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 |
$2$ |
$2$ |
4.4.8069.1 |
$4$ |
$[4, 0]$ |
5.1 |
\( 5 \) |
\( 5^{4} \) |
$9.81566$ |
$(-a^2-a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$262.4710411$ |
1.460970815 |
\( \frac{2937183550104}{625} a^{3} - \frac{3444473642517}{625} a^{2} - \frac{14095287030396}{625} a + \frac{17120317880357}{625} \) |
\( \bigl[a^{2} + a - 2\) , \( 0\) , \( a^{3} + a^{2} - 4 a - 2\) , \( 5 a^{3} - 5 a^{2} - 9 a - 6\) , \( a^{3} - 21 a^{2} + 40 a + 3\bigr] \) |
${y}^2+\left(a^{2}+a-2\right){x}{y}+\left(a^{3}+a^{2}-4a-2\right){y}={x}^{3}+\left(5a^{3}-5a^{2}-9a-6\right){x}+a^{3}-21a^{2}+40a+3$ |
5.1-a2 |
5.1-a |
$2$ |
$2$ |
4.4.8069.1 |
$4$ |
$[4, 0]$ |
5.1 |
\( 5 \) |
\( 5^{2} \) |
$9.81566$ |
$(-a^2-a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$262.4710411$ |
1.460970815 |
\( -\frac{526503}{25} a^{3} + \frac{958419}{25} a^{2} + \frac{2894547}{25} a - \frac{3922624}{25} \) |
\( \bigl[a^{2} + a - 2\) , \( 0\) , \( a^{3} + a^{2} - 4 a - 2\) , \( a - 1\) , \( a^{3} - 3 a - 1\bigr] \) |
${y}^2+\left(a^{2}+a-2\right){x}{y}+\left(a^{3}+a^{2}-4a-2\right){y}={x}^{3}+\left(a-1\right){x}+a^{3}-3a-1$ |
5.1-b1 |
5.1-b |
$2$ |
$2$ |
4.4.8069.1 |
$4$ |
$[4, 0]$ |
5.1 |
\( 5 \) |
\( 5^{4} \) |
$9.81566$ |
$(-a^2-a+2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.017299536$ |
$2174.132549$ |
1.674829594 |
\( \frac{2937183550104}{625} a^{3} - \frac{3444473642517}{625} a^{2} - \frac{14095287030396}{625} a + \frac{17120317880357}{625} \) |
\( \bigl[a^{3} + a^{2} - 4 a - 1\) , \( -1\) , \( a + 1\) , \( 69 a^{3} + 16 a^{2} - 324 a - 58\) , \( -456 a^{3} - 106 a^{2} + 2148 a + 372\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-4a-1\right){x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(69a^{3}+16a^{2}-324a-58\right){x}-456a^{3}-106a^{2}+2148a+372$ |
5.1-b2 |
5.1-b |
$2$ |
$2$ |
4.4.8069.1 |
$4$ |
$[4, 0]$ |
5.1 |
\( 5 \) |
\( 5^{2} \) |
$9.81566$ |
$(-a^2-a+2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.034599073$ |
$2174.132549$ |
1.674829594 |
\( -\frac{526503}{25} a^{3} + \frac{958419}{25} a^{2} + \frac{2894547}{25} a - \frac{3922624}{25} \) |
\( \bigl[a^{3} + a^{2} - 4 a - 1\) , \( -1\) , \( a + 1\) , \( 4 a^{3} + a^{2} - 19 a - 3\) , \( -5 a^{3} - a^{2} + 24 a + 4\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-4a-1\right){x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(4a^{3}+a^{2}-19a-3\right){x}-5a^{3}-a^{2}+24a+4$ |
7.1-a1 |
7.1-a |
$6$ |
$8$ |
4.4.8069.1 |
$4$ |
$[4, 0]$ |
7.1 |
\( 7 \) |
\( 7^{4} \) |
$10.23731$ |
$(-a-1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$16$ |
\( 2 \) |
$1$ |
$64.37704336$ |
1.433346416 |
\( \frac{1090950826513421409}{2401} a^{3} - \frac{1278489943416427617}{2401} a^{2} - \frac{5235283189978195968}{2401} a + \frac{6354702898520183792}{2401} \) |
\( \bigl[a^{2} + a - 2\) , \( -a^{3} + a^{2} + 3 a - 3\) , \( 0\) , \( -30 a^{3} - 4 a^{2} + 123 a - 94\) , \( -3 a^{3} - 229 a^{2} - 167 a + 555\bigr] \) |
${y}^2+\left(a^{2}+a-2\right){x}{y}={x}^{3}+\left(-a^{3}+a^{2}+3a-3\right){x}^{2}+\left(-30a^{3}-4a^{2}+123a-94\right){x}-3a^{3}-229a^{2}-167a+555$ |
7.1-a2 |
7.1-a |
$6$ |
$8$ |
4.4.8069.1 |
$4$ |
$[4, 0]$ |
7.1 |
\( 7 \) |
\( 7^{8} \) |
$10.23731$ |
$(-a-1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$4$ |
\( 2 \) |
$1$ |
$257.5081734$ |
1.433346416 |
\( \frac{47042604735051}{5764801} a^{3} - \frac{55967329253427}{5764801} a^{2} - \frac{226247884349976}{5764801} a + \frac{278958254354747}{5764801} \) |
\( \bigl[a^{2} + a - 2\) , \( -a^{3} + a^{2} + 3 a - 3\) , \( 0\) , \( -4 a^{2} + 8 a - 4\) , \( 8 a^{3} - 31 a^{2} + 13 a + 16\bigr] \) |
${y}^2+\left(a^{2}+a-2\right){x}{y}={x}^{3}+\left(-a^{3}+a^{2}+3a-3\right){x}^{2}+\left(-4a^{2}+8a-4\right){x}+8a^{3}-31a^{2}+13a+16$ |
7.1-a3 |
7.1-a |
$6$ |
$8$ |
4.4.8069.1 |
$4$ |
$[4, 0]$ |
7.1 |
\( 7 \) |
\( 7^{4} \) |
$10.23731$ |
$(-a-1)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$1030.032693$ |
1.433346416 |
\( \frac{1479733}{2401} a^{3} + \frac{8160419}{2401} a^{2} + \frac{3837720}{2401} a - \frac{15624676}{2401} \) |
\( \bigl[a^{2} + a - 2\) , \( -a^{3} + a^{2} + 3 a - 3\) , \( 0\) , \( a^{2} - 2 a + 1\) , \( 0\bigr] \) |
${y}^2+\left(a^{2}+a-2\right){x}{y}={x}^{3}+\left(-a^{3}+a^{2}+3a-3\right){x}^{2}+\left(a^{2}-2a+1\right){x}$ |
