| 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 |
| 1.1-a1 |
1.1-a |
$6$ |
$8$ |
4.4.11324.1 |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$9.50908$ |
$\textsf{none}$ |
0 |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
✓ |
$2$ |
2Cs |
$1$ |
\( 1 \) |
$1$ |
$3934.265394$ |
0.577675233 |
\( -224626 a^{3} - 29044 a^{2} + 1105288 a + 394939 \) |
\( \bigl[a^{3} + a^{2} - 4 a - 3\) , \( -a^{3} + a^{2} + 5 a - 4\) , \( 1\) , \( -4 a^{3} - 5 a^{2} + 15 a + 15\) , \( -2 a^{3} + 2 a^{2} + 12 a - 1\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-4a-3\right){x}{y}+{y}={x}^{3}+\left(-a^{3}+a^{2}+5a-4\right){x}^{2}+\left(-4a^{3}-5a^{2}+15a+15\right){x}-2a^{3}+2a^{2}+12a-1$ |
| 1.1-a2 |
1.1-a |
$6$ |
$8$ |
4.4.11324.1 |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$9.50908$ |
$\textsf{none}$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
✓ |
$2$ |
2Cs |
$1$ |
\( 1 \) |
$1$ |
$983.5663485$ |
0.577675233 |
\( 6250036 a^{3} - 8477824 a^{2} - 28229184 a + 35066649 \) |
\( \bigl[a^{2} - 3\) , \( a^{2} - 4\) , \( a^{3} + a^{2} - 3 a - 3\) , \( -a^{3} - 2 a^{2} + a - 1\) , \( -2 a^{3} - 3 a^{2} + 5 a + 1\bigr] \) |
${y}^2+\left(a^{2}-3\right){x}{y}+\left(a^{3}+a^{2}-3a-3\right){y}={x}^{3}+\left(a^{2}-4\right){x}^{2}+\left(-a^{3}-2a^{2}+a-1\right){x}-2a^{3}-3a^{2}+5a+1$ |
| 1.1-a3 |
1.1-a |
$6$ |
$8$ |
4.4.11324.1 |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$9.50908$ |
$\textsf{none}$ |
0 |
$\Z/8\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
✓ |
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$3934.265394$ |
0.577675233 |
\( -2155689 a^{3} + 6662753 a^{2} - 3147109 a - 2057725 \) |
\( \bigl[a^{3} - 3 a + 1\) , \( -a^{3} + a^{2} + 3 a - 4\) , \( 1\) , \( a^{2} - a\) , \( a^{3} - 4 a + 3\bigr] \) |
${y}^2+\left(a^{3}-3a+1\right){x}{y}+{y}={x}^{3}+\left(-a^{3}+a^{2}+3a-4\right){x}^{2}+\left(a^{2}-a\right){x}+a^{3}-4a+3$ |
| 1.1-a4 |
1.1-a |
$6$ |
$8$ |
4.4.11324.1 |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( -1 \) |
$9.50908$ |
$\textsf{none}$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
✓ |
$2$ |
2B |
$4$ |
\( 1 \) |
$1$ |
$61.47289678$ |
0.577675233 |
\( 273577301639170 a^{3} - 371107593060366 a^{2} - 1235586673541100 a + 1534795780915977 \) |
\( \bigl[a^{3} - 3 a + 1\) , \( a - 1\) , \( a^{3} - 4 a\) , \( -6 a^{3} + 21 a^{2} + 10 a - 38\) , \( 26 a^{3} - 86 a^{2} + 92 a - 39\bigr] \) |
${y}^2+\left(a^{3}-3a+1\right){x}{y}+\left(a^{3}-4a\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-6a^{3}+21a^{2}+10a-38\right){x}+26a^{3}-86a^{2}+92a-39$ |
| 1.1-a5 |
1.1-a |
$6$ |
$8$ |
4.4.11324.1 |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$9.50908$ |
$\textsf{none}$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
✓ |
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$983.5663485$ |
0.577675233 |
\( -305523916811 a^{3} - 55768842233 a^{2} + 1464100257869 a + 515196650157 \) |
