| 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 |
| 12.1-a1 |
12.1-a |
$6$ |
$8$ |
4.4.13068.1 |
$4$ |
$[4, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( 2^{16} \cdot 3^{2} \) |
$13.93608$ |
$(2a^3-3a^2-10a+2), (a^2+a-1)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$0.873972424$ |
$112.3141724$ |
3.434691376 |
\( -\frac{34451}{768} a^{3} + \frac{34451}{768} a^{2} + \frac{241157}{768} a + \frac{119659}{768} \) |
\( \bigl[-a^{3} + 2 a^{2} + 4 a - 2\) , \( -1\) , \( a^{3} - a^{2} - 5 a - 1\) , \( a^{3} - a^{2} - 7 a + 2\) , \( -3 a^{3} + 3 a^{2} + 21 a - 9\bigr] \) |
${y}^2+\left(-a^{3}+2a^{2}+4a-2\right){x}{y}+\left(a^{3}-a^{2}-5a-1\right){y}={x}^{3}-{x}^{2}+\left(a^{3}-a^{2}-7a+2\right){x}-3a^{3}+3a^{2}+21a-9$ |
| 12.1-a2 |
12.1-a |
$6$ |
$8$ |
4.4.13068.1 |
$4$ |
$[4, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( 2^{2} \cdot 3^{16} \) |
$13.93608$ |
$(2a^3-3a^2-10a+2), (a^2+a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.436986212$ |
$449.2566896$ |
3.434691376 |
\( -\frac{573965017}{54} a^{3} + \frac{573965017}{54} a^{2} + \frac{4017755119}{54} a + \frac{5806871057}{162} \) |
\( \bigl[-a^{3} + 2 a^{2} + 4 a - 2\) , \( a^{3} - a^{2} - 7 a\) , \( 0\) , \( 18 a^{3} - 18 a^{2} - 126 a - 47\) , \( -69 a^{3} + 69 a^{2} + 483 a + 243\bigr] \) |
${y}^2+\left(-a^{3}+2a^{2}+4a-2\right){x}{y}={x}^{3}+\left(a^{3}-a^{2}-7a\right){x}^{2}+\left(18a^{3}-18a^{2}-126a-47\right){x}-69a^{3}+69a^{2}+483a+243$ |
| 12.1-a3 |
12.1-a |
$6$ |
$8$ |
4.4.13068.1 |
$4$ |
$[4, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( 2^{4} \cdot 3^{8} \) |
$13.93608$ |
$(2a^3-3a^2-10a+2), (a^2+a-1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$0.218493106$ |
$1797.026758$ |
3.434691376 |
\( -\frac{11767}{12} a^{3} + \frac{11767}{12} a^{2} + \frac{82369}{12} a + \frac{225265}{36} \) |
\( \bigl[-a^{3} + 2 a^{2} + 4 a - 2\) , \( a^{3} - a^{2} - 7 a\) , \( 0\) , \( 3 a^{3} - 3 a^{2} - 21 a + 3\) , \( 9\bigr] \) |
${y}^2+\left(-a^{3}+2a^{2}+4a-2\right){x}{y}={x}^{3}+\left(a^{3}-a^{2}-7a\right){x}^{2}+\left(3a^{3}-3a^{2}-21a+3\right){x}+9$ |
| 12.1-a4 |
12.1-a |
$6$ |
$8$ |
4.4.13068.1 |
$4$ |
$[4, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( 2^{8} \cdot 3^{4} \) |
$13.93608$ |
$(2a^3-3a^2-10a+2), (a^2+a-1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$0.436986212$ |
$449.2566896$ |
3.434691376 |
\( \frac{65471}{16} a^{3} - \frac{65471}{16} a^{2} - \frac{458297}{16} a + \frac{824267}{48} \) |
\( \bigl[a^{3} - a^{2} - 6 a - 1\) , \( -a^{3} + a^{2} + 7 a\) , \( a^{2} - a - 2\) , \( 13 a^{3} - 36 a^{2} - 13 a + 9\) , \( 48 a^{3} - 135 a^{2} - 43 a + 24\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-6a-1\right){x}{y}+\left(a^{2}-a-2\right){y}={x}^{3}+\left(-a^{3}+a^{2}+7a\right){x}^{2}+\left(13a^{3}-36a^{2}-13a+9\right){x}+48a^{3}-135a^{2}-43a+24$ |
| 12.1-a5 |
12.1-a |
$6$ |
$8$ |
4.4.13068.1 |
$4$ |
$[4, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( 2^{4} \cdot 3^{2} \) |
$13.93608$ |
$(2a^3-3a^2-10a+2), (a^2+a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
✓ |
|
$2$ |
2B |
$4$ |
\( 2^{2} \) |
$0.873972424$ |
$28.07854310$ |
3.434691376 |
\( \frac{1814298623}{12} a^{3} - \frac{1814298623}{12} a^{2} - \frac{12700090361}{12} a + \frac{4841284613}{12} \) |
\( \bigl[a^{3} - a^{2} - 6 a - 1\) , \( -a^{3} + a^{2} + 7 a\) , \( a^{2} - a - 2\) , \( 208 a^{3} - 571 a^{2} - 218 a + 89\) , \( 3802 a^{3} - 10670 a^{2} - 3396 a + 1971\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-6a-1\right){x}{y}+\left(a^{2}-a-2\right){y}={x}^{3}+\left(-a^{3}+a^{2}+7a\right){x}^{2}+\left(208a^{3}-571a^{2}-218a+89\right){x}+3802a^{3}-10670a^{2}-3396a+1971$ |
