5} a - \frac{29}{5}\) , \( a\) , \( \frac{1}{5} a^{3} + a^{2} - \frac{2}{5} a - \frac{24}{5}\) , \( \frac{16}{5} a^{3} + 5 a^{2} - \frac{142}{5} a - \frac{224}{5}\) , \( -\frac{381}{5} a^{3} - 97 a^{2} + \frac{3467}{5} a + \frac{4839}{5}\bigr] \) |
${y}^2+\left(\frac{1}{5}a^{3}+a^{2}-\frac{7}{5}a-\frac{29}{5}\right){x}{y}+\left(\frac{1}{5}a^{3}+a^{2}-\frac{2}{5}a-\frac{24}{5}\right){y}={x}^{3}+a{x}^{2}+\left(\frac{16}{5}a^{3}+5a^{2}-\frac{142}{5}a-\frac{224}{5}\right){x}-\frac{381}{5}a^{3}-97a^{2}+\frac{3467}{5}a+\frac{4839}{5}$ |
| 9.1-c1 |
9.1-c |
$2$ |
$2$ |
4.4.13525.1 |
$4$ |
$[4, 0]$ |
9.1 |
\( 3^{2} \) |
\( - 3^{12} \) |
$13.67689$ |
$(-2/5a^3-a^2+19/5a+43/5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \cdot 3 \) |
$0.547652887$ |
$78.53844958$ |
2.219066511 |
\( -\frac{3920760259504}{729} a^{3} - \frac{5026538781991}{729} a^{2} + \frac{3953158349677}{81} a + \frac{49825009205279}{729} \) |
\( \bigl[a\) , \( \frac{1}{5} a^{3} - a^{2} - \frac{2}{5} a + \frac{31}{5}\) , \( \frac{1}{5} a^{3} + a^{2} - \frac{2}{5} a - \frac{24}{5}\) , \( -\frac{453}{5} a^{3} + 219 a^{2} + \frac{3841}{5} a - \frac{9088}{5}\) , \( -\frac{8734}{5} a^{3} + 4251 a^{2} + \frac{74273}{5} a - \frac{176414}{5}\bigr] \) |
${y}^2+a{x}{y}+\left(\frac{1}{5}a^{3}+a^{2}-\frac{2}{5}a-\frac{24}{5}\right){y}={x}^{3}+\left(\frac{1}{5}a^{3}-a^{2}-\frac{2}{5}a+\frac{31}{5}\right){x}^{2}+\left(-\frac{453}{5}a^{3}+219a^{2}+\frac{3841}{5}a-\frac{9088}{5}\right){x}-\frac{8734}{5}a^{3}+4251a^{2}+\frac{74273}{5}a-\frac{176414}{5}$ |
| 9.1-c2 |
9.1-c |
$2$ |
$2$ |
4.4.13525.1 |
$4$ |
$[4, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{6} \) |
$13.67689$ |
$(-2/5a^3-a^2+19/5a+43/5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 3 \) |
$0.273826443$ |
$314.1537983$ |
2.219066511 |
\( \frac{864767}{45} a^{3} + \frac{676385}{27} a^{2} - \frac{23459662}{135} a - \frac{32965924}{135} \) |
\( \bigl[a\) , \( \frac{1}{5} a^{3} - a^{2} - \frac{2}{5} a + \frac{31}{5}\) , \( \frac{1}{5} a^{3} + a^{2} - \frac{2}{5} a - \frac{24}{5}\) , \( -\frac{3}{5} a^{3} - a^{2} + \frac{16}{5} a + \frac{37}{5}\) , \( -\frac{366}{5} a^{3} + 174 a^{2} + \frac{3102}{5} a - \frac{7256}{5}\bigr] \) |
${y}^2+a{x}{y}+\left(\frac{1}{5}a^{3}+a^{2}-\frac{2}{5}a-\frac{24}{5}\right){y}={x}^{3}+\left(\frac{1}{5}a^{3}-a^{2}-\frac{2}{5}a+\frac{31}{5}\right){x}^{2}+\left(-\frac{3}{5}a^{3}-a^{2}+\frac{16}{5}a+\frac{37}{5}\right){x}-\frac{366}{5}a^{3}+174a^{2}+\frac{3102}{5}a-\frac{7256}{5}$ |
| 9.2-a1 |
9.2-a |
$1$ |
$1$ |
4.4.13525.1 |
$4$ |
$[4, 0]$ |
9.2 |
\( 3^{2} \) |
\( 3^{12} \) |
$13.67689$ |
$(-1/5a^3-a^2+7/5a+24/5)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \cdot 3 \) |
$0.054586874$ |
$270.1214392$ |
3.042915445 |
\( -\frac{321092231}{3645} a^{3} - \frac{93901877}{729} a^{2} + \frac{1967098972}{3645} a + \frac{1776885569}{3645} \) |
\( \bigl[\frac{1}{5} a^{3} + a^{2} - \frac{7}{5} a - \frac{24}{5}\) , \( \frac{1}{5} a^{3} - \frac{7}{5} a + \frac{6}{5}\) , \( \frac{1}{5} a^{3} + a^{2} - \frac{2}{5} a - \frac{24}{5}\) , \( \frac{1}{5} a^{3} + \frac{83}{5} a - \frac{199}{5}\) , \( -\frac{81}{5} a^{3} + 57 a^{2} + \frac{447}{5} a - \frac{1546}{5}\bigr] \) |
${y}^2+\left(\frac{1}{5}a^{3}+a^{2}-\frac{7}{5}a-\frac{24}{5}\right){x}{y}+\left(\frac{1}{5}a^{3}+a^{2}-\frac{2}{5}a-\frac{24}{5}\right){y}={x}^{3}+\left(\frac{1}{5}a^{3}-\frac{7}{5}a+\frac{6}{5}\right){x}^{2}+\left(\frac{1}{5}a^{3}+\frac{83}{5}a-\frac{199}{5}\right){x}-\frac{81}{5}a^{3}+57a^{2}+\frac{447}{5}a-\frac{1546}{5}$ |
| 9.2-b1 |
9.2-b |
$1$ |
$1$ |
4.4.13525.1 |
$4$ |
$[4, 0]$ |
9.2 |
\( 3^{2} \) |
\( 3^{4} \) |
$13.67689$ |
$(-1/5a^3-a^2+7/5a+24/5)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \) |
$0.028735632$ |
$1196.561040$ |
2.365249524 |
\( -\frac{3658}{45} a^{3} - \frac{970}{9} a^{2} + \frac{33341}{45} a + \frac{47257}{45} \) |
\( \bigl[\frac{1}{5} a^{3} + a^{2} - \frac{2}{5} a - \frac{24}{5}\) , \( -a^{2} + 5\) , \( a\) , \( 4 a^{3} + 6 a^{2} - 24 a - 26\) , \( \frac{38}{5} a^{3} + 16 a^{2} - \frac{286}{5} a - \frac{222}{5}\bigr] \) |
${y}^2+\left(\frac{1}{5}a^{3}+a^{2}-\frac{2}{5}a-\frac{24}{5}\right){x}{y}+a{y}={x}^{3}+\left(-a^{2}+5\right){x}^{2}+\left(4a^{3}+6a^{2}-24a-26\right){x}+\frac{38}{5}a^{3}+16a^{2}-\frac{286}{5}a-\frac{222}{5}$ |
| 9.2-c1 |
9.2-c |
$2$ |
$2$ |
4.4.13525.1 |
$4$ |
$[4, 0]$ |
9.2 |
\( 3^{2} \) |
\( - 3^{12} \) |
$13.67689$ |
$(-1/5a^3-a^2+7/5a+24/5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \cdot 3 \) |
$0.547652887$ |
$78.53844958$ |
2.219066511 |
\( -\frac{6444159184964}{3645} a^{3} + \frac{5026538781991}{729} a^{2} + \frac{4443597641923}{3645} a - \frac{64440332690464}{3645} \) |
\( \bigl[\frac{1}{5} a^{3} + a^{2} - \frac{2}{5} a - \frac{24}{5}\) , \( \frac{1}{5} a^{3} - \frac{12}{5} a + \frac{1}{5}\) , \( \frac{1}{5} a^{3} - \frac{2}{5} a + \frac{1}{5}\) , \( -\frac{54}{5} a^{3} - 26 a^{2} + \frac{328}{5} a + \frac{621}{5}\) , \( -\frac{951}{5} a^{3} - 400 a^{2} + \frac{5472}{5} a + \frac{9184}{5}\bigr] \) |
${y}^2+\left(\frac{1}{5}a^{3}+a^{2}-\frac{2}{5}a-\frac{24}{5}\right){x}{y}+\left(\frac{1}{5}a^{3}-\frac{2}{5}a+\frac{1}{5}\right){y}={x}^{3}+\left(\frac{1}{5}a^{3}-\frac{12}{5}a+\frac{1}{5}\right){x}^{2}+\left(-\frac{54}{5}a^{3}-26a^{2}+\frac{328}{5}a+\frac{621}{5}\right){x}-\frac{951}{5}a^{3}-400a^{2}+\frac{5472}{5}a+\frac{9184}{5}$ |