7.1-a4 |
7.1-a |
$6$ |
$8$ |
4.4.8069.1 |
$4$ |
$[4, 0]$ |
7.1 |
\( 7 \) |
\( 7^{2} \) |
$10.23731$ |
$(-a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$64$ |
\( 2 \) |
$1$ |
$4.023565210$ |
1.433346416 |
\( -\frac{903179504444842004658497}{49} a^{3} - \frac{210506064116712141630751}{49} a^{2} + \frac{4256328340089148297820838}{49} a + \frac{732462770570930887499093}{49} \) |
\( \bigl[a^{2} + a - 2\) , \( -a^{3} + a^{2} + 3 a - 3\) , \( 0\) , \( -270 a^{3} - 239 a^{2} + 643 a + 1\) , \( -5079 a^{3} - 5988 a^{2} + 12552 a + 2883\bigr] \) |
${y}^2+\left(a^{2}+a-2\right){x}{y}={x}^{3}+\left(-a^{3}+a^{2}+3a-3\right){x}^{2}+\left(-270a^{3}-239a^{2}+643a+1\right){x}-5079a^{3}-5988a^{2}+12552a+2883$ |
7.1-a5 |
7.1-a |
$6$ |
$8$ |
4.4.8069.1 |
$4$ |
$[4, 0]$ |
7.1 |
\( 7 \) |
\( 7^{2} \) |
$10.23731$ |
$(-a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$16$ |
\( 2 \) |
$1$ |
$16.09426084$ |
1.433346416 |
\( \frac{66871120728005420554207169448257}{49} a^{3} - \frac{78353160738203570395168782951137}{49} a^{2} - \frac{320902051243607226345493982558886}{49} a + \frac{389455774709698612801932562468731}{49} \) |
\( \bigl[a\) , \( a^{3} - 5 a\) , \( a^{3} - 3 a + 1\) , \( 205 a^{3} + 249 a^{2} - 971 a - 1165\) , \( 6904 a^{3} - 925 a^{2} - 32778 a + 6181\bigr] \) |
${y}^2+a{x}{y}+\left(a^{3}-3a+1\right){y}={x}^{3}+\left(a^{3}-5a\right){x}^{2}+\left(205a^{3}+249a^{2}-971a-1165\right){x}+6904a^{3}-925a^{2}-32778a+6181$ |
7.1-a6 |
7.1-a |
$6$ |
$8$ |
4.4.8069.1 |
$4$ |
$[4, 0]$ |
7.1 |
\( 7 \) |
\( 7^{16} \) |
$10.23731$ |
$(-a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$16$ |
\( 2 \) |
$1$ |
$16.09426084$ |
1.433346416 |
\( -\frac{126841224139522267347073}{33232930569601} a^{3} + \frac{406422195572792447137921}{33232930569601} a^{2} - \frac{261621582330064194508800}{33232930569601} a - \frac{57545552119111659197472}{33232930569601} \) |
\( \bigl[a\) , \( a^{3} - 5 a\) , \( a^{3} - 3 a + 1\) , \( 15 a^{3} + 4 a^{2} - 66 a - 15\) , \( 124 a^{3} + 24 a^{2} - 588 a - 100\bigr] \) |
${y}^2+a{x}{y}+\left(a^{3}-3a+1\right){y}={x}^{3}+\left(a^{3}-5a\right){x}^{2}+\left(15a^{3}+4a^{2}-66a-15\right){x}+124a^{3}+24a^{2}-588a-100$ |
7.1-b1 |
7.1-b |
$6$ |
$8$ |
4.4.8069.1 |
$4$ |
$[4, 0]$ |
7.1 |
\( 7 \) |
\( 7^{2} \) |
$10.23731$ |
$(-a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$16$ |
\( 2 \) |
$7.272519092$ |
$0.719059987$ |
1.862902449 |
\( \frac{66871120728005420554207169448257}{49} a^{3} - \frac{78353160738203570395168782951137}{49} a^{2} - \frac{320902051243607226345493982558886}{49} a + \frac{389455774709698612801932562468731}{49} \) |
\( \bigl[a^{3} + a^{2} - 4 a - 1\) , \( -a^{2} + 2\) , \( 0\) , \( -195 a^{3} + 225 a^{2} + 930 a - 1209\) , \( -3045 a^{3} + 3507 a^{2} + 14508 a - 17887\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-4a-1\right){x}{y}={x}^{3}+\left(-a^{2}+2\right){x}^{2}+\left(-195a^{3}+225a^{2}+930a-1209\right){x}-3045a^{3}+3507a^{2}+14508a-17887$ |
7.1-b2 |
7.1-b |
$6$ |
$8$ |
4.4.8069.1 |
$4$ |
$[4, 0]$ |
7.1 |
\( 7 \) |
\( 7^{4} \) |
$10.23731$ |
$(-a-1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$4$ |
\( 2^{2} \) |
$3.636259546$ |
$11.50495980$ |
1.862902449 |
\( \frac{1090950826513421409}{2401} a^{3} - \frac{1278489943416427617}{2401} a^{2} - \frac{5235283189978195968}{2401} a + \frac{6354702898520183792}{2401} \) |
\( \bigl[a^{3} + a^{2} - 4 a - 1\) , \( -a^{2} + 2\) , \( 0\) , \( -5 a^{3} + 5 a^{2} - 84\) , \( -34 a^{3} + 10 a^{2} + 24 a - 355\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-4a-1\right){x}{y}={x}^{3}+\left(-a^{2}+2\right){x}^{2}+\left(-5a^{3}+5a^{2}-84\right){x}-34a^{3}+10a^{2}+24a-355$ |
7.1-b3 |
7.1-b |
$6$ |
$8$ |
4.4.8069.1 |
$4$ |
$[4, 0]$ |
7.1 |
\( 7 \) |
\( 7^{16} \) |
$10.23731$ |
$(-a-1)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$0.909064886$ |
$46.01983922$ |
1.862902449 |
\( -\frac{126841224139522267347073}{33232930569601} a^{3} + \frac{406422195572792447137921}{33232930569601} a^{2} - \frac{261621582330064194508800}{33232930569601} a - \frac{57545552119111659197472}{33232930569601} \) |
\( \bigl[a^{3} + a^{2} - 4 a - 1\) , \( -a^{2} + 2\) , \( 0\) , \( 5 a^{3} - 5 a^{2} - 4\) , \( -12 a^{3} + 36 a^{2} - 24 a - 13\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-4a-1\right){x}{y}={x}^{3}+\left(-a^{2}+2\right){x}^{2}+\left(5a^{3}-5a^{2}-4\right){x}-12a^{3}+36a^{2}-24a-13$ |
