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 |
4.2-a1 |
4.2-a |
$16$ |
$48$ |
4.4.9248.1 |
$4$ |
$[4, 0]$ |
4.2 |
\( 2^{2} \) |
\( 2^{9} \) |
$10.21927$ |
$(a), (-a^3+4a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$144$ |
\( 2 \) |
$1$ |
$0.813617215$ |
0.609156265 |
\( -\frac{2598999057507859430840814142230563}{8} a^{3} - 215117023039975647450343147847680 a^{2} + 1481933932657809377628672524686862 a + 981267661531062863922029372621544 \) |
\( \bigl[a^{2} + a - 3\) , \( a^{3} - 5 a + 1\) , \( a^{3} + a^{2} - 4 a - 2\) , \( -986 a^{3} + 2462 a^{2} + 7270 a - 5617\) , \( -24055 a^{3} + 130017 a^{2} + 277176 a - 233563\bigr] \) |
${y}^2+\left(a^{2}+a-3\right){x}{y}+\left(a^{3}+a^{2}-4a-2\right){y}={x}^{3}+\left(a^{3}-5a+1\right){x}^{2}+\left(-986a^{3}+2462a^{2}+7270a-5617\right){x}-24055a^{3}+130017a^{2}+277176a-233563$ |
4.2-a2 |
4.2-a |
$16$ |
$48$ |
4.4.9248.1 |
$4$ |
$[4, 0]$ |
4.2 |
\( 2^{2} \) |
\( 2^{9} \) |
$10.21927$ |
$(a), (-a^3+4a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$144$ |
\( 2 \) |
$1$ |
$0.813617215$ |
0.609156265 |
\( \frac{2598999057507859430840814142230563}{8} a^{3} - 215117023039975647450343147847680 a^{2} - 1481933932657809377628672524686862 a + 981267661531062863922029372621544 \) |
\( \bigl[a^{2} + a - 3\) , \( a^{3} - 4 a + 1\) , \( a^{3} - 4 a\) , \( 993 a^{3} + 2463 a^{2} - 7301 a - 5617\) , \( 20899 a^{3} + 125700 a^{2} - 259626 a - 220971\bigr] \) |
${y}^2+\left(a^{2}+a-3\right){x}{y}+\left(a^{3}-4a\right){y}={x}^{3}+\left(a^{3}-4a+1\right){x}^{2}+\left(993a^{3}+2463a^{2}-7301a-5617\right){x}+20899a^{3}+125700a^{2}-259626a-220971$ |
4.2-a3 |
4.2-a |
$16$ |
$48$ |
4.4.9248.1 |
$4$ |
$[4, 0]$ |
4.2 |
\( 2^{2} \) |
\( 2^{18} \) |
$10.21927$ |
$(a), (-a^3+4a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2Cs, 3B.1.2 |
$36$ |
\( 2^{2} \) |
$1$ |
$6.508937725$ |
0.609156265 |
\( -\frac{653762688677050897}{64} a^{2} + \frac{1491086515722280627}{32} \) |
\( \bigl[1\) , \( a^{2} - 2\) , \( a^{2} - 3\) , \( 981 a^{2} - 4478\) , \( 23629 a^{2} - 107786\bigr] \) |
${y}^2+{x}{y}+\left(a^{2}-3\right){y}={x}^{3}+\left(a^{2}-2\right){x}^{2}+\left(981a^{2}-4478\right){x}+23629a^{2}-107786$ |
4.2-a4 |
4.2-a |
$16$ |
$48$ |
4.4.9248.1 |
$4$ |
$[4, 0]$ |
4.2 |
\( 2^{2} \) |
\( 2^{3} \) |
$10.21927$ |
$(a), (-a^3+4a+1)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$16$ |
\( 2 \) |
$1$ |
$65.90299447$ |
0.609156265 |
\( -179213540276326839556 a^{3} + 382760552527098253312 a^{2} + \frac{157151345464271319581}{2} a - 167820287562717580568 \) |
\( \bigl[1\) , \( a^{2} - 2\) , \( a^{2} - 3\) , \( 145 a^{3} + 91 a^{2} - 645 a - 453\) , \( 1478 a^{3} + 1064 a^{2} - 6784 a - 4764\bigr] \) |
${y}^2+{x}{y}+\left(a^{2}-3\right){y}={x}^{3}+\left(a^{2}-2\right){x}^{2}+\left(145a^{3}+91a^{2}-645a-453\right){x}+1478a^{3}+1064a^{2}-6784a-4764$ |
4.2-a5 |
4.2-a |
$16$ |
$48$ |
4.4.9248.1 |
$4$ |
$[4, 0]$ |
4.2 |
\( 2^{2} \) |
\( 2^{3} \) |
$10.21927$ |
$(a), (-a^3+4a+1)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$16$ |
\( 2 \) |
$1$ |
$65.90299447$ |
0.609156265 |
\( 179213540276326839556 a^{3} + 382760552527098253312 a^{2} - \frac{157151345464271319581}{2} a - 167820287562717580568 \) |
\( \bigl[1\) , \( a^{2} - 2\) , \( a^{2} - 3\) , \( -145 a^{3} + 91 a^{2} + 645 a - 453\) , \( -1478 a^{3} + 1064 a^{2} + 6784 a - 4764\bigr] \) |
${y}^2+{x}{y}+\left(a^{2}-3\right){y}={x}^{3}+\left(a^{2}-2\right){x}^{2}+\left(-145a^{3}+91a^{2}+645a-453\right){x}-1478a^{3}+1064a^{2}+6784a-4764$ |
4.2-a6 |
4.2-a |
$16$ |
$48$ |
4.4.9248.1 |
$4$ |
$[4, 0]$ |
4.2 |
\( 2^{2} \) |
\( 2^{36} \) |
$10.21927$ |
$(a), (-a^3+4a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2Cs, 3B.1.2 |