| 9.2-c2 |
9.2-c |
$2$ |
$2$ |
4.4.13525.1 |
$4$ |
$[4, 0]$ |
9.2 |
\( 3^{2} \) |
\( 3^{6} \) |
$13.67689$ |
$(-1/5a^3-a^2+7/5a+24/5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 3 \) |
$0.273826443$ |
$314.1537983$ |
2.219066511 |
\( \frac{171601}{27} a^{3} - \frac{676385}{27} a^{2} - \frac{141296}{27} a + \frac{1852561}{27} \) |
\( \bigl[\frac{1}{5} a^{3} - \frac{2}{5} a + \frac{1}{5}\) , \( -\frac{1}{5} a^{3} + \frac{2}{5} a - \frac{6}{5}\) , \( \frac{1}{5} a^{3} - \frac{2}{5} a + \frac{6}{5}\) , \( -\frac{4}{5} a^{3} - a^{2} + \frac{18}{5} a + \frac{26}{5}\) , \( -86 a^{3} - 176 a^{2} + 492 a + 814\bigr] \) |
${y}^2+\left(\frac{1}{5}a^{3}-\frac{2}{5}a+\frac{1}{5}\right){x}{y}+\left(\frac{1}{5}a^{3}-\frac{2}{5}a+\frac{6}{5}\right){y}={x}^{3}+\left(-\frac{1}{5}a^{3}+\frac{2}{5}a-\frac{6}{5}\right){x}^{2}+\left(-\frac{4}{5}a^{3}-a^{2}+\frac{18}{5}a+\frac{26}{5}\right){x}-86a^{3}-176a^{2}+492a+814$ |
| 25.1-a1 |
25.1-a |
$2$ |
$3$ |
4.4.13525.1 |
$4$ |
$[4, 0]$ |
25.1 |
\( 5^{2} \) |
\( 5^{6} \) |
$15.53995$ |
$(3/5a^3+a^2-16/5a-22/5), (2/5a^3-19/5a+2/5)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 3 \) |
$0.271401812$ |
$128.7283259$ |
3.604951897 |
\( \frac{8200212}{125} a^{3} - 141235 a^{2} - \frac{70053934}{125} a + \frac{145349182}{125} \) |
\( \bigl[a^{2} - 5\) , \( \frac{1}{5} a^{3} + a^{2} - \frac{12}{5} a - \frac{24}{5}\) , \( a^{2} - 5\) , \( -a^{3} + a^{2} + 4 a - 2\) , \( -3 a^{3} - 3 a^{2} + 15 a + 17\bigr] \) |
${y}^2+\left(a^{2}-5\right){x}{y}+\left(a^{2}-5\right){y}={x}^{3}+\left(\frac{1}{5}a^{3}+a^{2}-\frac{12}{5}a-\frac{24}{5}\right){x}^{2}+\left(-a^{3}+a^{2}+4a-2\right){x}-3a^{3}-3a^{2}+15a+17$ |
| 25.1-a2 |
25.1-a |
$2$ |
$3$ |
4.4.13525.1 |
$4$ |
$[4, 0]$ |
25.1 |
\( 5^{2} \) |
\( 5^{2} \) |
$15.53995$ |
$(3/5a^3+a^2-16/5a-22/5), (2/5a^3-19/5a+2/5)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 1 \) |
$0.814205437$ |
$128.7283259$ |
3.604951897 |
\( \frac{3007101002}{25} a^{3} + 246864964 a^{2} - \frac{17231600714}{25} a - \frac{28553182703}{25} \) |
\( \bigl[a + 1\) , \( -\frac{1}{5} a^{3} - a^{2} + \frac{2}{5} a + \frac{29}{5}\) , \( \frac{1}{5} a^{3} + a^{2} - \frac{2}{5} a - \frac{29}{5}\) , \( -\frac{144}{5} a^{3} + 67 a^{2} + \frac{1218}{5} a - \frac{2799}{5}\) , \( \frac{969}{5} a^{3} - 476 a^{2} - \frac{8253}{5} a + \frac{19714}{5}\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(\frac{1}{5}a^{3}+a^{2}-\frac{2}{5}a-\frac{29}{5}\right){y}={x}^{3}+\left(-\frac{1}{5}a^{3}-a^{2}+\frac{2}{5}a+\frac{29}{5}\right){x}^{2}+\left(-\frac{144}{5}a^{3}+67a^{2}+\frac{1218}{5}a-\frac{2799}{5}\right){x}+\frac{969}{5}a^{3}-476a^{2}-\frac{8253}{5}a+\frac{19714}{5}$ |
| 25.1-b1 |
25.1-b |
$2$ |
$3$ |
4.4.13525.1 |
$4$ |
$[4, 0]$ |
25.1 |
\( 5^{2} \) |
\( 5^{6} \) |
$15.53995$ |
$(3/5a^3+a^2-16/5a-22/5), (2/5a^3-19/5a+2/5)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 3 \) |
$0.271401812$ |
$128.7283259$ |
3.604951897 |
\( \frac{9200597}{125} a^{3} + 141235 a^{2} - \frac{51751729}{125} a - \frac{83157308}{125} \) |
\( \bigl[\frac{1}{5} a^{3} + a^{2} - \frac{7}{5} a - \frac{29}{5}\) , \( \frac{1}{5} a^{3} + a^{2} - \frac{2}{5} a - \frac{29}{5}\) , \( a + 1\) , \( \frac{9}{5} a^{3} + 7 a^{2} - \frac{38}{5} a - \frac{186}{5}\) , \( 5 a^{3} + 10 a^{2} - 29 a - 48\bigr] \) |
${y}^2+\left(\frac{1}{5}a^{3}+a^{2}-\frac{7}{5}a-\frac{29}{5}\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(\frac{1}{5}a^{3}+a^{2}-\frac{2}{5}a-\frac{29}{5}\right){x}^{2}+\left(\frac{9}{5}a^{3}+7a^{2}-\frac{38}{5}a-\frac{186}{5}\right){x}+5a^{3}+10a^{2}-29a-48$ |
| 25.1-b2 |
25.1-b |
$2$ |
$3$ |
4.4.13525.1 |
$4$ |
$[4, 0]$ |
25.1 |
\( 5^{2} \) |
\( 5^{2} \) |
$15.53995$ |
$(3/5a^3+a^2-16/5a-22/5), (2/5a^3-19/5a+2/5)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 1 \) |
$0.814205437$ |
$128.7283259$ |
3.604951897 |
\( \frac{2536397442}{25} a^{3} - 246864964 a^{2} - \frac{21572888394}{25} a + \frac{51207227037}{25} \) |
\( \bigl[\frac{1}{5} a^{3} - \frac{2}{5} a + \frac{6}{5}\) , \( \frac{1}{5} a^{3} - \frac{7}{5} a - \frac{4}{5}\) , \( a\) , \( -\frac{162}{5} a^{3} - 67 a^{2} + \frac{924}{5} a + \frac{1543}{5}\) , \( 178 a^{3} + 365 a^{2} - 1020 a - 1690\bigr] \) |
${y}^2+\left(\frac{1}{5}a^{3}-\frac{2}{5}a+\frac{6}{5}\right){x}{y}+a{y}={x}^{3}+\left(\frac{1}{5}a^{3}-\frac{7}{5}a-\frac{4}{5}\right){x}^{2}+\left(-\frac{162}{5}a^{3}-67a^{2}+\frac{924}{5}a+\frac{1543}{5}\right){x}+178a^{3}+365a^{2}-1020a-1690$ |
| 25.2-a1 |
25.2-a |
$2$ |
$5$ |
4.4.13525.1 |
$4$ |
$[4, 0]$ |
25.2 |
\( 5^{2} \) |
\( 5^{11} \) |
$15.53995$ |
$(3/5a^3+a^2-16/5a-22/5)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$5$ |
5B.1.4[2] |
$1$ |
\( 2^{2} \) |
$1$ |
$75.89636249$ |
2.610431589 |
\( \frac{12961}{125} a^{3} - \frac{49314}{125} a^{2} - \frac{11203}{25} a + \frac{275468}{125} \) |
\( \bigl[\frac{1}{5} a^{3} + a^{2} - \frac{7}{5} a - \frac{29}{5}\) , \( -\frac{1}{5} a^{3} + \frac{2}{5} a - \frac{1}{5}\) , \( \frac{1}{5} a^{3} + a^{2} - \frac{7}{5} a - \frac{29}{5}\) , \( a^{3} + 3 a^{2} - 6 a - 14\) , \( -\frac{74}{5} a^{3} - 30 a^{2} + \frac{423}{5} a + \frac{691}{5}\bigr] \) |