| 12.1-a6 |
12.1-a |
$6$ |
$8$ |
4.4.13068.1 |
$4$ |
$[4, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( 2^{2} \cdot 3^{4} \) |
$13.93608$ |
$(2a^3-3a^2-10a+2), (a^2+a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.109246553$ |
$1797.026758$ |
3.434691376 |
\( \frac{1547627}{2} a^{3} - \frac{1547627}{2} a^{2} - \frac{10833389}{2} a + \frac{11015453}{6} \) |
\( \bigl[a\) , \( 2 a^{3} - 3 a^{2} - 9 a + 2\) , \( a^{3} - a^{2} - 6 a - 1\) , \( 3 a^{3} + 3 a^{2} - 3 a + 6\) , \( 25 a^{3} + 52 a^{2} + 10 a - 4\bigr] \) |
${y}^2+a{x}{y}+\left(a^{3}-a^{2}-6a-1\right){y}={x}^{3}+\left(2a^{3}-3a^{2}-9a+2\right){x}^{2}+\left(3a^{3}+3a^{2}-3a+6\right){x}+25a^{3}+52a^{2}+10a-4$ |
| 12.1-b1 |
12.1-b |
$6$ |
$8$ |
4.4.13068.1 |
$4$ |
$[4, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( 2^{2} \cdot 3^{2} \) |
$13.93608$ |
$(2a^3-3a^2-10a+2), (a^2+a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$64$ |
\( 2 \) |
$1$ |
$4.675406230$ |
1.308774325 |
\( \frac{531321664281818146491712479}{2} a^{3} + \frac{1628823353887694808578099945}{3} a^{2} + \frac{351632875218067854416257885}{6} a - \frac{261843337348254999766538248}{3} \) |
\( \bigl[a^{2} - 2 a - 2\) , \( a^{3} - a^{2} - 5 a\) , \( a^{3} - a^{2} - 5 a\) , \( -207 a^{3} + 330 a^{2} + 1047 a - 427\) , \( -2696 a^{3} + 4177 a^{2} + 13864 a - 4949\bigr] \) |
${y}^2+\left(a^{2}-2a-2\right){x}{y}+\left(a^{3}-a^{2}-5a\right){y}={x}^{3}+\left(a^{3}-a^{2}-5a\right){x}^{2}+\left(-207a^{3}+330a^{2}+1047a-427\right){x}-2696a^{3}+4177a^{2}+13864a-4949$ |
| 12.1-b2 |
12.1-b |
$6$ |
$8$ |
4.4.13068.1 |
$4$ |
$[4, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( 2^{4} \cdot 3^{4} \) |
$13.93608$ |
$(2a^3-3a^2-10a+2), (a^2+a-1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$4$ |
\( 2^{3} \) |
$1$ |
$74.80649968$ |
1.308774325 |
\( \frac{7097336741951}{3} a^{3} + \frac{58010293511921}{12} a^{2} + 520639444971 a - \frac{9321083623331}{12} \) |
\( \bigl[-a^{3} + 2 a^{2} + 4 a - 2\) , \( 2 a^{3} - 3 a^{2} - 11 a + 1\) , \( -a^{3} + 2 a^{2} + 4 a - 2\) , \( -16 a^{3} + 13 a^{2} + 77 a - 24\) , \( -128 a^{3} + 170 a^{2} + 614 a - 216\bigr] \) |
${y}^2+\left(-a^{3}+2a^{2}+4a-2\right){x}{y}+\left(-a^{3}+2a^{2}+4a-2\right){y}={x}^{3}+\left(2a^{3}-3a^{2}-11a+1\right){x}^{2}+\left(-16a^{3}+13a^{2}+77a-24\right){x}-128a^{3}+170a^{2}+614a-216$ |
| 12.1-b3 |
12.1-b |
$6$ |
$8$ |
4.4.13068.1 |
$4$ |
$[4, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( 2^{4} \cdot 3^{16} \) |
$13.93608$ |
$(2a^3-3a^2-10a+2), (a^2+a-1)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$1$ |
$74.80649968$ |
1.308774325 |
\( -\frac{1036683181417999625476}{27} a^{3} + \frac{8353053198845987180365}{324} a^{2} + \frac{716532680943578841493}{3} a + \frac{467465469036373740445}{4} \) |
\( \bigl[a^{3} - a^{2} - 6 a - 1\) , \( -a^{3} + 2 a^{2} + 4 a - 2\) , \( a^{2} - 2 a - 2\) , \( 3207 a^{3} - 9050 a^{2} - 2740 a + 1750\) , \( -371722 a^{3} + 1049757 a^{2} + 315527 a - 203788\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-6a-1\right){x}{y}+\left(a^{2}-2a-2\right){y}={x}^{3}+\left(-a^{3}+2a^{2}+4a-2\right){x}^{2}+\left(3207a^{3}-9050a^{2}-2740a+1750\right){x}-371722a^{3}+1049757a^{2}+315527a-203788$ |
| 12.1-b4 |
12.1-b |
$6$ |
$8$ |
4.4.13068.1 |
$4$ |