$9$ |
\( 2^{2} \) |
$1$ |
$26.03575090$ |
0.609156265 |
\( -\frac{203862548967}{4096} a^{2} + \frac{464995782961}{2048} \) |
\( \bigl[1\) , \( a^{2} - 2\) , \( a^{2} - 3\) , \( 61 a^{2} - 278\) , \( 349 a^{2} - 1594\bigr] \) |
${y}^2+{x}{y}+\left(a^{2}-3\right){y}={x}^{3}+\left(a^{2}-2\right){x}^{2}+\left(61a^{2}-278\right){x}+349a^{2}-1594$ |
4.2-a7 |
4.2-a |
$16$ |
$48$ |
4.4.9248.1 |
$4$ |
$[4, 0]$ |
4.2 |
\( 2^{2} \) |
\( 2^{6} \) |
$10.21927$ |
$(a), (-a^3+4a+1)$ |
0 |
$\Z/2\Z\oplus\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2Cs, 3B.1.1 |
$4$ |
\( 2^{2} \) |
$1$ |
$527.2239557$ |
0.609156265 |
\( \frac{54503407609}{4} a^{2} - 5973867768 \) |
\( \bigl[1\) , \( a^{2} - 2\) , \( a^{2} - 3\) , \( 11 a^{2} - 53\) , \( 28 a^{2} - 128\bigr] \) |
${y}^2+{x}{y}+\left(a^{2}-3\right){y}={x}^{3}+\left(a^{2}-2\right){x}^{2}+\left(11a^{2}-53\right){x}+28a^{2}-128$ |
4.2-a8 |
4.2-a |
$16$ |
$48$ |
4.4.9248.1 |
$4$ |
$[4, 0]$ |
4.2 |
\( 2^{2} \) |
\( 2^{12} \) |
$10.21927$ |
$(a), (-a^3+4a+1)$ |
0 |
$\Z/2\Z\oplus\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2Cs, 3B.1.1 |
$1$ |
\( 2^{2} \) |
$1$ |
$2108.895823$ |
0.609156265 |
\( \frac{915957}{16} a^{2} - \frac{186929}{8} \) |
\( \bigl[1\) , \( a^{2} - 2\) , \( a^{2} - 3\) , \( a^{2} - 3\) , \( 0\bigr] \) |
${y}^2+{x}{y}+\left(a^{2}-3\right){y}={x}^{3}+\left(a^{2}-2\right){x}^{2}+\left(a^{2}-3\right){x}$ |
4.2-a9 |
4.2-a |
$16$ |
$48$ |
4.4.9248.1 |
$4$ |
$[4, 0]$ |
4.2 |
\( 2^{2} \) |
\( 2^{18} \) |
$10.21927$ |
$(a), (-a^3+4a+1)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{2} \) |
$1$ |
$527.2239557$ |
0.609156265 |
\( \frac{110887}{256} a^{2} - \frac{64929}{256} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( a^{2} - 5\) , \( -4 a^{2} + 18\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(a^{2}-5\right){x}-4a^{2}+18$ |
4.2-a10 |
4.2-a |
$16$ |
$48$ |
4.4.9248.1 |
$4$ |
$[4, 0]$ |
4.2 |
\( 2^{2} \) |
\( 2^{54} \) |
$10.21927$ |
$(a), (-a^3+4a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$9$ |
\( 2^{2} \) |
$1$ |
$6.508937725$ |
0.609156265 |
\( \frac{55573026649}{16777216} a^{2} - \frac{126228971439}{8388608} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( 9 a^{2} - 5\) , \( -106 a^{2} + 46\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(9a^{2}-5\right){x}-106a^{2}+46$ |
4.2-a11 |
4.2-a |
$16$ |
$48$ |
4.4.9248.1 |
$4$ |
$[4, 0]$ |
4.2 |
\( 2^{2} \) |
\( 2^{18} \) |
$10.21927$ |
$(a), (-a^3+4a+1)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{2} \) |
$1$ |
$527.2239557$ |
0.609156265 |
\( -\frac{110887}{256} a^{2} + \frac{244753}{128} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -a^{2}\) , \( 4 a^{2} - 2\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-a^{2}{x}+4a^{2}-2$ |
4.2-a12 |
4.2-a |
$16$ |
$48$ |
4.4.9248.1 |
$4$ |
$[4, 0]$ |
4.2 |
\( 2^{2} \) |
\( 2^{54} \) |
$10.21927$ |
$(a), (-a^3+4a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$9$ |
\( 2^{2} \) |
$1$ |
$6.508937725$ |
0.609156265 |
\( -\frac{55573026649}{16777216} a^{2} + \frac{25407190367}{16777216} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -9 a^{2} + 40\) , \( 106 a^{2} - 484\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(-9a^{2}+40\right){x}+106a^{2}-484$ |
4.2-a13 |
4.2-a |
$16$ |
$48$ |
4.4.9248.1 |
$4$ |
$[4, 0]$ |
4.2 |
\( 2^{2} \) |
\( 2^{6} \) |
$10.21927$ |
$(a), (-a^3+4a+1)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{2} \) |
$1$ |
$527.2239557$ |
0.609156265 |
\( -\frac{54503407609}{4} a^{2} + \frac{248621566973}{4} \) |
\( \bigl[1\) , \( -a^{2} + 3\) , \( a^{2} - 2\) , \( -12 a^{2} + 4\) , \( -28 a^{2} + 12\bigr] \) |