${y}^2+\left(\frac{1}{5}a^{3}+a^{2}-\frac{7}{5}a-\frac{29}{5}\right){x}{y}+\left(\frac{1}{5}a^{3}+a^{2}-\frac{7}{5}a-\frac{29}{5}\right){y}={x}^{3}+\left(-\frac{1}{5}a^{3}+\frac{2}{5}a-\frac{1}{5}\right){x}^{2}+\left(a^{3}+3a^{2}-6a-14\right){x}-\frac{74}{5}a^{3}-30a^{2}+\frac{423}{5}a+\frac{691}{5}$ |
| 25.2-a2 |
25.2-a |
$2$ |
$5$ |
4.4.13525.1 |
$4$ |
$[4, 0]$ |
25.2 |
\( 5^{2} \) |
\( 5^{7} \) |
$15.53995$ |
$(3/5a^3+a^2-16/5a-22/5)$ |
0 |
$\Z/5\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$5$ |
5B.1.1[2] |
$1$ |
\( 2^{2} \) |
$1$ |
$1897.409062$ |
2.610431589 |
\( -\frac{1402799}{5} a^{3} + \frac{3494916}{5} a^{2} + 2377163 a - \frac{29139337}{5} \) |
\( \bigl[\frac{1}{5} a^{3} - \frac{2}{5} a + \frac{1}{5}\) , \( -\frac{1}{5} a^{3} - a^{2} + \frac{7}{5} a + \frac{34}{5}\) , \( a^{2} + a - 6\) , \( \frac{17}{5} a^{3} + 2 a^{2} - \frac{194}{5} a - \frac{228}{5}\) , \( -\frac{62}{5} a^{3} - 13 a^{2} + \frac{604}{5} a + \frac{788}{5}\bigr] \) |
${y}^2+\left(\frac{1}{5}a^{3}-\frac{2}{5}a+\frac{1}{5}\right){x}{y}+\left(a^{2}+a-6\right){y}={x}^{3}+\left(-\frac{1}{5}a^{3}-a^{2}+\frac{7}{5}a+\frac{34}{5}\right){x}^{2}+\left(\frac{17}{5}a^{3}+2a^{2}-\frac{194}{5}a-\frac{228}{5}\right){x}-\frac{62}{5}a^{3}-13a^{2}+\frac{604}{5}a+\frac{788}{5}$ |
| 25.3-a1 |
25.3-a |
$2$ |
$5$ |
4.4.13525.1 |
$4$ |
$[4, 0]$ |
25.3 |
\( 5^{2} \) |
\( 5^{7} \) |
$15.53995$ |
$(2/5a^3-19/5a+2/5)$ |
0 |
$\Z/5\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$5$ |
5B.1.1[2] |
$1$ |
\( 2^{2} \) |
$1$ |
$1897.409062$ |
2.610431589 |
\( -\frac{8442689}{25} a^{3} - \frac{3494916}{5} a^{2} + \frac{48767713}{25} a + \frac{80044161}{25} \) |
\( \bigl[\frac{1}{5} a^{3} + a^{2} - \frac{7}{5} a - \frac{29}{5}\) , \( \frac{1}{5} a^{3} - \frac{7}{5} a + \frac{6}{5}\) , \( a^{2} + a - 5\) , \( -\frac{46}{5} a^{3} + 23 a^{2} + \frac{407}{5} a - \frac{971}{5}\) , \( 46 a^{3} - 109 a^{2} - 392 a + 914\bigr] \) |
${y}^2+\left(\frac{1}{5}a^{3}+a^{2}-\frac{7}{5}a-\frac{29}{5}\right){x}{y}+\left(a^{2}+a-5\right){y}={x}^{3}+\left(\frac{1}{5}a^{3}-\frac{7}{5}a+\frac{6}{5}\right){x}^{2}+\left(-\frac{46}{5}a^{3}+23a^{2}+\frac{407}{5}a-\frac{971}{5}\right){x}+46a^{3}-109a^{2}-392a+914$ |
| 25.3-a2 |
25.3-a |
$2$ |
$5$ |
4.4.13525.1 |
$4$ |
$[4, 0]$ |
25.3 |
\( 5^{2} \) |
\( 5^{11} \) |
$15.53995$ |
$(2/5a^3-19/5a+2/5)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$5$ |
5B.1.4[2] |
$1$ |
\( 2^{2} \) |
$1$ |
$75.89636249$ |
2.610431589 |
\( \frac{148831}{625} a^{3} + \frac{49314}{125} a^{2} - \frac{1215377}{625} a - \frac{1744044}{625} \) |
\( \bigl[a^{2} - 5\) , \( \frac{1}{5} a^{3} - a^{2} - \frac{2}{5} a + \frac{31}{5}\) , \( \frac{1}{5} a^{3} - \frac{2}{5} a + \frac{1}{5}\) , \( \frac{9}{5} a^{3} - 4 a^{2} - \frac{83}{5} a + \frac{194}{5}\) , \( -\frac{46}{5} a^{3} + 23 a^{2} + \frac{397}{5} a - \frac{961}{5}\bigr] \) |
${y}^2+\left(a^{2}-5\right){x}{y}+\left(\frac{1}{5}a^{3}-\frac{2}{5}a+\frac{1}{5}\right){y}={x}^{3}+\left(\frac{1}{5}a^{3}-a^{2}-\frac{2}{5}a+\frac{31}{5}\right){x}^{2}+\left(\frac{9}{5}a^{3}-4a^{2}-\frac{83}{5}a+\frac{194}{5}\right){x}-\frac{46}{5}a^{3}+23a^{2}+\frac{397}{5}a-\frac{961}{5}$ |
| 41.1-a1 |
41.1-a |
$2$ |
$2$ |
4.4.13525.1 |
$4$ |
$[4, 0]$ |
41.1 |
\( 41 \) |
\( - 41^{6} \) |
$16.53123$ |
$(2/5a^3+a^2-14/5a-38/5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \cdot 3 \) |
$0.351546268$ |
$216.6408462$ |
3.929211889 |
\( -\frac{741302826572035}{4750104241} a^{3} + \frac{2993781687054115}{4750104241} a^{2} + \frac{80756069372560}{4750104241} a - \frac{6965117713033177}{4750104241} \) |
\( \bigl[\frac{1}{5} a^{3} + a^{2} - \frac{7}{5} a - \frac{29}{5}\) , \( a^{2} - a - 7\) , \( \frac{1}{5} a^{3} - \frac{2}{5} a + \frac{1}{5}\) , \( -5 a^{3} - 5 a^{2} + 43 a + 55\) , \( -110 a^{3} - 141 a^{2} + 998 a + 1397\bigr] \) |
${y}^2+\left(\frac{1}{5}a^{3}+a^{2}-\frac{7}{5}a-\frac{29}{5}\right){x}{y}+\left(\frac{1}{5}a^{3}-\frac{2}{5}a+\frac{1}{5}\right){y}={x}^{3}+\left(a^{2}-a-7\right){x}^{2}+\left(-5a^{3}-5a^{2}+43a+55\right){x}-110a^{3}-141a^{2}+998a+1397$ |
| 41.1-a2 |
41.1-a |
$2$ |
$2$ |
4.4.13525.1 |
$4$ |
$[4, 0]$ |
41.1 |
\( 41 \) |
\( 41^{3} \) |
$16.53123$ |
$(2/5a^3+a^2-14/5a-38/5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 3 \) |
$0.175773134$ |
$866.5633850$ |
3.929211889 |
\( -\frac{85157746}{68921} a^{3} - \frac{114647803}{68921} a^{2} + \frac{843124349}{68921} a + \frac{1188953373}{68921} \) |
\( \bigl[\frac{1}{5} a^{3} + a^{2} - \frac{2}{5} a - \frac{29}{5}\) , \( \frac{1}{5} a^{3} + a^{2} - \frac{7}{5} a - \frac{24}{5}\) , \( a^{2} + a - 6\) , \( \frac{36}{5} a^{3} + 16 a^{2} - \frac{222}{5} a - \frac{424}{5}\) , \( 16 a^{3} + 36 a^{2} - 85 a - 158\bigr] \) |
${y}^2+\left(\frac{1}{5}a^{3}+a^{2}-\frac{2}{5}a-\frac{29}{5}\right){x}{y}+\left(a^{2}+a-6\right){y}={x}^{3}+\left(\frac{1}{5}a^{3}+a^{2}-\frac{7}{5}a-\frac{24}{5}\right){x}^{2}+\left(\frac{36}{5}a^{3}+16a^{2}-\frac{222}{5}a-\frac{424}{5}\right){x}+16a^{3}+36a^{2}-85a-158$ |
| 41.2-a1 |
41.2-a |
$1$ |
$1$ |
4.4.13525.1 |
$4$ |
$[4, 0]$ |
41.2 |
\( 41 \) |
\( 41 \) |
$16.53123$ |
