| 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 |
| 1.1-a1 |
1.1-a |
$4$ |
$35$ |
4.4.2525.1 |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$4.49024$ |
$\textsf{none}$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
✓ |
$5, 7$ |
5B.4.1[2], 7B.1.3 |
$49$ |
\( 1 \) |
$1$ |
$0.428696290$ |
0.418037376 |
\( -17038484321262621392677 a^{3} + 47324121859575160666349 a^{2} + 31360177851679811257113 a - 109574465986214263634831 \) |
\( \bigl[a^{3} - 3 a - 3\) , \( -a^{3} + 3 a + 3\) , \( a^{2} - 2\) , \( 304 a^{3} - 80 a^{2} - 1373 a - 884\) , \( 5992 a^{3} - 1423 a^{2} - 26497 a - 16937\bigr] \) |
${y}^2+\left(a^{3}-3a-3\right){x}{y}+\left(a^{2}-2\right){y}={x}^{3}+\left(-a^{3}+3a+3\right){x}^{2}+\left(304a^{3}-80a^{2}-1373a-884\right){x}+5992a^{3}-1423a^{2}-26497a-16937$ |
| 1.1-a2 |
1.1-a |
$4$ |
$35$ |
4.4.2525.1 |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$4.49024$ |
$\textsf{none}$ |
0 |
$\Z/7\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
✓ |
$5, 7$ |
5B.4.1[2], 7B.1.1 |
$1$ |
\( 1 \) |
$1$ |
$1029.299792$ |
0.418037376 |
\( -15961 a^{3} - 7274 a^{2} + 44865 a + 31594 \) |
\( \bigl[a^{2} - a - 3\) , \( -a^{3} + 2 a^{2} + a - 3\) , \( a^{3} - 3 a - 2\) , \( 2 a^{2} - 3 a - 3\) , \( -a^{3} + 2 a + 1\bigr] \) |
${y}^2+\left(a^{2}-a-3\right){x}{y}+\left(a^{3}-3a-2\right){y}={x}^{3}+\left(-a^{3}+2a^{2}+a-3\right){x}^{2}+\left(2a^{2}-3a-3\right){x}-a^{3}+2a+1$ |
| 1.1-a3 |
1.1-a |
$4$ |
$35$ |
4.4.2525.1 |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$4.49024$ |
$\textsf{none}$ |
0 |
$\Z/7\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
✓ |
$5, 7$ |
5B.4.1[2], 7B.1.1 |
$1$ |
\( 1 \) |
$1$ |
$1029.299792$ |
0.418037376 |
\( 15961 a^{3} - 55157 a^{2} + 17566 a + 53224 \) |
\( \bigl[a^{2} - a - 3\) , \( a^{3} - a^{2} - 2 a - 1\) , \( a^{3} - a^{2} - 2 a\) , \( 2 a^{2} - 2 a - 3\) , \( -a^{2} + a + 1\bigr] \) |
${y}^2+\left(a^{2}-a-3\right){x}{y}+\left(a^{3}-a^{2}-2a\right){y}={x}^{3}+\left(a^{3}-a^{2}-2a-1\right){x}^{2}+\left(2a^{2}-2a-3\right){x}-a^{2}+a+1$ |
| 1.1-a4 |
1.1-a |
$4$ |
$35$ |
4.4.2525.1 |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$4.49024$ |
$\textsf{none}$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
✓ |
$5, 7$ |
5B.4.1[2], 7B.1.3 |
$49$ |
\( 1 \) |
$1$ |
$0.428696290$ |
0.418037376 |
\( 17038484321262621392677 a^{3} - 3791331104212703511682 a^{2} - 74892968607042268411780 a - 47928650596221913104046 \) |
\( \bigl[a^{3} - a^{2} - 2 a + 1\) , \( a^{2} - 2 a - 3\) , \( 0\) , \( -307 a^{3} + 841 a^{2} + 624 a - 2046\) , \( -5450 a^{3} + 15034 a^{2} + 10411 a - 35399\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-2a+1\right){x}{y}={x}^{3}+\left(a^{2}-2a-3\right){x}^{2}+\left(-307a^{3}+841a^{2}+624a-2046\right){x}-5450a^{3}+15034a^{2}+10411a-35399$ |
| 25.1-a1 |
25.1-a |
$4$ |
$35$ |
4.4.2525.1 |
$4$ |
$[4, 0]$ |
25.1 |
\( 5^{2} \) |
\( 5^{6} \) |
$6.71447$ |
$(-a)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$5, 7$ |
5B.1.4[2], 7B.6.1 |
$1$ |
\( 1 \) |
$1$ |
$58.67010323$ |
1.167578693 |
\( -15961 a^{3} - 7274 a^{2} + 44865 a + 31594 \) |
\( \bigl[a^{2} - 3\) , \( a^{2} - a - 4\) , \( a^{3} - a^{2} - 2 a + 1\) , \( -a^{2} - a + 2\) , \( -a^{2}\bigr] \) |
${y}^2+\left(a^{2}-3\right){x}{y}+\left(a^{3}-a^{2}-2a+1\right){y}={x}^{3}+\left(a^{2}-a-4\right){x}^{2}+\left(-a^{2}-a+2\right){x}-a^{2}$ |
| 25.1-a2 |
25.1-a |
$4$ |
$35$ |
4.4.2525.1 |
$4$ |
$[4, 0]$ |
25.1 |
\( 5^{2} \) |
\( 5^{6} \) |
$6.71447$ |
$(-a)$ |
0 |
$\Z/5\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$5, 7$ |
5B.1.1[2], 7B.6.1 |
$1$ |
\( 1 \) |
$1$ |
$1466.752580$ |
1.167578693 |
\( 15961 a^{3} - 55157 a^{2} + 17566 a + 53224 \) |
\( \bigl[a^{2} - 3\) , \( -a^{2} + 2\) , \( a^{2} - 2\) , \( 0\) , \( 0\bigr] \) |
${y}^2+\left(a^{2}-3\right){x}{y}+\left(a^{2}-2\right){y}={x}^{3}+\left(-a^{2}+2\right){x}^{2}$ |
| 25.1-a3 |
25.1-a |
$4$ |
$35$ |
4.4.2525.1 |
$4$ |
$[4, 0]$ |
25.1 |
\( 5^{2} \) |
\( 5^{6} \) |
$6.71447$ |
$(-a)$ |
0 |
$\Z/5\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$5, 7$ |
5B.1.1[2], 7B.6.3 |
$49$ |
\( 1 \) |
$1$ |
$29.93372613$ |
1.167578693 |
\( -17038484321262621392677 a^{3} + 47324121859575160666349 a^{2} + 31360177851679811257113 a - 109574465986214263634831 \) |
\( \bigl[a^{3} - a^{2} - 2 a\) , \( -a^{2} + 2\) , \( a^{3} - a^{2} - 3 a\) , \( -71 a^{3} + 171 a^{2} + 265 a - 652\) , \( 6986 a^{3} - 23297 a^{2} + 3840 a + 27464\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-2a\right){x}{y}+\left(a^{3}-a^{2}-3a\right){y}={x}^{3}+\left(-a^{2}+2\right){x}^{2}+\left(-71a^{3}+171a^{2}+265a-652\right){x}+6986a^{3}-23297a^{2}+3840a+27464$ |