${y}^2+{x}{y}+\left(a^{2}-2\right){y}={x}^{3}+\left(-a^{2}+3\right){x}^{2}+\left(-12a^{2}+4\right){x}-28a^{2}+12$ |
4.2-a14 |
4.2-a |
$16$ |
$48$ |
4.4.9248.1 |
$4$ |
$[4, 0]$ |
4.2 |
\( 2^{2} \) |
\( 2^{12} \) |
$10.21927$ |
$(a), (-a^3+4a+1)$ |
0 |
$\Z/2\Z\oplus\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2Cs, 3B.1.1 |
$1$ |
\( 2^{2} \) |
$1$ |
$2108.895823$ |
0.609156265 |
\( -\frac{915957}{16} a^{2} + \frac{4205927}{16} \) |
\( \bigl[1\) , \( -a^{2} + 3\) , \( a^{2} - 2\) , \( -2 a^{2} + 4\) , \( 0\bigr] \) |
${y}^2+{x}{y}+\left(a^{2}-2\right){y}={x}^{3}+\left(-a^{2}+3\right){x}^{2}+\left(-2a^{2}+4\right){x}$ |
4.2-a15 |
4.2-a |
$16$ |
$48$ |
4.4.9248.1 |
$4$ |
$[4, 0]$ |
4.2 |
\( 2^{2} \) |
\( 2^{36} \) |
$10.21927$ |
$(a), (-a^3+4a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2Cs, 3B.1.2 |
$9$ |
\( 2^{2} \) |
$1$ |
$26.03575090$ |
0.609156265 |
\( \frac{203862548967}{4096} a^{2} - \frac{89321178913}{4096} \) |
\( \bigl[1\) , \( -a^{2} + 3\) , \( a^{2} - 2\) , \( -62 a^{2} + 29\) , \( -349 a^{2} + 151\bigr] \) |
${y}^2+{x}{y}+\left(a^{2}-2\right){y}={x}^{3}+\left(-a^{2}+3\right){x}^{2}+\left(-62a^{2}+29\right){x}-349a^{2}+151$ |
4.2-a16 |
4.2-a |
$16$ |
$48$ |
4.4.9248.1 |
$4$ |
$[4, 0]$ |
4.2 |
\( 2^{2} \) |
\( 2^{18} \) |
$10.21927$ |
$(a), (-a^3+4a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$9$ |
\( 2^{2} \) |
$1$ |
$6.508937725$ |
0.609156265 |
\( \frac{653762688677050897}{64} a^{2} - \frac{286640411940693231}{64} \) |
\( \bigl[1\) , \( -a^{2} + 3\) , \( a^{2} - 2\) , \( -982 a^{2} + 429\) , \( -23629 a^{2} + 10359\bigr] \) |
${y}^2+{x}{y}+\left(a^{2}-2\right){y}={x}^{3}+\left(-a^{2}+3\right){x}^{2}+\left(-982a^{2}+429\right){x}-23629a^{2}+10359$ |
4.2-b1 |
4.2-b |
$16$ |
$48$ |
4.4.9248.1 |
$4$ |
$[4, 0]$ |
4.2 |
\( 2^{2} \) |
\( 2^{9} \) |
$10.21927$ |
$(a), (-a^3+4a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 3$ |
2B, 3B |
$256$ |
\( 2 \cdot 3^{2} \) |
$1$ |
$0.235926723$ |
2.826218305 |
\( -\frac{2598999057507859430840814142230563}{8} a^{3} - 215117023039975647450343147847680 a^{2} + 1481933932657809377628672524686862 a + 981267661531062863922029372621544 \) |
\( \bigl[a^{3} + a^{2} - 4 a - 3\) , \( a^{3} + a^{2} - 5 a - 4\) , \( a^{3} - 4 a\) , \( 491 a^{3} - 384 a^{2} - 915 a - 356\) , \( 9226 a^{3} - 16357 a^{2} - 12726 a + 1248\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-4a-3\right){x}{y}+\left(a^{3}-4a\right){y}={x}^{3}+\left(a^{3}+a^{2}-5a-4\right){x}^{2}+\left(491a^{3}-384a^{2}-915a-356\right){x}+9226a^{3}-16357a^{2}-12726a+1248$ |
4.2-b2 |
4.2-b |
$16$ |
$48$ |
4.4.9248.1 |
$4$ |
$[4, 0]$ |
4.2 |
\( 2^{2} \) |
\( 2^{9} \) |
$10.21927$ |
$(a), (-a^3+4a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 3$ |
2B, 3B |
$256$ |
\( 2 \cdot 3^{2} \) |
$1$ |
$0.235926723$ |
2.826218305 |
\( \frac{2598999057507859430840814142230563}{8} a^{3} - 215117023039975647450343147847680 a^{2} - 1481933932657809377628672524686862 a + 981267661531062863922029372621544 \) |
\( \bigl[a^{3} + a^{2} - 4 a - 3\) , \( a^{3} + a^{2} - 5 a - 4\) , \( a^{3} - 4 a\) , \( -489 a^{3} - 384 a^{2} + 905 a - 356\) , \( -9226 a^{3} - 16357 a^{2} + 12726 a + 1248\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-4a-3\right){x}{y}+\left(a^{3}-4a\right){y}={x}^{3}+\left(a^{3}+a^{2}-5a-4\right){x}^{2}+\left(-489a^{3}-384a^{2}+905a-356\right){x}-9226a^{3}-16357a^{2}+12726a+1248$ |
4.2-b3 |
4.2-b |
$16$ |
$48$ |
4.4.9248.1 |
$4$ |
$[4, 0]$ |
4.2 |
\( 2^{2} \) |
\( 2^{18} \) |
$10.21927$ |
$(a), (-a^3+4a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2Cs, 3B |
$16$ |
\( 2^{3} \cdot 3^{2} \) |
$1$ |
$3.774827576$ |
2.826218305 |