$(-4/5a^3+33/5a+11/5)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$1$ |
$53.58543739$ |
0.460763579 |
\( -\frac{3675856}{205} a^{3} - \frac{2095031}{41} a^{2} + \frac{23550632}{205} a + \frac{44487594}{205} \) |
\( \bigl[\frac{1}{5} a^{3} + a^{2} - \frac{2}{5} a - \frac{24}{5}\) , \( 1\) , \( 1\) , \( \frac{36}{5} a^{3} + 14 a^{2} - \frac{207}{5} a - \frac{319}{5}\) , \( 17 a^{3} + 35 a^{2} - 97 a - 163\bigr] \) |
${y}^2+\left(\frac{1}{5}a^{3}+a^{2}-\frac{2}{5}a-\frac{24}{5}\right){x}{y}+{y}={x}^{3}+{x}^{2}+\left(\frac{36}{5}a^{3}+14a^{2}-\frac{207}{5}a-\frac{319}{5}\right){x}+17a^{3}+35a^{2}-97a-163$ |
| 41.2-b1 |
41.2-b |
$1$ |
$1$ |
4.4.13525.1 |
$4$ |
$[4, 0]$ |
41.2 |
\( 41 \) |
\( -41 \) |
$16.53123$ |
$(-4/5a^3+33/5a+11/5)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$1$ |
$367.9763622$ |
3.164107898 |
\( \frac{44216}{205} a^{3} - \frac{38839}{41} a^{2} - \frac{360917}{205} a + \frac{1654521}{205} \) |
\( \bigl[\frac{1}{5} a^{3} - \frac{2}{5} a + \frac{6}{5}\) , \( -\frac{1}{5} a^{3} + \frac{2}{5} a - \frac{1}{5}\) , \( 0\) , \( -\frac{24}{5} a^{3} - 5 a^{2} + \frac{213}{5} a + \frac{286}{5}\) , \( -\frac{14}{5} a^{3} - 3 a^{2} + \frac{123}{5} a + \frac{166}{5}\bigr] \) |
${y}^2+\left(\frac{1}{5}a^{3}-\frac{2}{5}a+\frac{6}{5}\right){x}{y}={x}^{3}+\left(-\frac{1}{5}a^{3}+\frac{2}{5}a-\frac{1}{5}\right){x}^{2}+\left(-\frac{24}{5}a^{3}-5a^{2}+\frac{213}{5}a+\frac{286}{5}\right){x}-\frac{14}{5}a^{3}-3a^{2}+\frac{123}{5}a+\frac{166}{5}$ |
| 41.2-c1 |
41.2-c |
$1$ |
$1$ |
4.4.13525.1 |
$4$ |
$[4, 0]$ |
41.2 |
\( 41 \) |
\( 41^{5} \) |
$16.53123$ |
$(-4/5a^3+33/5a+11/5)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5Ns.2.1[2] |
$1$ |
\( 1 \) |
$1$ |
$80.16388967$ |
0.689302962 |
\( \frac{837131435827}{115856201} a^{3} + \frac{1226642945595}{115856201} a^{2} - \frac{7604205172724}{115856201} a - \frac{11951355585799}{115856201} \) |
\( \bigl[a^{2} - 6\) , \( a^{2} - a - 6\) , \( \frac{1}{5} a^{3} + a^{2} - \frac{2}{5} a - \frac{24}{5}\) , \( \frac{49}{5} a^{3} + 15 a^{2} - \frac{468}{5} a - \frac{716}{5}\) , \( \frac{219}{5} a^{3} + 57 a^{2} - \frac{2013}{5} a - \frac{2836}{5}\bigr] \) |
${y}^2+\left(a^{2}-6\right){x}{y}+\left(\frac{1}{5}a^{3}+a^{2}-\frac{2}{5}a-\frac{24}{5}\right){y}={x}^{3}+\left(a^{2}-a-6\right){x}^{2}+\left(\frac{49}{5}a^{3}+15a^{2}-\frac{468}{5}a-\frac{716}{5}\right){x}+\frac{219}{5}a^{3}+57a^{2}-\frac{2013}{5}a-\frac{2836}{5}$ |
| 41.3-a1 |
41.3-a |
$1$ |
$1$ |
4.4.13525.1 |
$4$ |
$[4, 0]$ |
41.3 |
\( 41 \) |
\( 41 \) |
$16.53123$ |
$(-4/5a^3-a^2+23/5a+26/5)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$1$ |
$53.58543739$ |
0.460763579 |
\( -\frac{2016897}{205} a^{3} + \frac{2095031}{41} a^{2} + \frac{16298639}{205} a - \frac{90030462}{205} \) |
\( \bigl[\frac{1}{5} a^{3} + a^{2} - \frac{2}{5} a - \frac{29}{5}\) , \( a\) , \( \frac{1}{5} a^{3} - \frac{2}{5} a + \frac{1}{5}\) , \( 5 a^{3} + 10 a^{2} - 29 a - 46\) , \( 12 a^{3} + 24 a^{2} - 69 a - 113\bigr] \) |
${y}^2+\left(\frac{1}{5}a^{3}+a^{2}-\frac{2}{5}a-\frac{29}{5}\right){x}{y}+\left(\frac{1}{5}a^{3}-\frac{2}{5}a+\frac{1}{5}\right){y}={x}^{3}+a{x}^{2}+\left(5a^{3}+10a^{2}-29a-46\right){x}+12a^{3}+24a^{2}-69a-113$ |
| 41.3-b1 |
41.3-b |
$1$ |
$1$ |
4.4.13525.1 |
$4$ |
$[4, 0]$ |
41.3 |
\( 41 \) |
\( -41 \) |
$16.53123$ |
$(-4/5a^3-a^2+23/5a+26/5)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$1$ |
$367.9763622$ |
3.164107898 |
\( \frac{72774}{205} a^{3} + \frac{38839}{41} a^{2} - \frac{458013}{205} a - \frac{841456}{205} \) |
\( \bigl[a + 1\) , \( -\frac{1}{5} a^{3} - a^{2} + \frac{7}{5} a + \frac{34}{5}\) , \( 0\) , \( -2 a^{3} + 5 a^{2} + 5 a - 5\) , \( -\frac{6}{5} a^{3} + 3 a^{2} + \frac{17}{5} a - \frac{21}{5}\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-\frac{1}{5}a^{3}-a^{2}+\frac{7}{5}a+\frac{34}{5}\right){x}^{2}+\left(-2a^{3}+5a^{2}+5a-5\right){x}-\frac{6}{5}a^{3}+3a^{2}+\frac{17}{5}a-\frac{21}{5}$ |
| 41.3-c1 |
41.3-c |
$1$ |
$1$ |
4.4.13525.1 |
$4$ |
$[4, 0]$ |
41.3 |
\( 41 \) |
\( 41^{5} \) |
$16.53123$ |
$(-4/5a^3-a^2+23/5a+26/5)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5Ns.2.1[2] |
$1$ |
\( 1 \) |
$1$ |
$80.16388967$ |
0.689302962 |
\( \frac{242945822321}{115856201} a^{3} - \frac{1226642945595}{115856201} a^{2} + \frac{43664365688}{115856201} a + \frac{3400817093430}{115856201} \) |
\( \bigl[\frac{1}{5} a^{3} + a^{2} - \frac{7}{5} a - \frac{24}{5}\) , \( a^{2} + a - 5\) , \( 1\) , \( \frac{39}{5} a^{3} - 7 a^{2} - \frac{133}{5} a + \frac{34}{5}\) , \( \frac{141}{5} a^{3} - 68 a^{2} - \frac{267}{5} a + \frac{706}{5}\bigr] \) |
${y}^2+\left(\frac{1}{5}a^{3}+a^{2}-\frac{7}{5}a-\frac{24}{5}\right){x}{y}+{y}={x}^{3}+\left(a^{2}+a-5\right){x}^{2}+\left(\frac{39}{5}a^{3}-7a^{2}-\frac{133}{5}a+\frac{34}{5}\right){x}+\frac{141}{5}a^{3}-68a^{2}-\frac{267}{5}a+\frac{706}{5}$ |
| 41.4-a1 |
41.4-a |
$2$ |
$2$ |
4.4.13525.1 |
$4$ |
$[4, 0]$ |
41.4 |
\( 41 \) |
\( 41^{3} \) |
$16.53123$ |
$(1/5a^3-2/5a-14/5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 3 \) |
$0.175773134$ |
$866.5633850$ |
3.929211889 |
\( -\frac{12824160}{68921} a^{3} + \frac{114647803}{68921} a^{2} - \frac{157251007}{68921} a - \frac{229134480}{68921} \) |