| 25.1-a4 |
25.1-a |
$4$ |
$35$ |
4.4.2525.1 |
$4$ |
$[4, 0]$ |
25.1 |
\( 5^{2} \) |
\( 5^{6} \) |
$6.71447$ |
$(-a)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$5, 7$ |
5B.1.4[2], 7B.6.3 |
$49$ |
\( 1 \) |
$1$ |
$1.197349045$ |
1.167578693 |
\( 17038484321262621392677 a^{3} - 3791331104212703511682 a^{2} - 74892968607042268411780 a - 47928650596221913104046 \) |
\( \bigl[a\) , \( a^{3} - 2 a^{2} - a + 3\) , \( a^{3} - a^{2} - 2 a + 1\) , \( 38 a^{3} - 205 a^{2} + 280 a - 72\) , \( 2217 a^{3} - 6230 a^{2} - 320 a + 7787\bigr] \) |
${y}^2+a{x}{y}+\left(a^{3}-a^{2}-2a+1\right){y}={x}^{3}+\left(a^{3}-2a^{2}-a+3\right){x}^{2}+\left(38a^{3}-205a^{2}+280a-72\right){x}+2217a^{3}-6230a^{2}-320a+7787$ |
| 25.2-a1 |
25.2-a |
$4$ |
$15$ |
4.4.2525.1 |
$4$ |
$[4, 0]$ |
25.2 |
\( 5^{2} \) |
\( 5^{6} \) |
$6.71447$ |
$(-a), (a^3-2a^2-2a+3)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3, 5$ |
3B.1.1, 5B.4.1[2] |
$1$ |
\( 1 \) |
$1$ |
$470.1284370$ |
1.039545064 |
\( -\frac{41394176}{125} a^{3} + \frac{114860032}{125} a^{2} + \frac{76365824}{125} a - \frac{53194752}{25} \) |
\( \bigl[0\) , \( a^{3} - 4 a - 4\) , \( 1\) , \( -a^{3} - 3 a^{2} + 10 a + 9\) , \( 3 a^{3} - 5 a^{2} - 6 a\bigr] \) |
${y}^2+{y}={x}^{3}+\left(a^{3}-4a-4\right){x}^{2}+\left(-a^{3}-3a^{2}+10a+9\right){x}+3a^{3}-5a^{2}-6a$ |
| 25.2-a2 |
25.2-a |
$4$ |
$15$ |
4.4.2525.1 |
$4$ |
$[4, 0]$ |
25.2 |
\( 5^{2} \) |
\( 5^{18} \) |
$6.71447$ |
$(-a), (a^3-2a^2-2a+3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3, 5$ |
3B.1.2, 5B.4.1[2] |
$9$ |
\( 1 \) |
$1$ |
$5.804054778$ |
1.039545064 |
\( \frac{1003957168152576}{390625} a^{3} - \frac{3480444164882432}{390625} a^{2} + \frac{1089048124850176}{390625} a + \frac{684483524145152}{78125} \) |
\( \bigl[0\) , \( a^{2} - a - 3\) , \( a^{3} - 3 a - 2\) , \( 31 a^{3} - 90 a^{2} - 36 a + 175\) , \( 592 a^{3} - 1668 a^{2} - 1018 a + 3754\bigr] \) |
${y}^2+\left(a^{3}-3a-2\right){y}={x}^{3}+\left(a^{2}-a-3\right){x}^{2}+\left(31a^{3}-90a^{2}-36a+175\right){x}+592a^{3}-1668a^{2}-1018a+3754$ |
| 25.2-a3 |
25.2-a |
$4$ |
$15$ |
4.4.2525.1 |
$4$ |
$[4, 0]$ |
25.2 |
\( 5^{2} \) |
\( 5^{18} \) |
$6.71447$ |
$(-a), (a^3-2a^2-2a+3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3, 5$ |
3B.1.2, 5B.4.1[2] |
$9$ |
\( 1 \) |
$1$ |
$5.804054778$ |
1.039545064 |
\( -\frac{1003957168152576}{390625} a^{3} - \frac{468572660424704}{390625} a^{2} + \frac{571993740091392}{78125} a + \frac{406995749769216}{78125} \) |
\( \bigl[0\) , \( -a^{2} + a + 2\) , \( a^{3} - a^{2} - 2 a\) , \( -161 a^{3} + 36 a^{2} + 705 a + 450\) , \( -10496 a^{3} + 2334 a^{2} + 46135 a + 29525\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-2a\right){y}={x}^{3}+\left(-a^{2}+a+2\right){x}^{2}+\left(-161a^{3}+36a^{2}+705a+450\right){x}-10496a^{3}+2334a^{2}+46135a+29525$ |
| 25.2-a4 |
25.2-a |
$4$ |
$15$ |
4.4.2525.1 |
$4$ |
$[4, 0]$ |
25.2 |
\( 5^{2} \) |
\( 5^{6} \) |
$6.71447$ |
$(-a), (a^3-2a^2-2a+3)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3, 5$ |
3B.1.1, 5B.4.1[2] |
$1$ |
\( 1 \) |
$1$ |
$470.1284370$ |
1.039545064 |
\( \frac{41394176}{125} a^{3} - \frac{9322496}{125} a^{2} - \frac{36380672}{25} a - \frac{23228416}{25} \) |
\( \bigl[0\) , \( -a^{3} + 4 a + 2\) , \( 1\) , \( -a^{3} - a^{2} + 4 a + 5\) , \( -a^{3} + 3 a + 1\bigr] \) |
${y}^2+{y}={x}^{3}+\left(-a^{3}+4a+2\right){x}^{2}+\left(-a^{3}-a^{2}+4a+5\right){x}-a^{3}+3a+1$ |
| 25.3-a1 |
25.3-a |
$4$ |
$35$ |
4.4.2525.1 |
$4$ |
$[4, 0]$ |
25.3 |
\( 5^{2} \) |
\( 5^{6} \) |
$6.71447$ |
$(a^3-2a^2-2a+3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$5, 7$ |
5B.1.4[2], 7B.6.3 |
$49$ |
\( 1 \) |
$1$ |
$1.197349045$ |
1.167578693 |
\( -17038484321262621392677 a^{3} + 47324121859575160666349 a^{2} + 31360177851679811257113 a - 109574465986214263634831 \) |
\( \bigl[a^{3} - 4 a - 3\) , \( -a^{2} + 4\) , \( a^{3} - 3 a - 3\) , \( 492 a^{3} - 98 a^{2} - 2212 a - 1489\) , \( -10279 a^{3} + 2401 a^{2} + 44861 a + 28331\bigr] \) |
${y}^2+\left(a^{3}-4a-3\right){x}{y}+\left(a^{3}-3a-3\right){y}={x}^{3}+\left(-a^{2}+4\right){x}^{2}+\left(492a^{3}-98a^{2}-2212a-1489\right){x}-10279a^{3}+2401a^{2}+44861a+28331$ |
| 25.3-a2 |
25.3-a |
$4$ |
$35$ |
4.4.2525.1 |
$4$ |
$[4, 0]$ |
25.3 |
\( 5^{2} \) |
\( 5^{6} \) |
$6.71447$ |
$(a^3-2a^2-2a+3)$ |
0 |
$\Z/5\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$5, 7$ |
5B.1.1[2], 7B.6.3 |
$49$ |
\( 1 \) |
$1$ |