$[4, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( 2^{8} \cdot 3^{8} \) |
$13.93608$ |
$(2a^3-3a^2-10a+2), (a^2+a-1)$ |
0 |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$1$ |
$299.2259987$ |
1.308774325 |
\( -\frac{43797924767}{16} a^{3} + \frac{11036174117}{6} a^{2} + \frac{2451988535401}{144} a + 8331250974 \) |
\( \bigl[a^{3} - a^{2} - 6 a - 1\) , \( -a^{3} + 2 a^{2} + 4 a - 2\) , \( a^{2} - 2 a - 2\) , \( 3607 a^{3} - 10185 a^{2} - 3065 a + 1975\) , \( -300545 a^{3} + 848755 a^{2} + 255097 a - 164769\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-6a-1\right){x}{y}+\left(a^{2}-2a-2\right){y}={x}^{3}+\left(-a^{3}+2a^{2}+4a-2\right){x}^{2}+\left(3607a^{3}-10185a^{2}-3065a+1975\right){x}-300545a^{3}+848755a^{2}+255097a-164769$ |
| 12.1-b5 |
12.1-b |
$6$ |
$8$ |
4.4.13068.1 |
$4$ |
$[4, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( 2^{2} \cdot 3^{2} \) |
$13.93608$ |
$(2a^3-3a^2-10a+2), (a^2+a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$16$ |
\( 2 \) |
$1$ |
$18.70162492$ |
1.308774325 |
\( \frac{440549763666604197}{2} a^{3} - \frac{1023108718588004999}{3} a^{2} - \frac{6808097410236460801}{6} a + \frac{1205377891391042896}{3} \) |
\( \bigl[a^{3} - a^{2} - 6 a - 1\) , \( -2 a^{3} + 3 a^{2} + 11 a\) , \( a + 1\) , \( 13 a^{3} - 47 a^{2} - 3 a + 19\) , \( 88 a^{3} - 288 a^{2} - 66 a + 63\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-6a-1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-2a^{3}+3a^{2}+11a\right){x}^{2}+\left(13a^{3}-47a^{2}-3a+19\right){x}+88a^{3}-288a^{2}-66a+63$ |
| 12.1-b6 |
12.1-b |
$6$ |
$8$ |
4.4.13068.1 |
$4$ |
$[4, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( 2^{16} \cdot 3^{4} \) |
$13.93608$ |
$(2a^3-3a^2-10a+2), (a^2+a-1)$ |
0 |
$\Z/8\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$1$ |
$299.2259987$ |
1.308774325 |
\( -\frac{75343375421525}{48} a^{3} + \frac{3404376659285269}{768} a^{2} + \frac{42633632439585}{32} a - \frac{660888366058603}{768} \) |
\( \bigl[a\) , \( a^{2} - 2 a - 2\) , \( -a^{3} + 2 a^{2} + 4 a - 2\) , \( -26 a^{3} - 11 a^{2} + 51 a - 14\) , \( -194 a^{3} - 454 a^{2} - 130 a + 100\bigr] \) |
${y}^2+a{x}{y}+\left(-a^{3}+2a^{2}+4a-2\right){y}={x}^{3}+\left(a^{2}-2a-2\right){x}^{2}+\left(-26a^{3}-11a^{2}+51a-14\right){x}-194a^{3}-454a^{2}-130a+100$ |
| 12.1-c1 |
12.1-c |
$6$ |
$8$ |
4.4.13068.1 |
$4$ |
$[4, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( 2^{4} \cdot 3^{4} \) |
$13.93608$ |
$(2a^3-3a^2-10a+2), (a^2+a-1)$ |
$0 \le r \le 2$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$4$ |
\( 2^{3} \) |
$1$ |
$74.80649968$ |
1.308774325 |
\( -\frac{262983395626201}{12} a^{3} + 14715312928873 a^{2} + \frac{1635910667269127}{12} a + \frac{200112375462256}{3} \) |
\( \bigl[-a^{3} + 2 a^{2} + 4 a - 2\) , \( a^{2} - 3 a - 3\) , \( -a^{3} + 2 a^{2} + 4 a - 2\) , \( 22 a^{3} - 19 a^{2} - 119 a - 80\) , \( 112 a^{3} - 154 a^{2} - 502 a - 204\bigr] \) |
${y}^2+\left(-a^{3}+2a^{2}+4a-2\right){x}{y}+\left(-a^{3}+2a^{2}+4a-2\right){y}={x}^{3}+\left(a^{2}-3a-3\right){x}^{2}+\left(22a^{3}-19a^{2}-119a-80\right){x}+112a^{3}-154a^{2}-502a-204$ |
| 12.1-c2 |
12.1-c |
$6$ |
$8$ |
4.4.13068.1 |
$4$ |
$[4, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( 2^{4} \cdot 3^{16} \) |
$13.93608$ |
$(2a^3-3a^2-10a+2), (a^2+a-1)$ |
$0 \le r \le 2$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$1$ |
$74.80649968$ |
1.308774325 |
\( \frac{1342804498359466478375}{324} a^{3} + \frac{76231679994737273527}{9} a^{2} + \frac{296226208689188310115}{324} a - \frac{110292388112309740031}{81} \) |