7.1-b4 |
7.1-b |
$6$ |
$8$ |
4.4.8069.1 |
$4$ |
$[4, 0]$ |
7.1 |
\( 7 \) |
\( 7^{8} \) |
$10.23731$ |
$(-a-1)$ |
$1$ |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1.818129773$ |
$184.0793568$ |
1.862902449 |
\( \frac{47042604735051}{5764801} a^{3} - \frac{55967329253427}{5764801} a^{2} - \frac{226247884349976}{5764801} a + \frac{278958254354747}{5764801} \) |
\( \bigl[a^{3} + a^{2} - 4 a - 1\) , \( -a^{2} + 2\) , \( 0\) , \( -4\) , \( -a^{3} + a^{2} - 8\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-4a-1\right){x}{y}={x}^{3}+\left(-a^{2}+2\right){x}^{2}-4{x}-a^{3}+a^{2}-8$ |
7.1-b5 |
7.1-b |
$6$ |
$8$ |
4.4.8069.1 |
$4$ |
$[4, 0]$ |
7.1 |
\( 7 \) |
\( 7^{4} \) |
$10.23731$ |
$(-a-1)$ |
$1$ |
$\Z/8\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.909064886$ |
$736.3174275$ |
1.862902449 |
\( \frac{1479733}{2401} a^{3} + \frac{8160419}{2401} a^{2} + \frac{3837720}{2401} a - \frac{15624676}{2401} \) |
\( \bigl[a^{3} + a^{2} - 4 a - 1\) , \( -a^{2} + 2\) , \( 0\) , \( 1\) , \( 0\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-4a-1\right){x}{y}={x}^{3}+\left(-a^{2}+2\right){x}^{2}+{x}$ |
7.1-b6 |
7.1-b |
$6$ |
$8$ |
4.4.8069.1 |
$4$ |
$[4, 0]$ |
7.1 |
\( 7 \) |
\( 7^{2} \) |
$10.23731$ |
$(-a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$16$ |
\( 2 \) |
$7.272519092$ |
$0.719059987$ |
1.862902449 |
\( -\frac{903179504444842004658497}{49} a^{3} - \frac{210506064116712141630751}{49} a^{2} + \frac{4256328340089148297820838}{49} a + \frac{732462770570930887499093}{49} \) |
\( \bigl[a^{3} - 4 a + 2\) , \( a^{3} + a^{2} - 3 a - 2\) , \( a^{2} + a - 2\) , \( -463 a^{3} - 31 a^{2} + 763 a - 28\) , \( -8458 a^{3} - 9079 a^{2} + 21525 a + 3119\bigr] \) |
${y}^2+\left(a^{3}-4a+2\right){x}{y}+\left(a^{2}+a-2\right){y}={x}^{3}+\left(a^{3}+a^{2}-3a-2\right){x}^{2}+\left(-463a^{3}-31a^{2}+763a-28\right){x}-8458a^{3}-9079a^{2}+21525a+3119$ |
16.1-a1 |
16.1-a |
$2$ |
$2$ |
4.4.8069.1 |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( - 2^{4} \) |
$11.35177$ |
$(2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 1 \) |
$0.119941158$ |
$514.3903601$ |
2.747332318 |
\( -\frac{20486535511999}{2} a^{3} + \frac{65642625237009}{2} a^{2} - 21127692026009 a - \frac{9294418278973}{2} \) |
\( \bigl[a^{3} + a^{2} - 4 a - 2\) , \( -a^{3} - a^{2} + 3 a + 3\) , \( a^{3} - 3 a + 1\) , \( -7 a^{3} - 11 a^{2} + 44 a + 11\) , \( -69 a^{3} + a^{2} + 288 a + 49\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-4a-2\right){x}{y}+\left(a^{3}-3a+1\right){y}={x}^{3}+\left(-a^{3}-a^{2}+3a+3\right){x}^{2}+\left(-7a^{3}-11a^{2}+44a+11\right){x}-69a^{3}+a^{2}+288a+49$ |
16.1-a2 |
16.1-a |
$2$ |
$2$ |
4.4.8069.1 |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{8} \) |
$11.35177$ |
$(2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.059970579$ |
$2057.561440$ |
2.747332318 |
\( \frac{2313553}{4} a^{3} - \frac{7441197}{4} a^{2} + 1211326 a + 265361 \) |
\( \bigl[a^{2} + a - 2\) , \( a^{3} - 4 a + 2\) , \( a^{3} + a^{2} - 4 a - 1\) , \( 7 a^{2} + 4 a - 26\) , \( 16 a^{3} - 19 a^{2} - 72 a + 104\bigr] \) |
${y}^2+\left(a^{2}+a-2\right){x}{y}+\left(a^{3}+a^{2}-4a-1\right){y}={x}^{3}+\left(a^{3}-4a+2\right){x}^{2}+\left(7a^{2}+4a-26\right){x}+16a^{3}-19a^{2}-72a+104$ |
16.1-b1 |
16.1-b |
$2$ |
$2$ |
4.4.8069.1 |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( - 2^{4} \) |
$11.35177$ |
$(2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 1 \) |
$1.171712054$ |
$44.27984755$ |
2.310346656 |
\( -\frac{20486535511999}{2} a^{3} + \frac{65642625237009}{2} a^{2} - 21127692026009 a - \frac{9294418278973}{2} \) |
\( \bigl[a^{2} - 3\) , \( -a^{3} - a^{2} + 3 a + 1\) , \( a^{2} - 3\) , \( -96 a^{3} - 22 a^{2} + 456 a + 76\) , \( -3964 a^{3} - 925 a^{2} + 18682 a + 3213\bigr] \) |
${y}^2+\left(a^{2}-3\right){x}{y}+\left(a^{2}-3\right){y}={x}^{3}+\left(-a^{3}-a^{2}+3a+1\right){x}^{2}+\left(-96a^{3}-22a^{2}+456a+76\right){x}-3964a^{3}-925a^{2}+18682a+3213$ |
16.1-b2 |
16.1-b |
$2$ |
$2$ |
4.4.8069.1 |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{8} \) |
$11.35177$ |
$(2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.585856027$ |
$177.1193902$ |
2.310346656 |