\( -\frac{653762688677050897}{64} a^{2} + \frac{1491086515722280627}{32} \) |
\( \bigl[a^{3} + a^{2} - 4 a - 3\) , \( a^{3} + a^{2} - 5 a - 4\) , \( a^{3} - 4 a\) , \( a^{3} - 64 a^{2} - 5 a - 36\) , \( -437 a^{2} + 16\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-4a-3\right){x}{y}+\left(a^{3}-4a\right){y}={x}^{3}+\left(a^{3}+a^{2}-5a-4\right){x}^{2}+\left(a^{3}-64a^{2}-5a-36\right){x}-437a^{2}+16$ |
4.2-b4 |
4.2-b |
$16$ |
$48$ |
4.4.9248.1 |
$4$ |
$[4, 0]$ |
4.2 |
\( 2^{2} \) |
\( 2^{12} \) |
$10.21927$ |
$(a), (-a^3+4a+1)$ |
0 |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2Cs, 3B |
$1$ |
\( 2^{5} \) |
$1$ |
$543.5751710$ |
2.826218305 |
\( \frac{915957}{16} a^{2} - \frac{186929}{8} \) |
\( \bigl[a^{3} + a^{2} - 4 a - 3\) , \( a^{3} + a^{2} - 5 a - 4\) , \( a^{3} - 4 a\) , \( a^{3} - 4 a^{2} - 5 a - 1\) , \( -10 a^{2} + 3\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-4a-3\right){x}{y}+\left(a^{3}-4a\right){y}={x}^{3}+\left(a^{3}+a^{2}-5a-4\right){x}^{2}+\left(a^{3}-4a^{2}-5a-1\right){x}-10a^{2}+3$ |
4.2-b5 |
4.2-b |
$16$ |
$48$ |
4.4.9248.1 |
$4$ |
$[4, 0]$ |
4.2 |
\( 2^{2} \) |
\( 2^{36} \) |
$10.21927$ |
$(a), (-a^3+4a+1)$ |
0 |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2Cs, 3B |
$1$ |
\( 2^{5} \cdot 3^{2} \) |
$1$ |
$60.39724122$ |
2.826218305 |
\( -\frac{203862548967}{4096} a^{2} + \frac{464995782961}{2048} \) |
\( \bigl[a^{3} + a^{2} - 4 a - 3\) , \( a^{3} + a^{2} - 5 a - 4\) , \( a^{3} - 4 a\) , \( a^{3} - 24 a^{2} - 5 a + 4\) , \( 83 a^{2} - 40\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-4a-3\right){x}{y}+\left(a^{3}-4a\right){y}={x}^{3}+\left(a^{3}+a^{2}-5a-4\right){x}^{2}+\left(a^{3}-24a^{2}-5a+4\right){x}+83a^{2}-40$ |
4.2-b6 |
4.2-b |
$16$ |
$48$ |
4.4.9248.1 |
$4$ |
$[4, 0]$ |
4.2 |
\( 2^{2} \) |
\( 2^{6} \) |
$10.21927$ |
$(a), (-a^3+4a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2Cs, 3B |
$16$ |
\( 2^{3} \) |
$1$ |
$33.97344818$ |
2.826218305 |
\( \frac{54503407609}{4} a^{2} - 5973867768 \) |
\( \bigl[a^{3} + a^{2} - 4 a - 3\) , \( a^{3} + a^{2} - 5 a - 4\) , \( a^{3} - 4 a\) , \( a^{3} - 74 a^{2} - 5 a + 29\) , \( -544 a^{2} + 237\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-4a-3\right){x}{y}+\left(a^{3}-4a\right){y}={x}^{3}+\left(a^{3}+a^{2}-5a-4\right){x}^{2}+\left(a^{3}-74a^{2}-5a+29\right){x}-544a^{2}+237$ |
4.2-b7 |
4.2-b |
$16$ |
$48$ |
4.4.9248.1 |
$4$ |
$[4, 0]$ |
4.2 |
\( 2^{2} \) |
\( 2^{18} \) |
$10.21927$ |
$(a), (-a^3+4a+1)$ |
0 |
$\Z/8\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \cdot 3^{2} \) |
$1$ |
$241.5889648$ |
2.826218305 |
\( \frac{653762688677050897}{64} a^{2} - \frac{286640411940693231}{64} \) |
\( \bigl[a^{3} + a^{2} - 4 a - 3\) , \( a^{3} + a^{2} - 5 a - 2\) , \( a^{3} - 4 a\) , \( a^{3} + 66 a^{2} - 5 a - 359\) , \( -372 a^{2} + 1811\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-4a-3\right){x}{y}+\left(a^{3}-4a\right){y}={x}^{3}+\left(a^{3}+a^{2}-5a-2\right){x}^{2}+\left(a^{3}+66a^{2}-5a-359\right){x}-372a^{2}+1811$ |
4.2-b8 |
4.2-b |
$16$ |
$48$ |
4.4.9248.1 |
$4$ |
$[4, 0]$ |
4.2 |
\( 2^{2} \) |
\( 2^{6} \) |
$10.21927$ |
$(a), (-a^3+4a+1)$ |
0 |
$\Z/8\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \) |
$1$ |
$2174.300684$ |
2.826218305 |
\( -\frac{54503407609}{4} a^{2} + \frac{248621566973}{4} \) |
\( \bigl[a^{3} + a^{2} - 4 a - 3\) , \( a^{3} + a^{2} - 5 a - 2\) , \( a^{3} - 4 a\) , \( a^{3} + 76 a^{2} - 5 a - 344\) , \( -469 a^{2} + 2140\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-4a-3\right){x}{y}+\left(a^{3}-4a\right){y}={x}^{3}+\left(a^{3}+a^{2}-5a-2\right){x}^{2}+\left(a^{3}+76a^{2}-5a-344\right){x}-469a^{2}+2140$ |
4.2-b9 |
4.2-b |
$16$ |
