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 |
19.1-a1 |
19.1-a |
$1$ |
$1$ |
4.4.5125.1 |
$4$ |
$[4, 0]$ |
19.1 |
\( 19 \) |
\( 19^{2} \) |
$9.24336$ |
$(a^3-2a^2-3a+2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \) |
$1$ |
$57.02749930$ |
1.593189328 |
\( -\frac{97722368}{361} a^{3} - \frac{69640192}{361} a^{2} + \frac{21032960}{19} a + \frac{398553088}{361} \) |
\( \bigl[0\) , \( -a^{3} + 2 a^{2} + 2 a - 3\) , \( a^{2} - a - 4\) , \( a^{3} - 2 a^{2} - 4 a + 8\) , \( -a^{3} + 3 a^{2} + 3 a - 11\bigr] \) |
${y}^2+\left(a^{2}-a-4\right){y}={x}^{3}+\left(-a^{3}+2a^{2}+2a-3\right){x}^{2}+\left(a^{3}-2a^{2}-4a+8\right){x}-a^{3}+3a^{2}+3a-11$ |
19.1-b1 |
19.1-b |
$1$ |
$1$ |
4.4.5125.1 |
$4$ |
$[4, 0]$ |
19.1 |
\( 19 \) |
\( 19^{2} \) |
$9.24336$ |
$(a^3-2a^2-3a+2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \) |
$0.008997105$ |
$2008.533719$ |
2.019412344 |
\( -\frac{97722368}{361} a^{3} - \frac{69640192}{361} a^{2} + \frac{21032960}{19} a + \frac{398553088}{361} \) |
\( \bigl[0\) , \( -a^{3} + 6 a + 4\) , \( a^{2} - 3\) , \( -7 a^{3} - 4 a^{2} + 32 a + 32\) , \( 11 a^{3} + 9 a^{2} - 43 a - 45\bigr] \) |
${y}^2+\left(a^{2}-3\right){y}={x}^{3}+\left(-a^{3}+6a+4\right){x}^{2}+\left(-7a^{3}-4a^{2}+32a+32\right){x}+11a^{3}+9a^{2}-43a-45$ |
19.2-a1 |
19.2-a |
$1$ |
$1$ |
4.4.5125.1 |
$4$ |
$[4, 0]$ |
19.2 |
\( 19 \) |
\( 19^{2} \) |
$9.24336$ |
$(2a^2-a-6)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \) |
$1$ |
$57.02749930$ |
1.593189328 |
\( \frac{97722368}{361} a^{3} - \frac{362807296}{361} a^{2} + \frac{32821248}{361} a + \frac{630816768}{361} \) |
\( \bigl[0\) , \( a^{3} - a^{2} - 3 a\) , \( a^{2} - a - 4\) , \( -a^{3} + a^{2} + 5 a + 3\) , \( a^{3} - 6 a - 6\bigr] \) |
${y}^2+\left(a^{2}-a-4\right){y}={x}^{3}+\left(a^{3}-a^{2}-3a\right){x}^{2}+\left(-a^{3}+a^{2}+5a+3\right){x}+a^{3}-6a-6$ |
19.2-b1 |
19.2-b |
$1$ |
$1$ |
4.4.5125.1 |
$4$ |
$[4, 0]$ |
19.2 |
\( 19 \) |
\( 19^{2} \) |
$9.24336$ |
$(2a^2-a-6)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \) |
$0.008997105$ |
$2008.533719$ |
2.019412344 |
\( \frac{97722368}{361} a^{3} - \frac{362807296}{361} a^{2} + \frac{32821248}{361} a + \frac{630816768}{361} \) |
\( \bigl[0\) , \( a^{3} - 6 a - 3\) , \( a^{2} - 4\) , \( 3 a^{3} - 18 a^{2} + 12 a + 40\) , \( -9 a^{3} + 37 a^{2} - 9 a - 71\bigr] \) |
${y}^2+\left(a^{2}-4\right){y}={x}^{3}+\left(a^{3}-6a-3\right){x}^{2}+\left(3a^{3}-18a^{2}+12a+40\right){x}-9a^{3}+37a^{2}-9a-71$ |
29.1-a1 |
29.1-a |
$2$ |
$7$ |
4.4.5125.1 |
$4$ |
$[4, 0]$ |
29.1 |
\( 29 \) |
\( - 29^{7} \) |
$9.74508$ |
$(a^3-4a-4)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$7$ |
7B.6.3 |
$1$ |
\( 1 \) |
$1$ |
$125.2260233$ |
1.749232970 |
\( \frac{3402532667241798182971657}{17249876309} a^{3} - \frac{12539596288688205884294718}{17249876309} a^{2} + \frac{1032346455977317685746157}{17249876309} a + \frac{21764174988792336404044948}{17249876309} \) |
\( \bigl[a^{3} - 4 a - 4\) , \( -a - 1\) , \( a^{3} - a^{2} - 4 a + 1\) , \( -64 a^{3} + 32 a^{2} + 393 a - 43\) , \( 43 a^{3} - 491 a^{2} - 169 a + 3203\bigr] \) |
${y}^2+\left(a^{3}-4a-4\right){x}{y}+\left(a^{3}-a^{2}-4a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-64a^{3}+32a^{2}+393a-43\right){x}+43a^{3}-491a^{2}-169a+3203$ |
29.1-a2 |
29.1-a |
$2$ |
$7$ |
4.4.5125.1 |
$4$ |
$[4, 0]$ |
29.1 |
\( 29 \) |
\( -29 \) |
$9.74508$ |
$(a^3-4a-4)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$7$ |
7B.6.1 |
$1$ |
\( 1 \) |
$1$ |
$125.2260233$ |
1.749232970 |
\( \frac{1067314607}{29} a^{3} + \frac{130599537}{29} a^{2} - \frac{6126735575}{29} a - \frac{5531882051}{29} \) |
\( \bigl[a^{3} - a^{2} - 4 a + 1\) , \( 0\) , \( a^{3} - 4 a - 4\) , \( a^{3} - a^{2} - 6 a - 2\) , \( a^{3} - 7 a - 7\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-4a+1\right){x}{y}+\left(a^{3}-4a-4\right){y}={x}^{3}+\left(a^{3}-a^{2}-6a-2\right){x}+a^{3}-7a-7$ |
29.1-b1 |
29.1-b |
$2$ |
$7$ |
4.4.5125.1 |
$4$ |
$[4, 0]$ |
29.1 |
\( 29 \) |
\( - 29^{7} \) |
$9.74508$ |
$(a^3-4a-4)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$7$ |
7B.1.3 |
$1$ |
\( 7 \) |
$7.395445215$ |
$0.692045361$ |
2.001750670 |
\( \frac{3402532667241798182971657}{17249876309} a^{3} - \frac{12539596288688205884294718}{17249876309} a^{2} + \frac{1032346455977317685746157}{17249876309} a + \frac{21764174988792336404044948}{17249876309} \) |