\( \bigl[a + 1\) , \( a^{3} - 5 a + 1\) , \( a^{3} - 4 a\) , \( 24 a^{3} - 31 a^{2} - 117 a + 147\) , \( -299 a^{3} + 423 a^{2} + 1293 a - 1636\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{3}-4a\right){y}={x}^{3}+\left(a^{3}-5a+1\right){x}^{2}+\left(24a^{3}-31a^{2}-117a+147\right){x}-299a^{3}+423a^{2}+1293a-1636$ |
| 1.1-a6 |
1.1-a |
$6$ |
$8$ |
4.4.11324.1 |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( -1 \) |
$9.50908$ |
$\textsf{none}$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
✓ |
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$245.8915871$ |
0.577675233 |
\( -2075320 a^{3} + 6410242 a^{2} - 3015868 a - 1989779 \) |
\( \bigl[a + 1\) , \( -a^{3} - a^{2} + 3 a + 4\) , \( a^{3} + a^{2} - 3 a - 3\) , \( -4 a^{3} - a^{2} + 17 a + 5\) , \( -4 a^{3} + 16 a - 3\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{3}+a^{2}-3a-3\right){y}={x}^{3}+\left(-a^{3}-a^{2}+3a+4\right){x}^{2}+\left(-4a^{3}-a^{2}+17a+5\right){x}-4a^{3}+16a-3$ |
| 4.2-a1 |
4.2-a |
$2$ |
$5$ |
4.4.11324.1 |
$4$ |
$[4, 0]$ |
4.2 |
\( 2^{2} \) |
\( 2^{4} \) |
$11.30827$ |
$(-a^2+a+3)$ |
0 |
$\Z/5\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.1.1 |
$1$ |
\( 2 \) |
$1$ |
$732.6819323$ |
0.550814721 |
\( -154 a^{3} - \frac{3315}{4} a^{2} + \frac{837}{2} a + \frac{2407}{2} \) |
\( \bigl[a^{3} + a^{2} - 4 a - 2\) , \( a^{3} + a^{2} - 4 a - 4\) , \( 1\) , \( 2 a^{3} + 2 a^{2} - 3 a + 1\) , \( -a^{3} - a^{2} + 2 a\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-4a-2\right){x}{y}+{y}={x}^{3}+\left(a^{3}+a^{2}-4a-4\right){x}^{2}+\left(2a^{3}+2a^{2}-3a+1\right){x}-a^{3}-a^{2}+2a$ |
| 4.2-a2 |
4.2-a |
$2$ |
$5$ |
4.4.11324.1 |
$4$ |
$[4, 0]$ |
4.2 |
\( 2^{2} \) |
\( 2^{20} \) |
$11.30827$ |
$(-a^2+a+3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.1.2 |
$25$ |
\( 2 \) |
$1$ |
$1.172291091$ |
0.550814721 |
\( -\frac{163373769935391127101}{1024} a^{3} - \frac{205228455081736078125}{1024} a^{2} + \frac{88458628269022521363}{256} a + \frac{72411360787586364791}{512} \) |
\( \bigl[a^{3} + a^{2} - 4 a - 2\) , \( -a^{2} + 4\) , \( a^{3} - 3 a + 1\) , \( -371 a^{3} + 485 a^{2} + 1727 a - 2107\) , \( -7793 a^{3} + 10190 a^{2} + 36503 a - 44728\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-4a-2\right){x}{y}+\left(a^{3}-3a+1\right){y}={x}^{3}+\left(-a^{2}+4\right){x}^{2}+\left(-371a^{3}+485a^{2}+1727a-2107\right){x}-7793a^{3}+10190a^{2}+36503a-44728$ |
| 5.1-a1 |
5.1-a |
$4$ |
$6$ |
4.4.11324.1 |
$4$ |
$[4, 0]$ |
5.1 |
\( 5 \) |
\( - 5^{2} \) |
$11.62813$ |
$(a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$9$ |
\( 2 \) |
$1.815388587$ |
$5.783243990$ |
1.775880305 |
\( \frac{353245317217433658367}{25} a^{3} - \frac{479177251473660210479}{25} a^{2} - \frac{1595399924873532170816}{25} a + \frac{1981741245744593173394}{25} \) |
\( \bigl[a^{2} + a - 2\) , \( a^{2} - 3\) , \( a^{2} + a - 3\) , \( 69 a^{3} - 79 a^{2} - 147 a - 47\) , \( 520 a^{3} - 921 a^{2} - 542 a - 57\bigr] \) |