\( \bigl[a^{3} - a^{2} - 6 a - 1\) , \( a^{3} - a^{2} - 7 a - 2\) , \( a^{2} - a - 3\) , \( -306 a^{3} + 871 a^{2} + 246 a - 183\) , \( 154713 a^{3} - 436911 a^{2} - 131338 a + 84814\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-6a-1\right){x}{y}+\left(a^{2}-a-3\right){y}={x}^{3}+\left(a^{3}-a^{2}-7a-2\right){x}^{2}+\left(-306a^{3}+871a^{2}+246a-183\right){x}+154713a^{3}-436911a^{2}-131338a+84814$ |
| 12.1-c3 |
12.1-c |
$6$ |
$8$ |
4.4.13068.1 |
$4$ |
$[4, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( 2^{8} \cdot 3^{8} \) |
$13.93608$ |
$(2a^3-3a^2-10a+2), (a^2+a-1)$ |
$0 \le r \le 2$ |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$1$ |
$299.2259987$ |
1.308774325 |
\( \frac{2650784132}{9} a^{3} + \frac{86900597983}{144} a^{2} + \frac{144345863}{2} a - \frac{12772593329}{144} \) |
\( \bigl[a^{3} - a^{2} - 6 a - 1\) , \( a^{3} - a^{2} - 7 a - 2\) , \( a^{2} - a - 3\) , \( 1034 a^{3} - 2914 a^{2} - 889 a + 552\) , \( 45861 a^{3} - 129507 a^{2} - 38946 a + 25134\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-6a-1\right){x}{y}+\left(a^{2}-a-3\right){y}={x}^{3}+\left(a^{3}-a^{2}-7a-2\right){x}^{2}+\left(1034a^{3}-2914a^{2}-889a+552\right){x}+45861a^{3}-129507a^{2}-38946a+25134$ |
| 12.1-c4 |
12.1-c |
$6$ |
$8$ |
4.4.13068.1 |
$4$ |
$[4, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( 2^{2} \cdot 3^{2} \) |
$13.93608$ |
$(2a^3-3a^2-10a+2), (a^2+a-1)$ |
$0 \le r \le 2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$64$ |
\( 2 \) |
$1$ |
$4.675406230$ |
1.308774325 |
\( -\frac{7383517266455819273949209917}{3} a^{3} + \frac{9915422832290794491267082507}{6} a^{2} + \frac{45929926952622610452273359447}{3} a + \frac{14982327684928549109209501579}{2} \) |
\( \bigl[-a^{3} + 2 a^{2} + 5 a - 1\) , \( -a^{2} + 3 a + 4\) , \( a + 1\) , \( 70 a^{3} - 191 a^{2} - 89 a + 32\) , \( 708 a^{3} - 1980 a^{2} - 702 a + 341\bigr] \) |
${y}^2+\left(-a^{3}+2a^{2}+5a-1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a^{2}+3a+4\right){x}^{2}+\left(70a^{3}-191a^{2}-89a+32\right){x}+708a^{3}-1980a^{2}-702a+341$ |
| 12.1-c5 |
12.1-c |
$6$ |
$8$ |
4.4.13068.1 |
$4$ |
$[4, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( 2^{16} \cdot 3^{4} \) |
$13.93608$ |
$(2a^3-3a^2-10a+2), (a^2+a-1)$ |
$0 \le r \le 2$ |
$\Z/8\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$1$ |
$299.2259987$ |
1.308774325 |
\( \frac{4010874209375491}{768} a^{3} - \frac{258739869246515}{32} a^{2} - \frac{20660868596967677}{768} a + \frac{228626229158335}{24} \) |
\( \bigl[a\) , \( 2 a^{3} - 3 a^{2} - 11 a\) , \( a^{3} - a^{2} - 6 a\) , \( -224 a^{3} + 349 a^{2} + 1144 a - 432\) , \( 2338 a^{3} - 3603 a^{2} - 12042 a + 4211\bigr] \) |
${y}^2+a{x}{y}+\left(a^{3}-a^{2}-6a\right){y}={x}^{3}+\left(2a^{3}-3a^{2}-11a\right){x}^{2}+\left(-224a^{3}+349a^{2}+1144a-432\right){x}+2338a^{3}-3603a^{2}-12042a+4211$ |
| 12.1-c6 |
12.1-c |
$6$ |
$8$ |
4.4.13068.1 |
$4$ |
$[4, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( 2^{2} \cdot 3^{2} \) |
$13.93608$ |
$(2a^3-3a^2-10a+2), (a^2+a-1)$ |
$0 \le r \le 2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$16$ |
\( 2 \) |
$1$ |
$18.70162492$ |
1.308774325 |
\( -\frac{198615094793108669}{3} a^{3} + \frac{1121798335762414745}{6} a^{2} + \frac{168581850170647015}{3} a - \frac{72591204563022907}{2} \) |
\( \bigl[a\) , \( -a^{2} + 3 a + 4\) , \( a^{3} - a^{2} - 6 a\) , \( -41 a^{3} + 75 a^{2} + 198 a - 131\) , \( -263 a^{3} + 463 a^{2} + 1290 a - 786\bigr] \) |