\( \bigl[\frac{1}{5} a^{3} + a^{2} - \frac{2}{5} a - \frac{24}{5}\) , \( -\frac{1}{5} a^{3} - a^{2} + \frac{12}{5} a + \frac{29}{5}\) , \( \frac{1}{5} a^{3} - \frac{2}{5} a + \frac{6}{5}\) , \( \frac{21}{5} a^{3} + 7 a^{2} - \frac{112}{5} a - \frac{154}{5}\) , \( \frac{46}{5} a^{3} + 25 a^{2} - \frac{287}{5} a - \frac{534}{5}\bigr] \) |
${y}^2+\left(\frac{1}{5}a^{3}+a^{2}-\frac{2}{5}a-\frac{24}{5}\right){x}{y}+\left(\frac{1}{5}a^{3}-\frac{2}{5}a+\frac{6}{5}\right){y}={x}^{3}+\left(-\frac{1}{5}a^{3}-a^{2}+\frac{12}{5}a+\frac{29}{5}\right){x}^{2}+\left(\frac{21}{5}a^{3}+7a^{2}-\frac{112}{5}a-\frac{154}{5}\right){x}+\frac{46}{5}a^{3}+25a^{2}-\frac{287}{5}a-\frac{534}{5}$ |
| 41.4-a2 |
41.4-a |
$2$ |
$2$ |
4.4.13525.1 |
$4$ |
$[4, 0]$ |
41.4 |
\( 41 \) |
\( - 41^{6} \) |
$16.53123$ |
$(1/5a^3-2/5a-14/5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \cdot 3 \) |
$0.351546268$ |
$216.6408462$ |
3.929211889 |
\( -\frac{2361731907309195}{4750104241} a^{3} - \frac{2993781687054115}{4750104241} a^{2} + \frac{21640487067796050}{4750104241} a + \frac{30333615137933158}{4750104241} \) |
\( \bigl[\frac{1}{5} a^{3} + a^{2} - \frac{2}{5} a - \frac{24}{5}\) , \( -\frac{1}{5} a^{3} - a^{2} + \frac{12}{5} a + \frac{29}{5}\) , \( \frac{1}{5} a^{3} - \frac{2}{5} a + \frac{6}{5}\) , \( \frac{11}{5} a^{3} + 7 a^{2} - \frac{67}{5} a - \frac{139}{5}\) , \( -\frac{11}{5} a^{3} + 7 a^{2} + \frac{27}{5} a - \frac{106}{5}\bigr] \) |
${y}^2+\left(\frac{1}{5}a^{3}+a^{2}-\frac{2}{5}a-\frac{24}{5}\right){x}{y}+\left(\frac{1}{5}a^{3}-\frac{2}{5}a+\frac{6}{5}\right){y}={x}^{3}+\left(-\frac{1}{5}a^{3}-a^{2}+\frac{12}{5}a+\frac{29}{5}\right){x}^{2}+\left(\frac{11}{5}a^{3}+7a^{2}-\frac{67}{5}a-\frac{139}{5}\right){x}-\frac{11}{5}a^{3}+7a^{2}+\frac{27}{5}a-\frac{106}{5}$ |
| 45.1-a1 |
45.1-a |
$1$ |
$1$ |
4.4.13525.1 |
$4$ |
$[4, 0]$ |
45.1 |
\( 3^{2} \cdot 5 \) |
\( 3^{2} \cdot 5 \) |
$16.72472$ |
$(3/5a^3+a^2-16/5a-22/5), (-2/5a^3-a^2+19/5a+43/5)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$1$ |
$463.6560988$ |
3.986826533 |
\( -\frac{114023}{5} a^{3} + \frac{405149}{15} a^{2} + \frac{5219281}{15} a - \frac{9956996}{15} \) |
\( \bigl[a + 1\) , \( a^{2} + a - 6\) , \( a^{2} - 6\) , \( \frac{9}{5} a^{3} - \frac{33}{5} a + \frac{4}{5}\) , \( \frac{4}{5} a^{3} + 9 a^{2} - \frac{43}{5} a - \frac{171}{5}\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{2}-6\right){y}={x}^{3}+\left(a^{2}+a-6\right){x}^{2}+\left(\frac{9}{5}a^{3}-\frac{33}{5}a+\frac{4}{5}\right){x}+\frac{4}{5}a^{3}+9a^{2}-\frac{43}{5}a-\frac{171}{5}$ |
| 45.1-b1 |
45.1-b |
$2$ |
$2$ |
4.4.13525.1 |
$4$ |
$[4, 0]$ |
45.1 |
\( 3^{2} \cdot 5 \) |
\( - 3^{4} \cdot 5^{4} \) |
$16.72472$ |
$(3/5a^3+a^2-16/5a-22/5), (-2/5a^3-a^2+19/5a+43/5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 2^{3} \) |
$1$ |
$46.97125407$ |
3.231123110 |
\( \frac{3826912461601}{225} a^{3} - \frac{376124214242}{225} a^{2} - \frac{3002241843276}{25} a + \frac{725754518578}{9} \) |
\( \bigl[\frac{1}{5} a^{3} - \frac{7}{5} a + \frac{1}{5}\) , \( -\frac{1}{5} a^{3} + \frac{2}{5} a - \frac{6}{5}\) , \( a^{2} + a - 5\) , \( -\frac{507}{5} a^{3} + 249 a^{2} + \frac{4234}{5} a - \frac{10107}{5}\) , \( \frac{9727}{5} a^{3} - 4806 a^{2} - \frac{80984}{5} a + \frac{194342}{5}\bigr] \) |
${y}^2+\left(\frac{1}{5}a^{3}-\frac{7}{5}a+\frac{1}{5}\right){x}{y}+\left(a^{2}+a-5\right){y}={x}^{3}+\left(-\frac{1}{5}a^{3}+\frac{2}{5}a-\frac{6}{5}\right){x}^{2}+\left(-\frac{507}{5}a^{3}+249a^{2}+\frac{4234}{5}a-\frac{10107}{5}\right){x}+\frac{9727}{5}a^{3}-4806a^{2}-\frac{80984}{5}a+\frac{194342}{5}$ |
| 45.1-b2 |
45.1-b |
$2$ |
$2$ |
4.4.13525.1 |
$4$ |
$[4, 0]$ |
45.1 |
\( 3^{2} \cdot 5 \) |
\( 3^{2} \cdot 5^{8} \) |
$16.72472$ |
$(3/5a^3+a^2-16/5a-22/5), (-2/5a^3-a^2+19/5a+43/5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$187.8850162$ |
3.231123110 |
\( \frac{4408151}{1875} a^{3} + \frac{166648333}{1875} a^{2} + \frac{64439341}{1875} a - \frac{14311189}{25} \) |
\( \bigl[\frac{1}{5} a^{3} - \frac{7}{5} a + \frac{1}{5}\) , \( -\frac{1}{5} a^{3} + \frac{2}{5} a - \frac{6}{5}\) , \( a^{2} + a - 5\) , \( -\frac{17}{5} a^{3} + 4 a^{2} + \frac{254}{5} a - \frac{467}{5}\) , \( \frac{218}{5} a^{3} - 130 a^{2} - \frac{1321}{5} a + \frac{3798}{5}\bigr] \) |
${y}^2+\left(\frac{1}{5}a^{3}-\frac{7}{5}a+\frac{1}{5}\right){x}{y}+\left(a^{2}+a-5\right){y}={x}^{3}+\left(-\frac{1}{5}a^{3}+\frac{2}{5}a-\frac{6}{5}\right){x}^{2}+\left(-\frac{17}{5}a^{3}+4a^{2}+\frac{254}{5}a-\frac{467}{5}\right){x}+\frac{218}{5}a^{3}-130a^{2}-\frac{1321}{5}a+\frac{3798}{5}$ |
| 45.1-c1 |
45.1-c |
$2$ |
$2$ |
4.4.13525.1 |
$4$ |
$[4, 0]$ |
45.1 |
\( 3^{2} \cdot 5 \) |
\( 3^{6} \cdot 5^{2} \) |
$16.72472$ |
$(3/5a^3+a^2-16/5a-22/5), (-2/5a^3-a^2+19/5a+43/5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$146.8909155$ |
1.894600117 |
\( -\frac{873720511}{45} a^{3} + \frac{10471578184}{135} a^{2} + \frac{1596010592}{135} a - \frac{27027109603}{135} \) |
\( \bigl[\frac{1}{5} a^{3} + a^{2} - \frac{7}{5} a - \frac{29}{5}\) , \( -\frac{1}{5} a^{3} + a^{2} + \frac{12}{5} a - \frac{36}{5}\) , \( \frac{1}{5} a^{3} + a^{2} - \frac{2}{5} a - \frac{24}{5}\) , \( \frac{6}{5} a^{3} - 3 a^{2} - \frac{27}{5} a + \frac{76}{5}\) , \( \frac{3}{5} a^{3} - 2 a^{2} + \frac{14}{5} a - \frac{22}{5}\bigr] \) |