$48$ |
4.4.9248.1 |
$4$ |
$[4, 0]$ |
4.2 |
\( 2^{2} \) |
\( 2^{36} \) |
$10.21927$ |
$(a), (-a^3+4a+1)$ |
0 |
$\Z/2\Z\oplus\Z/8\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2Cs, 3B |
$1$ |
\( 2^{5} \cdot 3^{2} \) |
$1$ |
$241.5889648$ |
2.826218305 |
\( \frac{203862548967}{4096} a^{2} - \frac{89321178913}{4096} \) |
\( \bigl[a^{3} + a^{2} - 4 a - 3\) , \( a^{3} + a^{2} - 5 a - 2\) , \( a^{3} - 4 a\) , \( a^{3} + 26 a^{2} - 5 a - 119\) , \( 108 a^{2} - 493\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-4a-3\right){x}{y}+\left(a^{3}-4a\right){y}={x}^{3}+\left(a^{3}+a^{2}-5a-2\right){x}^{2}+\left(a^{3}+26a^{2}-5a-119\right){x}+108a^{2}-493$ |
4.2-b10 |
4.2-b |
$16$ |
$48$ |
4.4.9248.1 |
$4$ |
$[4, 0]$ |
4.2 |
\( 2^{2} \) |
\( 2^{12} \) |
$10.21927$ |
$(a), (-a^3+4a+1)$ |
0 |
$\Z/2\Z\oplus\Z/8\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2Cs, 3B |
$1$ |
\( 2^{5} \) |
$1$ |
$2174.300684$ |
2.826218305 |
\( -\frac{915957}{16} a^{2} + \frac{4205927}{16} \) |
\( \bigl[a^{3} + a^{2} - 4 a - 3\) , \( a^{3} + a^{2} - 5 a - 2\) , \( a^{3} - 4 a\) , \( a^{3} + 6 a^{2} - 5 a - 24\) , \( -5 a^{2} + 24\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-4a-3\right){x}{y}+\left(a^{3}-4a\right){y}={x}^{3}+\left(a^{3}+a^{2}-5a-2\right){x}^{2}+\left(a^{3}+6a^{2}-5a-24\right){x}-5a^{2}+24$ |
4.2-b11 |
4.2-b |
$16$ |
$48$ |
4.4.9248.1 |
$4$ |
$[4, 0]$ |
4.2 |
\( 2^{2} \) |
\( 2^{54} \) |
$10.21927$ |
$(a), (-a^3+4a+1)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{5} \cdot 3^{2} \) |
$1$ |
$15.09931030$ |
2.826218305 |
\( \frac{55573026649}{16777216} a^{2} - \frac{126228971439}{8388608} \) |
\( \bigl[a^{3} + a^{2} - 4 a - 3\) , \( a^{3} - 5 a - 1\) , \( a^{3} + a^{2} - 4 a - 3\) , \( 2 a^{3} + 10 a^{2} - 10 a - 47\) , \( a^{3} + 30 a^{2} - 5 a - 137\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-4a-3\right){x}{y}+\left(a^{3}+a^{2}-4a-3\right){y}={x}^{3}+\left(a^{3}-5a-1\right){x}^{2}+\left(2a^{3}+10a^{2}-10a-47\right){x}+a^{3}+30a^{2}-5a-137$ |
4.2-b12 |
4.2-b |
$16$ |
$48$ |
4.4.9248.1 |
$4$ |
$[4, 0]$ |
4.2 |
\( 2^{2} \) |
\( 2^{18} \) |
$10.21927$ |
$(a), (-a^3+4a+1)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{5} \) |
$1$ |
$135.8937927$ |
2.826218305 |
\( -\frac{110887}{256} a^{2} + \frac{244753}{128} \) |
\( \bigl[a^{3} + a^{2} - 4 a - 3\) , \( a^{3} - 5 a - 1\) , \( a^{3} + a^{2} - 4 a - 3\) , \( 2 a^{3} - 10 a - 2\) , \( a^{3} - 5 a - 1\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-4a-3\right){x}{y}+\left(a^{3}+a^{2}-4a-3\right){y}={x}^{3}+\left(a^{3}-5a-1\right){x}^{2}+\left(2a^{3}-10a-2\right){x}+a^{3}-5a-1$ |
4.2-b13 |
4.2-b |
$16$ |
$48$ |
4.4.9248.1 |
$4$ |
$[4, 0]$ |
4.2 |
\( 2^{2} \) |
\( 2^{18} \) |
$10.21927$ |
$(a), (-a^3+4a+1)$ |
0 |
$\Z/8\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{5} \) |
$1$ |
$543.5751710$ |
2.826218305 |
\( \frac{110887}{256} a^{2} - \frac{64929}{256} \) |
\( \bigl[a^{3} + a^{2} - 4 a - 3\) , \( a^{3} - 5 a\) , \( 0\) , \( 3\) , \( 1\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-4a-3\right){x}{y}={x}^{3}+\left(a^{3}-5a\right){x}^{2}+3{x}+1$ |
4.2-b14 |
4.2-b |
$16$ |
$48$ |
4.4.9248.1 |
$4$ |
$[4, 0]$ |
4.2 |
\( 2^{2} \) |
\( 2^{54} \) |
$10.21927$ |
$(a), (-a^3+4a+1)$ |
0 |
$\Z/8\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{5} \cdot 3^{2} \) |
$1$ |
$60.39724122$ |
2.826218305 |
\( -\frac{55573026649}{16777216} a^{2} + \frac{25407190367}{16777216} \) |
\( \bigl[a^{3} + a^{2} - 4 a - 3\) , \( a^{3} - 5 a\) , \( 0\) , \( -10 a^{2} + 8\) , \( 20 a^{2} - 8\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-4a-3\right){x}{y}={x}^{3}+\left(a^{3}-5a\right){x}^{2}+\left(-10a^{2}+8\right){x}+20a^{2}-8$ |