\( \bigl[a^{3} - 5 a - 4\) , \( -a^{3} + 4 a + 4\) , \( a + 1\) , \( -1238 a^{3} - 283 a^{2} + 6707 a + 6118\) , \( 9222 a^{3} - 1273 a^{2} - 59782 a - 52486\bigr] \) |
${y}^2+\left(a^{3}-5a-4\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a^{3}+4a+4\right){x}^{2}+\left(-1238a^{3}-283a^{2}+6707a+6118\right){x}+9222a^{3}-1273a^{2}-59782a-52486$ |
29.1-b2 |
29.1-b |
$2$ |
$7$ |
4.4.5125.1 |
$4$ |
$[4, 0]$ |
29.1 |
\( 29 \) |
\( -29 \) |
$9.74508$ |
$(a^3-4a-4)$ |
$1$ |
$\Z/7\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$7$ |
7B.1.1 |
$1$ |
\( 1 \) |
$1.056492173$ |
$1661.600912$ |
2.001750670 |
\( \frac{1067314607}{29} a^{3} + \frac{130599537}{29} a^{2} - \frac{6126735575}{29} a - \frac{5531882051}{29} \) |
\( \bigl[a^{2} - a - 3\) , \( a^{3} - 2 a^{2} - 3 a + 3\) , \( a^{3} - a^{2} - 3 a\) , \( -3 a^{3} + 7 a^{2} + 8 a - 18\) , \( 4 a^{3} - 14 a^{2} - 9 a + 43\bigr] \) |
${y}^2+\left(a^{2}-a-3\right){x}{y}+\left(a^{3}-a^{2}-3a\right){y}={x}^{3}+\left(a^{3}-2a^{2}-3a+3\right){x}^{2}+\left(-3a^{3}+7a^{2}+8a-18\right){x}+4a^{3}-14a^{2}-9a+43$ |
29.2-a1 |
29.2-a |
$2$ |
$7$ |
4.4.5125.1 |
$4$ |
$[4, 0]$ |
29.2 |
\( 29 \) |
\( -29 \) |
$9.74508$ |
$(a^2-6)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$7$ |
7B.6.1 |
$1$ |
\( 1 \) |
$1$ |
$125.2260233$ |
1.749232970 |
\( -\frac{1067314607}{29} a^{3} + \frac{3332543358}{29} a^{2} + \frac{2663592680}{29} a - \frac{10460703482}{29} \) |
\( \bigl[a^{3} - 5 a - 3\) , \( -a\) , \( a^{3} - a^{2} - 3 a + 1\) , \( -2 a^{3} + 3 a^{2} + 6 a - 7\) , \( -2 a^{3} + 4 a^{2} + 6 a - 12\bigr] \) |
${y}^2+\left(a^{3}-5a-3\right){x}{y}+\left(a^{3}-a^{2}-3a+1\right){y}={x}^{3}-a{x}^{2}+\left(-2a^{3}+3a^{2}+6a-7\right){x}-2a^{3}+4a^{2}+6a-12$ |
29.2-a2 |
29.2-a |
$2$ |
$7$ |
4.4.5125.1 |
$4$ |
$[4, 0]$ |
29.2 |
\( 29 \) |
\( - 29^{7} \) |
$9.74508$ |
$(a^2-6)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$7$ |
7B.6.3 |
$1$ |
\( 1 \) |
$1$ |
$125.2260233$ |
1.749232970 |
\( -\frac{3402532667241798182971657}{17249876309} a^{3} - \frac{2331998286962811335379747}{17249876309} a^{2} + \frac{13839248119673699533928308}{17249876309} a + \frac{13659457823323246388468044}{17249876309} \) |
\( \bigl[a^{3} - a^{2} - 3 a + 1\) , \( -a^{3} + a^{2} + 3 a - 1\) , \( a^{3} - 5 a - 3\) , \( 63 a^{3} - 159 a^{2} - 264 a + 319\) , \( -43 a^{3} - 362 a^{2} + 1021 a + 2586\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-3a+1\right){x}{y}+\left(a^{3}-5a-3\right){y}={x}^{3}+\left(-a^{3}+a^{2}+3a-1\right){x}^{2}+\left(63a^{3}-159a^{2}-264a+319\right){x}-43a^{3}-362a^{2}+1021a+2586$ |
29.2-b1 |
29.2-b |
$2$ |
$7$ |
4.4.5125.1 |
$4$ |
$[4, 0]$ |
29.2 |
\( 29 \) |
\( -29 \) |
$9.74508$ |
$(a^2-6)$ |
$1$ |
$\Z/7\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$7$ |
7B.1.1 |
$1$ |
\( 1 \) |
$1.056492173$ |
$1661.600912$ |
2.001750670 |
\( -\frac{1067314607}{29} a^{3} + \frac{3332543358}{29} a^{2} + \frac{2663592680}{29} a - \frac{10460703482}{29} \) |
\( \bigl[a^{2} - a - 3\) , \( -a^{3} + a^{2} + 4 a - 1\) , \( a^{3} - 4 a - 3\) , \( 2 a^{3} - a^{2} - 11 a - 6\) , \( -5 a^{3} - a^{2} + 27 a + 24\bigr] \) |
${y}^2+\left(a^{2}-a-3\right){x}{y}+\left(a^{3}-4a-3\right){y}={x}^{3}+\left(-a^{3}+a^{2}+4a-1\right){x}^{2}+\left(2a^{3}-a^{2}-11a-6\right){x}-5a^{3}-a^{2}+27a+24$ |
29.2-b2 |
29.2-b |
$2$ |
$7$ |
4.4.5125.1 |
$4$ |
$[4, 0]$ |
29.2 |
\( 29 \) |
\( - 29^{7} \) |
$9.74508$ |
$(a^2-6)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$7$ |
7B.1.3 |
$1$ |
\( 7 \) |
$7.395445215$ |
$0.692045361$ |
2.001750670 |
\( -\frac{3402532667241798182971657}{17249876309} a^{3} - \frac{2331998286962811335379747}{17249876309} a^{2} + \frac{13839248119673699533928308}{17249876309} a + \frac{13659457823323246388468044}{17249876309} \) |
\( \bigl[a^{3} - a^{2} - 4 a\) , \( -a^{3} + a^{2} + 4 a\) , \( a + 1\) , \( 1230 a^{3} - 3982 a^{2} - 2398 a + 11270\) , \( -12237 a^{3} + 35584 a^{2} + 43296 a - 135242\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-4a\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a^{3}+a^{2}+4a\right){x}^{2}+\left(1230a^{3}-3982a^{2}-2398a+11270\right){x}-12237a^{3}+35584a^{2}+43296a-135242$ |
41.1-a1 |
41.1-a |
$1$ |
$1$ |
4.4.5125.1 |
$4$ |
$[4, 0]$ |
41.1 |
\( 41 \) |
\( 41^{4} \) |
$10.17615$ |
$(a^3-a^2-4a-3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2^{2} \) |