$29.93372613$ |
1.167578693 |
\( 17038484321262621392677 a^{3} - 3791331104212703511682 a^{2} - 74892968607042268411780 a - 47928650596221913104046 \) |
\( \bigl[a^{3} - 3 a - 2\) , \( -a^{3} + 3 a + 4\) , \( a + 1\) , \( 69 a^{3} - 41 a^{2} - 388 a - 281\) , \( -6915 a^{3} - 2381 a^{2} + 21401 a + 14709\bigr] \) |
${y}^2+\left(a^{3}-3a-2\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a^{3}+3a+4\right){x}^{2}+\left(69a^{3}-41a^{2}-388a-281\right){x}-6915a^{3}-2381a^{2}+21401a+14709$ |
| 25.3-a3 |
25.3-a |
$4$ |
$35$ |
4.4.2525.1 |
$4$ |
$[4, 0]$ |
25.3 |
\( 5^{2} \) |
\( 5^{6} \) |
$6.71447$ |
$(a^3-2a^2-2a+3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$5, 7$ |
5B.1.4[2], 7B.6.1 |
$1$ |
\( 1 \) |
$1$ |
$58.67010323$ |
1.167578693 |
\( 15961 a^{3} - 55157 a^{2} + 17566 a + 53224 \) |
\( \bigl[a^{2} - 2\) , \( -a^{3} + 2 a^{2} + a - 4\) , \( a^{3} - 3 a - 3\) , \( -2 a^{3} + 2 a^{2} + 5 a - 2\) , \( -a^{3} + a^{2} + 2 a - 3\bigr] \) |
${y}^2+\left(a^{2}-2\right){x}{y}+\left(a^{3}-3a-3\right){y}={x}^{3}+\left(-a^{3}+2a^{2}+a-4\right){x}^{2}+\left(-2a^{3}+2a^{2}+5a-2\right){x}-a^{3}+a^{2}+2a-3$ |
| 25.3-a4 |
25.3-a |
$4$ |
$35$ |
4.4.2525.1 |
$4$ |
$[4, 0]$ |
25.3 |
\( 5^{2} \) |
\( 5^{6} \) |
$6.71447$ |
$(a^3-2a^2-2a+3)$ |
0 |
$\Z/5\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$5, 7$ |
5B.1.1[2], 7B.6.1 |
$1$ |
\( 1 \) |
$1$ |
$1466.752580$ |
1.167578693 |
\( -15961 a^{3} - 7274 a^{2} + 44865 a + 31594 \) |
\( \bigl[a^{2} - 2\) , \( -a^{3} + 4 a + 4\) , \( 1\) , \( -2 a^{3} + 2 a^{2} + 6 a + 4\) , \( -2 a^{3} + 4 a^{2} + 3 a - 1\bigr] \) |
${y}^2+\left(a^{2}-2\right){x}{y}+{y}={x}^{3}+\left(-a^{3}+4a+4\right){x}^{2}+\left(-2a^{3}+2a^{2}+6a+4\right){x}-2a^{3}+4a^{2}+3a-1$ |
| 29.1-a1 |
29.1-a |
$1$ |
$1$ |
4.4.2525.1 |
$4$ |
$[4, 0]$ |
29.1 |
\( 29 \) |
\( 29 \) |
$6.84020$ |
$(-a^3+4a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$1$ |
$64.61768313$ |
1.285939957 |
\( \frac{16401989}{29} a^{3} - \frac{21549477}{29} a^{2} - \frac{41847288}{29} a - \frac{11836024}{29} \) |
\( \bigl[a^{3} - a^{2} - 3 a + 1\) , \( a^{3} - 4 a - 2\) , \( a^{2} - 2\) , \( -a^{3} + 2 a^{2} + 3 a - 3\) , \( -2 a^{3} + 7 a^{2} + 3 a - 17\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-3a+1\right){x}{y}+\left(a^{2}-2\right){y}={x}^{3}+\left(a^{3}-4a-2\right){x}^{2}+\left(-a^{3}+2a^{2}+3a-3\right){x}-2a^{3}+7a^{2}+3a-17$ |
| 29.1-b1 |
29.1-b |
$2$ |
$5$ |
4.4.2525.1 |
$4$ |
$[4, 0]$ |
29.1 |
\( 29 \) |
\( 29^{5} \) |
$6.84020$ |
$(-a^3+4a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.4.1[2] |
$1$ |
\( 1 \) |
$1$ |
$69.98222523$ |
1.392698335 |
\( \frac{271921578873}{20511149} a^{3} - \frac{951668263827}{20511149} a^{2} + \frac{308150023595}{20511149} a + \frac{949181429351}{20511149} \) |
\( \bigl[a^{3} - a^{2} - 2 a\) , \( a^{3} - 4 a - 2\) , \( a^{2} - a - 2\) , \( 6 a^{3} - 13 a^{2} - 11 a + 30\) , \( 24 a^{3} - 62 a^{2} - 44 a + 138\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-2a\right){x}{y}+\left(a^{2}-a-2\right){y}={x}^{3}+\left(a^{3}-4a-2\right){x}^{2}+\left(6a^{3}-13a^{2}-11a+30\right){x}+24a^{3}-62a^{2}-44a+138$ |
| 29.1-b2 |
29.1-b |
$2$ |
$5$ |
4.4.2525.1 |
$4$ |
$[4, 0]$ |
29.1 |
\( 29 \) |
\( 29 \) |
$6.84020$ |
$(-a^3+4a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.4.1[2] |
$1$ |
\( 1 \) |
$1$ |
$69.98222523$ |
1.392698335 |
\( -\frac{816199082965}{29} a^{3} - \frac{380945698076}{29} a^{2} + \frac{2325101717112}{29} a + \frac{1654408977036}{29} \) |
\( \bigl[1\) , \( -a^{3} + 3 a + 4\) , \( a^{2} - 3\) , \( 45 a^{3} - 10 a^{2} - 201 a - 126\) , \( -235 a^{3} + 54 a^{2} + 1029 a + 656\bigr] \) |
${y}^2+{x}{y}+\left(a^{2}-3\right){y}={x}^{3}+\left(-a^{3}+3a+4\right){x}^{2}+\left(45a^{3}-10a^{2}-201a-126\right){x}-235a^{3}+54a^{2}+1029a+656$ |
| 29.2-a1 |
29.2-a |
$1$ |
$1$ |
4.4.2525.1 |
$4$ |
$[4, 0]$ |
29.2 |
\( 29 \) |
\( 29 \) |
$6.84020$ |
$(-a^3+a^2+4a-2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$1$ |
$64.61768313$ |
1.285939957 |
\( -\frac{16401989}{29} a^{3} + \frac{27656490}{29} a^{2} + \frac{35740275}{29} a - \frac{58830800}{29} \) |
\( \bigl[a^{3} - 4 a - 2\) , \( -a^{3} + 3 a + 4\) , \( a^{3} - 4 a - 2\) , \( -a^{3} + 3 a + 3\) , \( 2 a^{3} + a^{2} - 12 a - 9\bigr] \) |
${y}^2+\left(a^{3}-4a-2\right){x}{y}+\left(a^{3}-4a-2\right){y}={x}^{3}+\left(-a^{3}+3a+4\right){x}^{2}+\left(-a^{3}+3a+3\right){x}+2a^{3}+a^{2}-12a-9$ |
| 29.2-b1 |
29.2-b |
$2$ |
$5$ |
4.4.2525.1 |
$4$ |
$[4, 0]$ |
29.2 |
\( 29 \) |
\( 29^{5} \) |
$6.84020$ |