4.2-b15 |
4.2-b |
$16$ |
$48$ |
4.4.9248.1 |
$4$ |
$[4, 0]$ |
4.2 |
\( 2^{2} \) |
\( 2^{3} \) |
$10.21927$ |
$(a), (-a^3+4a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 3$ |
2B, 3B |
$256$ |
\( 2 \) |
$1$ |
$2.123340511$ |
2.826218305 |
\( 179213540276326839556 a^{3} + 382760552527098253312 a^{2} - \frac{157151345464271319581}{2} a - 167820287562717580568 \) |
\( \bigl[a^{3} - 3 a + 1\) , \( 0\) , \( a^{3} + a^{2} - 4 a - 2\) , \( 815 a^{3} + 529 a^{2} - 3702 a - 2452\) , \( 81105 a^{3} + 53660 a^{2} - 369901 a - 244920\bigr] \) |
${y}^2+\left(a^{3}-3a+1\right){x}{y}+\left(a^{3}+a^{2}-4a-2\right){y}={x}^{3}+\left(815a^{3}+529a^{2}-3702a-2452\right){x}+81105a^{3}+53660a^{2}-369901a-244920$ |
4.2-b16 |
4.2-b |
$16$ |
$48$ |
4.4.9248.1 |
$4$ |
$[4, 0]$ |
4.2 |
\( 2^{2} \) |
\( 2^{3} \) |
$10.21927$ |
$(a), (-a^3+4a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 3$ |
2B, 3B |
$256$ |
\( 2 \) |
$1$ |
$2.123340511$ |
2.826218305 |
\( -179213540276326839556 a^{3} + 382760552527098253312 a^{2} + \frac{157151345464271319581}{2} a - 167820287562717580568 \) |
\( \bigl[a^{3} - 3 a + 1\) , \( -a^{3} + 3 a\) , \( a^{3} + a^{2} - 4 a - 2\) , \( -816 a^{3} + 529 a^{2} + 3702 a - 2452\) , \( -81104 a^{3} + 53660 a^{2} + 369895 a - 244920\bigr] \) |
${y}^2+\left(a^{3}-3a+1\right){x}{y}+\left(a^{3}+a^{2}-4a-2\right){y}={x}^{3}+\left(-a^{3}+3a\right){x}^{2}+\left(-816a^{3}+529a^{2}+3702a-2452\right){x}-81104a^{3}+53660a^{2}+369895a-244920$ |
8.3-a1 |
8.3-a |
$8$ |
$16$ |
4.4.9248.1 |
$4$ |
$[4, 0]$ |
8.3 |
\( 2^{3} \) |
\( 2^{8} \) |
$11.14420$ |
$(a)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$644.2027085$ |
1.674706263 |
\( -7659605 a^{2} + 34939686 \) |
\( \bigl[a^{2} - 2\) , \( -a^{2} + 3\) , \( a^{2} - 2\) , \( 3 a^{2} - 17\) , \( -3 a^{2} + 12\bigr] \) |
${y}^2+\left(a^{2}-2\right){x}{y}+\left(a^{2}-2\right){y}={x}^{3}+\left(-a^{2}+3\right){x}^{2}+\left(3a^{2}-17\right){x}-3a^{2}+12$ |
8.3-a2 |
8.3-a |
$8$ |
$16$ |
4.4.9248.1 |
$4$ |
$[4, 0]$ |
8.3 |
\( 2^{3} \) |
\( 2^{10} \) |
$11.14420$ |
$(a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$322.1013542$ |
1.674706263 |
\( 343 a^{2} \) |
\( \bigl[a\) , \( a^{2} - 4\) , \( 0\) , \( 4\) , \( a^{2} - 2\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(a^{2}-4\right){x}^{2}+4{x}+a^{2}-2$ |
8.3-a3 |
8.3-a |
$8$ |
$16$ |
4.4.9248.1 |
$4$ |
$[4, 0]$ |
8.3 |
\( 2^{3} \) |
\( 2^{4} \) |
$11.14420$ |
$(a)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2 \) |
$1$ |
$1288.405417$ |
1.674706263 |
\( 24225 a^{2} - 4222 \) |
\( \bigl[a\) , \( a^{2} - 3\) , \( a\) , \( -a^{2} + 2\) , \( -a^{2}\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(a^{2}-3\right){x}^{2}+\left(-a^{2}+2\right){x}-a^{2}$ |
8.3-a4 |
8.3-a |
$8$ |
$16$ |
4.4.9248.1 |
$4$ |
$[4, 0]$ |
8.3 |
\( 2^{3} \) |
\( 2^{8} \) |
$11.14420$ |
$(a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
|
✓ |
$2$ |
2B |
$4$ |
\( 2 \) |
$1$ |
$80.52533856$ |
1.674706263 |
\( 2701312025 a^{2} - 1184382322 \) |
\( \bigl[a\) , \( a^{2} - 3\) , \( a\) , \( -11 a^{2} + 7\) , \( -36 a^{2} + 15\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(a^{2}-3\right){x}^{2}+\left(-11a^{2}+7\right){x}-36a^{2}+15$ |
8.3-a5 |
8.3-a |
$8$ |
$16$ |
4.4.9248.1 |
$4$ |
$[4, 0]$ |
8.3 |
\( 2^{3} \) |
\( 2^{11} \) |
$11.14420$ |
$(a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$16$ |
\( 1 \) |
$1$ |
$40.26266928$ |
1.674706263 |
\( -1409277718922882 a^{3} - 933097728375808 a^{2} + 6428663656193677 a + 4256735329251048 \) |
\( \bigl[a\) , \( 0\) , \( a^{3} - 4 a\) , \( 425 a^{3} + 317 a^{2} - 1940 a - 1450\) , \( 8542 a^{3} + 5847 a^{2} - 38964 a - 26670\bigr] \) |