\( \frac{2313553}{4} a^{3} - \frac{7441197}{4} a^{2} + 1211326 a + 265361 \) |
\( \bigl[a^{3} - 4 a + 2\) , \( -a^{2} - a + 3\) , \( a^{3} + a^{2} - 4 a - 2\) , \( -5 a^{3} + 5 a^{2} + 23 a - 29\) , \( -47 a^{3} + 55 a^{2} + 225 a - 276\bigr] \) |
${y}^2+\left(a^{3}-4a+2\right){x}{y}+\left(a^{3}+a^{2}-4a-2\right){y}={x}^{3}+\left(-a^{2}-a+3\right){x}^{2}+\left(-5a^{3}+5a^{2}+23a-29\right){x}-47a^{3}+55a^{2}+225a-276$ |
17.2-a1 |
17.2-a |
$2$ |
$2$ |
4.4.8069.1 |
$4$ |
$[4, 0]$ |
17.2 |
\( 17 \) |
\( 17^{8} \) |
$11.43812$ |
$(a^3-5a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 2 \) |
$1$ |
$84.87565438$ |
1.889745298 |
\( \frac{118616089394579979749}{6975757441} a^{3} - \frac{138982947419741442893}{6975757441} a^{2} - \frac{33483325262751701604}{410338673} a + \frac{690817225520342777793}{6975757441} \) |
\( \bigl[a^{2} + a - 3\) , \( -a^{3} + a^{2} + 3 a - 3\) , \( a^{2} + a - 3\) , \( -6 a^{3} + 2 a^{2} + 30 a - 21\) , \( 13 a^{3} - 16 a^{2} - 44 a + 36\bigr] \) |
${y}^2+\left(a^{2}+a-3\right){x}{y}+\left(a^{2}+a-3\right){y}={x}^{3}+\left(-a^{3}+a^{2}+3a-3\right){x}^{2}+\left(-6a^{3}+2a^{2}+30a-21\right){x}+13a^{3}-16a^{2}-44a+36$ |
17.2-a2 |
17.2-a |
$2$ |
$2$ |
4.4.8069.1 |
$4$ |
$[4, 0]$ |
17.2 |
\( 17 \) |
\( 17^{4} \) |
$11.43812$ |
$(a^3-5a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$339.5026175$ |
1.889745298 |
\( \frac{19928724333}{83521} a^{3} + \frac{32687561571}{83521} a^{2} - \frac{2414479368}{4913} a - \frac{35845946212}{83521} \) |
\( \bigl[a^{2} + a - 3\) , \( -a^{3} + a^{2} + 3 a - 3\) , \( a^{2} + a - 3\) , \( -a^{3} + 2 a^{2} - 6\) , \( a^{2} - 3 a - 2\bigr] \) |
${y}^2+\left(a^{2}+a-3\right){x}{y}+\left(a^{2}+a-3\right){y}={x}^{3}+\left(-a^{3}+a^{2}+3a-3\right){x}^{2}+\left(-a^{3}+2a^{2}-6\right){x}+a^{2}-3a-2$ |
17.2-b1 |
17.2-b |
$4$ |
$6$ |
4.4.8069.1 |
$4$ |
$[4, 0]$ |
17.2 |
\( 17 \) |
\( 17^{3} \) |
$11.43812$ |
$(a^3-5a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$36$ |
\( 1 \) |
$1$ |
$16.00555019$ |
1.603626629 |
\( \frac{608317232029322053436309872924}{4913} a^{3} + \frac{695192015586732468129853495461}{4913} a^{2} - \frac{91289447930238578250453833931}{289} a - \frac{283887402763415859894268217441}{4913} \) |
\( \bigl[a^{2} + a - 3\) , \( a - 1\) , \( a^{3} - 3 a + 2\) , \( 2646 a^{3} + 642 a^{2} - 12468 a - 2269\) , \( 727 a^{3} + 142 a^{2} - 3431 a - 458\bigr] \) |
${y}^2+\left(a^{2}+a-3\right){x}{y}+\left(a^{3}-3a+2\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(2646a^{3}+642a^{2}-12468a-2269\right){x}+727a^{3}+142a^{2}-3431a-458$ |
17.2-b2 |
17.2-b |
$4$ |
$6$ |
4.4.8069.1 |
$4$ |
$[4, 0]$ |
17.2 |
\( 17 \) |
\( 17^{6} \) |
$11.43812$ |
$(a^3-5a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$9$ |
\( 2 \) |
$1$ |
$32.01110039$ |
1.603626629 |
\( \frac{88777362057426946523}{24137569} a^{3} + \frac{101455804469795506868}{24137569} a^{2} - \frac{13322713579046234527}{1419857} a - \frac{41430314735614644056}{24137569} \) |
\( \bigl[a\) , \( a^{3} + a^{2} - 5 a - 1\) , \( a\) , \( -36 a^{3} - 35 a^{2} + 84 a + 20\) , \( -288 a^{3} - 304 a^{2} + 706 a + 130\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(a^{3}+a^{2}-5a-1\right){x}^{2}+\left(-36a^{3}-35a^{2}+84a+20\right){x}-288a^{3}-304a^{2}+706a+130$ |
17.2-b3 |
17.2-b |
$4$ |
$6$ |
4.4.8069.1 |
$4$ |
$[4, 0]$ |
17.2 |
\( 17 \) |
\( 17 \) |
$11.43812$ |
$(a^3-5a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$4$ |
\( 1 \) |
$1$ |
$144.0499517$ |
1.603626629 |
\( \frac{1426063358}{17} a^{3} + \frac{1999831039}{17} a^{2} - 150601727 a - \frac{3329290}{17} \) |
\( \bigl[a^{3} - 3 a + 1\) , \( -a^{3} + 3 a\) , \( a^{2} - 3\) , \( 10 a^{3} + a^{2} - 60 a - 14\) , \( -52 a^{3} - 20 a^{2} + 219 a + 30\bigr] \) |
${y}^2+\left(a^{3}-3a+1\right){x}{y}+\left(a^{2}-3\right){y}={x}^{3}+\left(-a^{3}+3a\right){x}^{2}+\left(10a^{3}+a^{2}-60a-14\right){x}-52a^{3}-20a^{2}+219a+30$ |
17.2-b4 |
17.2-b |
$4$ |
$6$ |
4.4.8069.1 |
$4$ |
$[4, 0]$ |
17.2 |
\( 17 \) |
\( 17^{2} \) |
$11.43812$ |
$(a^3-5a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$1$ |
$288.0999035$ |
1.603626629 |
\( -\frac{1645}{289} a^{3} + \frac{1182998}{289} a^{2} + \frac{140071}{17} a - \frac{969813}{289} \) |
\( \bigl[a^{3} - 3 a + 1\) , \( -a^{3} + 3 a\) , \( a^{2} - 3\) , \( a^{2} - 5 a + 1\) , \( -a^{3} + a^{2} + 2 a - 2\bigr] \) |