$0.009312090$ |
$1120.903857$ |
2.332859573 |
\( -\frac{71073792}{1681} a^{3} + \frac{148373504}{1681} a^{2} + \frac{213286912}{1681} a - \frac{439844864}{1681} \) |
\( \bigl[0\) , \( -a^{2} + 2 a + 3\) , \( a^{2} - 4\) , \( -6 a^{3} - 2 a^{2} + 25 a + 22\) , \( 8 a^{3} + 7 a^{2} - 30 a - 33\bigr] \) |
${y}^2+\left(a^{2}-4\right){y}={x}^{3}+\left(-a^{2}+2a+3\right){x}^{2}+\left(-6a^{3}-2a^{2}+25a+22\right){x}+8a^{3}+7a^{2}-30a-33$ |
41.1-b1 |
41.1-b |
$1$ |
$1$ |
4.4.5125.1 |
$4$ |
$[4, 0]$ |
41.1 |
\( 41 \) |
\( 41^{4} \) |
$10.17615$ |
$(a^3-a^2-4a-3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2^{2} \) |
$0.485050994$ |
$21.35387477$ |
2.314926137 |
\( \frac{71073792}{1681} a^{3} - \frac{64847872}{1681} a^{2} - \frac{296812544}{1681} a - \frac{149258240}{1681} \) |
\( \bigl[0\) , \( -a^{3} + a^{2} + 4 a\) , \( a^{3} - a^{2} - 3 a\) , \( -9 a^{3} - 7 a^{2} + 37 a + 39\) , \( -31 a^{3} - 23 a^{2} + 126 a + 126\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-3a\right){y}={x}^{3}+\left(-a^{3}+a^{2}+4a\right){x}^{2}+\left(-9a^{3}-7a^{2}+37a+39\right){x}-31a^{3}-23a^{2}+126a+126$ |
41.1-c1 |
41.1-c |
$2$ |
$7$ |
4.4.5125.1 |
$4$ |
$[4, 0]$ |
41.1 |
\( 41 \) |
\( 41^{2} \) |
$10.17615$ |
$(a^3-a^2-4a-3)$ |
0 |
$\Z/7\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
✓ |
|
$7$ |
7B.1.1 |
$1$ |
\( 2 \) |
$1$ |
$2140.068876$ |
1.220154235 |
\( \frac{176128}{41} a^{2} - \frac{176128}{41} a - \frac{815104}{41} \) |
\( \bigl[0\) , \( a^{2} - a - 4\) , \( a^{2} - a - 4\) , \( 0\) , \( 0\bigr] \) |
${y}^2+\left(a^{2}-a-4\right){y}={x}^{3}+\left(a^{2}-a-4\right){x}^{2}$ |
41.1-c2 |
41.1-c |
$2$ |
$7$ |
4.4.5125.1 |
$4$ |
$[4, 0]$ |
41.1 |
\( 41 \) |
\( 41^{14} \) |
$10.17615$ |
$(a^3-a^2-4a-3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
✓ |
|
$7$ |
7B.1.3 |
$49$ |
\( 2 \) |
$1$ |
$0.891323980$ |
1.220154235 |
\( -\frac{7215644871110656}{194754273881} a^{2} + \frac{7215644871110656}{194754273881} a + \frac{16969651353047040}{194754273881} \) |
\( \bigl[0\) , \( a^{2} - a - 4\) , \( a^{2} - a - 4\) , \( -10 a^{2} + 10 a\) , \( -31 a^{2} + 31 a + 11\bigr] \) |
${y}^2+\left(a^{2}-a-4\right){y}={x}^{3}+\left(a^{2}-a-4\right){x}^{2}+\left(-10a^{2}+10a\right){x}-31a^{2}+31a+11$ |
41.1-d1 |
41.1-d |
$2$ |
$7$ |
4.4.5125.1 |
$4$ |
$[4, 0]$ |
41.1 |
\( 41 \) |
\( 41^{14} \) |
$10.17615$ |
$(a^3-a^2-4a-3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
✓ |
|
$7$ |
7B.6.3 |
$1$ |
\( 2 \) |
$1$ |
$65.76400479$ |
1.837262932 |
\( -\frac{7215644871110656}{194754273881} a^{2} + \frac{7215644871110656}{194754273881} a + \frac{16969651353047040}{194754273881} \) |
\( \bigl[0\) , \( -a^{3} + 2 a^{2} + 4 a - 4\) , \( a^{3} - 4 a - 3\) , \( 144 a^{3} - 153 a^{2} - 559 a - 225\) , \( -1890 a^{3} + 1126 a^{2} + 8698 a + 5670\bigr] \) |
${y}^2+\left(a^{3}-4a-3\right){y}={x}^{3}+\left(-a^{3}+2a^{2}+4a-4\right){x}^{2}+\left(144a^{3}-153a^{2}-559a-225\right){x}-1890a^{3}+1126a^{2}+8698a+5670$ |
41.1-d2 |
41.1-d |
$2$ |
$7$ |
4.4.5125.1 |
$4$ |
$[4, 0]$ |
41.1 |
\( 41 \) |
\( 41^{2} \) |
$10.17615$ |
$(a^3-a^2-4a-3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
✓ |
|
$7$ |
7B.6.1 |
$1$ |
\( 2 \) |
$1$ |
$65.76400479$ |
1.837262932 |
\( \frac{176128}{41} a^{2} - \frac{176128}{41} a - \frac{815104}{41} \) |
\( \bigl[0\) , \( -a^{3} + 2 a^{2} + 4 a - 4\) , \( a^{3} - 4 a - 3\) , \( 4 a^{3} - 3 a^{2} - 19 a - 5\) , \( 11 a^{3} + a^{2} - 64 a - 61\bigr] \) |
${y}^2+\left(a^{3}-4a-3\right){y}={x}^{3}+\left(-a^{3}+2a^{2}+4a-4\right){x}^{2}+\left(4a^{3}-3a^{2}-19a-5\right){x}+11a^{3}+a^{2}-64a-61$ |
41.1-e1 |
41.1-e |
$1$ |
$1$ |
4.4.5125.1 |
$4$ |
$[4, 0]$ |
41.1 |
\( 41 \) |
\( 41^{4} \) |
$10.17615$ |
$(a^3-a^2-4a-3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2^{2} \) |
$0.009312090$ |
$1120.903857$ |
2.332859573 |
\( \frac{71073792}{1681} a^{3} - \frac{64847872}{1681} a^{2} - \frac{296812544}{1681} a - \frac{149258240}{1681} \) |
\( \bigl[0\) , \( -a^{2} + 4\) , \( a^{2} - 3\) , \( 6 a^{3} - 20 a^{2} - 3 a + 39\) , \( -9 a^{3} + 32 a^{2} - 5 a - 48\bigr] \) |
${y}^2+\left(a^{2}-3\right){y}={x}^{3}+\left(-a^{2}+4\right){x}^{2}+\left(6a^{3}-20a^{2}-3a+39\right){x}-9a^{3}+32a^{2}-5a-48$ |
41.1-f1 |
41.1-f |
$1$ |
$1$ |
4.4.5125.1 |
$4$ |
$[4, 0]$ |
41.1 |
\( 41 \) |
\( 41^{4} \) |
$10.17615$ |
$(a^3-a^2-4a-3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2^{2} \) |
