| 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 |
| 16.1-a1 |
16.1-a |
$1$ |
$1$ |
4.4.16225.1 |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{12} \) |
$16.09704$ |
$(1/3a^3-1/3a^2-10/3a+2), (1/3a^3+2/3a^2-4/3a-3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2^{3} \) |
$0.024957901$ |
$530.4436783$ |
3.325867710 |
\( -\frac{31557625}{96} a^{3} + \frac{87395431}{96} a^{2} + \frac{255480511}{96} a - \frac{53452375}{8} \) |
\( \bigl[1\) , \( -\frac{1}{6} a^{3} - \frac{5}{6} a^{2} + \frac{19}{6} a + 8\) , \( \frac{1}{6} a^{3} - \frac{1}{6} a^{2} - \frac{7}{6} a\) , \( -\frac{11}{2} a^{3} + \frac{21}{2} a^{2} + \frac{95}{2} a - 65\) , \( \frac{37}{3} a^{3} - \frac{118}{3} a^{2} - \frac{289}{3} a + 299\bigr] \) |
${y}^2+{x}{y}+\left(\frac{1}{6}a^{3}-\frac{1}{6}a^{2}-\frac{7}{6}a\right){y}={x}^{3}+\left(-\frac{1}{6}a^{3}-\frac{5}{6}a^{2}+\frac{19}{6}a+8\right){x}^{2}+\left(-\frac{11}{2}a^{3}+\frac{21}{2}a^{2}+\frac{95}{2}a-65\right){x}+\frac{37}{3}a^{3}-\frac{118}{3}a^{2}-\frac{289}{3}a+299$ |
| 16.1-b1 |
16.1-b |
$1$ |
$1$ |
4.4.16225.1 |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{12} \) |
$16.09704$ |
$(1/3a^3-1/3a^2-10/3a+2), (1/3a^3+2/3a^2-4/3a-3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2^{3} \) |
$0.024957901$ |
$530.4436783$ |
3.325867710 |
\( -\frac{1374039}{8} a^{3} - \frac{6558223}{16} a^{2} + \frac{6736845}{8} a + 1821645 \) |
\( \bigl[1\) , \( a^{2} - 2 a - 7\) , \( \frac{1}{6} a^{3} - \frac{1}{6} a^{2} - \frac{7}{6} a + 1\) , \( -\frac{19}{6} a^{3} - \frac{23}{6} a^{2} + \frac{103}{6} a + 24\) , \( \frac{55}{6} a^{3} + \frac{143}{6} a^{2} - \frac{283}{6} a - 108\bigr] \) |
${y}^2+{x}{y}+\left(\frac{1}{6}a^{3}-\frac{1}{6}a^{2}-\frac{7}{6}a+1\right){y}={x}^{3}+\left(a^{2}-2a-7\right){x}^{2}+\left(-\frac{19}{6}a^{3}-\frac{23}{6}a^{2}+\frac{103}{6}a+24\right){x}+\frac{55}{6}a^{3}+\frac{143}{6}a^{2}-\frac{283}{6}a-108$ |
| 16.1-c1 |
16.1-c |
$1$ |
$1$ |
4.4.16225.1 |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{12} \) |
$16.09704$ |
$(1/3a^3-1/3a^2-10/3a+2), (1/3a^3+2/3a^2-4/3a-3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2^{2} \) |
$0.015455278$ |
$1590.760758$ |
3.088227834 |
\( -\frac{31557625}{96} a^{3} + \frac{87395431}{96} a^{2} + \frac{255480511}{96} a - \frac{53452375}{8} \) |
\( \bigl[\frac{1}{6} a^{3} - \frac{1}{6} a^{2} - \frac{1}{6} a\) , \( -\frac{1}{6} a^{3} + \frac{7}{6} a^{2} + \frac{7}{6} a - 7\) , \( \frac{1}{6} a^{3} + \frac{5}{6} a^{2} - \frac{7}{6} a - 6\) , \( \frac{89}{6} a^{3} - \frac{329}{6} a^{2} - \frac{227}{6} a + 189\) , \( -130 a^{3} + 493 a^{2} + 324 a - 1692\bigr] \) |
${y}^2+\left(\frac{1}{6}a^{3}-\frac{1}{6}a^{2}-\frac{1}{6}a\right){x}{y}+\left(\frac{1}{6}a^{3}+\frac{5}{6}a^{2}-\frac{7}{6}a-6\right){y}={x}^{3}+\left(-\frac{1}{6}a^{3}+\frac{7}{6}a^{2}+\frac{7}{6}a-7\right){x}^{2}+\left(\frac{89}{6}a^{3}-\frac{329}{6}a^{2}-\frac{227}{6}a+189\right){x}-130a^{3}+493a^{2}+324a-1692$ |
| 16.1-d1 |
16.1-d |
$1$ |
$1$ |
4.4.16225.1 |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{12} \) |
$16.09704$ |
$(1/3a^3-1/3a^2-10/3a+2), (1/3a^3+2/3a^2-4/3a-3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2^{2} \) |
$0.015455278$ |
$1590.760758$ |
3.088227834 |
\( -\frac{1374039}{8} a^{3} - \frac{6558223}{16} a^{2} + \frac{6736845}{8} a + 1821645 \) |
\( \bigl[a + 1\) , \( a^{2} - 7\) , \( a^{2} - 7\) , \( \frac{119}{6} a^{3} + \frac{139}{6} a^{2} - \frac{1235}{6} a - 324\) , \( -\frac{637}{3} a^{3} - \frac{734}{3} a^{2} + \frac{6691}{3} a + 3532\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{2}-7\right){y}={x}^{3}+\left(a^{2}-7\right){x}^{2}+\left(\frac{119}{6}a^{3}+\frac{139}{6}a^{2}-\frac{1235}{6}a-324\right){x}-\frac{637}{3}a^{3}-\frac{734}{3}a^{2}+\frac{6691}{3}a+3532$ |
| 25.1-a1 |
25.1-a |
$2$ |
$2$ |
4.4.16225.1 |
$4$ |
$[4, 0]$ |
25.1 |
\( 5^{2} \) |
\( 5^{12} \) |
$17.02054$ |
$(1/3a^3-1/3a^2-7/3a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3Ns |
$1$ |
\( 2 \) |
$1$ |
$639.4904919$ |
2.510219756 |
\( -\frac{196733}{75} a^{3} + \frac{196733}{75} a^{2} + \frac{1377131}{75} a + \frac{15889551}{125} \) |
\( \bigl[\frac{1}{6} a^{3} + \frac{5}{6} a^{2} - \frac{13}{6} a - 7\) , \( a - 1\) , \( \frac{1}{6} a^{3} - \frac{1}{6} a^{2} - \frac{1}{6} a\) , \( -\frac{471}{2} a^{3} + \frac{1291}{2} a^{2} + \frac{3827}{2} a - 4733\) , \( \frac{12751}{2} a^{3} - \frac{35345}{2} a^{2} - \frac{103191}{2} a + 129687\bigr] \) |
${y}^2+\left(\frac{1}{6}a^{3}+\frac{5}{6}a^{2}-\frac{13}{6}a-7\right){x}{y}+\left(\frac{1}{6}a^{3}-\frac{1}{6}a^{2}-\frac{1}{6}a\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-\frac{471}{2}a^{3}+\frac{1291}{2}a^{2}+\frac{3827}{2}a-4733\right){x}+\frac{12751}{2}a^{3}-\frac{35345}{2}a^{2}-\frac{103191}{2}a+129687$ |
| 25.1-a2 |
25.1-a |
$2$ |
$2$ |
4.4.16225.1 |
$4$ |
$[4, 0]$ |
25.1 |
\( 5^{2} \) |
\( 5^{6} \) |
$17.02054$ |
$(1/3a^3-1/3a^2-7/3a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3Ns |
$1$ |
\( 1 \) |
$1$ |
$1278.980983$ |
2.510219756 |
\( -\frac{10096}{75} a^{3} + \frac{10096}{75} a^{2} + \frac{70672}{75} a + \frac{12229}{25} \) |
\( \bigl[\frac{1}{6} a^{3} - \frac{1}{6} a^{2} - \frac{1}{6} a\) , \( -\frac{1}{6} a^{3} + \frac{7}{6} a^{2} + \frac{7}{6} a - 8\) , \( \frac{1}{6} a^{3} - \frac{1}{6} a^{2} - \frac{7}{6} a + 1\) , \( \frac{58}{3} a^{3} + \frac{68}{3} a^{2} - \frac{610}{3} a - 314\) , \( \frac{121}{6} a^{3} + \frac{161}{6} a^{2} - \frac{1261}{6} a - 350\bigr] \) |