${y}^2+a{x}{y}+\left(a^{3}-a^{2}-6a\right){y}={x}^{3}+\left(-a^{2}+3a+4\right){x}^{2}+\left(-41a^{3}+75a^{2}+198a-131\right){x}-263a^{3}+463a^{2}+1290a-786$ |
| 12.1-d1 |
12.1-d |
$6$ |
$8$ |
4.4.13068.1 |
$4$ |
$[4, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( 2^{2} \cdot 3^{2} \) |
$13.93608$ |
$(2a^3-3a^2-10a+2), (a^2+a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 2 \) |
$1$ |
$139.5459291$ |
2.441420599 |
\( -\frac{7383517266455819273949209917}{3} a^{3} + \frac{9915422832290794491267082507}{6} a^{2} + \frac{45929926952622610452273359447}{3} a + \frac{14982327684928549109209501579}{2} \) |
\( \bigl[a^{2} - 2 a - 2\) , \( a^{3} - a^{2} - 5 a\) , \( a^{2} - a - 2\) , \( 84 a^{3} - 148 a^{2} - 459 a + 156\) , \( -490 a^{3} + 763 a^{2} + 2533 a - 894\bigr] \) |
${y}^2+\left(a^{2}-2a-2\right){x}{y}+\left(a^{2}-a-2\right){y}={x}^{3}+\left(a^{3}-a^{2}-5a\right){x}^{2}+\left(84a^{3}-148a^{2}-459a+156\right){x}-490a^{3}+763a^{2}+2533a-894$ |
| 12.1-d2 |
12.1-d |
$6$ |
$8$ |
4.4.13068.1 |
$4$ |
$[4, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( 2^{16} \cdot 3^{4} \) |
$13.93608$ |
$(2a^3-3a^2-10a+2), (a^2+a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$1$ |
$34.88648229$ |
2.441420599 |
\( \frac{4010874209375491}{768} a^{3} - \frac{258739869246515}{32} a^{2} - \frac{20660868596967677}{768} a + \frac{228626229158335}{24} \) |
\( \bigl[-a^{3} + 2 a^{2} + 4 a - 2\) , \( a^{2} - 3 a - 3\) , \( 0\) , \( 23 a^{3} - 9 a^{2} - 157 a - 92\) , \( -221 a^{3} + 158 a^{2} + 1358 a + 633\bigr] \) |
${y}^2+\left(-a^{3}+2a^{2}+4a-2\right){x}{y}={x}^{3}+\left(a^{2}-3a-3\right){x}^{2}+\left(23a^{3}-9a^{2}-157a-92\right){x}-221a^{3}+158a^{2}+1358a+633$ |
| 12.1-d3 |
12.1-d |
$6$ |
$8$ |
4.4.13068.1 |
$4$ |
$[4, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( 2^{2} \cdot 3^{2} \) |
$13.93608$ |
$(2a^3-3a^2-10a+2), (a^2+a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$558.1837167$ |
2.441420599 |
\( -\frac{198615094793108669}{3} a^{3} + \frac{1121798335762414745}{6} a^{2} + \frac{168581850170647015}{3} a - \frac{72591204563022907}{2} \) |
\( \bigl[-a^{3} + 2 a^{2} + 4 a - 2\) , \( 2 a^{3} - 3 a^{2} - 10 a\) , \( a + 1\) , \( 67 a^{3} - 53 a^{2} - 401 a - 178\) , \( -500 a^{3} + 346 a^{2} + 3081 a + 1511\bigr] \) |
${y}^2+\left(-a^{3}+2a^{2}+4a-2\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(2a^{3}-3a^{2}-10a\right){x}^{2}+\left(67a^{3}-53a^{2}-401a-178\right){x}-500a^{3}+346a^{2}+3081a+1511$ |
| 12.1-d4 |
12.1-d |
$6$ |
$8$ |
4.4.13068.1 |
$4$ |
$[4, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( 2^{8} \cdot 3^{8} \) |
$13.93608$ |
$(2a^3-3a^2-10a+2), (a^2+a-1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$1$ |
$139.5459291$ |
2.441420599 |
\( \frac{2650784132}{9} a^{3} + \frac{86900597983}{144} a^{2} + \frac{144345863}{2} a - \frac{12772593329}{144} \) |
\( \bigl[-a^{3} + 2 a^{2} + 4 a - 2\) , \( a^{3} - a^{2} - 5 a\) , \( -a^{3} + 2 a^{2} + 4 a - 1\) , \( -159 a^{3} + 227 a^{2} + 886 a - 312\) , \( -2178 a^{3} + 3457 a^{2} + 10932 a - 3884\bigr] \) |
${y}^2+\left(-a^{3}+2a^{2}+4a-2\right){x}{y}+\left(-a^{3}+2a^{2}+4a-1\right){y}={x}^{3}+\left(a^{3}-a^{2}-5a\right){x}^{2}+\left(-159a^{3}+227a^{2}+886a-312\right){x}-2178a^{3}+3457a^{2}+10932a-3884$ |
| 12.1-d5 |
12.1-d |
$6$ |
$8$ |
4.4.13068.1 |
$4$ |
$[4, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( 2^{4} \cdot 3^{16} \) |
$13.93608$ |