$(-a^3+a^2+4a-2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.4.1[2] |
$1$ |
\( 1 \) |
$1$ |
$69.98222523$ |
1.392698335 |
\( -\frac{271921578873}{20511149} a^{3} - \frac{135903527208}{20511149} a^{2} + \frac{779421767440}{20511149} a + \frac{577584767992}{20511149} \) |
\( \bigl[a^{3} - 3 a - 2\) , \( a^{3} - 2 a^{2} - a + 4\) , \( a^{2} - 2\) , \( -a^{3} + 2 a^{2} + 11 a + 10\) , \( -19 a^{3} + 7 a^{2} + 92 a + 59\bigr] \) |
${y}^2+\left(a^{3}-3a-2\right){x}{y}+\left(a^{2}-2\right){y}={x}^{3}+\left(a^{3}-2a^{2}-a+4\right){x}^{2}+\left(-a^{3}+2a^{2}+11a+10\right){x}-19a^{3}+7a^{2}+92a+59$ |
| 29.2-b2 |
29.2-b |
$2$ |
$5$ |
4.4.2525.1 |
$4$ |
$[4, 0]$ |
29.2 |
\( 29 \) |
\( 29 \) |
$6.84020$ |
$(-a^3+a^2+4a-2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.4.1[2] |
$1$ |
\( 1 \) |
$1$ |
$69.98222523$ |
1.392698335 |
\( \frac{816199082965}{29} a^{3} - \frac{2829542946971}{29} a^{2} + \frac{885386927935}{29} a + \frac{2782365913107}{29} \) |
\( \bigl[1\) , \( a^{3} - 3 a - 3\) , \( a + 1\) , \( -45 a^{3} + 127 a^{2} + 85 a - 299\) , \( 311 a^{3} - 861 a^{2} - 572 a + 1988\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a^{3}-3a-3\right){x}^{2}+\left(-45a^{3}+127a^{2}+85a-299\right){x}+311a^{3}-861a^{2}-572a+1988$ |
| 55.1-a1 |
55.1-a |
$2$ |
$3$ |
4.4.2525.1 |
$4$ |
$[4, 0]$ |
55.1 |
\( 5 \cdot 11 \) |
\( 5 \cdot 11 \) |
$7.40994$ |
$(a^3-2a^2-2a+3), (a^3-a^2-3a+2)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1 |
$1$ |
\( 1 \) |
$1$ |
$650.2841186$ |
1.437904182 |
\( \frac{1751719}{55} a^{3} - \frac{6053969}{55} a^{2} + \frac{375313}{11} a + \frac{1183328}{11} \) |
\( \bigl[a^{3} - a^{2} - 2 a + 1\) , \( a^{3} - 2 a^{2} - 2 a + 3\) , \( a + 1\) , \( 2 a^{3} - 3 a^{2} - 3 a + 4\) , \( 2 a^{3} - a^{2} - 5 a - 1\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-2a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a^{3}-2a^{2}-2a+3\right){x}^{2}+\left(2a^{3}-3a^{2}-3a+4\right){x}+2a^{3}-a^{2}-5a-1$ |
| 55.1-a2 |
55.1-a |
$2$ |
$3$ |
4.4.2525.1 |
$4$ |
$[4, 0]$ |
55.1 |
\( 5 \cdot 11 \) |
\( 5^{3} \cdot 11^{3} \) |
$7.40994$ |
$(a^3-2a^2-2a+3), (a^3-a^2-3a+2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.2 |
$9$ |
\( 1 \) |
$1$ |
$8.028198996$ |
1.437904182 |
\( \frac{83501071203538687206}{33275} a^{3} - \frac{289475819206939412276}{33275} a^{2} + \frac{18115821139427454458}{6655} a + \frac{56930020183303906389}{6655} \) |
\( \bigl[a^{3} - a^{2} - 2 a + 1\) , \( a^{3} - 2 a^{2} - 2 a + 3\) , \( a + 1\) , \( 42 a^{3} - 143 a^{2} + 42 a + 144\) , \( 284 a^{3} - 978 a^{2} + 299 a + 959\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-2a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a^{3}-2a^{2}-2a+3\right){x}^{2}+\left(42a^{3}-143a^{2}+42a+144\right){x}+284a^{3}-978a^{2}+299a+959$ |
| 55.1-b1 |
55.1-b |
$2$ |
$7$ |
4.4.2525.1 |
$4$ |
$[4, 0]$ |
55.1 |
\( 5 \cdot 11 \) |
\( 5 \cdot 11 \) |
$7.40994$ |
$(a^3-2a^2-2a+3), (a^3-a^2-3a+2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$7$ |
7B.1.3 |
$2401$ |
\( 1 \) |
$1$ |
$0.028981244$ |
1.384772715 |
\( -\frac{51807617749024903893654570531}{55} a^{3} - \frac{24180264547435014338329319864}{55} a^{2} + \frac{29516849829890003181366807638}{11} a + \frac{21002534120116238691361707660}{11} \) |
\( \bigl[a^{3} - a^{2} - 2 a\) , \( a^{3} - 4 a - 2\) , \( a^{2} - a - 2\) , \( -2415 a^{3} + 6527 a^{2} + 5201 a - 16455\) , \( -441575 a^{3} + 1222531 a^{2} + 828478 a - 2855897\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-2a\right){x}{y}+\left(a^{2}-a-2\right){y}={x}^{3}+\left(a^{3}-4a-2\right){x}^{2}+\left(-2415a^{3}+6527a^{2}+5201a-16455\right){x}-441575a^{3}+1222531a^{2}+828478a-2855897$ |
| 55.1-b2 |
55.1-b |
$2$ |
$7$ |
4.4.2525.1 |
$4$ |
$[4, 0]$ |
55.1 |
\( 5 \cdot 11 \) |
\( 5^{7} \cdot 11^{7} \) |
$7.40994$ |
$(a^3-2a^2-2a+3), (a^3-a^2-3a+2)$ |
0 |
$\Z/7\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$7$ |
7B.1.1 |
$1$ |
\( 7^{2} \) |
$1$ |
$69.58396776$ |
1.384772715 |
\( -\frac{102774237182609}{12179481875} a^{3} + \frac{246276827356634}{12179481875} a^{2} + \frac{40200038794063}{2435896375} a - \frac{112301783366486}{2435896375} \) |
\( \bigl[a\) , \( a^{3} - a^{2} - 3 a + 1\) , \( a^{3} - 4 a - 3\) , \( -2 a^{3} + a^{2} + 16 a - 16\) , \( 32 a^{3} - 106 a^{2} + 13 a + 127\bigr] \) |
${y}^2+a{x}{y}+\left(a^{3}-4a-3\right){y}={x}^{3}+\left(a^{3}-a^{2}-3a+1\right){x}^{2}+\left(-2a^{3}+a^{2}+16a-16\right){x}+32a^{3}-106a^{2}+13a+127$ |
| 55.1-c1 |
55.1-c |
$2$ |
$5$ |
4.4.2525.1 |
$4$ |
$[4, 0]$ |
55.1 |
\( 5 \cdot 11 \) |