$0.485050994$ |
$21.35387477$ |
2.314926137 |
\( -\frac{71073792}{1681} a^{3} + \frac{148373504}{1681} a^{2} + \frac{213286912}{1681} a - \frac{439844864}{1681} \) |
\( \bigl[0\) , \( a^{3} - 2 a^{2} - 3 a + 4\) , \( a^{3} - 4 a - 3\) , \( 9 a^{3} - 34 a^{2} + 4 a + 60\) , \( 30 a^{3} - 115 a^{2} + 15 a + 198\bigr] \) |
${y}^2+\left(a^{3}-4a-3\right){y}={x}^{3}+\left(a^{3}-2a^{2}-3a+4\right){x}^{2}+\left(9a^{3}-34a^{2}+4a+60\right){x}+30a^{3}-115a^{2}+15a+198$ |
55.1-a1 |
55.1-a |
$2$ |
$2$ |
4.4.5125.1 |
$4$ |
$[4, 0]$ |
55.1 |
\( 5 \cdot 11 \) |
\( 5^{2} \cdot 11^{2} \) |
$10.55676$ |
$(-a^3+a^2+4a+1), (-a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$134.2078364$ |
1.874696378 |
\( -\frac{287491768525988172527}{605} a^{3} + \frac{1065548612442610734672}{605} a^{2} - \frac{93261222637284540808}{605} a - \frac{370660991375398969213}{121} \) |
\( \bigl[a^{3} - a^{2} - 3 a + 1\) , \( -a^{3} + a^{2} + 3 a - 1\) , \( a + 1\) , \( -66 a^{3} + 194 a^{2} + 198 a - 666\) , \( -655 a^{3} + 2069 a^{2} + 1528 a - 6306\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-3a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a^{3}+a^{2}+3a-1\right){x}^{2}+\left(-66a^{3}+194a^{2}+198a-666\right){x}-655a^{3}+2069a^{2}+1528a-6306$ |
55.1-a2 |
55.1-a |
$2$ |
$2$ |
4.4.5125.1 |
$4$ |
$[4, 0]$ |
55.1 |
\( 5 \cdot 11 \) |
\( 5^{4} \cdot 11^{4} \) |
$10.55676$ |
$(-a^3+a^2+4a+1), (-a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$134.2078364$ |
1.874696378 |
\( \frac{16065231177563}{73205} a^{3} - \frac{59542537050681}{73205} a^{2} + \frac{5209876385716}{73205} a + \frac{103560802379479}{73205} \) |
\( \bigl[a^{3} - a^{2} - 3 a + 1\) , \( -a^{3} + a^{2} + 3 a - 1\) , \( a + 1\) , \( 4 a^{3} - 16 a^{2} - 7 a + 49\) , \( -45 a^{3} + 141 a^{2} + 111 a - 443\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-3a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a^{3}+a^{2}+3a-1\right){x}^{2}+\left(4a^{3}-16a^{2}-7a+49\right){x}-45a^{3}+141a^{2}+111a-443$ |
55.1-b1 |
55.1-b |
$2$ |
$2$ |
4.4.5125.1 |
$4$ |
$[4, 0]$ |
55.1 |
\( 5 \cdot 11 \) |
\( 5^{4} \cdot 11^{4} \) |
$10.55676$ |
$(-a^3+a^2+4a+1), (-a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.768685734$ |
$30.87409782$ |
2.652077121 |
\( \frac{5932926689}{73205} a^{3} - \frac{21993206812}{73205} a^{2} + \frac{1922722402}{73205} a + \frac{38257458108}{73205} \) |
\( \bigl[a^{2} - a - 4\) , \( a^{3} - 4 a - 3\) , \( a^{2} - a - 4\) , \( a^{3} - 4 a - 2\) , \( -2 a^{3} + a^{2} + 7 a - 1\bigr] \) |
${y}^2+\left(a^{2}-a-4\right){x}{y}+\left(a^{2}-a-4\right){y}={x}^{3}+\left(a^{3}-4a-3\right){x}^{2}+\left(a^{3}-4a-2\right){x}-2a^{3}+a^{2}+7a-1$ |
55.1-b2 |
55.1-b |
$2$ |
$2$ |
4.4.5125.1 |
$4$ |
$[4, 0]$ |
55.1 |
\( 5 \cdot 11 \) |
\( 5^{8} \cdot 11^{2} \) |
$10.55676$ |
$(-a^3+a^2+4a+1), (-a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1.537371468$ |
$30.87409782$ |
2.652077121 |
\( -\frac{196392867540579}{3025} a^{3} + \frac{727903424191802}{3025} a^{2} - \frac{12741819493871}{605} a - \frac{1266039682540334}{3025} \) |
\( \bigl[a^{2} - a - 4\) , \( a^{3} - 4 a - 3\) , \( a^{2} - a - 4\) , \( -14 a^{3} + 5 a^{2} + 51 a - 2\) , \( -82 a^{3} - 21 a^{2} + 320 a + 197\bigr] \) |
${y}^2+\left(a^{2}-a-4\right){x}{y}+\left(a^{2}-a-4\right){y}={x}^{3}+\left(a^{3}-4a-3\right){x}^{2}+\left(-14a^{3}+5a^{2}+51a-2\right){x}-82a^{3}-21a^{2}+320a+197$ |
55.1-c1 |
55.1-c |
$4$ |
$6$ |
4.4.5125.1 |
$4$ |
$[4, 0]$ |
55.1 |
\( 5 \cdot 11 \) |
\( 5 \cdot 11 \) |
$10.55676$ |
$(-a^3+a^2+4a+1), (-a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$4$ |
\( 1 \) |
$1$ |
$117.3818148$ |
1.639660313 |
\( -\frac{19204557701238}{55} a^{3} - \frac{2347403181723}{55} a^{2} + \frac{110246499123534}{55} a + \frac{99540191518811}{55} \) |
\( \bigl[a^{2} - 4\) , \( -a\) , \( 1\) , \( 32 a^{3} - 33 a^{2} - 128 a - 53\) , \( 141 a^{3} - 137 a^{2} - 564 a - 261\bigr] \) |
${y}^2+\left(a^{2}-4\right){x}{y}+{y}={x}^{3}-a{x}^{2}+\left(32a^{3}-33a^{2}-128a-53\right){x}+141a^{3}-137a^{2}-564a-261$ |
55.1-c2 |
55.1-c |
$4$ |
$6$ |
4.4.5125.1 |
$4$ |
$[4, 0]$ |
55.1 |
\( 5 \cdot 11 \) |
\( 5^{2} \cdot 11^{2} \) |
$10.55676$ |
$(-a^3+a^2+4a+1), (-a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \) |
$1$ |
$117.3818148$ |
1.639660313 |