$(2a^3-3a^2-10a+2), (a^2+a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 2^{5} \) |
$1$ |
$8.721620573$ |
2.441420599 |
\( \frac{1342804498359466478375}{324} a^{3} + \frac{76231679994737273527}{9} a^{2} + \frac{296226208689188310115}{324} a - \frac{110292388112309740031}{81} \) |
\( \bigl[-a^{3} + 2 a^{2} + 4 a - 2\) , \( a^{3} - a^{2} - 5 a\) , \( -a^{3} + 2 a^{2} + 4 a - 1\) , \( -159 a^{3} + 252 a^{2} + 801 a - 287\) , \( -2775 a^{3} + 4652 a^{2} + 13093 a - 4702\bigr] \) |
${y}^2+\left(-a^{3}+2a^{2}+4a-2\right){x}{y}+\left(-a^{3}+2a^{2}+4a-1\right){y}={x}^{3}+\left(a^{3}-a^{2}-5a\right){x}^{2}+\left(-159a^{3}+252a^{2}+801a-287\right){x}-2775a^{3}+4652a^{2}+13093a-4702$ |
| 12.1-d6 |
12.1-d |
$6$ |
$8$ |
4.4.13068.1 |
$4$ |
$[4, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( 2^{4} \cdot 3^{4} \) |
$13.93608$ |
$(2a^3-3a^2-10a+2), (a^2+a-1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1$ |
$558.1837167$ |
2.441420599 |
\( -\frac{262983395626201}{12} a^{3} + 14715312928873 a^{2} + \frac{1635910667269127}{12} a + \frac{200112375462256}{3} \) |
\( \bigl[a\) , \( 2 a^{3} - 3 a^{2} - 11 a\) , \( a^{2} - 2 a - 2\) , \( -323 a^{3} + 504 a^{2} + 1658 a - 609\) , \( -3531 a^{3} + 5452 a^{2} + 18208 a - 6362\bigr] \) |
${y}^2+a{x}{y}+\left(a^{2}-2a-2\right){y}={x}^{3}+\left(2a^{3}-3a^{2}-11a\right){x}^{2}+\left(-323a^{3}+504a^{2}+1658a-609\right){x}-3531a^{3}+5452a^{2}+18208a-6362$ |
| 12.1-e1 |
12.1-e |
$6$ |
$8$ |
4.4.13068.1 |
$4$ |
$[4, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( 2^{2} \cdot 3^{2} \) |
$13.93608$ |
$(2a^3-3a^2-10a+2), (a^2+a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$558.1837167$ |
2.441420599 |
\( \frac{440549763666604197}{2} a^{3} - \frac{1023108718588004999}{3} a^{2} - \frac{6808097410236460801}{6} a + \frac{1205377891391042896}{3} \) |
\( \bigl[-a^{3} + 2 a^{2} + 4 a - 2\) , \( -a^{3} + 2 a^{2} + 3 a - 3\) , \( a^{3} - a^{2} - 6 a\) , \( -14 a^{3} - a^{2} + 33 a - 10\) , \( 72 a^{3} + 82 a^{2} - 86 a + 15\bigr] \) |
${y}^2+\left(-a^{3}+2a^{2}+4a-2\right){x}{y}+\left(a^{3}-a^{2}-6a\right){y}={x}^{3}+\left(-a^{3}+2a^{2}+3a-3\right){x}^{2}+\left(-14a^{3}-a^{2}+33a-10\right){x}+72a^{3}+82a^{2}-86a+15$ |
| 12.1-e2 |
12.1-e |
$6$ |
$8$ |
4.4.13068.1 |
$4$ |
$[4, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( 2^{16} \cdot 3^{4} \) |
$13.93608$ |
$(2a^3-3a^2-10a+2), (a^2+a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$1$ |
$34.88648229$ |
2.441420599 |
\( -\frac{75343375421525}{48} a^{3} + \frac{3404376659285269}{768} a^{2} + \frac{42633632439585}{32} a - \frac{660888366058603}{768} \) |
\( \bigl[-a^{3} + 2 a^{2} + 4 a - 2\) , \( 2 a^{3} - 3 a^{2} - 11 a + 1\) , \( 0\) , \( 5 a^{3} - 19 a^{2} - 39 a + 10\) , \( 31 a^{3} + 32 a^{2} - 28 a + 3\bigr] \) |
${y}^2+\left(-a^{3}+2a^{2}+4a-2\right){x}{y}={x}^{3}+\left(2a^{3}-3a^{2}-11a+1\right){x}^{2}+\left(5a^{3}-19a^{2}-39a+10\right){x}+31a^{3}+32a^{2}-28a+3$ |
| 12.1-e3 |
12.1-e |
$6$ |
$8$ |
4.4.13068.1 |
$4$ |
$[4, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( 2^{8} \cdot 3^{8} \) |
$13.93608$ |
$(2a^3-3a^2-10a+2), (a^2+a-1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$1$ |
$139.5459291$ |
2.441420599 |
\( -\frac{43797924767}{16} a^{3} + \frac{11036174117}{6} a^{2} + \frac{2451988535401}{144} a + 8331250974 \) |
\( \bigl[-a^{3} + 2 a^{2} + 4 a - 2\) , \( -a^{3} + a^{2} + 5 a + 2\) , \( -a^{3} + 2 a^{2} + 4 a - 1\) , \( a^{3} - 70 a^{2} + 223 a - 61\) , \( 858 a^{3} - 2138 a^{2} - 1689 a + 757\bigr] \) |