${y}^2+\left(\frac{1}{6}a^{3}-\frac{1}{6}a^{2}-\frac{1}{6}a\right){x}{y}+\left(\frac{1}{6}a^{3}-\frac{1}{6}a^{2}-\frac{7}{6}a+1\right){y}={x}^{3}+\left(-\frac{1}{6}a^{3}+\frac{7}{6}a^{2}+\frac{7}{6}a-8\right){x}^{2}+\left(\frac{58}{3}a^{3}+\frac{68}{3}a^{2}-\frac{610}{3}a-314\right){x}+\frac{121}{6}a^{3}+\frac{161}{6}a^{2}-\frac{1261}{6}a-350$ |
| 25.1-b1 |
25.1-b |
$2$ |
$2$ |
4.4.16225.1 |
$4$ |
$[4, 0]$ |
25.1 |
\( 5^{2} \) |
\( 5^{6} \) |
$17.02054$ |
$(1/3a^3-1/3a^2-7/3a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3Ns |
$1$ |
\( 1 \) |
$1$ |
$1278.980983$ |
2.510219756 |
\( -\frac{10096}{75} a^{3} + \frac{10096}{75} a^{2} + \frac{70672}{75} a + \frac{12229}{25} \) |
\( \bigl[a + 1\) , \( a^{2} - 8\) , \( \frac{1}{6} a^{3} - \frac{1}{6} a^{2} - \frac{7}{6} a\) , \( \frac{31}{2} a^{3} - \frac{111}{2} a^{2} - \frac{81}{2} a + 193\) , \( 28 a^{3} - 101 a^{2} - 79 a + 359\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(\frac{1}{6}a^{3}-\frac{1}{6}a^{2}-\frac{7}{6}a\right){y}={x}^{3}+\left(a^{2}-8\right){x}^{2}+\left(\frac{31}{2}a^{3}-\frac{111}{2}a^{2}-\frac{81}{2}a+193\right){x}+28a^{3}-101a^{2}-79a+359$ |
| 25.1-b2 |
25.1-b |
$2$ |
$2$ |
4.4.16225.1 |
$4$ |
$[4, 0]$ |
25.1 |
\( 5^{2} \) |
\( 5^{12} \) |
$17.02054$ |
$(1/3a^3-1/3a^2-7/3a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3Ns |
$1$ |
\( 2 \) |
$1$ |
$639.4904919$ |
2.510219756 |
\( -\frac{196733}{75} a^{3} + \frac{196733}{75} a^{2} + \frac{1377131}{75} a + \frac{15889551}{125} \) |
\( \bigl[a + 1\) , \( a^{2} - 8\) , \( \frac{1}{6} a^{3} - \frac{1}{6} a^{2} - \frac{7}{6} a\) , \( \frac{833}{6} a^{3} - \frac{3173}{6} a^{2} - \frac{1853}{6} a + 1738\) , \( -\frac{21869}{6} a^{3} + \frac{82919}{6} a^{2} + \frac{53225}{6} a - 46906\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(\frac{1}{6}a^{3}-\frac{1}{6}a^{2}-\frac{7}{6}a\right){y}={x}^{3}+\left(a^{2}-8\right){x}^{2}+\left(\frac{833}{6}a^{3}-\frac{3173}{6}a^{2}-\frac{1853}{6}a+1738\right){x}-\frac{21869}{6}a^{3}+\frac{82919}{6}a^{2}+\frac{53225}{6}a-46906$ |
| 44.1-a1 |
44.1-a |
$1$ |
$1$ |
4.4.16225.1 |
$4$ |
$[4, 0]$ |
44.1 |
\( 2^{2} \cdot 11 \) |
\( 2^{16} \cdot 11^{4} \) |
$18.26680$ |
$(1/6a^3+5/6a^2-13/6a-8), (1/3a^3+2/3a^2-4/3a-3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2^{5} \) |
$1$ |
$14.08223842$ |
3.537767750 |
\( -\frac{73387874633}{15488} a^{3} + \frac{406673355373}{30976} a^{2} + \frac{594023130065}{15488} a - \frac{746087195411}{7744} \) |
\( \bigl[\frac{1}{6} a^{3} - \frac{1}{6} a^{2} - \frac{1}{6} a\) , \( a^{2} - 7\) , \( \frac{1}{6} a^{3} + \frac{5}{6} a^{2} - \frac{13}{6} a - 7\) , \( \frac{181}{6} a^{3} + \frac{227}{6} a^{2} - \frac{1903}{6} a - 512\) , \( \frac{1249}{3} a^{3} + \frac{1454}{3} a^{2} - \frac{13102}{3} a - 6942\bigr] \) |
${y}^2+\left(\frac{1}{6}a^{3}-\frac{1}{6}a^{2}-\frac{1}{6}a\right){x}{y}+\left(\frac{1}{6}a^{3}+\frac{5}{6}a^{2}-\frac{13}{6}a-7\right){y}={x}^{3}+\left(a^{2}-7\right){x}^{2}+\left(\frac{181}{6}a^{3}+\frac{227}{6}a^{2}-\frac{1903}{6}a-512\right){x}+\frac{1249}{3}a^{3}+\frac{1454}{3}a^{2}-\frac{13102}{3}a-6942$ |
| 44.1-b1 |
44.1-b |
$1$ |
$1$ |
4.4.16225.1 |
$4$ |
$[4, 0]$ |
44.1 |
\( 2^{2} \cdot 11 \) |
\( 2^{16} \cdot 11^{4} \) |
$18.26680$ |
$(1/6a^3+5/6a^2-13/6a-8), (1/3a^3+2/3a^2-4/3a-3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2^{2} \) |
$1$ |
$74.00610094$ |
2.323994855 |
\( -\frac{73387874633}{15488} a^{3} + \frac{406673355373}{30976} a^{2} + \frac{594023130065}{15488} a - \frac{746087195411}{7744} \) |
\( \bigl[\frac{1}{6} a^{3} + \frac{5}{6} a^{2} - \frac{13}{6} a - 6\) , \( -\frac{1}{6} a^{3} - \frac{5}{6} a^{2} + \frac{7}{6} a + 6\) , \( a^{2} - 6\) , \( -\frac{1}{6} a^{3} + \frac{1}{6} a^{2} + \frac{37}{6} a + 10\) , \( -\frac{19}{6} a^{3} - \frac{35}{6} a^{2} + \frac{127}{6} a + 36\bigr] \) |
${y}^2+\left(\frac{1}{6}a^{3}+\frac{5}{6}a^{2}-\frac{13}{6}a-6\right){x}{y}+\left(a^{2}-6\right){y}={x}^{3}+\left(-\frac{1}{6}a^{3}-\frac{5}{6}a^{2}+\frac{7}{6}a+6\right){x}^{2}+\left(-\frac{1}{6}a^{3}+\frac{1}{6}a^{2}+\frac{37}{6}a+10\right){x}-\frac{19}{6}a^{3}-\frac{35}{6}a^{2}+\frac{127}{6}a+36$ |
| 44.2-a1 |
44.2-a |
$1$ |
$1$ |
4.4.16225.1 |
$4$ |
$[4, 0]$ |
44.2 |
\( 2^{2} \cdot 11 \) |
\( 2^{16} \cdot 11^{4} \) |
$18.26680$ |
$(1/6a^3+5/6a^2-13/6a-8), (1/3a^3-1/3a^2-10/3a+2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2^{5} \) |
$1$ |
$14.08223842$ |
3.537767750 |
\( -\frac{153380291407}{61952} a^{3} - \frac{366414920807}{61952} a^{2} + \frac{752430009313}{61952} a + \frac{407416859561}{15488} \) |
\( \bigl[\frac{1}{6} a^{3} + \frac{5}{6} a^{2} - \frac{7}{6} a - 7\) , \( \frac{1}{6} a^{3} - \frac{1}{6} a^{2} - \frac{1}{6} a - 1\) , \( \frac{1}{6} a^{3} - \frac{1}{6} a^{2} - \frac{1}{6} a + 1\) , \( \frac{19}{6} a^{3} - \frac{79}{6} a^{2} - \frac{43}{6} a + 52\) , \( \frac{35}{3} a^{3} - \frac{161}{3} a^{2} - \frac{74}{3} a + 187\bigr] \) |
${y}^2+\left(\frac{1}{6}a^{3}+\frac{5}{6}a^{2}-\frac{7}{6}a-7\right){x}{y}+\left(\frac{1}{6}a^{3}-\frac{1}{6}a^{2}-\frac{1}{6}a+1\right){y}={x}^{3}+\left(\frac{1}{6}a^{3}-\frac{1}{6}a^{2}-\frac{1}{6}a-1\right){x}^{2}+\left(\frac{19}{6}a^{3}-\frac{79}{6}a^{2}-\frac{43}{6}a+52\right){x}+\frac{35}{3}a^{3}-\frac{161}{3}a^{2}-\frac{74}{3}a+187$ |
| 44.2-b1 |
44.2-b |
$1$ |
$1$ |
4.4.16225.1 |
$4$ |
$[4, 0]$ |
44.2 |
\( 2^{2} \cdot 11 \) |
\( 2^{16} \cdot 11^{4} \) |
$18.26680$ |
$(1/6a^3+5/6a^2-13/6a-8), (1/3a^3-1/3a^2-10/3a+2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2^{2} \) |
$1$ |
$74.00610094$ |
2.323994855 |
\( -\frac{153380291407}{61952} a^{3} - \frac{366414920807}{61952} a^{2} + \frac{752430009313}{61952} a + \frac{407416859561}{15488} \) |