\( \frac{131300318}{605} a^{3} + \frac{14981064}{605} a^{2} - \frac{151139983}{121} a - \frac{681395002}{605} \) |
\( \bigl[a^{2} - 4\) , \( -a\) , \( 1\) , \( 2 a^{3} - 3 a^{2} - 8 a + 2\) , \( 2 a^{3} - 4 a^{2} - 5 a + 3\bigr] \) |
${y}^2+\left(a^{2}-4\right){x}{y}+{y}={x}^{3}-a{x}^{2}+\left(2a^{3}-3a^{2}-8a+2\right){x}+2a^{3}-4a^{2}-5a+3$ |
55.1-c3 |
55.1-c |
$4$ |
$6$ |
4.4.5125.1 |
$4$ |
$[4, 0]$ |
55.1 |
\( 5 \cdot 11 \) |
\( 5^{3} \cdot 11^{3} \) |
$10.55676$ |
$(-a^3+a^2+4a+1), (-a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$4$ |
\( 1 \) |
$1$ |
$117.3818148$ |
1.639660313 |
\( \frac{133990069789633150033955762628}{6655} a^{3} + \frac{94645515348052450445056005699}{6655} a^{2} - \frac{547795377221621290762673298852}{6655} a - \frac{544602192760246793271514751626}{6655} \) |
\( \bigl[a^{3} - 5 a - 3\) , \( -a^{3} + 6 a + 4\) , \( a^{3} - 4 a - 3\) , \( 149 a^{3} + 15 a^{2} - 859 a - 806\) , \( 2623 a^{3} + 320 a^{2} - 15049 a - 13499\bigr] \) |
${y}^2+\left(a^{3}-5a-3\right){x}{y}+\left(a^{3}-4a-3\right){y}={x}^{3}+\left(-a^{3}+6a+4\right){x}^{2}+\left(149a^{3}+15a^{2}-859a-806\right){x}+2623a^{3}+320a^{2}-15049a-13499$ |
55.1-c4 |
55.1-c |
$4$ |
$6$ |
4.4.5125.1 |
$4$ |
$[4, 0]$ |
55.1 |
\( 5 \cdot 11 \) |
\( 5^{6} \cdot 11^{6} \) |
$10.55676$ |
$(-a^3+a^2+4a+1), (-a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \) |
$1$ |
$117.3818148$ |
1.639660313 |
\( -\frac{63264852088520783254}{44289025} a^{3} - \frac{8937579533749840902}{8857805} a^{2} + \frac{258647477139845380633}{44289025} a + \frac{257139780743870750929}{44289025} \) |
\( \bigl[a^{3} - 5 a - 3\) , \( -a^{3} + 6 a + 4\) , \( a^{3} - 4 a - 3\) , \( -16 a^{3} + 86 a + 74\) , \( 94 a^{3} + 11 a^{2} - 542 a - 486\bigr] \) |
${y}^2+\left(a^{3}-5a-3\right){x}{y}+\left(a^{3}-4a-3\right){y}={x}^{3}+\left(-a^{3}+6a+4\right){x}^{2}+\left(-16a^{3}+86a+74\right){x}+94a^{3}+11a^{2}-542a-486$ |
55.1-d1 |
55.1-d |
$4$ |
$6$ |
4.4.5125.1 |
$4$ |
$[4, 0]$ |
55.1 |
\( 5 \cdot 11 \) |
\( 5^{2} \cdot 11^{2} \) |
$10.55676$ |
$(-a^3+a^2+4a+1), (-a)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{2} \) |
$1$ |
$669.0430099$ |
1.038399794 |
\( \frac{131300318}{605} a^{3} + \frac{14981064}{605} a^{2} - \frac{151139983}{121} a - \frac{681395002}{605} \) |
\( \bigl[a^{3} - 4 a - 3\) , \( 0\) , \( a^{3} - 4 a - 3\) , \( a^{3} - 4 a - 3\) , \( a^{3} - 4 a - 2\bigr] \) |
${y}^2+\left(a^{3}-4a-3\right){x}{y}+\left(a^{3}-4a-3\right){y}={x}^{3}+\left(a^{3}-4a-3\right){x}+a^{3}-4a-2$ |
55.1-d2 |
55.1-d |
$4$ |
$6$ |
4.4.5125.1 |
$4$ |
$[4, 0]$ |
55.1 |
\( 5 \cdot 11 \) |
\( 5 \cdot 11 \) |
$10.55676$ |
$(-a^3+a^2+4a+1), (-a)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$4$ |
\( 1 \) |
$1$ |
$669.0430099$ |
1.038399794 |
\( -\frac{19204557701238}{55} a^{3} - \frac{2347403181723}{55} a^{2} + \frac{110246499123534}{55} a + \frac{99540191518811}{55} \) |
\( \bigl[a^{3} - 4 a - 3\) , \( 0\) , \( a^{3} - 4 a - 3\) , \( -4 a^{3} + 16 a - 3\) , \( -24 a^{3} - 24 a^{2} + 99 a + 130\bigr] \) |
${y}^2+\left(a^{3}-4a-3\right){x}{y}+\left(a^{3}-4a-3\right){y}={x}^{3}+\left(-4a^{3}+16a-3\right){x}-24a^{3}-24a^{2}+99a+130$ |
55.1-d3 |
55.1-d |
$4$ |
$6$ |
4.4.5125.1 |
$4$ |
$[4, 0]$ |
55.1 |
\( 5 \cdot 11 \) |
\( 5^{3} \cdot 11^{3} \) |
$10.55676$ |
$(-a^3+a^2+4a+1), (-a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$36$ |
\( 1 \) |
$1$ |
$8.259790245$ |
1.038399794 |
\( \frac{133990069789633150033955762628}{6655} a^{3} + \frac{94645515348052450445056005699}{6655} a^{2} - \frac{547795377221621290762673298852}{6655} a - \frac{544602192760246793271514751626}{6655} \) |
\( \bigl[a + 1\) , \( 0\) , \( a^{3} - 4 a - 3\) , \( -191 a^{3} + 389 a^{2} + 555 a - 1139\) , \( -2260 a^{3} + 4761 a^{2} + 6611 a - 13813\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{3}-4a-3\right){y}={x}^{3}+\left(-191a^{3}+389a^{2}+555a-1139\right){x}-2260a^{3}+4761a^{2}+6611a-13813$ |
55.1-d4 |
55.1-d |
$4$ |
$6$ |
4.4.5125.1 |
$4$ |
$[4, 0]$ |
55.1 |
\( 5 \cdot 11 \) |
\( 5^{6} \cdot 11^{6} \) |
$10.55676$ |
$(-a^3+a^2+4a+1), (-a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$9$ |
\( 2^{2} \) |
$1$ |
$8.259790245$ |
1.038399794 |
\( -\frac{63264852088520783254}{44289025} a^{3} - \frac{8937579533749840902}{8857805} a^{2} + \frac{258647477139845380633}{44289025} a + \frac{257139780743870750929}{44289025} \) |