${y}^2+\left(-a^{3}+2a^{2}+4a-2\right){x}{y}+\left(-a^{3}+2a^{2}+4a-1\right){y}={x}^{3}+\left(-a^{3}+a^{2}+5a+2\right){x}^{2}+\left(a^{3}-70a^{2}+223a-61\right){x}+858a^{3}-2138a^{2}-1689a+757$ |
| 12.1-e4 |
12.1-e |
$6$ |
$8$ |
4.4.13068.1 |
$4$ |
$[4, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( 2^{4} \cdot 3^{16} \) |
$13.93608$ |
$(2a^3-3a^2-10a+2), (a^2+a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 2^{5} \) |
$1$ |
$8.721620573$ |
2.441420599 |
\( -\frac{1036683181417999625476}{27} a^{3} + \frac{8353053198845987180365}{324} a^{2} + \frac{716532680943578841493}{3} a + \frac{467465469036373740445}{4} \) |
\( \bigl[-a^{3} + 2 a^{2} + 4 a - 2\) , \( -a^{3} + a^{2} + 5 a + 2\) , \( -a^{3} + 2 a^{2} + 4 a - 1\) , \( 61 a^{3} - 155 a^{2} - 112 a + 54\) , \( 1681 a^{3} - 3559 a^{2} - 5432 a + 2107\bigr] \) |
${y}^2+\left(-a^{3}+2a^{2}+4a-2\right){x}{y}+\left(-a^{3}+2a^{2}+4a-1\right){y}={x}^{3}+\left(-a^{3}+a^{2}+5a+2\right){x}^{2}+\left(61a^{3}-155a^{2}-112a+54\right){x}+1681a^{3}-3559a^{2}-5432a+2107$ |
| 12.1-e5 |
12.1-e |
$6$ |
$8$ |
4.4.13068.1 |
$4$ |
$[4, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( 2^{4} \cdot 3^{4} \) |
$13.93608$ |
$(2a^3-3a^2-10a+2), (a^2+a-1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1$ |
$558.1837167$ |
2.441420599 |
\( \frac{7097336741951}{3} a^{3} + \frac{58010293511921}{12} a^{2} + 520639444971 a - \frac{9321083623331}{12} \) |
\( \bigl[a^{3} - a^{2} - 6 a - 1\) , \( a^{2} - 3 a - 4\) , \( -a^{3} + 2 a^{2} + 5 a - 1\) , \( 98 a^{3} - 279 a^{2} - 84 a + 56\) , \( 1058 a^{3} - 2980 a^{2} - 895 a + 578\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-6a-1\right){x}{y}+\left(-a^{3}+2a^{2}+5a-1\right){y}={x}^{3}+\left(a^{2}-3a-4\right){x}^{2}+\left(98a^{3}-279a^{2}-84a+56\right){x}+1058a^{3}-2980a^{2}-895a+578$ |
| 12.1-e6 |
12.1-e |
$6$ |
$8$ |
4.4.13068.1 |
$4$ |
$[4, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( 2^{2} \cdot 3^{2} \) |
$13.93608$ |
$(2a^3-3a^2-10a+2), (a^2+a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 2 \) |
$1$ |
$139.5459291$ |
2.441420599 |
\( \frac{531321664281818146491712479}{2} a^{3} + \frac{1628823353887694808578099945}{3} a^{2} + \frac{351632875218067854416257885}{6} a - \frac{261843337348254999766538248}{3} \) |
\( \bigl[-a^{3} + 2 a^{2} + 5 a - 1\) , \( -a^{2} + 3 a + 4\) , \( -a^{3} + 2 a^{2} + 5 a - 1\) , \( 18 a^{3} + 47 a^{2} - 253 a - 161\) , \( 197 a^{3} - 552 a^{2} - 175 a + 103\bigr] \) |
${y}^2+\left(-a^{3}+2a^{2}+5a-1\right){x}{y}+\left(-a^{3}+2a^{2}+5a-1\right){y}={x}^{3}+\left(-a^{2}+3a+4\right){x}^{2}+\left(18a^{3}+47a^{2}-253a-161\right){x}+197a^{3}-552a^{2}-175a+103$ |
| 12.1-f1 |
12.1-f |
$6$ |
$8$ |
4.4.13068.1 |
$4$ |
$[4, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( 2^{2} \cdot 3^{4} \) |
$13.93608$ |
$(2a^3-3a^2-10a+2), (a^2+a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.636117744$ |
$148.7678610$ |
1.655663451 |
\( \frac{1547627}{2} a^{3} - \frac{1547627}{2} a^{2} - \frac{10833389}{2} a + \frac{11015453}{6} \) |
\( \bigl[-a^{3} + 2 a^{2} + 4 a - 2\) , \( -1\) , \( a^{2} - a - 3\) , \( -4 a^{3} + 4 a^{2} + 28 a + 11\) , \( 19 a^{3} - 19 a^{2} - 133 a - 65\bigr] \) |
${y}^2+\left(-a^{3}+2a^{2}+4a-2\right){x}{y}+\left(a^{2}-a-3\right){y}={x}^{3}-{x}^{2}+\left(-4a^{3}+4a^{2}+28a+11\right){x}+19a^{3}-19a^{2}-133a-65$ |
| 12.1-f2 |
12.1-f |
$6$ |
$8$ |
4.4.13068.1 |
$4$ |
$[4, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( 2^{4} \cdot 3^{2} \) |