${y}^2+a{x}{y}+\left(a^{3}-4a\right){y}={x}^{3}+\left(425a^{3}+317a^{2}-1940a-1450\right){x}+8542a^{3}+5847a^{2}-38964a-26670$ |
8.3-a6 |
8.3-a |
$8$ |
$16$ |
4.4.9248.1 |
$4$ |
$[4, 0]$ |
8.3 |
\( 2^{3} \) |
\( 2^{11} \) |
$11.14420$ |
$(a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$16$ |
\( 1 \) |
$1$ |
$40.26266928$ |
1.674706263 |
\( 1409277718922882 a^{3} - 933097728375808 a^{2} - 6428663656193677 a + 4256735329251048 \) |
\( \bigl[a\) , \( 0\) , \( a^{3} - 4 a\) , \( -425 a^{3} + 317 a^{2} + 1940 a - 1450\) , \( -8542 a^{3} + 5847 a^{2} + 38964 a - 26670\bigr] \) |
${y}^2+a{x}{y}+\left(a^{3}-4a\right){y}={x}^{3}+\left(-425a^{3}+317a^{2}+1940a-1450\right){x}-8542a^{3}+5847a^{2}+38964a-26670$ |
8.3-a7 |
8.3-a |
$8$ |
$16$ |
4.4.9248.1 |
$4$ |
$[4, 0]$ |
8.3 |
\( 2^{3} \) |
\( 2^{10} \) |
$11.14420$ |
$(a)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
|
✓ |
$2$ |
2Cs |
$4$ |
\( 2 \) |
$1$ |
$322.1013542$ |
1.674706263 |
\( -21069823 a^{2} + 96961280 \) |
\( \bigl[a\) , \( 0\) , \( a^{3} - 4 a\) , \( 37 a^{2} - 170\) , \( 181 a^{2} - 826\bigr] \) |
${y}^2+a{x}{y}+\left(a^{3}-4a\right){y}={x}^{3}+\left(37a^{2}-170\right){x}+181a^{2}-826$ |
8.3-a8 |
8.3-a |
$8$ |
$16$ |
4.4.9248.1 |
$4$ |
$[4, 0]$ |
8.3 |
\( 2^{3} \) |
\( 2^{8} \) |
$11.14420$ |
$(a)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2 \) |
$1$ |
$1288.405417$ |
1.674706263 |
\( -1995 a^{2} + 11006 \) |
\( \bigl[a\) , \( 0\) , \( a^{3} - 4 a\) , \( 2 a^{2} - 10\) , \( 3 a^{2} - 14\bigr] \) |
${y}^2+a{x}{y}+\left(a^{3}-4a\right){y}={x}^{3}+\left(2a^{2}-10\right){x}+3a^{2}-14$ |
8.3-b1 |
8.3-b |
$8$ |
$16$ |
4.4.9248.1 |
$4$ |
$[4, 0]$ |
8.3 |
\( 2^{3} \) |
\( 2^{4} \) |
$11.14420$ |
$(a)$ |
$1$ |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2 \) |
$0.246667540$ |
$4366.360965$ |
1.399966817 |
\( 24225 a^{2} - 4222 \) |
\( \bigl[a^{3} + a^{2} - 3 a - 2\) , \( a^{2} + a - 2\) , \( a^{3} + a^{2} - 4 a - 2\) , \( 4 a^{3} + 10 a^{2} - 7 a - 21\) , \( 9 a^{3} + 6 a^{2} - 21 a + 15\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-3a-2\right){x}{y}+\left(a^{3}+a^{2}-4a-2\right){y}={x}^{3}+\left(a^{2}+a-2\right){x}^{2}+\left(4a^{3}+10a^{2}-7a-21\right){x}+9a^{3}+6a^{2}-21a+15$ |
8.3-b2 |
8.3-b |
$8$ |
$16$ |
4.4.9248.1 |
$4$ |
$[4, 0]$ |
8.3 |
\( 2^{3} \) |
\( 2^{8} \) |
$11.14420$ |
$(a)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.123333770$ |
$1091.590241$ |
1.399966817 |
\( 2701312025 a^{2} - 1184382322 \) |
\( \bigl[a^{3} + a^{2} - 3 a - 2\) , \( a^{2} + a - 2\) , \( a^{3} + a^{2} - 4 a - 2\) , \( 4 a^{3} - 7 a + 24\) , \( -a^{3} - 14 a^{2} + 24 a + 105\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-3a-2\right){x}{y}+\left(a^{3}+a^{2}-4a-2\right){y}={x}^{3}+\left(a^{2}+a-2\right){x}^{2}+\left(4a^{3}-7a+24\right){x}-a^{3}-14a^{2}+24a+105$ |
8.3-b3 |
8.3-b |
$8$ |
$16$ |
4.4.9248.1 |
$4$ |
$[4, 0]$ |
8.3 |
\( 2^{3} \) |
\( 2^{11} \) |
$11.14420$ |
$(a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$16$ |
\( 1 \) |
$1.973340325$ |
$4.264024380$ |
1.399966817 |
\( -1409277718922882 a^{3} - 933097728375808 a^{2} + 6428663656193677 a + 4256735329251048 \) |
\( \bigl[a^{3} + a^{2} - 3 a - 2\) , \( a\) , \( a^{3} - 4 a\) , \( -13 a^{3} - 41 a^{2} - 21 a - 2\) , \( -224 a^{3} - 527 a^{2} + 2 a + 165\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-3a-2\right){x}{y}+\left(a^{3}-4a\right){y}={x}^{3}+a{x}^{2}+\left(-13a^{3}-41a^{2}-21a-2\right){x}-224a^{3}-527a^{2}+2a+165$ |
8.3-b4 |
8.3-b |
$8$ |
$16$ |
4.4.9248.1 |
$4$ |
$[4, 0]$ |
8.3 |
\( 2^{3} \) |
\( 2^{10} \) |
$11.14420$ |
$(a)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
|
✓ |
$2$ |