${y}^2+\left(a^{3}-3a+1\right){x}{y}+\left(a^{2}-3\right){y}={x}^{3}+\left(-a^{3}+3a\right){x}^{2}+\left(a^{2}-5a+1\right){x}-a^{3}+a^{2}+2a-2$ |
17.2-c1 |
17.2-c |
$4$ |
$6$ |
4.4.8069.1 |
$4$ |
$[4, 0]$ |
17.2 |
\( 17 \) |
\( 17 \) |
$11.43812$ |
$(a^3-5a+2)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$4$ |
\( 1 \) |
$1$ |
$966.0995802$ |
1.195004460 |
\( \frac{1426063358}{17} a^{3} + \frac{1999831039}{17} a^{2} - 150601727 a - \frac{3329290}{17} \) |
\( \bigl[a^{3} + a^{2} - 3 a - 2\) , \( 0\) , \( a^{3} + a^{2} - 3 a - 2\) , \( -4 a^{3} - 4 a^{2} + 12 a - 7\) , \( -27 a^{3} - 32 a^{2} + 65 a + 19\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-3a-2\right){x}{y}+\left(a^{3}+a^{2}-3a-2\right){y}={x}^{3}+\left(-4a^{3}-4a^{2}+12a-7\right){x}-27a^{3}-32a^{2}+65a+19$ |
17.2-c2 |
17.2-c |
$4$ |
$6$ |
4.4.8069.1 |
$4$ |
$[4, 0]$ |
17.2 |
\( 17 \) |
\( 17^{2} \) |
$11.43812$ |
$(a^3-5a+2)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2 \) |
$1$ |
$1932.199160$ |
1.195004460 |
\( -\frac{1645}{289} a^{3} + \frac{1182998}{289} a^{2} + \frac{140071}{17} a - \frac{969813}{289} \) |
\( \bigl[a^{3} + a^{2} - 3 a - 2\) , \( 0\) , \( a^{3} + a^{2} - 3 a - 2\) , \( a^{3} + a^{2} - 3 a - 2\) , \( a^{3} + a^{2} - 3 a - 1\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-3a-2\right){x}{y}+\left(a^{3}+a^{2}-3a-2\right){y}={x}^{3}+\left(a^{3}+a^{2}-3a-2\right){x}+a^{3}+a^{2}-3a-1$ |
17.2-c3 |
17.2-c |
$4$ |
$6$ |
4.4.8069.1 |
$4$ |
$[4, 0]$ |
17.2 |
\( 17 \) |
\( 17^{6} \) |
$11.43812$ |
$(a^3-5a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$9$ |
\( 2 \) |
$1$ |
$23.85431062$ |
1.195004460 |
\( \frac{88777362057426946523}{24137569} a^{3} + \frac{101455804469795506868}{24137569} a^{2} - \frac{13322713579046234527}{1419857} a - \frac{41430314735614644056}{24137569} \) |
\( \bigl[a^{3} + a^{2} - 3 a - 2\) , \( 0\) , \( a^{3} + a^{2} - 3 a - 2\) , \( -24 a^{3} - 29 a^{2} + 57 a + 13\) , \( -236 a^{3} - 271 a^{2} + 600 a + 109\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-3a-2\right){x}{y}+\left(a^{3}+a^{2}-3a-2\right){y}={x}^{3}+\left(-24a^{3}-29a^{2}+57a+13\right){x}-236a^{3}-271a^{2}+600a+109$ |
17.2-c4 |
17.2-c |
$4$ |
$6$ |
4.4.8069.1 |
$4$ |
$[4, 0]$ |
17.2 |
\( 17 \) |
\( 17^{3} \) |
$11.43812$ |
$(a^3-5a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$36$ |
\( 1 \) |
$1$ |
$11.92715531$ |
1.195004460 |
\( \frac{608317232029322053436309872924}{4913} a^{3} + \frac{695192015586732468129853495461}{4913} a^{2} - \frac{91289447930238578250453833931}{289} a - \frac{283887402763415859894268217441}{4913} \) |
\( \bigl[1\) , \( -a^{2} - a + 4\) , \( a^{3} + a^{2} - 4 a - 1\) , \( 121 a^{3} + 56 a^{2} - 553 a - 264\) , \( 97 a^{2} + 46 a - 550\bigr] \) |
${y}^2+{x}{y}+\left(a^{3}+a^{2}-4a-1\right){y}={x}^{3}+\left(-a^{2}-a+4\right){x}^{2}+\left(121a^{3}+56a^{2}-553a-264\right){x}+97a^{2}+46a-550$ |
17.2-d1 |
17.2-d |
$2$ |
$2$ |
4.4.8069.1 |
$4$ |
$[4, 0]$ |
17.2 |
\( 17 \) |
\( 17^{4} \) |
$11.43812$ |
$(a^3-5a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$116.7709092$ |
0.649972239 |
\( \frac{19928724333}{83521} a^{3} + \frac{32687561571}{83521} a^{2} - \frac{2414479368}{4913} a - \frac{35845946212}{83521} \) |
\( \bigl[a^{3} - 3 a + 2\) , \( -a^{3} - a^{2} + 4 a + 3\) , \( a^{3} + a^{2} - 4 a - 2\) , \( 19 a^{3} + 3 a^{2} - 91 a - 10\) , \( 95 a^{3} + 22 a^{2} - 448 a - 77\bigr] \) |
${y}^2+\left(a^{3}-3a+2\right){x}{y}+\left(a^{3}+a^{2}-4a-2\right){y}={x}^{3}+\left(-a^{3}-a^{2}+4a+3\right){x}^{2}+\left(19a^{3}+3a^{2}-91a-10\right){x}+95a^{3}+22a^{2}-448a-77$ |
17.2-d2 |
17.2-d |
$2$ |
$2$ |
4.4.8069.1 |
$4$ |
$[4, 0]$ |
17.2 |
\( 17 \) |
\( 17^{8} \) |
$11.43812$ |
$(a^3-5a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 2 \) |
$1$ |
$29.19272730$ |
0.649972239 |
\( \frac{118616089394579979749}{6975757441} a^{3} - \frac{138982947419741442893}{6975757441} a^{2} - \frac{33483325262751701604}{410338673} a + \frac{690817225520342777793}{6975757441} \) |
\( \bigl[a^{3} - 3 a + 2\) , \( -a^{3} - a^{2} + 4 a + 3\) , \( a^{3} + a^{2} - 4 a - 2\) , \( -36 a^{3} - 7 a^{2} + 169 a + 20\) , \( 288 a^{3} + 76 a^{2} - 1357 a - 276\bigr] \) |