${y}^2+\left(a^{2}+a-2\right){x}{y}+\left(a^{2}+a-3\right){y}={x}^{3}+\left(a^{2}-3\right){x}^{2}+\left(69a^{3}-79a^{2}-147a-47\right){x}+520a^{3}-921a^{2}-542a-57$ |
| 5.1-a2 |
5.1-a |
$4$ |
$6$ |
4.4.11324.1 |
$4$ |
$[4, 0]$ |
5.1 |
\( 5 \) |
\( - 5^{6} \) |
$11.62813$ |
$(a+1)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2 \cdot 3 \) |
$0.605129529$ |
$468.4427632$ |
1.775880305 |
\( \frac{10282966402}{15625} a^{3} - \frac{14004905899}{15625} a^{2} - \frac{46437691346}{15625} a + \frac{57971011014}{15625} \) |
\( \bigl[a^{2} + a - 2\) , \( a^{2} - 3\) , \( a^{2} + a - 3\) , \( 4 a^{3} + a^{2} - 12 a - 7\) , \( -3 a^{3} + 2 a^{2} + 20 a + 4\bigr] \) |
${y}^2+\left(a^{2}+a-2\right){x}{y}+\left(a^{2}+a-3\right){y}={x}^{3}+\left(a^{2}-3\right){x}^{2}+\left(4a^{3}+a^{2}-12a-7\right){x}-3a^{3}+2a^{2}+20a+4$ |
| 5.1-a3 |
5.1-a |
$4$ |
$6$ |
4.4.11324.1 |
$4$ |
$[4, 0]$ |
5.1 |
\( 5 \) |
\( 5^{3} \) |
$11.62813$ |
$(a+1)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 3 \) |
$1.210259058$ |
$468.4427632$ |
1.775880305 |
\( -\frac{97899}{125} a^{3} + \frac{107813}{125} a^{2} + \frac{551252}{125} a - \frac{8318}{125} \) |
\( \bigl[a^{2} + a - 2\) , \( -a^{3} + 3 a - 1\) , \( a^{3} - 4 a + 1\) , \( -5 a^{3} - 7 a^{2} + 10 a + 7\) , \( -13 a^{3} - 16 a^{2} + 28 a + 10\bigr] \) |
${y}^2+\left(a^{2}+a-2\right){x}{y}+\left(a^{3}-4a+1\right){y}={x}^{3}+\left(-a^{3}+3a-1\right){x}^{2}+\left(-5a^{3}-7a^{2}+10a+7\right){x}-13a^{3}-16a^{2}+28a+10$ |
| 5.1-a4 |
5.1-a |
$4$ |
$6$ |
4.4.11324.1 |
$4$ |
$[4, 0]$ |
5.1 |
\( 5 \) |
\( 5 \) |
$11.62813$ |
$(a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$9$ |
\( 1 \) |
$3.630777175$ |
$5.783243990$ |
1.775880305 |
\( -\frac{42808556696}{5} a^{3} + \frac{42712897307}{5} a^{2} + \frac{300041550278}{5} a + \frac{49861471458}{5} \) |
\( \bigl[a^{2} + a - 2\) , \( -a^{3} + 3 a - 1\) , \( a^{3} - 4 a + 1\) , \( -345 a^{3} - 437 a^{2} + 735 a + 297\) , \( -8879 a^{3} - 11165 a^{2} + 19198 a + 7853\bigr] \) |
${y}^2+\left(a^{2}+a-2\right){x}{y}+\left(a^{3}-4a+1\right){y}={x}^{3}+\left(-a^{3}+3a-1\right){x}^{2}+\left(-345a^{3}-437a^{2}+735a+297\right){x}-8879a^{3}-11165a^{2}+19198a+7853$ |
| 5.1-b1 |
5.1-b |
$4$ |
$4$ |
4.4.11324.1 |
$4$ |
$[4, 0]$ |
5.1 |
\( 5 \) |
\( 5 \) |
$11.62813$ |
$(a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$254.4388762$ |
0.597755453 |
\( -\frac{6504999251}{5} a^{3} - \frac{1235566503}{5} a^{2} + \frac{31054752658}{5} a + \frac{10933319893}{5} \) |
\( \bigl[a^{3} + a^{2} - 3 a - 3\) , \( -a - 1\) , \( 1\) , \( 3 a^{3} + 2 a^{2} - 11 a - 3\) , \( 4 a^{3} + 2 a^{2} - 16 a - 6\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-3a-3\right){x}{y}+{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(3a^{3}+2a^{2}-11a-3\right){x}+4a^{3}+2a^{2}-16a-6$ |
| 5.1-b2 |
5.1-b |
$4$ |
$4$ |
4.4.11324.1 |
$4$ |
$[4, 0]$ |
5.1 |
\( 5 \) |
\( - 5^{4} \) |
$11.62813$ |
$(a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$127.2194381$ |