\( \bigl[\frac{1}{6} a^{3} + \frac{5}{6} a^{2} - \frac{13}{6} a - 7\) , \( -\frac{1}{6} a^{3} - \frac{5}{6} a^{2} + \frac{13}{6} a + 7\) , \( a^{2} - a - 7\) , \( -\frac{7}{6} a^{3} - \frac{47}{6} a^{2} + \frac{103}{6} a + 76\) , \( -\frac{37}{6} a^{3} - \frac{23}{6} a^{2} + \frac{373}{6} a + 73\bigr] \) |
${y}^2+\left(\frac{1}{6}a^{3}+\frac{5}{6}a^{2}-\frac{13}{6}a-7\right){x}{y}+\left(a^{2}-a-7\right){y}={x}^{3}+\left(-\frac{1}{6}a^{3}-\frac{5}{6}a^{2}+\frac{13}{6}a+7\right){x}^{2}+\left(-\frac{7}{6}a^{3}-\frac{47}{6}a^{2}+\frac{103}{6}a+76\right){x}-\frac{37}{6}a^{3}-\frac{23}{6}a^{2}+\frac{373}{6}a+73$ |
| 64.1-a1 |
64.1-a |
$2$ |
$3$ |
4.4.16225.1 |
$4$ |
$[4, 0]$ |
64.1 |
\( 2^{6} \) |
\( 2^{24} \) |
$19.14271$ |
$(1/3a^3-1/3a^2-10/3a+2), (1/3a^3+2/3a^2-4/3a-3)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.1 |
$1$ |
\( 2^{2} \cdot 3 \) |
$0.979038791$ |
$119.9966651$ |
4.918984473 |
\( \frac{1102525}{48} a^{3} + \frac{316721}{12} a^{2} - \frac{1451225}{6} a - \frac{766369}{2} \) |
\( \bigl[a^{2} - 6\) , \( -a^{2} + a + 7\) , \( 0\) , \( \frac{1}{3} a^{3} - \frac{1}{3} a^{2} - \frac{4}{3} a + 9\) , \( 10 a^{3} - 37 a^{2} - 25 a + 130\bigr] \) |
${y}^2+\left(a^{2}-6\right){x}{y}={x}^{3}+\left(-a^{2}+a+7\right){x}^{2}+\left(\frac{1}{3}a^{3}-\frac{1}{3}a^{2}-\frac{4}{3}a+9\right){x}+10a^{3}-37a^{2}-25a+130$ |
| 64.1-a2 |
64.1-a |
$2$ |
$3$ |
4.4.16225.1 |
$4$ |
$[4, 0]$ |
64.1 |
\( 2^{6} \) |
\( 2^{40} \) |
$19.14271$ |
$(1/3a^3-1/3a^2-10/3a+2), (1/3a^3+2/3a^2-4/3a-3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.2 |
$1$ |
\( 2^{2} \cdot 3^{2} \) |
$2.937116375$ |
$1.481440310$ |
4.918984473 |
\( -\frac{93154131986155}{12288} a^{3} - \frac{55635154580471}{3072} a^{2} + \frac{57124800666575}{1536} a + \frac{41239388864647}{512} \) |
\( \bigl[a^{2} - 6\) , \( -a^{2} + a + 7\) , \( 0\) , \( \frac{311}{3} a^{3} - \frac{1196}{3} a^{2} - \frac{674}{3} a + 1309\) , \( 2317 a^{3} - 8793 a^{2} - 5609 a + 29794\bigr] \) |
${y}^2+\left(a^{2}-6\right){x}{y}={x}^{3}+\left(-a^{2}+a+7\right){x}^{2}+\left(\frac{311}{3}a^{3}-\frac{1196}{3}a^{2}-\frac{674}{3}a+1309\right){x}+2317a^{3}-8793a^{2}-5609a+29794$ |
| 64.1-b1 |
64.1-b |
$2$ |
$3$ |
4.4.16225.1 |
$4$ |
$[4, 0]$ |
64.1 |
\( 2^{6} \) |
\( 2^{40} \) |
$19.14271$ |
$(1/3a^3-1/3a^2-10/3a+2), (1/3a^3+2/3a^2-4/3a-3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B |
$9$ |
\( 2 \) |
$1$ |
$5.476202669$ |
0.773855128 |
\( -\frac{93154131986155}{12288} a^{3} - \frac{55635154580471}{3072} a^{2} + \frac{57124800666575}{1536} a + \frac{41239388864647}{512} \) |
\( \bigl[a^{2} - 6\) , \( a - 1\) , \( 0\) , \( -\frac{383}{2} a^{3} + \frac{1065}{2} a^{2} + \frac{3113}{2} a - 3907\) , \( -\frac{13820}{3} a^{3} + \frac{38315}{3} a^{2} + \frac{111836}{3} a - 93700\bigr] \) |
${y}^2+\left(a^{2}-6\right){x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-\frac{383}{2}a^{3}+\frac{1065}{2}a^{2}+\frac{3113}{2}a-3907\right){x}-\frac{13820}{3}a^{3}+\frac{38315}{3}a^{2}+\frac{111836}{3}a-93700$ |
| 64.1-b2 |
64.1-b |
$2$ |
$3$ |
4.4.16225.1 |
$4$ |
$[4, 0]$ |
64.1 |
\( 2^{6} \) |
\( 2^{24} \) |
$19.14271$ |
$(1/3a^3-1/3a^2-10/3a+2), (1/3a^3+2/3a^2-4/3a-3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B |
$1$ |
\( 2 \) |
$1$ |
$49.28582402$ |
0.773855128 |
\( \frac{1102525}{48} a^{3} + \frac{316721}{12} a^{2} - \frac{1451225}{6} a - \frac{766369}{2} \) |
\( \bigl[a^{2} - 6\) , \( a - 1\) , \( 0\) , \( \frac{31}{6} a^{3} - \frac{55}{6} a^{2} - \frac{241}{6} a + 73\) , \( -\frac{95}{3} a^{3} + \frac{281}{3} a^{2} + \frac{776}{3} a - 684\bigr] \) |
${y}^2+\left(a^{2}-6\right){x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(\frac{31}{6}a^{3}-\frac{55}{6}a^{2}-\frac{241}{6}a+73\right){x}-\frac{95}{3}a^{3}+\frac{281}{3}a^{2}+\frac{776}{3}a-684$ |
| 64.2-a1 |
64.2-a |
$2$ |
$3$ |
4.4.16225.1 |
$4$ |
$[4, 0]$ |
64.2 |
\( 2^{6} \) |
\( 2^{40} \) |
$19.14271$ |
$(1/3a^3-1/3a^2-10/3a+2), (1/3a^3+2/3a^2-4/3a-3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.2 |
$1$ |
\( 2^{2} \cdot 3^{2} \) |
$2.937116375$ |
$1.481440310$ |
4.918984473 |
\( -\frac{59427781155303}{4096} a^{3} + \frac{41164841147829}{1024} a^{2} + \frac{60127663451327}{512} a - \frac{1208353896710501}{4096} \) |
\( \bigl[\frac{1}{6} a^{3} + \frac{5}{6} a^{2} - \frac{7}{6} a - 6\) , \( \frac{1}{6} a^{3} - \frac{1}{6} a^{2} - \frac{1}{6} a + 1\) , \( 0\) , \( 139 a^{3} + 162 a^{2} - 1469 a - 2347\) , \( \frac{6607}{2} a^{3} + \frac{7605}{2} a^{2} - \frac{69633}{2} a - 55246\bigr] \) |
${y}^2+\left(\frac{1}{6}a^{3}+\frac{5}{6}a^{2}-\frac{7}{6}a-6\right){x}{y}={x}^{3}+\left(\frac{1}{6}a^{3}-\frac{1}{6}a^{2}-\frac{1}{6}a+1\right){x}^{2}+\left(139a^{3}+162a^{2}-1469a-2347\right){x}+\frac{6607}{2}a^{3}+\frac{7605}{2}a^{2}-\frac{69633}{2}a-55246$ |
| 64.2-a2 |
64.2-a |
$2$ |
$3$ |
4.4.16225.1 |
$4$ |
$[4, 0]$ |
64.2 |
\( 2^{6} \) |
\( 2^{24} \) |
$19.14271$ |
$(1/3a^3-1/3a^2-10/3a+2), (1/3a^3+2/3a^2-4/3a-3)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.1 |
$1$ |
\( 2^{2} \cdot 3 \) |
$0.979038791$ |
$119.9966651$ |
4.918984473 |
\( \frac{282913}{16} a^{3} - \frac{268179}{4} a^{2} - \frac{85377}{2} a + \frac{3628915}{16} \) |
\( \bigl[\frac{1}{6} a^{3} + \frac{5}{6} a^{2} - \frac{7}{6} a - 6\) , \( \frac{1}{6} a^{3} - \frac{1}{6} a^{2} - \frac{1}{6} a + 1\) , \( 0\) , \( \frac{3}{2} a^{3} + \frac{9}{2} a^{2} - \frac{13}{2} a - 17\) , \( \frac{31}{2} a^{3} + \frac{43}{2} a^{2} - \frac{291}{2} a - 239\bigr] \) |
${y}^2+\left(\frac{1}{6}a^{3}+\frac{5}{6}a^{2}-\frac{7}{6}a-6\right){x}{y}={x}^{3}+\left(\frac{1}{6}a^{3}-\frac{1}{6}a^{2}-\frac{1}{6}a+1\right){x}^{2}+\left(\frac{3}{2}a^{3}+\frac{9}{2}a^{2}-\frac{13}{2}a-17\right){x}+\frac{31}{2}a^{3}+\frac{43}{2}a^{2}-\frac{291}{2}a-239$ |