${y}^2+\left(a^{3}-3a+2\right){x}{y}+\left(a^{3}+a^{2}-4a-2\right){y}={x}^{3}+\left(-a^{3}-a^{2}+4a+3\right){x}^{2}+\left(-36a^{3}-7a^{2}+169a+20\right){x}+288a^{3}+76a^{2}-1357a-276$ |
19.1-a1 |
19.1-a |
$4$ |
$10$ |
4.4.8069.1 |
$4$ |
$[4, 0]$ |
19.1 |
\( 19 \) |
\( 19^{5} \) |
$11.59825$ |
$(a^2+a-4)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B.4.2 |
$100$ |
\( 1 \) |
$1$ |
$8.546425211$ |
2.378562937 |
\( -\frac{16075947372441447683071219604597}{2476099} a^{3} - \frac{3746856964444343086453903380667}{2476099} a^{2} + \frac{75759591575353944746601364499055}{2476099} a + \frac{13037311952911337243612323131579}{2476099} \) |
\( \bigl[a^{3} + a^{2} - 3 a - 2\) , \( a^{2} + a - 3\) , \( a^{2} - 3\) , \( -416 a^{3} + 73 a^{2} + 1594 a - 1363\) , \( -4 a^{3} - 6042 a^{2} - 5981 a + 16343\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-3a-2\right){x}{y}+\left(a^{2}-3\right){y}={x}^{3}+\left(a^{2}+a-3\right){x}^{2}+\left(-416a^{3}+73a^{2}+1594a-1363\right){x}-4a^{3}-6042a^{2}-5981a+16343$ |
19.1-a2 |
19.1-a |
$4$ |
$10$ |
4.4.8069.1 |
$4$ |
$[4, 0]$ |
19.1 |
\( 19 \) |
\( 19 \) |
$11.59825$ |
$(a^2+a-4)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B.4.1 |
$4$ |
\( 1 \) |
$1$ |
$213.6606302$ |
2.378562937 |
\( \frac{1121092698094}{19} a^{3} - \frac{61710073984}{19} a^{2} - \frac{4164205346487}{19} a + \frac{3126720543036}{19} \) |
\( \bigl[a\) , \( -a^{3} - a^{2} + 4 a + 3\) , \( 0\) , \( 4 a^{3} - 16 a - 8\) , \( 22 a^{3} + 6 a^{2} - 98 a - 29\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-a^{3}-a^{2}+4a+3\right){x}^{2}+\left(4a^{3}-16a-8\right){x}+22a^{3}+6a^{2}-98a-29$ |
19.1-a3 |
19.1-a |
$4$ |
$10$ |
4.4.8069.1 |
$4$ |
$[4, 0]$ |
19.1 |
\( 19 \) |
\( 19^{2} \) |
$11.59825$ |
$(a^2+a-4)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B.4.1 |
$1$ |
\( 2 \) |
$1$ |
$427.3212605$ |
2.378562937 |
\( -\frac{4504636}{361} a^{3} + \frac{51759581}{361} a^{2} + \frac{66818656}{361} a - \frac{151977092}{361} \) |
\( \bigl[a\) , \( -a^{3} - a^{2} + 4 a + 3\) , \( 0\) , \( -a^{3} + 4 a + 2\) , \( 0\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-a^{3}-a^{2}+4a+3\right){x}^{2}+\left(-a^{3}+4a+2\right){x}$ |
19.1-a4 |
19.1-a |
$4$ |
$10$ |
4.4.8069.1 |
$4$ |
$[4, 0]$ |
19.1 |
\( 19 \) |
\( 19^{10} \) |
$11.59825$ |
$(a^2+a-4)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B.4.2 |
$25$ |
\( 2 \) |
$1$ |
$17.09285042$ |
2.378562937 |
\( -\frac{7453708100651023724731227}{6131066257801} a^{3} - \frac{1737250893512074261087546}{6131066257801} a^{2} + \frac{35126388668209027651898288}{6131066257801} a + \frac{6044827780477046155354082}{6131066257801} \) |
\( \bigl[1\) , \( -a^{3} + a^{2} + 4 a - 3\) , \( a^{2} + a - 2\) , \( 659 a^{3} - 621 a^{2} - 3152 a + 3119\) , \( 10968 a^{3} - 11477 a^{2} - 52551 a + 57385\bigr] \) |
${y}^2+{x}{y}+\left(a^{2}+a-2\right){y}={x}^{3}+\left(-a^{3}+a^{2}+4a-3\right){x}^{2}+\left(659a^{3}-621a^{2}-3152a+3119\right){x}+10968a^{3}-11477a^{2}-52551a+57385$ |
19.1-b1 |
19.1-b |
$2$ |
$2$ |
4.4.8069.1 |
$4$ |
$[4, 0]$ |
19.1 |
\( 19 \) |
\( 19^{2} \) |
$11.59825$ |
$(a^2+a-4)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$402.9403342$ |
2.242853406 |
\( \frac{921050783480}{361} a^{3} + \frac{1052547388417}{361} a^{2} - \frac{2349627001920}{361} a - \frac{429808776872}{361} \) |
\( \bigl[a^{3} + a^{2} - 4 a - 2\) , \( -a - 1\) , \( a\) , \( -11 a^{2} - 8 a + 29\) , \( -14 a^{3} - 5 a^{2} + 45 a - 22\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-4a-2\right){x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-11a^{2}-8a+29\right){x}-14a^{3}-5a^{2}+45a-22$ |
19.1-b2 |
19.1-b |
$2$ |
$2$ |
4.4.8069.1 |
$4$ |
$[4, 0]$ |
19.1 |
\( 19 \) |
\( 19^{4} \) |
$11.59825$ |
$(a^2+a-4)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$402.9403342$ |
2.242853406 |
\( -\frac{10354365223022612}{130321} a^{3} + \frac{21330013069525904}{130321} a^{2} + \frac{1995387782333409}{130321} a - \frac{338656947464676}{130321} \) |
\( \bigl[a^{2} - 2\) , \( -a^{3} - a^{2} + 4 a + 2\) , \( a^{3} + a^{2} - 4 a - 1\) , \( 32 a^{3} + 19 a^{2} - 155 a - 95\) , \( -218 a^{3} - 25 a^{2} + 1023 a + 41\bigr] \) |
${y}^2+\left(a^{2}-2\right){x}{y}+\left(a^{3}+a^{2}-4a-1\right){y}={x}^{3}+\left(-a^{3}-a^{2}+4a+2\right){x}^{2}+\left(32a^{3}+19a^{2}-155a-95\right){x}-218a^{3}-25a^{2}+1023a+41$ |
19.1-c1 |
19.1-c |
$4$ |
$6$ |
4.4.8069.1 |