0.597755453 |
\( -\frac{3252803325308247}{625} a^{3} + \frac{10049963651802539}{625} a^{2} - \frac{4736699380617094}{625} a - \frac{3113273290305929}{625} \) |
\( \bigl[a^{3} - 3 a + 1\) , \( a^{3} + a^{2} - 3 a - 4\) , \( a^{2} - 2\) , \( 4 a^{3} + 10 a^{2} - 10 a - 25\) , \( -254 a^{3} - 332 a^{2} + 552 a + 284\bigr] \) |
${y}^2+\left(a^{3}-3a+1\right){x}{y}+\left(a^{2}-2\right){y}={x}^{3}+\left(a^{3}+a^{2}-3a-4\right){x}^{2}+\left(4a^{3}+10a^{2}-10a-25\right){x}-254a^{3}-332a^{2}+552a+284$ |
| 5.1-b3 |
5.1-b |
$4$ |
$4$ |
4.4.11324.1 |
$4$ |
$[4, 0]$ |
5.1 |
\( 5 \) |
\( -5 \) |
$11.62813$ |
$(a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$254.4388762$ |
0.597755453 |
\( \frac{1355158991}{5} a^{3} + \frac{1702315023}{5} a^{2} - \frac{2935026028}{5} a - \frac{1201219253}{5} \) |
\( \bigl[a + 1\) , \( a^{3} + a^{2} - 4 a - 3\) , \( a^{2} + a - 3\) , \( -9 a^{3} + 13 a^{2} + 43 a - 50\) , \( -22 a^{3} + 32 a^{2} + 101 a - 130\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{2}+a-3\right){y}={x}^{3}+\left(a^{3}+a^{2}-4a-3\right){x}^{2}+\left(-9a^{3}+13a^{2}+43a-50\right){x}-22a^{3}+32a^{2}+101a-130$ |
| 5.1-b4 |
5.1-b |
$4$ |
$4$ |
4.4.11324.1 |
$4$ |
$[4, 0]$ |
5.1 |
\( 5 \) |
\( 5^{2} \) |
$11.62813$ |
$(a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2 \) |
$1$ |
$508.8777525$ |
0.597755453 |
\( -\frac{11729758}{25} a^{3} + \frac{35509221}{25} a^{2} - \frac{15183766}{25} a - \frac{10332681}{25} \) |
\( \bigl[a + 1\) , \( a^{3} + a^{2} - 4 a - 2\) , \( a^{2} - 2\) , \( 33 a^{3} + 7 a^{2} - 155 a - 54\) , \( 137 a^{3} + 25 a^{2} - 654 a - 231\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{2}-2\right){y}={x}^{3}+\left(a^{3}+a^{2}-4a-2\right){x}^{2}+\left(33a^{3}+7a^{2}-155a-54\right){x}+137a^{3}+25a^{2}-654a-231$ |
| 8.1-a1 |
8.1-a |
$2$ |
$2$ |
4.4.11324.1 |
$4$ |
$[4, 0]$ |
8.1 |
\( 2^{3} \) |
\( 2^{6} \) |
$12.33175$ |
$(a^3-5a), (-a^2+a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$340.3879291$ |
3.198705229 |
\( \frac{1404792715}{4} a^{3} - \frac{1905362155}{4} a^{2} - 1586175900 a + 1970002986 \) |
\( \bigl[a^{3} + a^{2} - 4 a - 3\) , \( a^{2} - 2\) , \( a^{2} - 2\) , \( -6 a^{3} + 7 a^{2} + 40 a - 41\) , \( -12 a^{3} + 10 a^{2} + 90 a - 97\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-4a-3\right){x}{y}+\left(a^{2}-2\right){y}={x}^{3}+\left(a^{2}-2\right){x}^{2}+\left(-6a^{3}+7a^{2}+40a-41\right){x}-12a^{3}+10a^{2}+90a-97$ |
| 8.1-a2 |
8.1-a |
$2$ |
$2$ |
4.4.11324.1 |
$4$ |
$[4, 0]$ |
8.1 |
\( 2^{3} \) |
\( 2^{6} \) |
$12.33175$ |
$(a^3-5a), (-a^2+a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$340.3879291$ |
3.198705229 |
\( -\frac{28279490875}{4} a^{3} - \frac{2685693575}{2} a^{2} + \frac{67502881775}{2} a + \frac{47530715137}{4} \) |
\( \bigl[a^{2} - 3\) , \( a^{3} + a^{2} - 5 a - 4\) , \( a^{3} + a^{2} - 3 a - 2\) , \( -2 a - 2\) , \( -4 a^{3} - 20 a^{2} + 50 a + 20\bigr] \) |