2Cs |
$4$ |
\( 2 \) |
$0.986670162$ |
$68.22439009$ |
1.399966817 |
\( -21069823 a^{2} + 96961280 \) |
\( \bigl[a^{3} + a^{2} - 3 a - 2\) , \( a\) , \( a^{3} - 4 a\) , \( 2 a^{3} - a^{2} - a - 2\) , \( -3 a^{3} - 14 a^{2} + 3\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-3a-2\right){x}{y}+\left(a^{3}-4a\right){y}={x}^{3}+a{x}^{2}+\left(2a^{3}-a^{2}-a-2\right){x}-3a^{3}-14a^{2}+3$ |
8.3-b5 |
8.3-b |
$8$ |
$16$ |
4.4.9248.1 |
$4$ |
$[4, 0]$ |
8.3 |
\( 2^{3} \) |
\( 2^{8} \) |
$11.14420$ |
$(a)$ |
$1$ |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$0.493335081$ |
$1091.590241$ |
1.399966817 |
\( -1995 a^{2} + 11006 \) |
\( \bigl[a^{3} + a^{2} - 3 a - 2\) , \( a\) , \( a^{3} - 4 a\) , \( 2 a^{3} + 4 a^{2} - a - 2\) , \( 2 a^{3} + 5 a^{2} - 3\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-3a-2\right){x}{y}+\left(a^{3}-4a\right){y}={x}^{3}+a{x}^{2}+\left(2a^{3}+4a^{2}-a-2\right){x}+2a^{3}+5a^{2}-3$ |
8.3-b6 |
8.3-b |
$8$ |
$16$ |
4.4.9248.1 |
$4$ |
$[4, 0]$ |
8.3 |
\( 2^{3} \) |
\( 2^{11} \) |
$11.14420$ |
$(a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$16$ |
\( 1 \) |
$1.973340325$ |
$4.264024380$ |
1.399966817 |
\( 1409277718922882 a^{3} - 933097728375808 a^{2} - 6428663656193677 a + 4256735329251048 \) |
\( \bigl[a^{3} + a^{2} - 3 a - 2\) , \( a\) , \( a^{3} - 4 a\) , \( 17 a^{3} - 41 a^{2} + 19 a - 2\) , \( 138 a^{3} - 337 a^{2} - 2 a + 105\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-3a-2\right){x}{y}+\left(a^{3}-4a\right){y}={x}^{3}+a{x}^{2}+\left(17a^{3}-41a^{2}+19a-2\right){x}+138a^{3}-337a^{2}-2a+105$ |
8.3-b7 |
8.3-b |
$8$ |
$16$ |
4.4.9248.1 |
$4$ |
$[4, 0]$ |
8.3 |
\( 2^{3} \) |
\( 2^{10} \) |
$11.14420$ |
$(a)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$0.986670162$ |
$272.8975603$ |
1.399966817 |
\( 343 a^{2} \) |
\( \bigl[a^{3} + a^{2} - 3 a - 2\) , \( a + 1\) , \( a^{2} + a - 2\) , \( a^{3} + 3 a^{2} + 3 a + 3\) , \( 2 a^{3} + 7 a^{2} + 4 a - 4\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-3a-2\right){x}{y}+\left(a^{2}+a-2\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(a^{3}+3a^{2}+3a+3\right){x}+2a^{3}+7a^{2}+4a-4$ |
8.3-b8 |
8.3-b |
$8$ |
$16$ |
4.4.9248.1 |
$4$ |
$[4, 0]$ |
8.3 |
\( 2^{3} \) |
\( 2^{8} \) |
$11.14420$ |
$(a)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$0.123333770$ |
$2183.180482$ |
1.399966817 |
\( -7659605 a^{2} + 34939686 \) |
\( \bigl[a^{3} - 4 a\) , \( -1\) , \( a^{3} - 4 a\) , \( -3\) , \( 6 a^{2} - 4\bigr] \) |
${y}^2+\left(a^{3}-4a\right){x}{y}+\left(a^{3}-4a\right){y}={x}^{3}-{x}^{2}-3{x}+6a^{2}-4$ |
8.4-a1 |
8.4-a |
$6$ |
$8$ |
4.4.9248.1 |
$4$ |
$[4, 0]$ |
8.4 |
\( 2^{3} \) |
\( 2^{8} \) |
$11.14420$ |
$(-a^3+4a+1)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$0.756986305$ |
$644.2027085$ |
2.535459413 |
\( 7659605 a^{2} - 3358339 \) |
\( \bigl[a^{2} - 3\) , \( a^{2} - 2\) , \( a^{2} - 3\) , \( -3 a^{2} - 2\) , \( 3 a^{2} - 3\bigr] \) |
${y}^2+\left(a^{2}-3\right){x}{y}+\left(a^{2}-3\right){y}={x}^{3}+\left(a^{2}-2\right){x}^{2}+\left(-3a^{2}-2\right){x}+3a^{2}-3$ |
8.4-a2 |
8.4-a |
$6$ |
$8$ |
4.4.9248.1 |
$4$ |
$[4, 0]$ |
8.4 |
\( 2^{3} \) |
\( 2^{10} \) |
$11.14420$ |
$(-a^3+4a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$0.378493152$ |
$322.1013542$ |
2.535459413 |
\( -343 a^{2} + 1715 \) |
\( \bigl[a + 1\) , \( -a^{3} + a^{2} + 5 a - 4\) , \( a^{3} - 4 a + 1\) , \( 3 a^{3} - 10 a + 8\) , \( -5 a^{3} - 4 a^{2} + 12 a - 5\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{3}-4a+1\right){y}={x}^{3}+\left(-a^{3}+a^{2}+5a-4\right){x}^{2}+\left(3a^{3}-10a+8\right){x}-5a^{3}-4a^{2}+12a-5$ |
*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.