${y}^2+\left(\frac{1}{5}a^{3}+a^{2}-\frac{7}{5}a-\frac{29}{5}\right){x}{y}+\left(\frac{1}{5}a^{3}+a^{2}-\frac{2}{5}a-\frac{24}{5}\right){y}={x}^{3}+\left(-\frac{1}{5}a^{3}+a^{2}+\frac{12}{5}a-\frac{36}{5}\right){x}^{2}+\left(\frac{6}{5}a^{3}-3a^{2}-\frac{27}{5}a+\frac{76}{5}\right){x}+\frac{3}{5}a^{3}-2a^{2}+\frac{14}{5}a-\frac{22}{5}$ |
| 45.1-c2 |
45.1-c |
$2$ |
$2$ |
4.4.13525.1 |
$4$ |
$[4, 0]$ |
45.1 |
\( 3^{2} \cdot 5 \) |
\( 3^{12} \cdot 5 \) |
$16.72472$ |
$(3/5a^3+a^2-16/5a-22/5), (-2/5a^3-a^2+19/5a+43/5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$146.8909155$ |
1.894600117 |
\( \frac{7150298296431604}{3645} a^{3} + \frac{14681250308973859}{3645} a^{2} - \frac{910629148427686}{81} a - \frac{67914310580967908}{3645} \) |
\( \bigl[\frac{1}{5} a^{3} + a^{2} - \frac{7}{5} a - \frac{29}{5}\) , \( -\frac{1}{5} a^{3} + a^{2} + \frac{12}{5} a - \frac{36}{5}\) , \( \frac{1}{5} a^{3} + a^{2} - \frac{2}{5} a - \frac{24}{5}\) , \( -\frac{14}{5} a^{3} - 8 a^{2} + \frac{88}{5} a + \frac{131}{5}\) , \( \frac{32}{5} a^{3} - 4 a^{2} - \frac{214}{5} a + \frac{112}{5}\bigr] \) |
${y}^2+\left(\frac{1}{5}a^{3}+a^{2}-\frac{7}{5}a-\frac{29}{5}\right){x}{y}+\left(\frac{1}{5}a^{3}+a^{2}-\frac{2}{5}a-\frac{24}{5}\right){y}={x}^{3}+\left(-\frac{1}{5}a^{3}+a^{2}+\frac{12}{5}a-\frac{36}{5}\right){x}^{2}+\left(-\frac{14}{5}a^{3}-8a^{2}+\frac{88}{5}a+\frac{131}{5}\right){x}+\frac{32}{5}a^{3}-4a^{2}-\frac{214}{5}a+\frac{112}{5}$ |
| 45.3-a1 |
45.3-a |
$1$ |
$1$ |
4.4.13525.1 |
$4$ |
$[4, 0]$ |
45.3 |
\( 3^{2} \cdot 5 \) |
\( 3^{2} \cdot 5 \) |
$16.72472$ |
$(2/5a^3-19/5a+2/5), (-1/5a^3-a^2+7/5a+24/5)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$1$ |
$463.6560988$ |
3.986826533 |
\( \frac{709304}{75} a^{3} - \frac{405149}{15} a^{2} - \frac{19089118}{75} a - \frac{21030646}{75} \) |
\( \bigl[a^{2} + a - 6\) , \( \frac{1}{5} a^{3} - \frac{2}{5} a - \frac{4}{5}\) , \( a^{2} - 6\) , \( \frac{73}{5} a^{3} + 21 a^{2} - \frac{626}{5} a - \frac{882}{5}\) , \( -53 a^{3} - 66 a^{2} + 497 a + 699\bigr] \) |
${y}^2+\left(a^{2}+a-6\right){x}{y}+\left(a^{2}-6\right){y}={x}^{3}+\left(\frac{1}{5}a^{3}-\frac{2}{5}a-\frac{4}{5}\right){x}^{2}+\left(\frac{73}{5}a^{3}+21a^{2}-\frac{626}{5}a-\frac{882}{5}\right){x}-53a^{3}-66a^{2}+497a+699$ |
| 45.3-b1 |
45.3-b |
$2$ |
$2$ |
4.4.13525.1 |
$4$ |
$[4, 0]$ |
45.3 |
\( 3^{2} \cdot 5 \) |
\( 3^{2} \cdot 5^{8} \) |
$16.72472$ |
$(2/5a^3-19/5a+2/5), (-1/5a^3-a^2+7/5a+24/5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$187.8850162$ |
3.231123110 |
\( -\frac{3287412}{625} a^{3} - \frac{166648333}{1875} a^{2} - \frac{8753582}{625} a + \frac{1078818767}{1875} \) |
\( \bigl[1\) , \( \frac{1}{5} a^{3} - a^{2} - \frac{12}{5} a + \frac{31}{5}\) , \( \frac{1}{5} a^{3} + a^{2} - \frac{7}{5} a - \frac{29}{5}\) , \( \frac{291}{5} a^{3} + 71 a^{2} - \frac{2652}{5} a - \frac{3584}{5}\) , \( \frac{2986}{5} a^{3} + 766 a^{2} - \frac{27042}{5} a - \frac{37809}{5}\bigr] \) |
${y}^2+{x}{y}+\left(\frac{1}{5}a^{3}+a^{2}-\frac{7}{5}a-\frac{29}{5}\right){y}={x}^{3}+\left(\frac{1}{5}a^{3}-a^{2}-\frac{12}{5}a+\frac{31}{5}\right){x}^{2}+\left(\frac{291}{5}a^{3}+71a^{2}-\frac{2652}{5}a-\frac{3584}{5}\right){x}+\frac{2986}{5}a^{3}+766a^{2}-\frac{27042}{5}a-\frac{37809}{5}$ |
| 45.3-b2 |
45.3-b |
$2$ |
$2$ |
4.4.13525.1 |
$4$ |
$[4, 0]$ |
45.3 |
\( 3^{2} \cdot 5 \) |
\( - 3^{4} \cdot 5^{4} \) |
$16.72472$ |
$(2/5a^3-19/5a+2/5), (-1/5a^3-a^2+7/5a+24/5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 2^{3} \) |
$1$ |
$46.97125407$ |
3.231123110 |
\( \frac{3855779432794}{225} a^{3} + \frac{376124214242}{225} a^{2} - \frac{26758666671281}{225} a + \frac{13283115150497}{225} \) |
\( \bigl[1\) , \( \frac{1}{5} a^{3} - a^{2} - \frac{12}{5} a + \frac{31}{5}\) , \( \frac{1}{5} a^{3} + a^{2} - \frac{7}{5} a - \frac{29}{5}\) , \( -\frac{284}{5} a^{3} - 89 a^{2} + \frac{2298}{5} a + \frac{3466}{5}\) , \( \frac{13601}{5} a^{3} + 3601 a^{2} - \frac{120912}{5} a - \frac{170354}{5}\bigr] \) |
${y}^2+{x}{y}+\left(\frac{1}{5}a^{3}+a^{2}-\frac{7}{5}a-\frac{29}{5}\right){y}={x}^{3}+\left(\frac{1}{5}a^{3}-a^{2}-\frac{12}{5}a+\frac{31}{5}\right){x}^{2}+\left(-\frac{284}{5}a^{3}-89a^{2}+\frac{2298}{5}a+\frac{3466}{5}\right){x}+\frac{13601}{5}a^{3}+3601a^{2}-\frac{120912}{5}a-\frac{170354}{5}$ |
| 45.3-c1 |
45.3-c |
$2$ |
$2$ |
4.4.13525.1 |
$4$ |
$[4, 0]$ |
45.3 |
\( 3^{2} \cdot 5 \) |
\( 3^{12} \cdot 5 \) |
$16.72472$ |
$(2/5a^3-19/5a+2/5), (-1/5a^3-a^2+7/5a+24/5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$146.8909155$ |
1.894600117 |
\( \frac{30144017568959519}{18225} a^{3} - \frac{14681250308973859}{3645} a^{2} - \frac{256377004961593423}{18225} a + \frac{609102243265262794}{18225} \) |
\( \bigl[a^{2} - 5\) , \( -\frac{1}{5} a^{3} + a^{2} + \frac{2}{5} a - \frac{31}{5}\) , \( 0\) , \( -3 a^{3} + 10 a^{2} + 20 a - 84\) , \( 17 a^{3} - 34 a^{2} - 141 a + 272\bigr] \) |
${y}^2+\left(a^{2}-5\right){x}{y}={x}^{3}+\left(-\frac{1}{5}a^{3}+a^{2}+\frac{2}{5}a-\frac{31}{5}\right){x}^{2}+\left(-3a^{3}+10a^{2}+20a-84\right){x}+17a^{3}-34a^{2}-141a+272$ |