${y}^2+\left(a^{2}-3\right){x}{y}+\left(a^{3}+a^{2}-3a-2\right){y}={x}^{3}+\left(a^{3}+a^{2}-5a-4\right){x}^{2}+\left(-2a-2\right){x}-4a^{3}-20a^{2}+50a+20$ |
| 8.1-b1 |
8.1-b |
$1$ |
$1$ |
4.4.11324.1 |
$4$ |
$[4, 0]$ |
8.1 |
\( 2^{3} \) |
\( 2^{9} \) |
$12.33175$ |
$(a^3-5a), (-a^2+a+3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$1$ |
$95.00683401$ |
0.892801509 |
\( -\frac{1448503}{16} a^{3} + \frac{2031095}{16} a^{2} + \frac{6530981}{16} a - \frac{4219149}{8} \) |
\( \bigl[a^{2} - 3\) , \( -a^{2} + 2\) , \( a^{2} - 3\) , \( a^{3} - 5 a - 1\) , \( a^{3} - 5 a - 2\bigr] \) |
${y}^2+\left(a^{2}-3\right){x}{y}+\left(a^{2}-3\right){y}={x}^{3}+\left(-a^{2}+2\right){x}^{2}+\left(a^{3}-5a-1\right){x}+a^{3}-5a-2$ |
| 8.1-c1 |
8.1-c |
$4$ |
$4$ |
4.4.11324.1 |
$4$ |
$[4, 0]$ |
8.1 |
\( 2^{3} \) |
\( 2^{10} \) |
$12.33175$ |
$(a^3-5a), (-a^2+a+3)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.093613475$ |
$1064.136859$ |
1.872258966 |
\( \frac{1148659}{16} a^{3} - 97391 a^{2} - \frac{2597693}{8} a + \frac{1618985}{4} \) |
\( \bigl[a^{3} + a^{2} - 4 a - 3\) , \( -a^{3} - a^{2} + 3 a + 3\) , \( a\) , \( -7 a^{3} + 32 a + 4\) , \( -5 a^{3} - 2 a^{2} + 24 a + 12\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-4a-3\right){x}{y}+a{y}={x}^{3}+\left(-a^{3}-a^{2}+3a+3\right){x}^{2}+\left(-7a^{3}+32a+4\right){x}-5a^{3}-2a^{2}+24a+12$ |
| 8.1-c2 |
8.1-c |
$4$ |
$4$ |
4.4.11324.1 |
$4$ |
$[4, 0]$ |
8.1 |
\( 2^{3} \) |
\( 2^{4} \) |
$12.33175$ |
$(a^3-5a), (-a^2+a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.374453900$ |
$266.0342149$ |
1.872258966 |
\( -802630664191 a^{3} + 2479833481214 a^{2} - 1168780558340 a - \frac{1536406845933}{2} \) |
\( \bigl[a^{3} + a^{2} - 3 a - 3\) , \( a^{2} + a - 3\) , \( a^{3} - 4 a\) , \( 242 a^{3} - 718 a^{2} + 323 a + 220\) , \( 6877 a^{3} - 21198 a^{2} + 9972 a + 6560\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-3a-3\right){x}{y}+\left(a^{3}-4a\right){y}={x}^{3}+\left(a^{2}+a-3\right){x}^{2}+\left(242a^{3}-718a^{2}+323a+220\right){x}+6877a^{3}-21198a^{2}+9972a+6560$ |
| 8.1-c3 |
8.1-c |
$4$ |
$4$ |
4.4.11324.1 |
$4$ |
$[4, 0]$ |
8.1 |
\( 2^{3} \) |
\( 2^{10} \) |
$12.33175$ |
$(a^3-5a), (-a^2+a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.374453900$ |
$266.0342149$ |
1.872258966 |
\( -\frac{174483}{16} a^{3} - 234 a^{2} + \frac{466917}{8} a + \frac{352373}{16} \) |
\( \bigl[a^{3} - 3 a + 1\) , \( -a^{3} + a^{2} + 3 a - 2\) , \( a^{3} - 4 a + 1\) , \( -a^{3} + a^{2} - 1\) , \( -3 a^{3} - 2 a^{2} + 5 a\bigr] \) |
${y}^2+\left(a^{3}-3a+1\right){x}{y}+\left(a^{3}-4a+1\right){y}={x}^{3}+\left(-a^{3}+a^{2}+3a-2\right){x}^{2}+\left(-a^{3}+a^{2}-1\right){x}-3a^{3}-2a^{2}+5a$ |
| 8.1-c4 |
8.1-c |
$4$ |
$4$ |
4.4.11324.1 |
$4$ |
$[4, 0]$ |
8.1 |
\( 2^{3} \) |
\( 2^{8} \) |
$12.33175$ |
$(a^3-5a), (-a^2+a+3)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$0.187226950$ |
$1064.136859$ |
1.872258966 |
\( -180162 a^{3} + 556938 a^{2} - 262398 a - \frac{682855}{4} \) |