$4$ |
$[4, 0]$ |
19.1 |
\( 19 \) |
\( 19^{3} \) |
$11.59825$ |
$(a^2+a-4)$ |
$0 \le r \le 1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
|
\( 3 \) |
$1$ |
$7.687728166$ |
2.402020858 |
\( \frac{22194249947282956334538362641}{6859} a^{3} - \frac{26005091804226993659513655139}{6859} a^{2} - \frac{106506071026766490646787756502}{6859} a + \frac{129258769902742562322216519975}{6859} \) |
\( \bigl[a^{3} + a^{2} - 3 a - 2\) , \( -a^{3} + 5 a\) , \( 1\) , \( 85 a^{3} + 459 a^{2} - 366 a - 2135\) , \( -10862 a^{3} + 5071 a^{2} + 51661 a - 27097\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-3a-2\right){x}{y}+{y}={x}^{3}+\left(-a^{3}+5a\right){x}^{2}+\left(85a^{3}+459a^{2}-366a-2135\right){x}-10862a^{3}+5071a^{2}+51661a-27097$ |
19.1-c2 |
19.1-c |
$4$ |
$6$ |
4.4.8069.1 |
$4$ |
$[4, 0]$ |
19.1 |
\( 19 \) |
\( 19^{6} \) |
$11.59825$ |
$(a^2+a-4)$ |
$0 \le r \le 1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
|
\( 2 \cdot 3 \) |
$1$ |
$7.687728166$ |
2.402020858 |
\( -\frac{32920179219067742335}{47045881} a^{3} + \frac{38573217360313423603}{47045881} a^{2} + \frac{157978303983605228544}{47045881} a - \frac{191727709378707559964}{47045881} \) |
\( \bigl[a^{3} + a^{2} - 3 a - 2\) , \( -a^{3} + 5 a\) , \( 1\) , \( 40 a^{3} + 39 a^{2} - 181 a - 160\) , \( 261 a^{3} + 179 a^{2} - 1219 a - 762\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-3a-2\right){x}{y}+{y}={x}^{3}+\left(-a^{3}+5a\right){x}^{2}+\left(40a^{3}+39a^{2}-181a-160\right){x}+261a^{3}+179a^{2}-1219a-762$ |
19.1-c3 |
19.1-c |
$4$ |
$6$ |
4.4.8069.1 |
$4$ |
$[4, 0]$ |
19.1 |
\( 19 \) |
\( 19 \) |
$11.59825$ |
$(a^2+a-4)$ |
$0 \le r \le 1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
|
\( 1 \) |
$1$ |
$622.7059815$ |
2.402020858 |
\( -\frac{140184437194705}{19} a^{3} - \frac{32674219622507}{19} a^{2} + \frac{660633828065334}{19} a + \frac{113692420421896}{19} \) |
\( \bigl[a^{3} + a^{2} - 4 a - 1\) , \( a^{3} + a^{2} - 3 a - 1\) , \( a^{3} + a^{2} - 3 a - 1\) , \( -a^{3} + 11 a^{2} + 19 a - 45\) , \( -13 a^{3} + 30 a^{2} + 74 a - 109\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-4a-1\right){x}{y}+\left(a^{3}+a^{2}-3a-1\right){y}={x}^{3}+\left(a^{3}+a^{2}-3a-1\right){x}^{2}+\left(-a^{3}+11a^{2}+19a-45\right){x}-13a^{3}+30a^{2}+74a-109$ |
19.1-c4 |
19.1-c |
$4$ |
$6$ |
4.4.8069.1 |
$4$ |
$[4, 0]$ |
19.1 |
\( 19 \) |
\( 19^{2} \) |
$11.59825$ |
$(a^2+a-4)$ |
$0 \le r \le 1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
|
\( 2 \) |
$1$ |
$622.7059815$ |
2.402020858 |
\( -\frac{468732461}{361} a^{3} - \frac{107902627}{361} a^{2} + \frac{2209071420}{361} a + \frac{374364855}{361} \) |
\( \bigl[a^{3} + a^{2} - 4 a - 1\) , \( a^{3} + a^{2} - 3 a - 1\) , \( a^{3} + a^{2} - 3 a - 1\) , \( 4 a^{3} + 6 a^{2} - 11 a - 5\) , \( 7 a^{3} + 9 a^{2} - 18 a - 5\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-4a-1\right){x}{y}+\left(a^{3}+a^{2}-3a-1\right){y}={x}^{3}+\left(a^{3}+a^{2}-3a-1\right){x}^{2}+\left(4a^{3}+6a^{2}-11a-5\right){x}+7a^{3}+9a^{2}-18a-5$ |
19.1-d1 |
19.1-d |
$4$ |
$6$ |
4.4.8069.1 |
$4$ |
$[4, 0]$ |
19.1 |
\( 19 \) |
\( 19^{3} \) |
$11.59825$ |
$(a^2+a-4)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 3 \) |
$0.422148619$ |
$189.7385750$ |
2.675053088 |
\( \frac{22194249947282956334538362641}{6859} a^{3} - \frac{26005091804226993659513655139}{6859} a^{2} - \frac{106506071026766490646787756502}{6859} a + \frac{129258769902742562322216519975}{6859} \) |
\( \bigl[a\) , \( a^{3} + a^{2} - 5 a - 3\) , \( a\) , \( -406 a^{3} + 495 a^{2} + 1969 a - 2505\) , \( 8935 a^{3} - 10618 a^{2} - 42945 a + 52855\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(a^{3}+a^{2}-5a-3\right){x}^{2}+\left(-406a^{3}+495a^{2}+1969a-2505\right){x}+8935a^{3}-10618a^{2}-42945a+52855$ |
19.1-d2 |
19.1-d |
$4$ |
$6$ |
4.4.8069.1 |
$4$ |
$[4, 0]$ |
19.1 |
\( 19 \) |
\( 19^{6} \) |
$11.59825$ |
$(a^2+a-4)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \cdot 3 \) |
$0.211074309$ |
$189.7385750$ |
2.675053088 |
\( -\frac{32920179219067742335}{47045881} a^{3} + \frac{38573217360313423603}{47045881} a^{2} + \frac{157978303983605228544}{47045881} a - \frac{191727709378707559964}{47045881} \) |