\( \bigl[a + 1\) , \( 0\) , \( a^{3} - 4 a - 3\) , \( -6 a^{3} - a^{2} + 25 a + 16\) , \( -86 a^{3} + 215 a^{2} + 239 a - 646\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{3}-4a-3\right){y}={x}^{3}+\left(-6a^{3}-a^{2}+25a+16\right){x}-86a^{3}+215a^{2}+239a-646$ |
55.1-e1 |
55.1-e |
$2$ |
$2$ |
4.4.5125.1 |
$4$ |
$[4, 0]$ |
55.1 |
\( 5 \cdot 11 \) |
\( 5^{8} \cdot 11^{2} \) |
$10.55676$ |
$(-a^3+a^2+4a+1), (-a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.047398503$ |
$856.4096892$ |
2.268084662 |
\( -\frac{196392867540579}{3025} a^{3} + \frac{727903424191802}{3025} a^{2} - \frac{12741819493871}{605} a - \frac{1266039682540334}{3025} \) |
\( \bigl[a^{2} - 3\) , \( a^{3} - 2 a^{2} - 4 a + 4\) , \( 0\) , \( 22 a^{3} - 20 a^{2} - 95 a - 42\) , \( -107 a^{3} + 34 a^{2} + 540 a + 416\bigr] \) |
${y}^2+\left(a^{2}-3\right){x}{y}={x}^{3}+\left(a^{3}-2a^{2}-4a+4\right){x}^{2}+\left(22a^{3}-20a^{2}-95a-42\right){x}-107a^{3}+34a^{2}+540a+416$ |
55.1-e2 |
55.1-e |
$2$ |
$2$ |
4.4.5125.1 |
$4$ |
$[4, 0]$ |
55.1 |
\( 5 \cdot 11 \) |
\( 5^{4} \cdot 11^{4} \) |
$10.55676$ |
$(-a^3+a^2+4a+1), (-a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.023699251$ |
$856.4096892$ |
2.268084662 |
\( \frac{5932926689}{73205} a^{3} - \frac{21993206812}{73205} a^{2} + \frac{1922722402}{73205} a + \frac{38257458108}{73205} \) |
\( \bigl[a^{2} - 3\) , \( a^{3} - 2 a^{2} - 4 a + 4\) , \( 0\) , \( 2 a^{3} - 5 a^{2} - 5 a + 13\) , \( -2 a^{3} - 2 a^{2} + 13 a + 20\bigr] \) |
${y}^2+\left(a^{2}-3\right){x}{y}={x}^{3}+\left(a^{3}-2a^{2}-4a+4\right){x}^{2}+\left(2a^{3}-5a^{2}-5a+13\right){x}-2a^{3}-2a^{2}+13a+20$ |
55.1-f1 |
55.1-f |
$2$ |
$2$ |
4.4.5125.1 |
$4$ |
$[4, 0]$ |
55.1 |
\( 5 \cdot 11 \) |
\( 5^{2} \cdot 11^{2} \) |
$10.55676$ |
$(-a^3+a^2+4a+1), (-a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$70.55402936$ |
0.985541431 |
\( -\frac{287491768525988172527}{605} a^{3} + \frac{1065548612442610734672}{605} a^{2} - \frac{93261222637284540808}{605} a - \frac{370660991375398969213}{121} \) |
\( \bigl[a^{3} - 4 a - 4\) , \( 1\) , \( 1\) , \( -218 a^{3} - 146 a^{2} + 869 a + 827\) , \( -4041 a^{3} - 2859 a^{2} + 16568 a + 16518\bigr] \) |
${y}^2+\left(a^{3}-4a-4\right){x}{y}+{y}={x}^{3}+{x}^{2}+\left(-218a^{3}-146a^{2}+869a+827\right){x}-4041a^{3}-2859a^{2}+16568a+16518$ |
55.1-f2 |
55.1-f |
$2$ |
$2$ |
4.4.5125.1 |
$4$ |
$[4, 0]$ |
55.1 |
\( 5 \cdot 11 \) |
\( 5^{4} \cdot 11^{4} \) |
$10.55676$ |
$(-a^3+a^2+4a+1), (-a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$70.55402936$ |
0.985541431 |
\( \frac{16065231177563}{73205} a^{3} - \frac{59542537050681}{73205} a^{2} + \frac{5209876385716}{73205} a + \frac{103560802379479}{73205} \) |
\( \bigl[1\) , \( a^{3} - 4 a - 5\) , \( a^{3} - 5 a - 4\) , \( 7 a^{3} - 24 a^{2} + 42\) , \( 14 a^{3} - 54 a^{2} + 8 a + 98\bigr] \) |
${y}^2+{x}{y}+\left(a^{3}-5a-4\right){y}={x}^{3}+\left(a^{3}-4a-5\right){x}^{2}+\left(7a^{3}-24a^{2}+42\right){x}+14a^{3}-54a^{2}+8a+98$ |
55.2-a1 |
55.2-a |
$2$ |
$2$ |
4.4.5125.1 |
$4$ |
$[4, 0]$ |
55.2 |
\( 5 \cdot 11 \) |
\( 5^{2} \cdot 11^{2} \) |
$10.55676$ |
$(-a^3+a^2+4a+1), (a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$134.2078364$ |
1.874696378 |
\( \frac{287491768525988172527}{605} a^{3} + \frac{203073306864646217091}{605} a^{2} - \frac{235072139333994482191}{121} a - \frac{106228121417968802248}{55} \) |
\( \bigl[a^{3} - 4 a - 4\) , \( -a - 1\) , \( a\) , \( 64 a^{3} - a^{2} - 383 a - 342\) , \( 655 a^{3} + 104 a^{2} - 3702 a - 3363\bigr] \) |
${y}^2+\left(a^{3}-4a-4\right){x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(64a^{3}-a^{2}-383a-342\right){x}+655a^{3}+104a^{2}-3702a-3363$ |
55.2-a2 |
55.2-a |
$2$ |
$2$ |
4.4.5125.1 |
$4$ |
$[4, 0]$ |
55.2 |
\( 5 \cdot 11 \) |
\( 5^{4} \cdot 11^{4} \) |
$10.55676$ |
$(-a^3+a^2+4a+1), (a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$134.2078364$ |
1.874696378 |
\( -\frac{16065231177563}{73205} a^{3} - \frac{11346843517992}{73205} a^{2} + \frac{65679504182957}{73205} a + \frac{5935761172007}{6655} \) |
\( \bigl[a^{3} - 4 a - 4\) , \( -a - 1\) , \( a\) , \( -6 a^{3} - a^{2} + 32 a + 28\) , \( 45 a^{3} + 6 a^{2} - 259 a - 235\bigr] \) |
${y}^2+\left(a^{3}-4a-4\right){x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-6a^{3}-a^{2}+32a+28\right){x}+45a^{3}+6a^{2}-259a-235$ |
55.2-b1 |
55.2-b |
$2$ |
$2$ |
4.4.5125.1 |
$4$ |