\( \bigl[1\) , \( 0\) , \( a^{3} + a^{2} - 3 a - 3\) , \( -3 a^{3} + 4 a^{2} + 12 a - 19\) , \( -2 a^{2} - 2 a + 4\bigr] \) |
${y}^2+{x}{y}+\left(a^{3}+a^{2}-3a-3\right){y}={x}^{3}+\left(-3a^{3}+4a^{2}+12a-19\right){x}-2a^{2}-2a+4$ |
| 8.1-d1 |
8.1-d |
$3$ |
$9$ |
4.4.11324.1 |
$4$ |
$[4, 0]$ |
8.1 |
\( 2^{3} \) |
\( 2^{27} \) |
$12.33175$ |
$(a^3-5a), (-a^2+a+3)$ |
0 |
$\Z/9\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1 |
$1$ |
\( 3^{4} \) |
$1$ |
$180.3949705$ |
1.695213861 |
\( -\frac{3175}{256} a^{3} + \frac{162185}{512} a^{2} - \frac{16573}{256} a - \frac{87921}{256} \) |
\( \bigl[1\) , \( a^{2} + a - 3\) , \( a^{3} - 4 a + 1\) , \( a^{3} + 3 a^{2} - 4 a\) , \( 2 a^{2} - a - 3\bigr] \) |
${y}^2+{x}{y}+\left(a^{3}-4a+1\right){y}={x}^{3}+\left(a^{2}+a-3\right){x}^{2}+\left(a^{3}+3a^{2}-4a\right){x}+2a^{2}-a-3$ |
| 8.1-d2 |
8.1-d |
$3$ |
$9$ |
4.4.11324.1 |
$4$ |
$[4, 0]$ |
8.1 |
\( 2^{3} \) |
\( 2^{57} \) |
$12.33175$ |
$(a^3-5a), (-a^2+a+3)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3Cs.1.1 |
$9$ |
\( 3^{4} \) |
$1$ |
$2.227098402$ |
1.695213861 |
\( \frac{112807378703683}{134217728} a^{3} + \frac{10131794073095}{67108864} a^{2} - \frac{270571608370495}{67108864} a - \frac{11896758820741}{8388608} \) |
\( \bigl[1\) , \( a^{2} + a - 3\) , \( a^{3} - 4 a + 1\) , \( -14 a^{3} - 47 a^{2} + 36 a + 20\) , \( -169 a^{3} - 350 a^{2} + 445 a + 193\bigr] \) |
${y}^2+{x}{y}+\left(a^{3}-4a+1\right){y}={x}^{3}+\left(a^{2}+a-3\right){x}^{2}+\left(-14a^{3}-47a^{2}+36a+20\right){x}-169a^{3}-350a^{2}+445a+193$ |
| 8.1-d3 |
8.1-d |
$3$ |
$9$ |
4.4.11324.1 |
$4$ |
$[4, 0]$ |
8.1 |
\( 2^{3} \) |
\( 2^{19} \) |
$12.33175$ |
$(a^3-5a), (-a^2+a+3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.2 |
$729$ |
\( 3^{2} \) |
$1$ |
$0.027495042$ |
1.695213861 |
\( \frac{9135977966106098429399}{512} a^{3} + \frac{867628940947068681587}{256} a^{2} - \frac{21807541432668180905747}{256} a - \frac{959710996587311585475}{32} \) |
\( \bigl[1\) , \( a^{2} + a - 3\) , \( a^{3} - 4 a + 1\) , \( -1149 a^{3} - 3922 a^{2} + 3071 a + 1540\) , \( -99521 a^{3} - 216742 a^{2} + 264677 a + 117393\bigr] \) |
${y}^2+{x}{y}+\left(a^{3}-4a+1\right){y}={x}^{3}+\left(a^{2}+a-3\right){x}^{2}+\left(-1149a^{3}-3922a^{2}+3071a+1540\right){x}-99521a^{3}-216742a^{2}+264677a+117393$ |
| 8.2-a1 |
8.2-a |
$1$ |
$1$ |
4.4.11324.1 |
$4$ |
$[4, 0]$ |
8.2 |
\( 2^{3} \) |
\( 2^{4} \) |
$12.33175$ |
$(a^3-5a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
|
|
$1$ |
\( 2 \) |
$0.033042447$ |
$773.0375144$ |
1.920272359 |
\( 621 a^{3} + 120 a^{2} - 2966 a - 1036 \) |
\( \bigl[a^{3} - 4 a\) , \( a^{2} - a - 3\) , \( a^{3} + a^{2} - 3 a - 2\) , \( 4 a^{3} - 6 a^{2} - 21 a + 23\) , \( -117 a^{3} + 156 a^{2} + 525 a - 650\bigr] \) |
${y}^2+\left(a^{3}-4a\right){x}{y}+\left(a^{3}+a^{2}-3a-2\right){y}={x}^{3}+\left(a^{2}-a-3\right){x}^{2}+\left(4a^{3}-6a^{2}-21a+23\right){x}-117a^{3}+156a^{2}+525a-650$ |