\( \bigl[a\) , \( a^{3} + a^{2} - 5 a - 3\) , \( a\) , \( -26 a^{3} + 30 a^{2} + 124 a - 155\) , \( 153 a^{3} - 184 a^{2} - 737 a + 908\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(a^{3}+a^{2}-5a-3\right){x}^{2}+\left(-26a^{3}+30a^{2}+124a-155\right){x}+153a^{3}-184a^{2}-737a+908$ |
19.1-d3 |
19.1-d |
$4$ |
$6$ |
4.4.8069.1 |
$4$ |
$[4, 0]$ |
19.1 |
\( 19 \) |
\( 19 \) |
$11.59825$ |
$(a^2+a-4)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 1 \) |
$0.140716206$ |
$1707.647175$ |
2.675053088 |
\( -\frac{140184437194705}{19} a^{3} - \frac{32674219622507}{19} a^{2} + \frac{660633828065334}{19} a + \frac{113692420421896}{19} \) |
\( \bigl[a\) , \( a^{3} + a^{2} - 5 a - 3\) , \( a\) , \( 14 a^{3} + 10 a^{2} - 66 a - 45\) , \( -101 a^{3} - 46 a^{2} + 475 a + 186\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(a^{3}+a^{2}-5a-3\right){x}^{2}+\left(14a^{3}+10a^{2}-66a-45\right){x}-101a^{3}-46a^{2}+475a+186$ |
19.1-d4 |
19.1-d |
$4$ |
$6$ |
4.4.8069.1 |
$4$ |
$[4, 0]$ |
19.1 |
\( 19 \) |
\( 19^{2} \) |
$11.59825$ |
$(a^2+a-4)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$0.070358103$ |
$1707.647175$ |
2.675053088 |
\( -\frac{468732461}{361} a^{3} - \frac{107902627}{361} a^{2} + \frac{2209071420}{361} a + \frac{374364855}{361} \) |
\( \bigl[a\) , \( a^{3} + a^{2} - 5 a - 3\) , \( a\) , \( -a^{3} + 4 a\) , \( -2 a^{3} - a^{2} + 9 a + 4\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(a^{3}+a^{2}-5a-3\right){x}^{2}+\left(-a^{3}+4a\right){x}-2a^{3}-a^{2}+9a+4$ |
19.1-e1 |
19.1-e |
$2$ |
$2$ |
4.4.8069.1 |
$4$ |
$[4, 0]$ |
19.1 |
\( 19 \) |
\( 19^{4} \) |
$11.59825$ |
$(a^2+a-4)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$99.74404697$ |
0.555197026 |
\( -\frac{10354365223022612}{130321} a^{3} + \frac{21330013069525904}{130321} a^{2} + \frac{1995387782333409}{130321} a - \frac{338656947464676}{130321} \) |
\( \bigl[a^{2} - 3\) , \( -a^{3} + 5 a - 1\) , \( a^{3} + a^{2} - 3 a - 1\) , \( -16 a^{3} + 12 a^{2} + 72 a - 84\) , \( 11 a^{3} - 32 a^{2} - 66 a + 111\bigr] \) |
${y}^2+\left(a^{2}-3\right){x}{y}+\left(a^{3}+a^{2}-3a-1\right){y}={x}^{3}+\left(-a^{3}+5a-1\right){x}^{2}+\left(-16a^{3}+12a^{2}+72a-84\right){x}+11a^{3}-32a^{2}-66a+111$ |
19.1-e2 |
19.1-e |
$2$ |
$2$ |
4.4.8069.1 |
$4$ |
$[4, 0]$ |
19.1 |
\( 19 \) |
\( 19^{2} \) |
$11.59825$ |
$(a^2+a-4)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$99.74404697$ |
0.555197026 |
\( \frac{921050783480}{361} a^{3} + \frac{1052547388417}{361} a^{2} - \frac{2349627001920}{361} a - \frac{429808776872}{361} \) |
\( \bigl[a^{2} - 3\) , \( -a^{3} + 5 a - 1\) , \( a^{3} + a^{2} - 3 a - 1\) , \( -a^{3} - 8 a^{2} - 3 a + 21\) , \( -5 a^{3} - 12 a^{2} + 7 a + 20\bigr] \) |
${y}^2+\left(a^{2}-3\right){x}{y}+\left(a^{3}+a^{2}-3a-1\right){y}={x}^{3}+\left(-a^{3}+5a-1\right){x}^{2}+\left(-a^{3}-8a^{2}-3a+21\right){x}-5a^{3}-12a^{2}+7a+20$ |
19.1-f1 |
19.1-f |
$4$ |
$10$ |
4.4.8069.1 |
$4$ |
$[4, 0]$ |
19.1 |
\( 19 \) |
\( 19^{2} \) |
$11.59825$ |
$(a^2+a-4)$ |
0 |
$\Z/10\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B.1.1 |
$1$ |
\( 2 \) |
$1$ |
$2054.093936$ |
0.457341317 |
\( -\frac{4504636}{361} a^{3} + \frac{51759581}{361} a^{2} + \frac{66818656}{361} a - \frac{151977092}{361} \) |
\( \bigl[a^{3} + a^{2} - 3 a - 2\) , \( a^{2} - a - 4\) , \( a^{2} - 3\) , \( 14 a^{3} + 5 a^{2} - 64 a - 10\) , \( -18 a^{3} - 2 a^{2} + 88 a + 12\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-3a-2\right){x}{y}+\left(a^{2}-3\right){y}={x}^{3}+\left(a^{2}-a-4\right){x}^{2}+\left(14a^{3}+5a^{2}-64a-10\right){x}-18a^{3}-2a^{2}+88a+12$ |
19.1-f2 |
19.1-f |
$4$ |
$10$ |
4.4.8069.1 |
$4$ |
$[4, 0]$ |
19.1 |
\( 19 \) |
\( 19 \) |
$11.59825$ |
$(a^2+a-4)$ |
0 |
$\Z/10\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B.1.1 |
$4$ |
\( 1 \) |
$1$ |
$1027.046968$ |
0.457341317 |
\( \frac{1121092698094}{19} a^{3} - \frac{61710073984}{19} a^{2} - \frac{4164205346487}{19} a + \frac{3126720543036}{19} \) |
\( \bigl[a^{3} + a^{2} - 4 a - 1\) , \( -a^{3} - a^{2} + 4 a + 1\) , \( a^{3} + a^{2} - 4 a - 1\) , \( 2 a^{3} - 18 a^{2} + 24 a - 5\) , \( -14 a^{3} + 48 a^{2} - 41 a + 2\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-4a-1\right){x}{y}+\left(a^{3}+a^{2}-4a-1\right){y}={x}^{3}+\left(-a^{3}-a^{2}+4a+1\right){x}^{2}+\left(2a^{3}-18a^{2}+24a-5\right){x}-14a^{3}+48a^{2}-41a+2$ |
*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.