\( 5 \cdot 11^{5} \) |
$7.40994$ |
$(a^3-2a^2-2a+3), (a^3-a^2-3a+2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.4.1[2] |
$1$ |
\( 1 \) |
$1$ |
$53.80734858$ |
1.070806258 |
\( \frac{2944570612696149}{805255} a^{3} - \frac{655213616419024}{805255} a^{2} - \frac{2588582683571638}{161051} a - \frac{1656594163874440}{161051} \) |
\( \bigl[a^{3} - 3 a - 3\) , \( -a^{2} + 2 a + 3\) , \( 0\) , \( 31 a^{3} - 82 a^{2} - 59 a + 199\) , \( 91 a^{3} - 246 a^{2} - 173 a + 579\bigr] \) |
${y}^2+\left(a^{3}-3a-3\right){x}{y}={x}^{3}+\left(-a^{2}+2a+3\right){x}^{2}+\left(31a^{3}-82a^{2}-59a+199\right){x}+91a^{3}-246a^{2}-173a+579$ |
| 55.1-c2 |
55.1-c |
$2$ |
$5$ |
4.4.2525.1 |
$4$ |
$[4, 0]$ |
55.1 |
\( 5 \cdot 11 \) |
\( 5^{5} \cdot 11 \) |
$7.40994$ |
$(a^3-2a^2-2a+3), (a^3-a^2-3a+2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.4.1[2] |
$1$ |
\( 1 \) |
$1$ |
$53.80734858$ |
1.070806258 |
\( \frac{168847603239}{1375} a^{3} - \frac{585922554419}{1375} a^{2} + \frac{36866686387}{275} a + \frac{115063357051}{275} \) |
\( \bigl[a^{3} - a^{2} - 3 a\) , \( a^{3} - a^{2} - 3 a + 1\) , \( 1\) , \( a^{3} - 11 a^{2} + 14 a + 19\) , \( 9 a^{3} + 19 a^{2} - 75 a - 66\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-3a\right){x}{y}+{y}={x}^{3}+\left(a^{3}-a^{2}-3a+1\right){x}^{2}+\left(a^{3}-11a^{2}+14a+19\right){x}+9a^{3}+19a^{2}-75a-66$ |
| 55.2-a1 |
55.2-a |
$4$ |
$10$ |
4.4.2525.1 |
$4$ |
$[4, 0]$ |
55.2 |
\( 5 \cdot 11 \) |
\( - 5^{5} \cdot 11 \) |
$7.40994$ |
$(a^3-2a^2-2a+3), (-a^3+5a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B.4.1[2] |
$1$ |
\( 1 \) |
$1$ |
$302.4912667$ |
1.504950300 |
\( -\frac{1430471161}{1375} a^{3} + \frac{7928609681}{1375} a^{2} - \frac{871481363}{275} a - \frac{1774299999}{275} \) |
\( \bigl[a^{3} - 4 a - 3\) , \( a^{3} - a^{2} - 2 a + 1\) , \( a^{2} - a - 3\) , \( -7 a^{3} + 15 a^{2} + 15 a - 32\) , \( -24 a^{3} + 40 a^{2} + 53 a - 84\bigr] \) |
${y}^2+\left(a^{3}-4a-3\right){x}{y}+\left(a^{2}-a-3\right){y}={x}^{3}+\left(a^{3}-a^{2}-2a+1\right){x}^{2}+\left(-7a^{3}+15a^{2}+15a-32\right){x}-24a^{3}+40a^{2}+53a-84$ |
| 55.2-a2 |
55.2-a |
$4$ |
$10$ |
4.4.2525.1 |
$4$ |
$[4, 0]$ |
55.2 |
\( 5 \cdot 11 \) |
\( - 5 \cdot 11^{5} \) |
$7.40994$ |
$(a^3-2a^2-2a+3), (-a^3+5a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B.4.1[2] |
$1$ |
\( 1 \) |
$1$ |
$302.4912667$ |
1.504950300 |
\( -\frac{904663159491}{805255} a^{3} + \frac{272075501886}{805255} a^{2} + \frac{788768413072}{161051} a + \frac{495329003734}{161051} \) |
\( \bigl[a^{2} - 2\) , \( a^{2} - 2\) , \( a^{3} - a^{2} - 3 a\) , \( 16 a^{3} - 39 a^{2} - 30 a + 89\) , \( 931 a^{3} - 2579 a^{2} - 1716 a + 5968\bigr] \) |
${y}^2+\left(a^{2}-2\right){x}{y}+\left(a^{3}-a^{2}-3a\right){y}={x}^{3}+\left(a^{2}-2\right){x}^{2}+\left(16a^{3}-39a^{2}-30a+89\right){x}+931a^{3}-2579a^{2}-1716a+5968$ |
| 55.2-a3 |
55.2-a |
$4$ |
$10$ |
4.4.2525.1 |
$4$ |
$[4, 0]$ |
55.2 |
\( 5 \cdot 11 \) |
\( - 5^{2} \cdot 11^{10} \) |
$7.40994$ |
$(a^3-2a^2-2a+3), (-a^3+5a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B.4.1[2] |
$1$ |
\( 2^{2} \) |
$1$ |
$75.62281668$ |
1.504950300 |
\( -\frac{392381810948767203121}{129687123005} a^{3} + \frac{272056546037232533612}{25937424601} a^{2} - \frac{85128797684737133901}{25937424601} a - \frac{267520650780877770522}{25937424601} \) |
\( \bigl[a^{3} - a^{2} - 2 a\) , \( -a^{2} + 2 a + 2\) , \( a^{3} - a^{2} - 3 a + 1\) , \( -18 a^{3} - 3 a^{2} + 48 a + 20\) , \( 297 a^{3} + 131 a^{2} - 847 a - 587\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-2a\right){x}{y}+\left(a^{3}-a^{2}-3a+1\right){y}={x}^{3}+\left(-a^{2}+2a+2\right){x}^{2}+\left(-18a^{3}-3a^{2}+48a+20\right){x}+297a^{3}+131a^{2}-847a-587$ |
| 55.2-a4 |
55.2-a |
$4$ |
$10$ |
4.4.2525.1 |
$4$ |
$[4, 0]$ |
55.2 |
\( 5 \cdot 11 \) |
\( - 5^{10} \cdot 11^{2} \) |
$7.40994$ |
$(a^3-2a^2-2a+3), (-a^3+5a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B.4.1[2] |
$1$ |
\( 2^{2} \) |
$1$ |
$75.62281668$ |
1.504950300 |
\( -\frac{5558430994512303}{378125} a^{3} + \frac{1202115147604197}{378125} a^{2} + \frac{4893381503722738}{75625} a + \frac{3152259928887352}{75625} \) |
\( \bigl[a + 1\) , \( -a^{3} + 2 a^{2} + 2 a - 4\) , \( a + 1\) , \( -26 a^{3} + 26 a^{2} + 61 a - 51\) , \( -123 a^{3} + 32 a^{2} + 322 a + 16\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a^{3}+2a^{2}+2a-4\right){x}^{2}+\left(-26a^{3}+26a^{2}+61a-51\right){x}-123a^{3}+32a^{2}+322a+16$ |
| 55.2-b1 |
55.2-b |
$4$ |
$6$ |
4.4.2525.1 |
$4$ |
$[4, 0]$ |
55.2 |
\( 5 \cdot 11 \) |