| 10.1-a1 |
10.1-a |
$2$ |
$3$ |
4.4.11324.1 |
$4$ |
$[4, 0]$ |
10.1 |
\( 2 \cdot 5 \) |
\( 2^{18} \cdot 5^{3} \) |
$12.68056$ |
$(a^3-5a), (a+1)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1 |
$1$ |
\( 2 \cdot 3 \) |
$0.331766971$ |
$299.5258831$ |
2.490211922 |
\( -\frac{18143260469}{64000} a^{3} + \frac{12173702639}{32000} a^{2} + \frac{20688063403}{16000} a - \frac{102310022683}{64000} \) |
\( \bigl[a^{3} - 4 a + 1\) , \( -a\) , \( a^{2} - 3\) , \( -4 a^{3} - 4 a^{2} + 9 a + 1\) , \( -17 a^{3} - 22 a^{2} + 36 a + 16\bigr] \) |
${y}^2+\left(a^{3}-4a+1\right){x}{y}+\left(a^{2}-3\right){y}={x}^{3}-a{x}^{2}+\left(-4a^{3}-4a^{2}+9a+1\right){x}-17a^{3}-22a^{2}+36a+16$ |
| 10.1-a2 |
10.1-a |
$2$ |
$3$ |
4.4.11324.1 |
$4$ |
$[4, 0]$ |
10.1 |
\( 2 \cdot 5 \) |
\( 2^{54} \cdot 5 \) |
$12.68056$ |
$(a^3-5a), (a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.2 |
$9$ |
\( 2 \) |
$0.995300915$ |
$3.697850409$ |
2.490211922 |
\( -\frac{104421194283869401}{671088640} a^{3} - \frac{65592039235049719}{335544320} a^{2} + \frac{28265898435686641}{83886080} a + \frac{92555681506655613}{671088640} \) |
\( \bigl[a^{3} - 4 a + 1\) , \( -a\) , \( a^{2} - 3\) , \( -339 a^{3} - 434 a^{2} + 719 a + 306\) , \( -8637 a^{3} - 10869 a^{2} + 18676 a + 7678\bigr] \) |
${y}^2+\left(a^{3}-4a+1\right){x}{y}+\left(a^{2}-3\right){y}={x}^{3}-a{x}^{2}+\left(-339a^{3}-434a^{2}+719a+306\right){x}-8637a^{3}-10869a^{2}+18676a+7678$ |
| 10.1-b1 |
10.1-b |
$8$ |
$12$ |
4.4.11324.1 |
$4$ |
$[4, 0]$ |
10.1 |
\( 2 \cdot 5 \) |
\( - 2^{12} \cdot 5^{3} \) |
$12.68056$ |
$(a^3-5a), (a+1)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{2} \cdot 3 \) |
$0.369583550$ |
$716.1018848$ |
3.316089596 |
\( -\frac{57583081}{8000} a^{3} + \frac{92313143}{2000} a^{2} - \frac{128192731}{4000} a - \frac{120790917}{8000} \) |
\( \bigl[a^{3} + a^{2} - 3 a - 3\) , \( -a^{3} - a^{2} + 4 a + 2\) , \( a^{3} - 4 a\) , \( -29 a^{3} - 35 a^{2} + 67 a + 28\) , \( -250 a^{3} - 312 a^{2} + 546 a + 222\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-3a-3\right){x}{y}+\left(a^{3}-4a\right){y}={x}^{3}+\left(-a^{3}-a^{2}+4a+2\right){x}^{2}+\left(-29a^{3}-35a^{2}+67a+28\right){x}-250a^{3}-312a^{2}+546a+222$ |
| 10.1-b2 |
10.1-b |
$8$ |
$12$ |
4.4.11324.1 |
$4$ |
$[4, 0]$ |
10.1 |
\( 2 \cdot 5 \) |
\( - 2^{4} \cdot 5^{9} \) |
$12.68056$ |
$(a^3-5a), (a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$9$ |
\( 2^{2} \) |
$1.108750650$ |
$8.840764010$ |
3.316089596 |
\( \frac{170246460623168112451}{7812500} a^{3} + \frac{53462209509857054872}{1953125} a^{2} - \frac{184365542195919851399}{3906250} a - \frac{150882643732061508493}{7812500} \) |
\( \bigl[a^{2} - 3\) , \( a^{3} + a^{2} - 3 a - 3\) , \( a^{2} + a - 3\) , \( 172 a^{3} - 551 a^{2} + 326 a + 110\) , \( 4341 a^{3} - 13428 a^{2} + 6464 a + 3927\bigr] \) |
${y}^2+\left(a^{2}-3\right){x}{y}+\left(a^{2}+a-3\right){y}={x}^{3}+\left(a^{3}+a^{2}-3a-3\right){x}^{2}+\left(172a^{3}-551a^{2}+326a+110\right){x}+4341a^{3}-13428a^{2}+6464a+3927$ |