| 64.2-b1 |
64.2-b |
$2$ |
$3$ |
4.4.16225.1 |
$4$ |
$[4, 0]$ |
64.2 |
\( 2^{6} \) |
\( 2^{24} \) |
$19.14271$ |
$(1/3a^3-1/3a^2-10/3a+2), (1/3a^3+2/3a^2-4/3a-3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B |
$1$ |
\( 2 \) |
$1$ |
$49.28582402$ |
0.773855128 |
\( \frac{282913}{16} a^{3} - \frac{268179}{4} a^{2} - \frac{85377}{2} a + \frac{3628915}{16} \) |
\( \bigl[\frac{1}{6} a^{3} + \frac{5}{6} a^{2} - \frac{7}{6} a - 6\) , \( -\frac{1}{6} a^{3} - \frac{5}{6} a^{2} + \frac{13}{6} a + 7\) , \( \frac{1}{6} a^{3} - \frac{1}{6} a^{2} - \frac{1}{6} a + 1\) , \( \frac{3}{2} a^{3} + \frac{7}{2} a^{2} - \frac{3}{2} a - 3\) , \( -\frac{23}{2} a^{3} - \frac{55}{2} a^{2} + \frac{123}{2} a + 132\bigr] \) |
${y}^2+\left(\frac{1}{6}a^{3}+\frac{5}{6}a^{2}-\frac{7}{6}a-6\right){x}{y}+\left(\frac{1}{6}a^{3}-\frac{1}{6}a^{2}-\frac{1}{6}a+1\right){y}={x}^{3}+\left(-\frac{1}{6}a^{3}-\frac{5}{6}a^{2}+\frac{13}{6}a+7\right){x}^{2}+\left(\frac{3}{2}a^{3}+\frac{7}{2}a^{2}-\frac{3}{2}a-3\right){x}-\frac{23}{2}a^{3}-\frac{55}{2}a^{2}+\frac{123}{2}a+132$ |
| 64.2-b2 |
64.2-b |
$2$ |
$3$ |
4.4.16225.1 |
$4$ |
$[4, 0]$ |
64.2 |
\( 2^{6} \) |
\( 2^{40} \) |
$19.14271$ |
$(1/3a^3-1/3a^2-10/3a+2), (1/3a^3+2/3a^2-4/3a-3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B |
$9$ |
\( 2 \) |
$1$ |
$5.476202669$ |
0.773855128 |
\( -\frac{59427781155303}{4096} a^{3} + \frac{41164841147829}{1024} a^{2} + \frac{60127663451327}{512} a - \frac{1208353896710501}{4096} \) |
\( \bigl[\frac{1}{6} a^{3} - \frac{1}{6} a^{2} - \frac{1}{6} a + 1\) , \( -\frac{1}{6} a^{3} + \frac{1}{6} a^{2} + \frac{13}{6} a - 1\) , \( a^{2} - a - 7\) , \( -\frac{65}{6} a^{3} - \frac{121}{6} a^{2} + \frac{107}{6} a + 38\) , \( -\frac{1079}{6} a^{3} - \frac{2923}{6} a^{2} + \frac{6107}{6} a + 2329\bigr] \) |
${y}^2+\left(\frac{1}{6}a^{3}-\frac{1}{6}a^{2}-\frac{1}{6}a+1\right){x}{y}+\left(a^{2}-a-7\right){y}={x}^{3}+\left(-\frac{1}{6}a^{3}+\frac{1}{6}a^{2}+\frac{13}{6}a-1\right){x}^{2}+\left(-\frac{65}{6}a^{3}-\frac{121}{6}a^{2}+\frac{107}{6}a+38\right){x}-\frac{1079}{6}a^{3}-\frac{2923}{6}a^{2}+\frac{6107}{6}a+2329$ |
| 64.3-a1 |
64.3-a |
$4$ |
$4$ |
4.4.16225.1 |
$4$ |
$[4, 0]$ |
64.3 |
\( 2^{6} \) |
\( - 2^{16} \) |
$19.14271$ |
$(1/3a^3-1/3a^2-10/3a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$462.9190080$ |
3.634232109 |
\( 69 a^{3} + 148 a^{2} - 248 a - 328 \) |
\( \bigl[a^{2} - a - 6\) , \( \frac{1}{6} a^{3} - \frac{1}{6} a^{2} - \frac{1}{6} a + 1\) , \( a^{2} - 6\) , \( -\frac{71}{6} a^{3} - \frac{169}{6} a^{2} + \frac{359}{6} a + 127\) , \( -\frac{181}{2} a^{3} - \frac{431}{2} a^{2} + \frac{891}{2} a + 960\bigr] \) |
${y}^2+\left(a^{2}-a-6\right){x}{y}+\left(a^{2}-6\right){y}={x}^{3}+\left(\frac{1}{6}a^{3}-\frac{1}{6}a^{2}-\frac{1}{6}a+1\right){x}^{2}+\left(-\frac{71}{6}a^{3}-\frac{169}{6}a^{2}+\frac{359}{6}a+127\right){x}-\frac{181}{2}a^{3}-\frac{431}{2}a^{2}+\frac{891}{2}a+960$ |
| 64.3-a2 |
64.3-a |
$4$ |
$4$ |
4.4.16225.1 |
$4$ |
$[4, 0]$ |
64.3 |
\( 2^{6} \) |
\( - 2^{16} \) |
$19.14271$ |
$(1/3a^3-1/3a^2-10/3a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$4$ |
\( 2 \) |
$1$ |
$231.4595040$ |
3.634232109 |
\( -\frac{32239801}{3} a^{3} + \frac{121806406}{3} a^{2} + \frac{42230668}{3} a - 95767152 \) |
\( \bigl[a^{2} - 6\) , \( \frac{1}{6} a^{3} + \frac{5}{6} a^{2} - \frac{7}{6} a - 8\) , \( a\) , \( -\frac{2}{3} a^{3} + \frac{8}{3} a^{2} + \frac{53}{3} a - 36\) , \( -\frac{21}{2} a^{3} + \frac{75}{2} a^{2} + \frac{111}{2} a - 193\bigr] \) |
${y}^2+\left(a^{2}-6\right){x}{y}+a{y}={x}^{3}+\left(\frac{1}{6}a^{3}+\frac{5}{6}a^{2}-\frac{7}{6}a-8\right){x}^{2}+\left(-\frac{2}{3}a^{3}+\frac{8}{3}a^{2}+\frac{53}{3}a-36\right){x}-\frac{21}{2}a^{3}+\frac{75}{2}a^{2}+\frac{111}{2}a-193$ |
| 64.3-a3 |
64.3-a |
$4$ |
$4$ |
4.4.16225.1 |
$4$ |
$[4, 0]$ |
64.3 |
\( 2^{6} \) |
\( 2^{8} \) |
$19.14271$ |
$(1/3a^3-1/3a^2-10/3a+2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2Cs |
$4$ |
\( 2 \) |
$1$ |
$925.8380161$ |
3.634232109 |
\( 145153 a^{3} + 348932 a^{2} - 713992 a - 1543480 \) |
\( \bigl[a\) , \( \frac{1}{6} a^{3} + \frac{5}{6} a^{2} - \frac{13}{6} a - 6\) , \( a^{2} - a - 6\) , \( -a^{2} + 3 a + 7\) , \( \frac{1}{6} a^{3} + \frac{5}{6} a^{2} - \frac{13}{6} a - 6\bigr] \) |
${y}^2+a{x}{y}+\left(a^{2}-a-6\right){y}={x}^{3}+\left(\frac{1}{6}a^{3}+\frac{5}{6}a^{2}-\frac{13}{6}a-6\right){x}^{2}+\left(-a^{2}+3a+7\right){x}+\frac{1}{6}a^{3}+\frac{5}{6}a^{2}-\frac{13}{6}a-6$ |
| 64.3-a4 |
64.3-a |
$4$ |
$4$ |
4.4.16225.1 |
$4$ |
$[4, 0]$ |
64.3 |
\( 2^{6} \) |
\( 2^{16} \) |
$19.14271$ |
$(1/3a^3-1/3a^2-10/3a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$4$ |
\( 2^{2} \) |
$1$ |
$115.7297520$ |
3.634232109 |
\( \frac{2485611978745}{3} a^{3} + \frac{5937258041354}{3} a^{2} - \frac{12193663889404}{3} a - 8802130701520 \) |
\( \bigl[a\) , \( \frac{1}{6} a^{3} + \frac{5}{6} a^{2} - \frac{13}{6} a - 6\) , \( a^{2} - a - 6\) , \( \frac{5}{6} a^{3} - \frac{41}{6} a^{2} + \frac{13}{6} a + 27\) , \( \frac{20}{3} a^{3} - \frac{101}{3} a^{2} - \frac{44}{3} a + 117\bigr] \) |
${y}^2+a{x}{y}+\left(a^{2}-a-6\right){y}={x}^{3}+\left(\frac{1}{6}a^{3}+\frac{5}{6}a^{2}-\frac{13}{6}a-6\right){x}^{2}+\left(\frac{5}{6}a^{3}-\frac{41}{6}a^{2}+\frac{13}{6}a+27\right){x}+\frac{20}{3}a^{3}-\frac{101}{3}a^{2}-\frac{44}{3}a+117$ |
| 64.3-b1 |
64.3-b |
$1$ |
$1$ |
4.4.16225.1 |
$4$ |
$[4, 0]$ |
64.3 |
\( 2^{6} \) |
\( - 2^{22} \) |
$19.14271$ |
$(1/3a^3-1/3a^2-10/3a+2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
|
|
$1$ |
\( 1 \) |
$0.398578148$ |
$467.5310675$ |
5.851828621 |
\( -\frac{5272}{3} a^{3} - \frac{5678}{3} a^{2} + \frac{54298}{3} a + 28246 \) |