$[4, 0]$ |
55.2 |
\( 5 \cdot 11 \) |
\( 5^{4} \cdot 11^{4} \) |
$10.55676$ |
$(-a^3+a^2+4a+1), (a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.768685734$ |
$30.87409782$ |
2.652077121 |
\( -\frac{5932926689}{73205} a^{3} - \frac{838885349}{14641} a^{2} + \frac{4852982231}{14641} a + \frac{2192718217}{6655} \) |
\( \bigl[a^{2} - a - 4\) , \( -a^{3} + 4 a + 3\) , \( a^{2} - a - 3\) , \( a^{3} - a^{2} - a + 1\) , \( a^{3} - 6 a^{2} + 2 a + 11\bigr] \) |
${y}^2+\left(a^{2}-a-4\right){x}{y}+\left(a^{2}-a-3\right){y}={x}^{3}+\left(-a^{3}+4a+3\right){x}^{2}+\left(a^{3}-a^{2}-a+1\right){x}+a^{3}-6a^{2}+2a+11$ |
55.2-b2 |
55.2-b |
$2$ |
$2$ |
4.4.5125.1 |
$4$ |
$[4, 0]$ |
55.2 |
\( 5 \cdot 11 \) |
\( 5^{8} \cdot 11^{2} \) |
$10.55676$ |
$(-a^3+a^2+4a+1), (a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1.537371468$ |
$30.87409782$ |
2.652077121 |
\( \frac{196392867540579}{3025} a^{3} + \frac{27744964314013}{605} a^{2} - \frac{802919148292512}{3025} a - \frac{72567111214406}{275} \) |
\( \bigl[a^{2} - a - 4\) , \( -a^{3} + 4 a + 3\) , \( a^{2} - a - 3\) , \( 16 a^{3} - 41 a^{2} - 21 a + 46\) , \( 66 a^{3} - 198 a^{2} - 52 a + 280\bigr] \) |
${y}^2+\left(a^{2}-a-4\right){x}{y}+\left(a^{2}-a-3\right){y}={x}^{3}+\left(-a^{3}+4a+3\right){x}^{2}+\left(16a^{3}-41a^{2}-21a+46\right){x}+66a^{3}-198a^{2}-52a+280$ |
55.2-c1 |
55.2-c |
$4$ |
$6$ |
4.4.5125.1 |
$4$ |
$[4, 0]$ |
55.2 |
\( 5 \cdot 11 \) |
\( 5 \cdot 11 \) |
$10.55676$ |
$(-a^3+a^2+4a+1), (a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$4$ |
\( 1 \) |
$1$ |
$117.3818148$ |
1.639660313 |
\( \frac{19204557701238}{55} a^{3} - \frac{59961076285437}{55} a^{2} - \frac{47938019656374}{55} a + \frac{17112248159944}{5} \) |
\( \bigl[a^{2} - 3\) , \( -a^{3} + a^{2} + 4 a - 1\) , \( 1\) , \( -32 a^{3} + 63 a^{2} + 97 a - 182\) , \( -141 a^{3} + 286 a^{2} + 415 a - 821\bigr] \) |
${y}^2+\left(a^{2}-3\right){x}{y}+{y}={x}^{3}+\left(-a^{3}+a^{2}+4a-1\right){x}^{2}+\left(-32a^{3}+63a^{2}+97a-182\right){x}-141a^{3}+286a^{2}+415a-821$ |
55.2-c2 |
55.2-c |
$4$ |
$6$ |
4.4.5125.1 |
$4$ |
$[4, 0]$ |
55.2 |
\( 5 \cdot 11 \) |
\( 5^{2} \cdot 11^{2} \) |
$10.55676$ |
$(-a^3+a^2+4a+1), (a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \) |
$1$ |
$117.3818148$ |
1.639660313 |
\( -\frac{131300318}{605} a^{3} + \frac{408882018}{605} a^{2} + \frac{331836833}{605} a - \frac{23469337}{11} \) |
\( \bigl[a^{2} - 3\) , \( -a^{3} + a^{2} + 4 a - 1\) , \( 1\) , \( -2 a^{3} + 3 a^{2} + 7 a - 7\) , \( -2 a^{3} + 2 a^{2} + 7 a - 4\bigr] \) |
${y}^2+\left(a^{2}-3\right){x}{y}+{y}={x}^{3}+\left(-a^{3}+a^{2}+4a-1\right){x}^{2}+\left(-2a^{3}+3a^{2}+7a-7\right){x}-2a^{3}+2a^{2}+7a-4$ |
55.2-c3 |
55.2-c |
$4$ |
$6$ |
4.4.5125.1 |
$4$ |
$[4, 0]$ |
55.2 |
\( 5 \cdot 11 \) |
\( 5^{3} \cdot 11^{3} \) |
$10.55676$ |
$(-a^3+a^2+4a+1), (a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$4$ |
\( 1 \) |
$1$ |
$117.3818148$ |
1.639660313 |
\( -\frac{133990069789633150033955762628}{6655} a^{3} + \frac{496615724716951900546923293583}{6655} a^{2} - \frac{8693172568676612045861200086}{1331} a - \frac{78523816804016589414106934741}{605} \) |
\( \bigl[a^{3} - a^{2} - 4 a + 1\) , \( a^{3} - 4 a - 5\) , \( a\) , \( -155 a^{3} + 482 a^{2} + 395 a - 1557\) , \( -2048 a^{3} + 6363 a^{2} + 5087 a - 19778\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-4a+1\right){x}{y}+a{y}={x}^{3}+\left(a^{3}-4a-5\right){x}^{2}+\left(-155a^{3}+482a^{2}+395a-1557\right){x}-2048a^{3}+6363a^{2}+5087a-19778$ |
55.2-c4 |
55.2-c |
$4$ |
$6$ |
4.4.5125.1 |
$4$ |
$[4, 0]$ |
55.2 |
\( 5 \cdot 11 \) |
\( 5^{6} \cdot 11^{6} \) |
$10.55676$ |
$(-a^3+a^2+4a+1), (a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \) |
$1$ |
$117.3818148$ |
1.639660313 |
\( \frac{63264852088520783254}{44289025} a^{3} - \frac{234482453934311554272}{44289025} a^{2} + \frac{20522874463215378149}{44289025} a + \frac{37075864375131467618}{4026275} \) |
\( \bigl[a^{3} - a^{2} - 4 a + 1\) , \( a^{3} - 4 a - 5\) , \( a\) , \( 10 a^{3} - 28 a^{2} - 25 a + 88\) , \( -134 a^{3} + 427 a^{2} + 330 a - 1341\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-4a+1\right){x}{y}+a{y}={x}^{3}+\left(a^{3}-4a-5\right){x}^{2}+\left(10a^{3}-28a^{2}-25a+88\right){x}-134a^{3}+427a^{2}+330a-1341$ |
55.2-d1 |
55.2-d |
$4$ |
$6$ |
4.4.5125.1 |
$4$ |
$[4, 0]$ |
55.2 |
\( 5 \cdot 11 \) |