$13.93608$ |
$(2a^3-3a^2-10a+2), (a^2+a-1)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.079514718$ |
$2380.285777$ |
1.655663451 |
\( \frac{1814298623}{12} a^{3} - \frac{1814298623}{12} a^{2} - \frac{12700090361}{12} a + \frac{4841284613}{12} \) |
\( \bigl[-a^{3} + 2 a^{2} + 4 a - 2\) , \( -a^{3} + a^{2} + 7 a + 1\) , \( 0\) , \( -6 a^{3} + 6 a^{2} + 42 a - 19\) , \( 15 a^{3} - 15 a^{2} - 105 a + 37\bigr] \) |
${y}^2+\left(-a^{3}+2a^{2}+4a-2\right){x}{y}={x}^{3}+\left(-a^{3}+a^{2}+7a+1\right){x}^{2}+\left(-6a^{3}+6a^{2}+42a-19\right){x}+15a^{3}-15a^{2}-105a+37$ |
| 12.1-f3 |
12.1-f |
$6$ |
$8$ |
4.4.13068.1 |
$4$ |
$[4, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( 2^{8} \cdot 3^{4} \) |
$13.93608$ |
$(2a^3-3a^2-10a+2), (a^2+a-1)$ |
$1$ |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$0.159029436$ |
$2380.285777$ |
1.655663451 |
\( \frac{65471}{16} a^{3} - \frac{65471}{16} a^{2} - \frac{458297}{16} a + \frac{824267}{48} \) |
\( \bigl[-a^{3} + 2 a^{2} + 4 a - 2\) , \( -a^{3} + a^{2} + 7 a + 1\) , \( 0\) , \( -a^{3} + a^{2} + 7 a + 1\) , \( 1\bigr] \) |
${y}^2+\left(-a^{3}+2a^{2}+4a-2\right){x}{y}={x}^{3}+\left(-a^{3}+a^{2}+7a+1\right){x}^{2}+\left(-a^{3}+a^{2}+7a+1\right){x}+1$ |
| 12.1-f4 |
12.1-f |
$6$ |
$8$ |
4.4.13068.1 |
$4$ |
$[4, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( 2^{16} \cdot 3^{2} \) |
$13.93608$ |
$(2a^3-3a^2-10a+2), (a^2+a-1)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$0.079514718$ |
$595.0714443$ |
1.655663451 |
\( -\frac{34451}{768} a^{3} + \frac{34451}{768} a^{2} + \frac{241157}{768} a + \frac{119659}{768} \) |
\( \bigl[a^{3} - a^{2} - 6 a - 1\) , \( -2 a^{3} + 3 a^{2} + 9 a\) , \( -a^{3} + 2 a^{2} + 5 a - 2\) , \( -11 a^{3} + 29 a^{2} + 13 a + 3\) , \( -872 a^{3} + 2458 a^{2} + 752 a - 475\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-6a-1\right){x}{y}+\left(-a^{3}+2a^{2}+5a-2\right){y}={x}^{3}+\left(-2a^{3}+3a^{2}+9a\right){x}^{2}+\left(-11a^{3}+29a^{2}+13a+3\right){x}-872a^{3}+2458a^{2}+752a-475$ |
| 12.1-f5 |
12.1-f |
$6$ |
$8$ |
4.4.13068.1 |
$4$ |
$[4, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( 2^{4} \cdot 3^{8} \) |
$13.93608$ |
$(2a^3-3a^2-10a+2), (a^2+a-1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$0.318058872$ |
$595.0714443$ |
1.655663451 |
\( -\frac{11767}{12} a^{3} + \frac{11767}{12} a^{2} + \frac{82369}{12} a + \frac{225265}{36} \) |
\( \bigl[a\) , \( -a^{3} + 2 a^{2} + 5 a - 2\) , \( a^{2} - a - 2\) , \( -2 a^{3} + 2 a^{2} + 6 a - 3\) , \( -a^{3} - 6 a^{2} - 6 a + 1\bigr] \) |
${y}^2+a{x}{y}+\left(a^{2}-a-2\right){y}={x}^{3}+\left(-a^{3}+2a^{2}+5a-2\right){x}^{2}+\left(-2a^{3}+2a^{2}+6a-3\right){x}-a^{3}-6a^{2}-6a+1$ |
| 12.1-f6 |
12.1-f |
$6$ |
$8$ |
4.4.13068.1 |
$4$ |
$[4, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( 2^{2} \cdot 3^{16} \) |
$13.93608$ |
$(2a^3-3a^2-10a+2), (a^2+a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
✓ |
|
$2$ |
2B |
$4$ |
\( 2 \) |
$0.636117744$ |
$37.19196527$ |
1.655663451 |
\( -\frac{573965017}{54} a^{3} + \frac{573965017}{54} a^{2} + \frac{4017755119}{54} a + \frac{5806871057}{162} \) |
\( \bigl[a\) , \( -a^{3} + 2 a^{2} + 5 a - 2\) , \( a^{2} - a - 2\) , \( 3 a^{3} - 33 a^{2} - 69 a + 7\) , \( -107 a^{3} - 151 a^{2} + 63 a - 34\bigr] \) |
${y}^2+a{x}{y}+\left(a^{2}-a-2\right){y}={x}^{3}+\left(-a^{3}+2a^{2}+5a-2\right){x}^{2}+\left(3a^{3}-33a^{2}-69a+7\right){x}-107a^{3}-151a^{2}+63a-34$ |
*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.