\( - 5^{3} \cdot 11^{3} \) |
$7.40994$ |
$(a^3-2a^2-2a+3), (-a^3+5a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$9$ |
\( 1 \) |
$1$ |
$26.09440830$ |
1.168420802 |
\( -\frac{6497565844347824}{33275} a^{3} + \frac{1456407629467884}{33275} a^{2} + \frac{5708457023802048}{6655} a + \frac{3651422298792739}{6655} \) |
\( \bigl[a^{3} - 3 a - 3\) , \( -a^{3} + 3 a + 4\) , \( a^{3} - a^{2} - 3 a + 1\) , \( 18 a^{3} - 19 a^{2} - 59 a - 21\) , \( 103 a^{3} - 73 a^{2} - 374 a - 192\bigr] \) |
${y}^2+\left(a^{3}-3a-3\right){x}{y}+\left(a^{3}-a^{2}-3a+1\right){y}={x}^{3}+\left(-a^{3}+3a+4\right){x}^{2}+\left(18a^{3}-19a^{2}-59a-21\right){x}+103a^{3}-73a^{2}-374a-192$ |
| 55.2-b2 |
55.2-b |
$4$ |
$6$ |
4.4.2525.1 |
$4$ |
$[4, 0]$ |
55.2 |
\( 5 \cdot 11 \) |
\( - 5 \cdot 11 \) |
$7.40994$ |
$(a^3-2a^2-2a+3), (-a^3+5a+2)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 1 \) |
$1$ |
$2113.647072$ |
1.168420802 |
\( -\frac{23406441}{55} a^{3} + \frac{64841646}{55} a^{2} + \frac{8657882}{11} a - \frac{29950059}{11} \) |
\( \bigl[a^{3} - 3 a - 3\) , \( -a^{3} + 3 a + 4\) , \( a^{3} - a^{2} - 3 a + 1\) , \( -2 a^{3} + a^{2} + 6 a + 4\) , \( -a^{3} + a^{2} + 3 a\bigr] \) |
${y}^2+\left(a^{3}-3a-3\right){x}{y}+\left(a^{3}-a^{2}-3a+1\right){y}={x}^{3}+\left(-a^{3}+3a+4\right){x}^{2}+\left(-2a^{3}+a^{2}+6a+4\right){x}-a^{3}+a^{2}+3a$ |
| 55.2-b3 |
55.2-b |
$4$ |
$6$ |
4.4.2525.1 |
$4$ |
$[4, 0]$ |
55.2 |
\( 5 \cdot 11 \) |
\( - 5^{6} \cdot 11^{6} \) |
$7.40994$ |
$(a^3-2a^2-2a+3), (-a^3+5a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$9$ |
\( 2^{2} \) |
$1$ |
$6.523602076$ |
1.168420802 |
\( -\frac{18753351407783692656432346}{221445125} a^{3} + \frac{13002567951254045423323246}{44289025} a^{2} - \frac{4068598821162040689721566}{44289025} a - \frac{2557161623814181929515881}{8857805} \) |
\( \bigl[a^{3} - 3 a - 3\) , \( -a^{3} + 3 a + 4\) , \( a^{3} - a^{2} - 3 a + 1\) , \( 73 a^{3} - 214 a^{2} + 21 a + 144\) , \( 789 a^{3} - 2446 a^{2} + 345 a + 2175\bigr] \) |
${y}^2+\left(a^{3}-3a-3\right){x}{y}+\left(a^{3}-a^{2}-3a+1\right){y}={x}^{3}+\left(-a^{3}+3a+4\right){x}^{2}+\left(73a^{3}-214a^{2}+21a+144\right){x}+789a^{3}-2446a^{2}+345a+2175$ |
| 55.2-b4 |
55.2-b |
$4$ |
$6$ |
4.4.2525.1 |
$4$ |
$[4, 0]$ |
55.2 |
\( 5 \cdot 11 \) |
\( - 5^{2} \cdot 11^{2} \) |
$7.40994$ |
$(a^3-2a^2-2a+3), (-a^3+5a+2)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{2} \) |
$1$ |
$528.4117682$ |
1.168420802 |
\( \frac{621594170868971}{605} a^{3} - \frac{1726467978493952}{605} a^{2} - \frac{228815033849085}{121} a + \frac{799494266717923}{121} \) |
\( \bigl[a^{3} - a^{2} - 3 a + 1\) , \( -a^{3} + a^{2} + 2 a - 1\) , \( a^{2} - 2\) , \( 5 a^{3} - 17 a^{2} + 7 a + 14\) , \( 18 a^{3} - 64 a^{2} + 19 a + 67\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-3a+1\right){x}{y}+\left(a^{2}-2\right){y}={x}^{3}+\left(-a^{3}+a^{2}+2a-1\right){x}^{2}+\left(5a^{3}-17a^{2}+7a+14\right){x}+18a^{3}-64a^{2}+19a+67$ |
| 55.2-c1 |
55.2-c |
$4$ |
$4$ |
4.4.2525.1 |
$4$ |
$[4, 0]$ |
55.2 |
\( 5 \cdot 11 \) |
\( 5^{4} \cdot 11 \) |
$7.40994$ |
$(a^3-2a^2-2a+3), (-a^3+5a+2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.167782605$ |
$242.4782834$ |
1.619269318 |
\( -\frac{25953922597562095509798}{275} a^{3} + \frac{5775156529361736202714}{275} a^{2} + \frac{22816188033512795949149}{55} a + \frac{14601492297156395688994}{55} \) |
\( \bigl[a^{2} - a - 3\) , \( -a^{3} + 5 a + 4\) , \( a^{3} - 3 a - 2\) , \( 111 a^{3} - 25 a^{2} - 489 a - 314\) , \( -906 a^{3} + 154 a^{2} + 3875 a + 2494\bigr] \) |
${y}^2+\left(a^{2}-a-3\right){x}{y}+\left(a^{3}-3a-2\right){y}={x}^{3}+\left(-a^{3}+5a+4\right){x}^{2}+\left(111a^{3}-25a^{2}-489a-314\right){x}-906a^{3}+154a^{2}+3875a+2494$ |
| 55.2-c2 |
55.2-c |
$4$ |
$4$ |
4.4.2525.1 |
$4$ |
$[4, 0]$ |
55.2 |
\( 5 \cdot 11 \) |
\( - 5 \cdot 11^{4} \) |
$7.40994$ |
$(a^3-2a^2-2a+3), (-a^3+5a+2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.167782605$ |
$121.2391417$ |
1.619269318 |
\( -\frac{144551574495955734}{73205} a^{3} + \frac{501250894564427754}{73205} a^{2} - \frac{31386808429453083}{14641} a - \frac{98589239350867390}{14641} \) |
\( \bigl[a^{2} - a - 2\) , \( -a^{2} + 2\) , \( a + 1\) , \( 28 a^{3} - 11 a^{2} - 158 a - 122\) , \( -413 a^{3} + 65 a^{2} + 1690 a + 1037\bigr] \) |
${y}^2+\left(a^{2}-a-2\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a^{2}+2\right){x}^{2}+\left(28a^{3}-11a^{2}-158a-122\right){x}-413a^{3}+65a^{2}+1690a+1037$ |
| 55.2-c3 |
55.2-c |
$4$ |
$4$ |
4.4.2525.1 |
$4$ |