| 45.3-c2 |
45.3-c |
$2$ |
$2$ |
4.4.13525.1 |
$4$ |
$[4, 0]$ |
45.3 |
\( 3^{2} \cdot 5 \) |
\( 3^{6} \cdot 5^{2} \) |
$16.72472$ |
$(2/5a^3-19/5a+2/5), (-1/5a^3-a^2+7/5a+24/5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$146.8909155$ |
1.894600117 |
\( -\frac{40329505988}{675} a^{3} - \frac{10471578184}{135} a^{2} + \frac{366067142611}{675} a + \frac{518293335622}{675} \) |
\( \bigl[a^{2} - 5\) , \( -\frac{1}{5} a^{3} + a^{2} + \frac{2}{5} a - \frac{31}{5}\) , \( 0\) , \( a^{3} + 5 a^{2} - 13 a - 30\) , \( \frac{9}{5} a^{3} + 4 a^{2} - \frac{98}{5} a - \frac{116}{5}\bigr] \) |
${y}^2+\left(a^{2}-5\right){x}{y}={x}^{3}+\left(-\frac{1}{5}a^{3}+a^{2}+\frac{2}{5}a-\frac{31}{5}\right){x}^{2}+\left(a^{3}+5a^{2}-13a-30\right){x}+\frac{9}{5}a^{3}+4a^{2}-\frac{98}{5}a-\frac{116}{5}$ |
| 55.1-a1 |
55.1-a |
$4$ |
$6$ |
4.4.13525.1 |
$4$ |
$[4, 0]$ |
55.1 |
\( 5 \cdot 11 \) |
\( - 5 \cdot 11^{3} \) |
$17.14954$ |
$(3/5a^3+a^2-16/5a-22/5), (-1/5a^3+12/5a-6/5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 1 \) |
$1$ |
$625.3404995$ |
1.344274399 |
\( -\frac{35021174}{6655} a^{3} - \frac{18726749}{6655} a^{2} + \frac{82326551}{1331} a + \frac{525612243}{6655} \) |
\( \bigl[a^{2} - 6\) , \( -a^{2} - a + 5\) , \( a^{2} + a - 5\) , \( -\frac{1}{5} a^{3} - 3 a^{2} + \frac{2}{5} a + \frac{99}{5}\) , \( \frac{4}{5} a^{3} - a^{2} - \frac{33}{5} a + \frac{44}{5}\bigr] \) |
${y}^2+\left(a^{2}-6\right){x}{y}+\left(a^{2}+a-5\right){y}={x}^{3}+\left(-a^{2}-a+5\right){x}^{2}+\left(-\frac{1}{5}a^{3}-3a^{2}+\frac{2}{5}a+\frac{99}{5}\right){x}+\frac{4}{5}a^{3}-a^{2}-\frac{33}{5}a+\frac{44}{5}$ |
| 55.1-a2 |
55.1-a |
$4$ |
$6$ |
4.4.13525.1 |
$4$ |
$[4, 0]$ |
55.1 |
\( 5 \cdot 11 \) |
\( - 5^{3} \cdot 11 \) |
$17.14954$ |
$(3/5a^3+a^2-16/5a-22/5), (-1/5a^3+12/5a-6/5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 1 \) |
$1$ |
$625.3404995$ |
1.344274399 |
\( -\frac{12294096}{275} a^{3} + \frac{48397429}{275} a^{2} + \frac{1950123}{55} a - \frac{122029048}{275} \) |
\( \bigl[a^{2} + a - 6\) , \( \frac{1}{5} a^{3} - a^{2} - \frac{2}{5} a + \frac{36}{5}\) , \( \frac{1}{5} a^{3} - \frac{2}{5} a + \frac{6}{5}\) , \( \frac{32}{5} a^{3} + 2 a^{2} - \frac{264}{5} a - \frac{33}{5}\) , \( \frac{13}{5} a^{3} - 6 a^{2} - \frac{56}{5} a + \frac{378}{5}\bigr] \) |
${y}^2+\left(a^{2}+a-6\right){x}{y}+\left(\frac{1}{5}a^{3}-\frac{2}{5}a+\frac{6}{5}\right){y}={x}^{3}+\left(\frac{1}{5}a^{3}-a^{2}-\frac{2}{5}a+\frac{36}{5}\right){x}^{2}+\left(\frac{32}{5}a^{3}+2a^{2}-\frac{264}{5}a-\frac{33}{5}\right){x}+\frac{13}{5}a^{3}-6a^{2}-\frac{56}{5}a+\frac{378}{5}$ |
| 55.1-a3 |
55.1-a |
$4$ |
$6$ |
4.4.13525.1 |
$4$ |
$[4, 0]$ |
55.1 |
\( 5 \cdot 11 \) |
\( - 5^{6} \cdot 11^{2} \) |
$17.14954$ |
$(3/5a^3+a^2-16/5a-22/5), (-1/5a^3+12/5a-6/5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \) |
$1$ |
$156.3351248$ |
1.344274399 |
\( -\frac{1370018490207413}{15125} a^{3} + \frac{5343160062680501}{15125} a^{2} + \frac{944714786707682}{15125} a - \frac{2739976330259044}{3025} \) |
\( \bigl[a^{2} + a - 6\) , \( \frac{1}{5} a^{3} - a^{2} - \frac{2}{5} a + \frac{36}{5}\) , \( \frac{1}{5} a^{3} - \frac{2}{5} a + \frac{6}{5}\) , \( \frac{7}{5} a^{3} - 3 a^{2} - \frac{39}{5} a + \frac{217}{5}\) , \( -\frac{126}{5} a^{3} - 37 a^{2} + \frac{1197}{5} a + \frac{1929}{5}\bigr] \) |
${y}^2+\left(a^{2}+a-6\right){x}{y}+\left(\frac{1}{5}a^{3}-\frac{2}{5}a+\frac{6}{5}\right){y}={x}^{3}+\left(\frac{1}{5}a^{3}-a^{2}-\frac{2}{5}a+\frac{36}{5}\right){x}^{2}+\left(\frac{7}{5}a^{3}-3a^{2}-\frac{39}{5}a+\frac{217}{5}\right){x}-\frac{126}{5}a^{3}-37a^{2}+\frac{1197}{5}a+\frac{1929}{5}$ |
| 55.1-a4 |
55.1-a |
$4$ |
$6$ |
4.4.13525.1 |
$4$ |
$[4, 0]$ |
55.1 |
\( 5 \cdot 11 \) |
\( - 5^{2} \cdot 11^{6} \) |
$17.14954$ |
$(3/5a^3+a^2-16/5a-22/5), (-1/5a^3+12/5a-6/5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \) |
$1$ |
$156.3351248$ |
1.344274399 |
\( \frac{3565196602907817}{8857805} a^{3} + \frac{7319897905379131}{8857805} a^{2} - \frac{20432459189748088}{8857805} a - \frac{6772201577919357}{1771561} \) |
\( \bigl[a + 1\) , \( -\frac{1}{5} a^{3} + \frac{12}{5} a - \frac{1}{5}\) , \( a^{2} + a - 6\) , \( -\frac{2}{5} a^{3} - 7 a^{2} + \frac{49}{5} a + \frac{133}{5}\) , \( \frac{7}{5} a^{3} - 10 a^{2} + \frac{31}{5} a + \frac{132}{5}\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{2}+a-6\right){y}={x}^{3}+\left(-\frac{1}{5}a^{3}+\frac{12}{5}a-\frac{1}{5}\right){x}^{2}+\left(-\frac{2}{5}a^{3}-7a^{2}+\frac{49}{5}a+\frac{133}{5}\right){x}+\frac{7}{5}a^{3}-10a^{2}+\frac{31}{5}a+\frac{132}{5}$ |
| 55.2-a1 |
55.2-a |
$2$ |
$2$ |
4.4.13525.1 |
$4$ |
$[4, 0]$ |
55.2 |
\( 5 \cdot 11 \) |
\( - 5^{22} \cdot 11^{2} \) |
$17.14954$ |
$(3/5a^3+a^2-16/5a-22/5), (2/5a^3+a^2-14/5a-28/5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \cdot 11 \) |
$0.271976694$ |
$39.89551052$ |
4.105251405 |
\( -\frac{13411008321949}{5908203125} a^{3} - \frac{48358554576758}{5908203125} a^{2} + \frac{24069628976738}{5908203125} a + \frac{416249632496594}{5908203125} \) |
\( \bigl[1\) , \( -\frac{1}{5} a^{3} - a^{2} + \frac{7}{5} a + \frac{29}{5}\) , \( a^{2} - 5\) , \( -496 a^{3} + 1220 a^{2} + 4218 a - 10129\) , \( \frac{102403}{5} a^{3} - 49843 a^{2} - \frac{870971}{5} a + \frac{2067788}{5}\bigr] \) |