\( \bigl[0\) , \( -a^{2} + 7\) , \( a\) , \( -2 a^{3} + 8 a^{2} + 4 a - 24\) , \( -\frac{31}{6} a^{3} + \frac{121}{6} a^{2} + \frac{73}{6} a - 69\bigr] \) |
${y}^2+a{y}={x}^{3}+\left(-a^{2}+7\right){x}^{2}+\left(-2a^{3}+8a^{2}+4a-24\right){x}-\frac{31}{6}a^{3}+\frac{121}{6}a^{2}+\frac{73}{6}a-69$ |
| 64.3-c1 |
64.3-c |
$1$ |
$1$ |
4.4.16225.1 |
$4$ |
$[4, 0]$ |
64.3 |
\( 2^{6} \) |
\( 2^{20} \) |
$19.14271$ |
$(1/3a^3-1/3a^2-10/3a+2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
|
|
$1$ |
\( 2 \) |
$1$ |
$109.7057975$ |
1.722531695 |
\( -\frac{28354015}{3} a^{3} - \frac{67765031}{3} a^{2} + \frac{139111738}{3} a + 100456208 \) |
\( \bigl[a^{2} - a - 6\) , \( -a - 1\) , \( a^{2} - 6\) , \( -\frac{5}{3} a^{3} - \frac{7}{3} a^{2} + \frac{29}{3} a + 14\) , \( -\frac{5}{3} a^{3} - \frac{10}{3} a^{2} + \frac{20}{3} a + 11\bigr] \) |
${y}^2+\left(a^{2}-a-6\right){x}{y}+\left(a^{2}-6\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-\frac{5}{3}a^{3}-\frac{7}{3}a^{2}+\frac{29}{3}a+14\right){x}-\frac{5}{3}a^{3}-\frac{10}{3}a^{2}+\frac{20}{3}a+11$ |
| 64.3-d1 |
64.3-d |
$4$ |
$4$ |
4.4.16225.1 |
$4$ |
$[4, 0]$ |
64.3 |
\( 2^{6} \) |
\( - 2^{16} \) |
$19.14271$ |
$(1/3a^3-1/3a^2-10/3a+2)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$4.240610387$ |
$222.4424047$ |
3.702743309 |
\( 69 a^{3} + 148 a^{2} - 248 a - 328 \) |
\( \bigl[a^{2} - 6\) , \( -\frac{1}{6} a^{3} - \frac{5}{6} a^{2} + \frac{7}{6} a + 6\) , \( 0\) , \( -\frac{20}{3} a^{3} - \frac{28}{3} a^{2} + \frac{206}{3} a + 120\) , \( 39 a^{3} + 44 a^{2} - 412 a - 648\bigr] \) |
${y}^2+\left(a^{2}-6\right){x}{y}={x}^{3}+\left(-\frac{1}{6}a^{3}-\frac{5}{6}a^{2}+\frac{7}{6}a+6\right){x}^{2}+\left(-\frac{20}{3}a^{3}-\frac{28}{3}a^{2}+\frac{206}{3}a+120\right){x}+39a^{3}+44a^{2}-412a-648$ |
| 64.3-d2 |
64.3-d |
$4$ |
$4$ |
4.4.16225.1 |
$4$ |
$[4, 0]$ |
64.3 |
\( 2^{6} \) |
\( - 2^{16} \) |
$19.14271$ |
$(1/3a^3-1/3a^2-10/3a+2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$4.240610387$ |
$27.80530059$ |
3.702743309 |
\( -\frac{32239801}{3} a^{3} + \frac{121806406}{3} a^{2} + \frac{42230668}{3} a - 95767152 \) |
\( \bigl[a\) , \( -\frac{1}{6} a^{3} + \frac{7}{6} a^{2} + \frac{7}{6} a - 6\) , \( 0\) , \( -\frac{19}{2} a^{3} + \frac{77}{2} a^{2} + \frac{143}{2} a - 295\) , \( -\frac{331}{6} a^{3} + \frac{1123}{6} a^{2} + \frac{2569}{6} a - 1437\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-\frac{1}{6}a^{3}+\frac{7}{6}a^{2}+\frac{7}{6}a-6\right){x}^{2}+\left(-\frac{19}{2}a^{3}+\frac{77}{2}a^{2}+\frac{143}{2}a-295\right){x}-\frac{331}{6}a^{3}+\frac{1123}{6}a^{2}+\frac{2569}{6}a-1437$ |
| 64.3-d3 |
64.3-d |
$4$ |
$4$ |
4.4.16225.1 |
$4$ |
$[4, 0]$ |
64.3 |
\( 2^{6} \) |
\( 2^{16} \) |
$19.14271$ |
$(1/3a^3-1/3a^2-10/3a+2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$1.060152596$ |
$222.4424047$ |
3.702743309 |
\( \frac{2485611978745}{3} a^{3} + \frac{5937258041354}{3} a^{2} - \frac{12193663889404}{3} a - 8802130701520 \) |
\( \bigl[a\) , \( -\frac{1}{6} a^{3} + \frac{7}{6} a^{2} + \frac{7}{6} a - 6\) , \( 0\) , \( -2 a^{3} + 11 a^{2} + 14 a - 80\) , \( \frac{29}{3} a^{3} - \frac{89}{3} a^{2} - \frac{230}{3} a + 228\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-\frac{1}{6}a^{3}+\frac{7}{6}a^{2}+\frac{7}{6}a-6\right){x}^{2}+\left(-2a^{3}+11a^{2}+14a-80\right){x}+\frac{29}{3}a^{3}-\frac{89}{3}a^{2}-\frac{230}{3}a+228$ |
| 64.3-d4 |
64.3-d |
$4$ |
$4$ |
4.4.16225.1 |
$4$ |
$[4, 0]$ |
64.3 |
\( 2^{6} \) |
\( 2^{8} \) |
$19.14271$ |
$(1/3a^3-1/3a^2-10/3a+2)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2 \) |
$2.120305193$ |
$444.8848094$ |
3.702743309 |
\( 145153 a^{3} + 348932 a^{2} - 713992 a - 1543480 \) |
\( \bigl[a\) , \( -\frac{1}{6} a^{3} + \frac{7}{6} a^{2} + \frac{7}{6} a - 6\) , \( 0\) , \( -\frac{1}{3} a^{3} + \frac{13}{3} a^{2} + \frac{7}{3} a - 25\) , \( 3 a^{2} - 18\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-\frac{1}{6}a^{3}+\frac{7}{6}a^{2}+\frac{7}{6}a-6\right){x}^{2}+\left(-\frac{1}{3}a^{3}+\frac{13}{3}a^{2}+\frac{7}{3}a-25\right){x}+3a^{2}-18$ |
| 64.3-e1 |
64.3-e |
$1$ |
$1$ |
4.4.16225.1 |
$4$ |
$[4, 0]$ |
64.3 |
\( 2^{6} \) |
\( 2^{20} \) |
$19.14271$ |
$(1/3a^3-1/3a^2-10/3a+2)$ |
$0 \le r \le 1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
|
|
|
\( 2 \) |
$1$ |
$35.64671152$ |
4.468649477 |
\( -\frac{28354015}{3} a^{3} - \frac{67765031}{3} a^{2} + \frac{139111738}{3} a + 100456208 \) |
\( \bigl[a^{2} - a - 6\) , \( -a^{2} + 7\) , \( 0\) , \( -\frac{21}{2} a^{3} - \frac{25}{2} a^{2} + \frac{217}{2} a + 179\) , \( -\frac{305}{6} a^{3} - \frac{355}{6} a^{2} + \frac{3197}{6} a + 850\bigr] \) |
${y}^2+\left(a^{2}-a-6\right){x}{y}={x}^{3}+\left(-a^{2}+7\right){x}^{2}+\left(-\frac{21}{2}a^{3}-\frac{25}{2}a^{2}+\frac{217}{2}a+179\right){x}-\frac{305}{6}a^{3}-\frac{355}{6}a^{2}+\frac{3197}{6}a+850$ |
| 64.3-f1 |
64.3-f |
$1$ |
$1$ |
4.4.16225.1 |
$4$ |
$[4, 0]$ |
64.3 |
\( 2^{6} \) |
\( - 2^{22} \) |
$19.14271$ |
$(1/3a^3-1/3a^2-10/3a+2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
|
|
$1$ |
\( 1 \) |
$1$ |
$230.1517432$ |
1.806849234 |
\( -\frac{5272}{3} a^{3} - \frac{5678}{3} a^{2} + \frac{54298}{3} a + 28246 \) |
\( \bigl[0\) , \( \frac{1}{6} a^{3} - \frac{7}{6} a^{2} - \frac{1}{6} a + 8\) , \( a\) , \( -\frac{1}{6} a^{3} + \frac{1}{6} a^{2} + \frac{1}{6} a + 4\) , \( \frac{1}{3} a^{3} - \frac{4}{3} a^{2} - \frac{4}{3} a + 4\bigr] \) |
${y}^2+a{y}={x}^{3}+\left(\frac{1}{6}a^{3}-\frac{7}{6}a^{2}-\frac{1}{6}a+8\right){x}^{2}+\left(-\frac{1}{6}a^{3}+\frac{1}{6}a^{2}+\frac{1}{6}a+4\right){x}+\frac{1}{3}a^{3}-\frac{4}{3}a^{2}-\frac{4}{3}a+4$ |