$[4, 0]$ |
55.2 |
\( 5 \cdot 11 \) |
\( - 5 \cdot 11 \) |
$7.40994$ |
$(a^3-2a^2-2a+3), (-a^3+5a+2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$0.041945651$ |
$1939.826267$ |
1.619269318 |
\( -\frac{1467546}{55} a^{3} + \frac{366356}{55} a^{2} + \frac{1280193}{11} a + \frac{825697}{11} \) |
\( \bigl[a^{3} - a^{2} - 3 a\) , \( -a^{3} + a^{2} + 2 a + 1\) , \( a^{3} - 4 a - 2\) , \( a^{3} - 4 a^{2} + a + 6\) , \( -a^{2} + a + 1\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-3a\right){x}{y}+\left(a^{3}-4a-2\right){y}={x}^{3}+\left(-a^{3}+a^{2}+2a+1\right){x}^{2}+\left(a^{3}-4a^{2}+a+6\right){x}-a^{2}+a+1$ |
| 55.2-c4 |
55.2-c |
$4$ |
$4$ |
4.4.2525.1 |
$4$ |
$[4, 0]$ |
55.2 |
\( 5 \cdot 11 \) |
\( 5^{2} \cdot 11^{2} \) |
$7.40994$ |
$(a^3-2a^2-2a+3), (-a^3+5a+2)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$0.083891302$ |
$969.9131338$ |
1.619269318 |
\( -\frac{491852727240}{121} a^{3} + \frac{548157473929}{605} a^{2} + \frac{2161634837932}{121} a + \frac{1383208602332}{121} \) |
\( \bigl[a^{3} - a^{2} - 2 a\) , \( a^{3} - a^{2} - 3 a\) , \( a^{3} - a^{2} - 3 a\) , \( -11 a^{3} + 31 a^{2} + 28 a - 86\) , \( -40 a^{3} + 117 a^{2} + 58 a - 250\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-2a\right){x}{y}+\left(a^{3}-a^{2}-3a\right){y}={x}^{3}+\left(a^{3}-a^{2}-3a\right){x}^{2}+\left(-11a^{3}+31a^{2}+28a-86\right){x}-40a^{3}+117a^{2}+58a-250$ |
| 55.3-a1 |
55.3-a |
$4$ |
$10$ |
4.4.2525.1 |
$4$ |
$[4, 0]$ |
55.3 |
\( 5 \cdot 11 \) |
\( - 5 \cdot 11^{5} \) |
$7.40994$ |
$(-a), (a^3-a^2-3a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B.4.1[2] |
$1$ |
\( 1 \) |
$1$ |
$302.4912667$ |
1.504950300 |
\( \frac{904663159491}{805255} a^{3} - \frac{2441913976587}{805255} a^{2} - \frac{1774003590659}{805255} a + \frac{1157579885285}{161051} \) |
\( \bigl[a^{2} - 3\) , \( -a^{3} + 5 a + 3\) , \( a^{3} - a^{2} - 3 a\) , \( -16 a^{3} + 2 a^{2} + 72 a + 49\) , \( -964 a^{3} + 215 a^{2} + 4236 a + 2710\bigr] \) |
${y}^2+\left(a^{2}-3\right){x}{y}+\left(a^{3}-a^{2}-3a\right){y}={x}^{3}+\left(-a^{3}+5a+3\right){x}^{2}+\left(-16a^{3}+2a^{2}+72a+49\right){x}-964a^{3}+215a^{2}+4236a+2710$ |
| 55.3-a2 |
55.3-a |
$4$ |
$10$ |
4.4.2525.1 |
$4$ |
$[4, 0]$ |
55.3 |
\( 5 \cdot 11 \) |
\( - 5^{2} \cdot 11^{10} \) |
$7.40994$ |
$(-a), (a^3-a^2-3a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B.4.1[2] |
$1$ |
\( 2^{2} \) |
$1$ |
$75.62281668$ |
1.504950300 |
\( \frac{392381810948767203121}{129687123005} a^{3} + \frac{183137297339861058697}{129687123005} a^{2} - \frac{1117776039102338057252}{129687123005} a - \frac{795346323090679057176}{129687123005} \) |
\( \bigl[a^{3} - 3 a - 2\) , \( -a^{3} + 4 a + 3\) , \( a^{3} - a^{2} - 3 a + 1\) , \( 17 a^{3} - 57 a^{2} + 18 a + 50\) , \( -319 a^{3} + 1107 a^{2} - 345 a - 1094\bigr] \) |
${y}^2+\left(a^{3}-3a-2\right){x}{y}+\left(a^{3}-a^{2}-3a+1\right){y}={x}^{3}+\left(-a^{3}+4a+3\right){x}^{2}+\left(17a^{3}-57a^{2}+18a+50\right){x}-319a^{3}+1107a^{2}-345a-1094$ |
| 55.3-a3 |
55.3-a |
$4$ |
$10$ |
4.4.2525.1 |
$4$ |
$[4, 0]$ |
55.3 |
\( 5 \cdot 11 \) |
\( - 5^{5} \cdot 11 \) |
$7.40994$ |
$(-a), (a^3-a^2-3a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B.4.1[2] |
$1$ |
\( 1 \) |
$1$ |
$302.4912667$ |
1.504950300 |
\( \frac{1430471161}{1375} a^{3} + \frac{3637196198}{1375} a^{2} - \frac{7208399064}{1375} a - \frac{1346153658}{275} \) |
\( \bigl[a^{3} - a^{2} - 3 a\) , \( a\) , \( a^{2} - a - 2\) , \( 7 a^{3} - 8 a^{2} - 19 a - 8\) , \( 23 a^{3} - 16 a^{2} - 83 a - 43\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-3a\right){x}{y}+\left(a^{2}-a-2\right){y}={x}^{3}+a{x}^{2}+\left(7a^{3}-8a^{2}-19a-8\right){x}+23a^{3}-16a^{2}-83a-43$ |
| 55.3-a4 |
55.3-a |
$4$ |
$10$ |
4.4.2525.1 |
$4$ |
$[4, 0]$ |
55.3 |
\( 5 \cdot 11 \) |
\( - 5^{10} \cdot 11^{2} \) |
$7.40994$ |
$(-a), (a^3-a^2-3a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B.4.1[2] |
$1$ |
\( 2^{2} \) |
$1$ |
$75.62281668$ |
1.504950300 |
\( \frac{5558430994512303}{378125} a^{3} - \frac{15473177835932712}{378125} a^{2} - \frac{407833793211407}{15125} a + \frac{35871891316142344}{378125} \) |
\( \bigl[a\) , \( a^{3} - a^{2} - 4 a\) , \( a\) , \( 26 a^{3} - 52 a^{2} - 37 a + 12\) , \( 123 a^{3} - 337 a^{2} - 18 a + 248\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(a^{3}-a^{2}-4a\right){x}^{2}+\left(26a^{3}-52a^{2}-37a+12\right){x}+123a^{3}-337a^{2}-18a+248$ |
| 55.3-b1 |
55.3-b |
$4$ |
$6$ |
4.4.2525.1 |
$4$ |
$[4, 0]$ |
55.3 |
\( 5 \cdot 11 \) |
\( - 5^{3} \cdot 11^{3} \) |
$7.40994$ |