${y}^2+{x}{y}+\left(a^{2}-5\right){y}={x}^{3}+\left(-\frac{1}{5}a^{3}-a^{2}+\frac{7}{5}a+\frac{29}{5}\right){x}^{2}+\left(-496a^{3}+1220a^{2}+4218a-10129\right){x}+\frac{102403}{5}a^{3}-49843a^{2}-\frac{870971}{5}a+\frac{2067788}{5}$ |
| 55.2-a2 |
55.2-a |
$2$ |
$2$ |
4.4.13525.1 |
$4$ |
$[4, 0]$ |
55.2 |
\( 5 \cdot 11 \) |
\( - 5^{11} \cdot 11 \) |
$17.14954$ |
$(3/5a^3+a^2-16/5a-22/5), (2/5a^3+a^2-14/5a-28/5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 11 \) |
$0.543953389$ |
$79.79102105$ |
4.105251405 |
\( \frac{28796619096163}{171875} a^{3} + \frac{59125971251753}{171875} a^{2} - \frac{6601378754243}{6875} a - \frac{273514607028291}{171875} \) |
\( \bigl[\frac{1}{5} a^{3} - \frac{7}{5} a + \frac{6}{5}\) , \( \frac{1}{5} a^{3} - a^{2} - \frac{2}{5} a + \frac{31}{5}\) , \( a^{2} - 6\) , \( -\frac{7}{5} a^{3} - 3 a^{2} + \frac{54}{5} a + \frac{168}{5}\) , \( \frac{307}{5} a^{3} - 119 a^{2} - \frac{2629}{5} a + \frac{4827}{5}\bigr] \) |
${y}^2+\left(\frac{1}{5}a^{3}-\frac{7}{5}a+\frac{6}{5}\right){x}{y}+\left(a^{2}-6\right){y}={x}^{3}+\left(\frac{1}{5}a^{3}-a^{2}-\frac{2}{5}a+\frac{31}{5}\right){x}^{2}+\left(-\frac{7}{5}a^{3}-3a^{2}+\frac{54}{5}a+\frac{168}{5}\right){x}+\frac{307}{5}a^{3}-119a^{2}-\frac{2629}{5}a+\frac{4827}{5}$ |
| 55.2-b1 |
55.2-b |
$2$ |
$2$ |
4.4.13525.1 |
$4$ |
$[4, 0]$ |
55.2 |
\( 5 \cdot 11 \) |
\( - 5^{2} \cdot 11^{6} \) |
$17.14954$ |
$(3/5a^3+a^2-16/5a-22/5), (2/5a^3+a^2-14/5a-28/5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.292855154$ |
$399.8924246$ |
4.027980916 |
\( \frac{75506328579686}{8857805} a^{3} - \frac{184199126675253}{8857805} a^{2} - \frac{642146204380567}{8857805} a + \frac{1528650347075539}{8857805} \) |
\( \bigl[\frac{1}{5} a^{3} + a^{2} - \frac{7}{5} a - \frac{29}{5}\) , \( \frac{1}{5} a^{3} - \frac{2}{5} a + \frac{6}{5}\) , \( \frac{1}{5} a^{3} + a^{2} - \frac{7}{5} a - \frac{29}{5}\) , \( \frac{202}{5} a^{3} + 76 a^{2} - \frac{1124}{5} a - \frac{1803}{5}\) , \( \frac{1886}{5} a^{3} + 797 a^{2} - \frac{10902}{5} a - \frac{18284}{5}\bigr] \) |
${y}^2+\left(\frac{1}{5}a^{3}+a^{2}-\frac{7}{5}a-\frac{29}{5}\right){x}{y}+\left(\frac{1}{5}a^{3}+a^{2}-\frac{7}{5}a-\frac{29}{5}\right){y}={x}^{3}+\left(\frac{1}{5}a^{3}-\frac{2}{5}a+\frac{6}{5}\right){x}^{2}+\left(\frac{202}{5}a^{3}+76a^{2}-\frac{1124}{5}a-\frac{1803}{5}\right){x}+\frac{1886}{5}a^{3}+797a^{2}-\frac{10902}{5}a-\frac{18284}{5}$ |
| 55.2-b2 |
55.2-b |
$2$ |
$2$ |
4.4.13525.1 |
$4$ |
$[4, 0]$ |
55.2 |
\( 5 \cdot 11 \) |
\( - 5 \cdot 11^{3} \) |
$17.14954$ |
$(3/5a^3+a^2-16/5a-22/5), (2/5a^3+a^2-14/5a-28/5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$0.585710309$ |
$799.7848493$ |
4.027980916 |
\( -\frac{3017327}{6655} a^{3} + \frac{10698093}{6655} a^{2} + \frac{5499218}{1331} a - \frac{82747216}{6655} \) |
\( \bigl[a^{2} - 5\) , \( -a^{2} - a + 5\) , \( \frac{1}{5} a^{3} + a^{2} - \frac{2}{5} a - \frac{24}{5}\) , \( 14 a^{3} + 16 a^{2} - 130 a - 168\) , \( \frac{3627}{5} a^{3} + 928 a^{2} - \frac{32929}{5} a - \frac{46053}{5}\bigr] \) |
${y}^2+\left(a^{2}-5\right){x}{y}+\left(\frac{1}{5}a^{3}+a^{2}-\frac{2}{5}a-\frac{24}{5}\right){y}={x}^{3}+\left(-a^{2}-a+5\right){x}^{2}+\left(14a^{3}+16a^{2}-130a-168\right){x}+\frac{3627}{5}a^{3}+928a^{2}-\frac{32929}{5}a-\frac{46053}{5}$ |
| 55.2-c1 |
55.2-c |
$2$ |
$3$ |
4.4.13525.1 |
$4$ |
$[4, 0]$ |
55.2 |
\( 5 \cdot 11 \) |
\( 5^{3} \cdot 11 \) |
$17.14954$ |
$(3/5a^3+a^2-16/5a-22/5), (2/5a^3+a^2-14/5a-28/5)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 3 \) |
$0.156635803$ |
$239.8474446$ |
3.876490678 |
\( \frac{4175439416}{275} a^{3} - \frac{10168297204}{275} a^{2} - \frac{7102437506}{55} a + \frac{84373152943}{275} \) |
\( \bigl[a^{2} - 6\) , \( -\frac{1}{5} a^{3} + a^{2} + \frac{7}{5} a - \frac{26}{5}\) , \( a\) , \( \frac{6}{5} a^{3} + 4 a^{2} - \frac{57}{5} a - \frac{119}{5}\) , \( \frac{9}{5} a^{3} + 3 a^{2} - \frac{83}{5} a - \frac{126}{5}\bigr] \) |
${y}^2+\left(a^{2}-6\right){x}{y}+a{y}={x}^{3}+\left(-\frac{1}{5}a^{3}+a^{2}+\frac{7}{5}a-\frac{26}{5}\right){x}^{2}+\left(\frac{6}{5}a^{3}+4a^{2}-\frac{57}{5}a-\frac{119}{5}\right){x}+\frac{9}{5}a^{3}+3a^{2}-\frac{83}{5}a-\frac{126}{5}$ |
| 55.2-c2 |
55.2-c |
$2$ |
$3$ |
4.4.13525.1 |
$4$ |
$[4, 0]$ |
55.2 |
\( 5 \cdot 11 \) |
\( 5 \cdot 11^{3} \) |
$17.14954$ |
$(3/5a^3+a^2-16/5a-22/5), (2/5a^3+a^2-14/5a-28/5)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 1 \) |
$0.469907410$ |
$239.8474446$ |
3.876490678 |
\( -\frac{821916543}{6655} a^{3} - \frac{1133719021}{6655} a^{2} + \frac{7120720929}{6655} a + \frac{2027386242}{1331} \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( \frac{1}{5} a^{3} + a^{2} - \frac{7}{5} a - \frac{29}{5}\) , \( \frac{11}{5} a^{3} - 13 a^{2} + \frac{28}{5} a + \frac{156}{5}\) , \( 49 a^{3} - 193 a^{2} - 31 a + 493\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(\frac{1}{5}a^{3}+a^{2}-\frac{7}{5}a-\frac{29}{5}\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(\frac{11}{5}a^{3}-13a^{2}+\frac{28}{5}a+\frac{156}{5}\right){x}+49a^{3}-193a^{2}-31a+493$ |
*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.