| 64.4-a1 |
64.4-a |
$4$ |
$4$ |
4.4.16225.1 |
$4$ |
$[4, 0]$ |
64.4 |
\( 2^{6} \) |
\( - 2^{16} \) |
$19.14271$ |
$(1/3a^3+2/3a^2-4/3a-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$462.9190080$ |
3.634232109 |
\( \frac{433}{3} a^{3} - \frac{1084}{3} a^{2} - \frac{3736}{3} a + 2945 \) |
\( \bigl[a^{2} - a - 7\) , \( -\frac{1}{6} a^{3} + \frac{1}{6} a^{2} + \frac{1}{6} a - 1\) , \( a^{2} - a - 7\) , \( -\frac{45}{2} a^{3} + \frac{129}{2} a^{2} + \frac{361}{2} a - 470\) , \( -\frac{273}{2} a^{3} + \frac{757}{2} a^{2} + \frac{2205}{2} a - 2775\bigr] \) |
${y}^2+\left(a^{2}-a-7\right){x}{y}+\left(a^{2}-a-7\right){y}={x}^{3}+\left(-\frac{1}{6}a^{3}+\frac{1}{6}a^{2}+\frac{1}{6}a-1\right){x}^{2}+\left(-\frac{45}{2}a^{3}+\frac{129}{2}a^{2}+\frac{361}{2}a-470\right){x}-\frac{273}{2}a^{3}+\frac{757}{2}a^{2}+\frac{2205}{2}a-2775$ |
| 64.4-a2 |
64.4-a |
$4$ |
$4$ |
4.4.16225.1 |
$4$ |
$[4, 0]$ |
64.4 |
\( 2^{6} \) |
\( - 2^{16} \) |
$19.14271$ |
$(1/3a^3+2/3a^2-4/3a-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$4$ |
\( 2 \) |
$1$ |
$231.4595040$ |
3.634232109 |
\( -15962230 a^{3} - 13893305 a^{2} + 172884923 a + 261061025 \) |
\( \bigl[\frac{1}{6} a^{3} - \frac{1}{6} a^{2} - \frac{1}{6} a + 1\) , \( \frac{1}{6} a^{3} + \frac{5}{6} a^{2} - \frac{19}{6} a - 8\) , \( \frac{1}{6} a^{3} + \frac{5}{6} a^{2} - \frac{7}{6} a - 6\) , \( \frac{79}{6} a^{3} + \frac{101}{6} a^{2} - \frac{865}{6} a - 236\) , \( -\frac{935}{6} a^{3} - \frac{1081}{6} a^{2} + \frac{9779}{6} a + 2584\bigr] \) |
${y}^2+\left(\frac{1}{6}a^{3}-\frac{1}{6}a^{2}-\frac{1}{6}a+1\right){x}{y}+\left(\frac{1}{6}a^{3}+\frac{5}{6}a^{2}-\frac{7}{6}a-6\right){y}={x}^{3}+\left(\frac{1}{6}a^{3}+\frac{5}{6}a^{2}-\frac{19}{6}a-8\right){x}^{2}+\left(\frac{79}{6}a^{3}+\frac{101}{6}a^{2}-\frac{865}{6}a-236\right){x}-\frac{935}{6}a^{3}-\frac{1081}{6}a^{2}+\frac{9779}{6}a+2584$ |
| 64.4-a3 |
64.4-a |
$4$ |
$4$ |
4.4.16225.1 |
$4$ |
$[4, 0]$ |
64.4 |
\( 2^{6} \) |
\( 2^{16} \) |
$19.14271$ |
$(1/3a^3+2/3a^2-4/3a-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$4$ |
\( 2^{2} \) |
$1$ |
$115.7297520$ |
3.634232109 |
\( \frac{4757026975730}{3} a^{3} - \frac{13179896995829}{3} a^{2} - \frac{38504808791921}{3} a + 32239802712879 \) |
\( \bigl[\frac{1}{6} a^{3} - \frac{1}{6} a^{2} - \frac{1}{6} a + 1\) , \( \frac{1}{6} a^{3} + \frac{5}{6} a^{2} - \frac{19}{6} a - 8\) , \( \frac{1}{6} a^{3} + \frac{5}{6} a^{2} - \frac{7}{6} a - 6\) , \( -\frac{1}{6} a^{3} + \frac{31}{6} a^{2} - \frac{35}{6} a - 46\) , \( -\frac{5}{2} a^{3} + \frac{7}{2} a^{2} + \frac{39}{2} a - 18\bigr] \) |
${y}^2+\left(\frac{1}{6}a^{3}-\frac{1}{6}a^{2}-\frac{1}{6}a+1\right){x}{y}+\left(\frac{1}{6}a^{3}+\frac{5}{6}a^{2}-\frac{7}{6}a-6\right){y}={x}^{3}+\left(\frac{1}{6}a^{3}+\frac{5}{6}a^{2}-\frac{19}{6}a-8\right){x}^{2}+\left(-\frac{1}{6}a^{3}+\frac{31}{6}a^{2}-\frac{35}{6}a-46\right){x}-\frac{5}{2}a^{3}+\frac{7}{2}a^{2}+\frac{39}{2}a-18$ |
| 64.4-a4 |
64.4-a |
$4$ |
$4$ |
4.4.16225.1 |
$4$ |
$[4, 0]$ |
64.4 |
\( 2^{6} \) |
\( 2^{8} \) |
$19.14271$ |
$(1/3a^3+2/3a^2-4/3a-3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2Cs |
$4$ |
\( 2 \) |
$1$ |
$925.8380161$ |
3.634232109 |
\( 277847 a^{3} - 771932 a^{2} - 2247008 a + 5675789 \) |
\( \bigl[\frac{1}{6} a^{3} - \frac{1}{6} a^{2} - \frac{1}{6} a + 1\) , \( \frac{1}{6} a^{3} + \frac{5}{6} a^{2} - \frac{19}{6} a - 8\) , \( \frac{1}{6} a^{3} + \frac{5}{6} a^{2} - \frac{7}{6} a - 6\) , \( -a^{3} + a^{2} + 5 a - 1\) , \( -4 a^{3} - 3 a^{2} + 38 a + 53\bigr] \) |
${y}^2+\left(\frac{1}{6}a^{3}-\frac{1}{6}a^{2}-\frac{1}{6}a+1\right){x}{y}+\left(\frac{1}{6}a^{3}+\frac{5}{6}a^{2}-\frac{7}{6}a-6\right){y}={x}^{3}+\left(\frac{1}{6}a^{3}+\frac{5}{6}a^{2}-\frac{19}{6}a-8\right){x}^{2}+\left(-a^{3}+a^{2}+5a-1\right){x}-4a^{3}-3a^{2}+38a+53$ |
| 64.4-b1 |
64.4-b |
$1$ |
$1$ |
4.4.16225.1 |
$4$ |
$[4, 0]$ |
64.4 |
\( 2^{6} \) |
\( - 2^{22} \) |
$19.14271$ |
$(1/3a^3+2/3a^2-4/3a-3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
|
|
$1$ |
\( 1 \) |
$0.398578148$ |
$467.5310675$ |
5.851828621 |
\( -\frac{4198}{3} a^{3} + \frac{15148}{3} a^{2} + \frac{11992}{3} a - 17056 \) |
\( \bigl[0\) , \( -\frac{1}{6} a^{3} + \frac{7}{6} a^{2} + \frac{7}{6} a - 7\) , \( \frac{1}{6} a^{3} - \frac{1}{6} a^{2} - \frac{1}{6} a + 1\) , \( -\frac{8}{3} a^{3} - \frac{10}{3} a^{2} + \frac{86}{3} a + 50\) , \( -\frac{20}{3} a^{3} - \frac{28}{3} a^{2} + \frac{212}{3} a + 123\bigr] \) |
${y}^2+\left(\frac{1}{6}a^{3}-\frac{1}{6}a^{2}-\frac{1}{6}a+1\right){y}={x}^{3}+\left(-\frac{1}{6}a^{3}+\frac{7}{6}a^{2}+\frac{7}{6}a-7\right){x}^{2}+\left(-\frac{8}{3}a^{3}-\frac{10}{3}a^{2}+\frac{86}{3}a+50\right){x}-\frac{20}{3}a^{3}-\frac{28}{3}a^{2}+\frac{212}{3}a+123$ |
| 64.4-c1 |
64.4-c |
$1$ |
$1$ |
4.4.16225.1 |
$4$ |
$[4, 0]$ |
64.4 |
\( 2^{6} \) |
\( 2^{20} \) |
$19.14271$ |
$(1/3a^3+2/3a^2-4/3a-3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
|
|
$1$ |
\( 2 \) |
$1$ |
$109.7057975$ |
1.722531695 |
\( -\frac{108536501}{6} a^{3} + \frac{300774593}{6} a^{2} + \frac{878488241}{6} a - 367888129 \) |
\( \bigl[\frac{1}{6} a^{3} - \frac{1}{6} a^{2} - \frac{1}{6} a + 1\) , \( a + 1\) , \( \frac{1}{6} a^{3} - \frac{1}{6} a^{2} - \frac{1}{6} a + 1\) , \( -\frac{41}{3} a^{3} + \frac{122}{3} a^{2} + \frac{341}{3} a - 295\) , \( -\frac{539}{6} a^{3} + \frac{1523}{6} a^{2} + \frac{4385}{6} a - 1857\bigr] \) |
${y}^2+\left(\frac{1}{6}a^{3}-\frac{1}{6}a^{2}-\frac{1}{6}a+1\right){x}{y}+\left(\frac{1}{6}a^{3}-\frac{1}{6}a^{2}-\frac{1}{6}a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-\frac{41}{3}a^{3}+\frac{122}{3}a^{2}+\frac{341}{3}a-295\right){x}-\frac{539}{6}a^{3}+\frac{1523}{6}a^{2}+\frac{4385}{6}a-1857$ |