$(-a), (a^3-a^2-3a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$9$ |
\( 1 \) |
$1$ |
$26.09440830$ |
1.168420802 |
\( \frac{6497565844347824}{33275} a^{3} - \frac{18036289903575588}{33275} a^{2} - \frac{11962402844902536}{33275} a + \frac{8351647679618799}{6655} \) |
\( \bigl[a^{3} - a^{2} - 2 a + 1\) , \( a^{2} - 2 a - 2\) , \( a^{3} - a^{2} - 2 a + 1\) , \( -21 a^{3} + 42 a^{2} + 46 a - 93\) , \( -80 a^{3} + 164 a^{2} + 171 a - 369\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-2a+1\right){x}{y}+\left(a^{3}-a^{2}-2a+1\right){y}={x}^{3}+\left(a^{2}-2a-2\right){x}^{2}+\left(-21a^{3}+42a^{2}+46a-93\right){x}-80a^{3}+164a^{2}+171a-369$ |
| 55.3-b2 |
55.3-b |
$4$ |
$6$ |
4.4.2525.1 |
$4$ |
$[4, 0]$ |
55.3 |
\( 5 \cdot 11 \) |
\( - 5^{2} \cdot 11^{2} \) |
$7.40994$ |
$(-a), (a^3-a^2-3a+2)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{2} \) |
$1$ |
$528.4117682$ |
1.168420802 |
\( -\frac{621594170868971}{605} a^{3} + \frac{138314534112961}{605} a^{2} + \frac{2732228613626416}{605} a + \frac{1748522356719209}{605} \) |
\( \bigl[a^{3} - a^{2} - 2 a + 1\) , \( a^{2} - 2 a - 2\) , \( a^{3} - a^{2} - 2 a + 1\) , \( 4 a^{3} + 2 a^{2} - 24 a - 23\) , \( -24 a^{3} + 4 a^{2} + 101 a + 66\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-2a+1\right){x}{y}+\left(a^{3}-a^{2}-2a+1\right){y}={x}^{3}+\left(a^{2}-2a-2\right){x}^{2}+\left(4a^{3}+2a^{2}-24a-23\right){x}-24a^{3}+4a^{2}+101a+66$ |
| 55.3-b3 |
55.3-b |
$4$ |
$6$ |
4.4.2525.1 |
$4$ |
$[4, 0]$ |
55.3 |
\( 5 \cdot 11 \) |
\( - 5 \cdot 11 \) |
$7.40994$ |
$(-a), (a^3-a^2-3a+2)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 1 \) |
$1$ |
$2113.647072$ |
1.168420802 |
\( \frac{23406441}{55} a^{3} - \frac{5377677}{55} a^{2} - \frac{102753379}{55} a - \frac{13005136}{11} \) |
\( \bigl[a^{3} - a^{2} - 2 a + 1\) , \( a^{2} - 2 a - 2\) , \( a^{3} - a^{2} - 2 a + 1\) , \( -a^{3} + 2 a^{2} + a - 3\) , \( -a^{3} + a^{2} + 3 a\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-2a+1\right){x}{y}+\left(a^{3}-a^{2}-2a+1\right){y}={x}^{3}+\left(a^{2}-2a-2\right){x}^{2}+\left(-a^{3}+2a^{2}+a-3\right){x}-a^{3}+a^{2}+3a$ |
| 55.3-b4 |
55.3-b |
$4$ |
$6$ |
4.4.2525.1 |
$4$ |
$[4, 0]$ |
55.3 |
\( 5 \cdot 11 \) |
\( - 5^{6} \cdot 11^{6} \) |
$7.40994$ |
$(-a), (a^3-a^2-3a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$9$ |
\( 2^{2} \) |
$1$ |
$6.523602076$ |
1.168420802 |
\( \frac{18753351407783692656432346}{221445125} a^{3} + \frac{8752785532919149147319192}{221445125} a^{2} - \frac{53422631183379172815327592}{221445125} a - \frac{38012546352678217226320971}{221445125} \) |
\( \bigl[a^{3} - a^{2} - 2 a + 1\) , \( a^{2} - 2 a - 2\) , \( a^{3} - a^{2} - 2 a + 1\) , \( -76 a^{3} + 12 a^{2} + 191 a + 12\) , \( -816 a^{3} - 166 a^{2} + 2300 a + 1140\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-2a+1\right){x}{y}+\left(a^{3}-a^{2}-2a+1\right){y}={x}^{3}+\left(a^{2}-2a-2\right){x}^{2}+\left(-76a^{3}+12a^{2}+191a+12\right){x}-816a^{3}-166a^{2}+2300a+1140$ |
| 55.3-c1 |
55.3-c |
$4$ |
$4$ |
4.4.2525.1 |
$4$ |
$[4, 0]$ |
55.3 |
\( 5 \cdot 11 \) |
\( - 5 \cdot 11^{4} \) |
$7.40994$ |
$(-a), (a^3-a^2-3a+2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.167782605$ |
$121.2391417$ |
1.619269318 |
\( \frac{144551574495955734}{73205} a^{3} + \frac{67596171076560552}{73205} a^{2} - \frac{411913023493722891}{73205} a - \frac{58636183766626069}{14641} \) |
\( \bigl[a^{2} - a - 3\) , \( a^{3} - 5 a - 4\) , \( a^{3} - a^{2} - 2 a + 1\) , \( 113 a^{3} - 412 a^{2} + 163 a + 389\) , \( 1616 a^{3} - 5572 a^{2} + 1681 a + 5535\bigr] \) |
${y}^2+\left(a^{2}-a-3\right){x}{y}+\left(a^{3}-a^{2}-2a+1\right){y}={x}^{3}+\left(a^{3}-5a-4\right){x}^{2}+\left(113a^{3}-412a^{2}+163a+389\right){x}+1616a^{3}-5572a^{2}+1681a+5535$ |
| 55.3-c2 |
55.3-c |
$4$ |
$4$ |
4.4.2525.1 |
$4$ |
$[4, 0]$ |
55.3 |
\( 5 \cdot 11 \) |
\( 5^{2} \cdot 11^{2} \) |
$7.40994$ |
$(-a), (a^3-a^2-3a+2)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$0.083891302$ |
$969.9131338$ |
1.619269318 |
\( \frac{491852727240}{121} a^{3} - \frac{6829633434671}{605} a^{2} - \frac{4526698228918}{605} a + \frac{15813111039049}{605} \) |
\( \bigl[a^{3} - 3 a - 2\) , \( a^{3} - 3 a - 3\) , \( a^{3} - 4 a - 2\) , \( 17 a^{3} - 2 a^{2} - 72 a - 47\) , \( 22 a^{3} - 4 a^{2} - 94 a - 60\bigr] \) |
${y}^2+\left(a^{3}-3a-2\right){x}{y}+\left(a^{3}-4a-2\right){y}={x}^{3}+\left(a^{3}-3a-3\right){x}^{2}+\left(17a^{3}-2a^{2}-72a-47\right){x}+22a^{3}-4a^{2}-94a-60$ |
*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.