\( 5^{2} \cdot 11^{2} \) |
$10.55676$ |
$(-a^3+a^2+4a+1), (a-1)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{2} \) |
$1$ |
$669.0430099$ |
1.038399794 |
\( -\frac{131300318}{605} a^{3} + \frac{408882018}{605} a^{2} + \frac{331836833}{605} a - \frac{23469337}{11} \) |
\( \bigl[a^{3} - a^{2} - 3 a\) , \( -a^{3} + 2 a^{2} + 4 a - 5\) , \( a^{3} - a^{2} - 3 a + 1\) , \( a^{3} - 6 a^{2} + a + 19\) , \( -a^{3} + a^{2} + 5 a - 3\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-3a\right){x}{y}+\left(a^{3}-a^{2}-3a+1\right){y}={x}^{3}+\left(-a^{3}+2a^{2}+4a-5\right){x}^{2}+\left(a^{3}-6a^{2}+a+19\right){x}-a^{3}+a^{2}+5a-3$ |
55.2-d2 |
55.2-d |
$4$ |
$6$ |
4.4.5125.1 |
$4$ |
$[4, 0]$ |
55.2 |
\( 5 \cdot 11 \) |
\( 5 \cdot 11 \) |
$10.55676$ |
$(-a^3+a^2+4a+1), (a-1)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$4$ |
\( 1 \) |
$1$ |
$669.0430099$ |
1.038399794 |
\( \frac{19204557701238}{55} a^{3} - \frac{59961076285437}{55} a^{2} - \frac{47938019656374}{55} a + \frac{17112248159944}{5} \) |
\( \bigl[a^{3} - a^{2} - 3 a\) , \( -a^{3} + 2 a^{2} + 4 a - 5\) , \( a^{3} - a^{2} - 3 a + 1\) , \( 6 a^{3} - 21 a^{2} - 4 a + 34\) , \( 14 a^{3} - 58 a^{2} + 10 a + 113\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-3a\right){x}{y}+\left(a^{3}-a^{2}-3a+1\right){y}={x}^{3}+\left(-a^{3}+2a^{2}+4a-5\right){x}^{2}+\left(6a^{3}-21a^{2}-4a+34\right){x}+14a^{3}-58a^{2}+10a+113$ |
55.2-d3 |
55.2-d |
$4$ |
$6$ |
4.4.5125.1 |
$4$ |
$[4, 0]$ |
55.2 |
\( 5 \cdot 11 \) |
\( 5^{3} \cdot 11^{3} \) |
$10.55676$ |
$(-a^3+a^2+4a+1), (a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$36$ |
\( 1 \) |
$1$ |
$8.259790245$ |
1.038399794 |
\( -\frac{133990069789633150033955762628}{6655} a^{3} + \frac{496615724716951900546923293583}{6655} a^{2} - \frac{8693172568676612045861200086}{1331} a - \frac{78523816804016589414106934741}{605} \) |
\( \bigl[a\) , \( -a + 1\) , \( a^{3} - a^{2} - 3 a\) , \( 189 a^{3} - 180 a^{2} - 756 a - 392\) , \( 2259 a^{3} - 2017 a^{2} - 9352 a - 4703\bigr] \) |
${y}^2+a{x}{y}+\left(a^{3}-a^{2}-3a\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(189a^{3}-180a^{2}-756a-392\right){x}+2259a^{3}-2017a^{2}-9352a-4703$ |
55.2-d4 |
55.2-d |
$4$ |
$6$ |
4.4.5125.1 |
$4$ |
$[4, 0]$ |
55.2 |
\( 5 \cdot 11 \) |
\( 5^{6} \cdot 11^{6} \) |
$10.55676$ |
$(-a^3+a^2+4a+1), (a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$9$ |
\( 2^{2} \) |
$1$ |
$8.259790245$ |
1.038399794 |
\( \frac{63264852088520783254}{44289025} a^{3} - \frac{234482453934311554272}{44289025} a^{2} + \frac{20522874463215378149}{44289025} a + \frac{37075864375131467618}{4026275} \) |
\( \bigl[a\) , \( -a + 1\) , \( a^{3} - a^{2} - 3 a\) , \( 4 a^{3} - 15 a^{2} - a + 28\) , \( 85 a^{3} - 41 a^{2} - 410 a - 280\bigr] \) |
${y}^2+a{x}{y}+\left(a^{3}-a^{2}-3a\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(4a^{3}-15a^{2}-a+28\right){x}+85a^{3}-41a^{2}-410a-280$ |
55.2-e1 |
55.2-e |
$2$ |
$2$ |
4.4.5125.1 |
$4$ |
$[4, 0]$ |
55.2 |
\( 5 \cdot 11 \) |
\( 5^{8} \cdot 11^{2} \) |
$10.55676$ |
$(-a^3+a^2+4a+1), (a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.047398503$ |
$856.4096892$ |
2.268084662 |
\( \frac{196392867540579}{3025} a^{3} + \frac{27744964314013}{605} a^{2} - \frac{802919148292512}{3025} a - \frac{72567111214406}{275} \) |
\( \bigl[a^{2} - 4\) , \( a^{3} - 5 a - 4\) , \( a^{2} - 3\) , \( -22 a^{3} + 47 a^{2} + 69 a - 141\) , \( 67 a^{3} - 189 a^{2} - 181 a + 592\bigr] \) |
${y}^2+\left(a^{2}-4\right){x}{y}+\left(a^{2}-3\right){y}={x}^{3}+\left(a^{3}-5a-4\right){x}^{2}+\left(-22a^{3}+47a^{2}+69a-141\right){x}+67a^{3}-189a^{2}-181a+592$ |
55.2-e2 |
55.2-e |
$2$ |
$2$ |
4.4.5125.1 |
$4$ |
$[4, 0]$ |
55.2 |
\( 5 \cdot 11 \) |
\( 5^{4} \cdot 11^{4} \) |
$10.55676$ |
$(-a^3+a^2+4a+1), (a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.023699251$ |
$856.4096892$ |
2.268084662 |
\( -\frac{5932926689}{73205} a^{3} - \frac{838885349}{14641} a^{2} + \frac{4852982231}{14641} a + \frac{2192718217}{6655} \) |
\( \bigl[a^{2} - 4\) , \( a^{3} - 5 a - 4\) , \( a^{2} - 3\) , \( -2 a^{3} + 2 a^{2} + 9 a - 1\) , \( 2 a^{3} - 5 a^{2} - 7 a + 13\bigr] \) |
${y}^2+\left(a^{2}-4\right){x}{y}+\left(a^{2}-3\right){y}={x}^{3}+\left(a^{3}-5a-4\right){x}^{2}+\left(-2a^{3}+2a^{2}+9a-1\right){x}+2a^{3}-5a^{2}-7a+13$ |
*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.