| 64.4-d1 |
64.4-d |
$4$ |
$4$ |
4.4.16225.1 |
$4$ |
$[4, 0]$ |
64.4 |
\( 2^{6} \) |
\( - 2^{16} \) |
$19.14271$ |
$(1/3a^3+2/3a^2-4/3a-3)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$4.240610387$ |
$222.4424047$ |
3.702743309 |
\( \frac{433}{3} a^{3} - \frac{1084}{3} a^{2} - \frac{3736}{3} a + 2945 \) |
\( \bigl[a^{2} - a - 7\) , \( \frac{1}{6} a^{3} + \frac{5}{6} a^{2} - \frac{7}{6} a - 6\) , \( \frac{1}{6} a^{3} - \frac{1}{6} a^{2} - \frac{1}{6} a + 1\) , \( -\frac{35}{6} a^{3} + \frac{107}{6} a^{2} + \frac{257}{6} a - 112\) , \( -\frac{19}{2} a^{3} + \frac{51}{2} a^{2} + \frac{169}{2} a - 206\bigr] \) |
${y}^2+\left(a^{2}-a-7\right){x}{y}+\left(\frac{1}{6}a^{3}-\frac{1}{6}a^{2}-\frac{1}{6}a+1\right){y}={x}^{3}+\left(\frac{1}{6}a^{3}+\frac{5}{6}a^{2}-\frac{7}{6}a-6\right){x}^{2}+\left(-\frac{35}{6}a^{3}+\frac{107}{6}a^{2}+\frac{257}{6}a-112\right){x}-\frac{19}{2}a^{3}+\frac{51}{2}a^{2}+\frac{169}{2}a-206$ |
| 64.4-d2 |
64.4-d |
$4$ |
$4$ |
4.4.16225.1 |
$4$ |
$[4, 0]$ |
64.4 |
\( 2^{6} \) |
\( 2^{8} \) |
$19.14271$ |
$(1/3a^3+2/3a^2-4/3a-3)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2 \) |
$2.120305193$ |
$444.8848094$ |
3.702743309 |
\( 277847 a^{3} - 771932 a^{2} - 2247008 a + 5675789 \) |
\( \bigl[\frac{1}{6} a^{3} - \frac{1}{6} a^{2} - \frac{1}{6} a + 1\) , \( a^{2} - 7\) , \( \frac{1}{6} a^{3} - \frac{1}{6} a^{2} - \frac{1}{6} a + 1\) , \( \frac{2}{3} a^{3} - \frac{2}{3} a^{2} - \frac{11}{3} a + 4\) , \( -\frac{5}{6} a^{3} - \frac{19}{6} a^{2} + \frac{29}{6} a + 12\bigr] \) |
${y}^2+\left(\frac{1}{6}a^{3}-\frac{1}{6}a^{2}-\frac{1}{6}a+1\right){x}{y}+\left(\frac{1}{6}a^{3}-\frac{1}{6}a^{2}-\frac{1}{6}a+1\right){y}={x}^{3}+\left(a^{2}-7\right){x}^{2}+\left(\frac{2}{3}a^{3}-\frac{2}{3}a^{2}-\frac{11}{3}a+4\right){x}-\frac{5}{6}a^{3}-\frac{19}{6}a^{2}+\frac{29}{6}a+12$ |
| 64.4-d3 |
64.4-d |
$4$ |
$4$ |
4.4.16225.1 |
$4$ |
$[4, 0]$ |
64.4 |
\( 2^{6} \) |
\( 2^{16} \) |
$19.14271$ |
$(1/3a^3+2/3a^2-4/3a-3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$1.060152596$ |
$222.4424047$ |
3.702743309 |
\( \frac{4757026975730}{3} a^{3} - \frac{13179896995829}{3} a^{2} - \frac{38504808791921}{3} a + 32239802712879 \) |
\( \bigl[\frac{1}{6} a^{3} - \frac{1}{6} a^{2} - \frac{1}{6} a + 1\) , \( a^{2} - 7\) , \( \frac{1}{6} a^{3} - \frac{1}{6} a^{2} - \frac{1}{6} a + 1\) , \( -\frac{1}{6} a^{3} - \frac{29}{6} a^{2} + \frac{13}{6} a + 19\) , \( -\frac{2}{3} a^{3} - \frac{1}{3} a^{2} + \frac{8}{3} a + 2\bigr] \) |
${y}^2+\left(\frac{1}{6}a^{3}-\frac{1}{6}a^{2}-\frac{1}{6}a+1\right){x}{y}+\left(\frac{1}{6}a^{3}-\frac{1}{6}a^{2}-\frac{1}{6}a+1\right){y}={x}^{3}+\left(a^{2}-7\right){x}^{2}+\left(-\frac{1}{6}a^{3}-\frac{29}{6}a^{2}+\frac{13}{6}a+19\right){x}-\frac{2}{3}a^{3}-\frac{1}{3}a^{2}+\frac{8}{3}a+2$ |
| 64.4-d4 |
64.4-d |
$4$ |
$4$ |
4.4.16225.1 |
$4$ |
$[4, 0]$ |
64.4 |
\( 2^{6} \) |
\( - 2^{16} \) |
$19.14271$ |
$(1/3a^3+2/3a^2-4/3a-3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$4.240610387$ |
$27.80530059$ |
3.702743309 |
\( -15962230 a^{3} - 13893305 a^{2} + 172884923 a + 261061025 \) |
\( \bigl[\frac{1}{6} a^{3} - \frac{1}{6} a^{2} - \frac{1}{6} a + 1\) , \( a^{2} - 7\) , \( \frac{1}{6} a^{3} - \frac{1}{6} a^{2} - \frac{1}{6} a + 1\) , \( -\frac{7}{2} a^{3} - \frac{43}{2} a^{2} + \frac{41}{2} a + 89\) , \( -\frac{160}{3} a^{3} - \frac{524}{3} a^{2} + \frac{841}{3} a + 746\bigr] \) |
${y}^2+\left(\frac{1}{6}a^{3}-\frac{1}{6}a^{2}-\frac{1}{6}a+1\right){x}{y}+\left(\frac{1}{6}a^{3}-\frac{1}{6}a^{2}-\frac{1}{6}a+1\right){y}={x}^{3}+\left(a^{2}-7\right){x}^{2}+\left(-\frac{7}{2}a^{3}-\frac{43}{2}a^{2}+\frac{41}{2}a+89\right){x}-\frac{160}{3}a^{3}-\frac{524}{3}a^{2}+\frac{841}{3}a+746$ |
| 64.4-e1 |
64.4-e |
$1$ |
$1$ |
4.4.16225.1 |
$4$ |
$[4, 0]$ |
64.4 |
\( 2^{6} \) |
\( 2^{20} \) |
$19.14271$ |
$(1/3a^3+2/3a^2-4/3a-3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
|
|
$1$ |
\( 2 \) |
$1.995993781$ |
$35.64671152$ |
4.468649477 |
\( -\frac{108536501}{6} a^{3} + \frac{300774593}{6} a^{2} + \frac{878488241}{6} a - 367888129 \) |
\( \bigl[a^{2} - a - 7\) , \( -\frac{1}{6} a^{3} + \frac{7}{6} a^{2} + \frac{7}{6} a - 7\) , \( 0\) , \( -\frac{17}{2} a^{3} + \frac{63}{2} a^{2} + \frac{49}{2} a - 108\) , \( -\frac{119}{3} a^{3} + \frac{449}{3} a^{2} + \frac{302}{3} a - 513\bigr] \) |
${y}^2+\left(a^{2}-a-7\right){x}{y}={x}^{3}+\left(-\frac{1}{6}a^{3}+\frac{7}{6}a^{2}+\frac{7}{6}a-7\right){x}^{2}+\left(-\frac{17}{2}a^{3}+\frac{63}{2}a^{2}+\frac{49}{2}a-108\right){x}-\frac{119}{3}a^{3}+\frac{449}{3}a^{2}+\frac{302}{3}a-513$ |
| 64.4-f1 |
64.4-f |
$1$ |
$1$ |
4.4.16225.1 |
$4$ |
$[4, 0]$ |
64.4 |
\( 2^{6} \) |
\( - 2^{22} \) |
$19.14271$ |
$(1/3a^3+2/3a^2-4/3a-3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
|
|
$1$ |
\( 1 \) |
$1$ |
$230.1517432$ |
1.806849234 |
\( -\frac{4198}{3} a^{3} + \frac{15148}{3} a^{2} + \frac{11992}{3} a - 17056 \) |
\( \bigl[0\) , \( \frac{1}{6} a^{3} + \frac{5}{6} a^{2} - \frac{13}{6} a - 8\) , \( \frac{1}{6} a^{3} - \frac{1}{6} a^{2} - \frac{1}{6} a + 1\) , \( -\frac{2}{3} a^{3} - \frac{4}{3} a^{2} + \frac{23}{3} a + 16\) , \( \frac{5}{6} a^{3} + \frac{1}{6} a^{2} - \frac{53}{6} a - 12\bigr] \) |
${y}^2+\left(\frac{1}{6}a^{3}-\frac{1}{6}a^{2}-\frac{1}{6}a+1\right){y}={x}^{3}+\left(\frac{1}{6}a^{3}+\frac{5}{6}a^{2}-\frac{13}{6}a-8\right){x}^{2}+\left(-\frac{2}{3}a^{3}-\frac{4}{3}a^{2}+\frac{23}{3}a+16\right){x}+\frac{5}{6}a^{3}+\frac{1}{6}a^{2}-\frac{53}{6}a-12$ |
| 76.2-a1 |
76.2-a |
$1$ |
$1$ |
4.4.16225.1 |
$4$ |
$[4, 0]$ |
76.2 |
\( 2^{2} \cdot 19 \) |
\( 2^{4} \cdot 19^{8} \) |
$19.55837$ |
$(1/6a^3+5/6a^2-7/6a-5), (1/3a^3-1/3a^2-10/3a+2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2^{4} \) |
$1$ |
$14.90163978$ |
1.871809689 |
\( \frac{17428257335143375475}{407605512984} a^{3} - \frac{65843784811728540029}{407605512984} a^{2} - \frac{43645308360297631757}{407605512984} a + \frac{18818048741697529469}{33967126082} \) |
\( \bigl[\frac{1}{6} a^{3} - \frac{1}{6} a^{2} - \frac{1}{6} a\) , \( -\frac{1}{6} a^{3} + \frac{7}{6} a^{2} - \frac{5}{6} a - 8\) , \( \frac{1}{6} a^{3} + \frac{5}{6} a^{2} - \frac{13}{6} a - 6\) , \( \frac{3419}{2} a^{3} + \frac{3989}{2} a^{2} - \frac{35883}{2} a - 28533\) , \( -\frac{420308}{3} a^{3} - \frac{487420}{3} a^{2} + \frac{4411274}{3} a + 2335211\bigr] \) |
${y}^2+\left(\frac{1}{6}a^{3}-\frac{1}{6}a^{2}-\frac{1}{6}a\right){x}{y}+\left(\frac{1}{6}a^{3}+\frac{5}{6}a^{2}-\frac{13}{6}a-6\right){y}={x}^{3}+\left(-\frac{1}{6}a^{3}+\frac{7}{6}a^{2}-\frac{5}{6}a-8\right){x}^{2}+\left(\frac{3419}{2}a^{3}+\frac{3989}{2}a^{2}-\frac{35883}{2}a-28533\right){x}-\frac{420308}{3}a^{3}-\frac{487420}{3}a^{2}+\frac{4411274}{3}a+2335211$ |
| 76.2-b1 |
76.2-b |
$1$ |
$1$ |
4.4.16225.1 |
$4$ |
$[4, 0]$ |
76.2 |
\( 2^{2} \cdot 19 \) |
\( 2^{4} \cdot 19^{8} \) |
$19.55837$ |
$(1/6a^3+5/6a^2-7/6a-5), (1/3a^3-1/3a^2-10/3a+2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2^{2} \) |
$1$ |
$30.34656030$ |
0.952965352 |
\( \frac{17428257335143375475}{407605512984} a^{3} - \frac{65843784811728540029}{407605512984} a^{2} - \frac{43645308360297631757}{407605512984} a + \frac{18818048741697529469}{33967126082} \) |
\( \bigl[\frac{1}{6} a^{3} + \frac{5}{6} a^{2} - \frac{7}{6} a - 7\) , \( -\frac{1}{6} a^{3} + \frac{7}{6} a^{2} - \frac{5}{6} a - 7\) , \( a^{2} - a - 7\) , \( 79 a^{3} + 110 a^{2} - 771 a - 1274\) , \( \frac{7435}{6} a^{3} + \frac{9971}{6} a^{2} - \frac{72001}{6} a - 19580\bigr] \) |
${y}^2+\left(\frac{1}{6}a^{3}+\frac{5}{6}a^{2}-\frac{7}{6}a-7\right){x}{y}+\left(a^{2}-a-7\right){y}={x}^{3}+\left(-\frac{1}{6}a^{3}+\frac{7}{6}a^{2}-\frac{5}{6}a-7\right){x}^{2}+\left(79a^{3}+110a^{2}-771a-1274\right){x}+\frac{7435}{6}a^{3}+\frac{9971}{6}a^{2}-\frac{72001}{6}a-19580$ |
| 76.2-c1 |
76.2-c |
$2$ |
$3$ |
4.4.16225.1 |
$4$ |
$[4, 0]$ |
76.2 |
\( 2^{2} \cdot 19 \) |
\( - 2^{6} \cdot 19^{2} \) |
$19.55837$ |
$(1/6a^3+5/6a^2-7/6a-5), (1/3a^3-1/3a^2-10/3a+2)$ |
$2$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 2 \) |
$0.023463441$ |
$881.3833876$ |
5.195342601 |
\( -\frac{15779143}{2166} a^{3} - \frac{53955503}{8664} a^{2} + \frac{651846229}{8664} a + \frac{289182259}{2888} \) |
\( \bigl[a^{2} - a - 7\) , \( 1\) , \( \frac{1}{6} a^{3} + \frac{5}{6} a^{2} - \frac{13}{6} a - 6\) , \( 0\) , \( 0\bigr] \) |
${y}^2+\left(a^{2}-a-7\right){x}{y}+\left(\frac{1}{6}a^{3}+\frac{5}{6}a^{2}-\frac{13}{6}a-6\right){y}={x}^{3}+{x}^{2}$ |
| 76.2-c2 |
76.2-c |
$2$ |
$3$ |
4.4.16225.1 |
$4$ |
$[4, 0]$ |
76.2 |
\( 2^{2} \cdot 19 \) |
\( - 2^{18} \cdot 19^{6} \) |
$19.55837$ |
$(1/6a^3+5/6a^2-7/6a-5), (1/3a^3-1/3a^2-10/3a+2)$ |
$2$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 2 \) |
$0.211170970$ |
$97.93148752$ |
5.195342601 |
\( \frac{758824281392413199}{9032809152} a^{3} - \frac{22934531625924522847}{72262473216} a^{2} - \frac{15207761590086801163}{72262473216} a + \frac{26224234042269258567}{24087491072} \) |
\( \bigl[a^{2} - a - 7\) , \( 1\) , \( \frac{1}{6} a^{3} + \frac{5}{6} a^{2} - \frac{13}{6} a - 6\) , \( \frac{5}{3} a^{3} - \frac{20}{3} a^{2} - \frac{20}{3} a + 25\) , \( -\frac{5}{2} a^{3} + \frac{7}{2} a^{2} + \frac{13}{2} a - 9\bigr] \) |
${y}^2+\left(a^{2}-a-7\right){x}{y}+\left(\frac{1}{6}a^{3}+\frac{5}{6}a^{2}-\frac{13}{6}a-6\right){y}={x}^{3}+{x}^{2}+\left(\frac{5}{3}a^{3}-\frac{20}{3}a^{2}-\frac{20}{3}a+25\right){x}-\frac{5}{2}a^{3}+\frac{7}{2}a^{2}+\frac{13}{2}a-9$ |
| 76.2-d1 |
76.2-d |
$2$ |
$3$ |
4.4.16225.1 |
$4$ |
$[4, 0]$ |
76.2 |
\( 2^{2} \cdot 19 \) |
\( - 2^{18} \cdot 19 \) |
$19.55837$ |
$(1/6a^3+5/6a^2-7/6a-5), (1/3a^3-1/3a^2-10/3a+2)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1 |
$1$ |
\( 3^{2} \) |
$1$ |
$235.3773227$ |
1.847873621 |
\( \frac{1283876395}{7296} a^{3} + \frac{12219646895}{29184} a^{2} - \frac{25175106325}{29184} a - \frac{18125906531}{9728} \) |
\( \bigl[a^{2} - 7\) , \( 0\) , \( a\) , \( \frac{53}{6} a^{3} + \frac{61}{6} a^{2} - \frac{557}{6} a - 146\) , \( -\frac{695}{2} a^{3} - \frac{807}{2} a^{2} + \frac{7295}{2} a + 5795\bigr] \) |
${y}^2+\left(a^{2}-7\right){x}{y}+a{y}={x}^{3}+\left(\frac{53}{6}a^{3}+\frac{61}{6}a^{2}-\frac{557}{6}a-146\right){x}-\frac{695}{2}a^{3}-\frac{807}{2}a^{2}+\frac{7295}{2}a+5795$ |
| 76.2-d2 |
76.2-d |
$2$ |
$3$ |
4.4.16225.1 |
$4$ |
$[4, 0]$ |
76.2 |
\( 2^{2} \cdot 19 \) |
\( - 2^{6} \cdot 19^{3} \) |
$19.55837$ |
$(1/6a^3+5/6a^2-7/6a-5), (1/3a^3-1/3a^2-10/3a+2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.2 |
$9$ |
\( 3^{2} \) |
$1$ |
$2.905892872$ |
1.847873621 |
\( \frac{2728474999953280805377885}{329232} a^{3} + \frac{6517372894619793685285643}{329232} a^{2} - \frac{13385076746015151259895653}{329232} a - \frac{4831082607194298347787901}{54872} \) |
\( \bigl[a^{2} - 7\) , \( 0\) , \( a\) , \( -\frac{169}{2} a^{3} - \frac{183}{2} a^{2} + \frac{1741}{2} a + 1314\) , \( \frac{55625}{6} a^{3} + \frac{64651}{6} a^{2} - \frac{584219}{6} a - 154901\bigr] \) |
${y}^2+\left(a^{2}-7\right){x}{y}+a{y}={x}^{3}+\left(-\frac{169}{2}a^{3}-\frac{183}{2}a^{2}+\frac{1741}{2}a+1314\right){x}+\frac{55625}{6}a^{3}+\frac{64651}{6}a^{2}-\frac{584219}{6}a-154901$ |
*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.