| 10.1-b3 |
10.1-b |
$8$ |
$12$ |
4.4.11324.1 |
$4$ |
$[4, 0]$ |
10.1 |
\( 2 \cdot 5 \) |
\( - 2 \cdot 5^{9} \) |
$12.68056$ |
$(a^3-5a), (a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$9$ |
\( 1 \) |
$4.435002603$ |
$8.840764010$ |
3.316089596 |
\( -\frac{2732063681131532298413}{3906250} a^{3} + \frac{8441065838478510499631}{3906250} a^{2} - \frac{3978392047229931711101}{3906250} a - \frac{1307437773480485111158}{1953125} \) |
\( \bigl[a^{2} - 3\) , \( a^{2} - 2\) , \( a\) , \( 24 a^{3} + 15 a^{2} - 118 a - 98\) , \( 175 a^{3} + 12 a^{2} - 839 a - 228\bigr] \) |
${y}^2+\left(a^{2}-3\right){x}{y}+a{y}={x}^{3}+\left(a^{2}-2\right){x}^{2}+\left(24a^{3}+15a^{2}-118a-98\right){x}+175a^{3}+12a^{2}-839a-228$ |
| 10.1-b4 |
10.1-b |
$8$ |
$12$ |
4.4.11324.1 |
$4$ |
$[4, 0]$ |
10.1 |
\( 2 \cdot 5 \) |
\( - 2^{3} \cdot 5^{3} \) |
$12.68056$ |
$(a^3-5a), (a+1)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 3 \) |
$1.478334201$ |
$716.1018848$ |
3.316089596 |
\( \frac{129742133341}{500} a^{3} - \frac{175986226817}{500} a^{2} - \frac{585999555143}{500} a + \frac{363945784931}{250} \) |
\( \bigl[a^{2} - 3\) , \( a^{2} - 2\) , \( a\) , \( -6 a^{3} + 10 a^{2} + 27 a - 38\) , \( 17 a^{3} - 22 a^{2} - 76 a + 92\bigr] \) |
${y}^2+\left(a^{2}-3\right){x}{y}+a{y}={x}^{3}+\left(a^{2}-2\right){x}^{2}+\left(-6a^{3}+10a^{2}+27a-38\right){x}+17a^{3}-22a^{2}-76a+92$ |
| 10.1-b5 |
10.1-b |
$8$ |
$12$ |
4.4.11324.1 |
$4$ |
$[4, 0]$ |
10.1 |
\( 2 \cdot 5 \) |
\( 2^{3} \cdot 5^{12} \) |
$12.68056$ |
$(a^3-5a), (a+1)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2 \cdot 3 \) |
$1.478334201$ |
$358.0509424$ |
3.316089596 |
\( -\frac{1943723921964277833}{976562500} a^{3} - \frac{369057274848591579}{976562500} a^{2} + \frac{9279632299215839059}{976562500} a + \frac{1633512853465750497}{488281250} \) |
\( \bigl[a + 1\) , \( -a^{2} + a + 3\) , \( a^{2} - 3\) , \( -6 a^{3} - 2 a^{2} + 5 a + 5\) , \( 12 a^{3} + 9 a^{2} - 20 a - 9\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{2}-3\right){y}={x}^{3}+\left(-a^{2}+a+3\right){x}^{2}+\left(-6a^{3}-2a^{2}+5a+5\right){x}+12a^{3}+9a^{2}-20a-9$ |
| 10.1-b6 |
10.1-b |
$8$ |
$12$ |
4.4.11324.1 |
$4$ |
$[4, 0]$ |
10.1 |
\( 2 \cdot 5 \) |
\( 2^{6} \cdot 5^{6} \) |
$12.68056$ |
$(a^3-5a), (a+1)$ |
$1$ |
$\Z/2\Z\oplus\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2Cs, 3B.1.1 |
$1$ |
\( 2^{2} \cdot 3 \) |
$0.739167100$ |
$1432.203769$ |
3.316089596 |
\( -\frac{406878961}{31250} a^{3} - \frac{1453963347}{125000} a^{2} + \frac{7973027737}{125000} a + \frac{8375457067}{125000} \) |
\( \bigl[a + 1\) , \( -a^{2} + a + 3\) , \( a^{2} - 3\) , \( -a^{3} - 2 a^{2} + 5 a + 5\) , \( -a^{3} + a^{2} + 2 a - 1\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{2}-3\right){y}={x}^{3}+\left(-a^{2}+a+3\right){x}^{2}+\left(-a^{3}-2a^{2}+5a+5\right){x}-a^{3}+a^{2}+2a-1$ |
| 10.1-b7 |
10.1-b |
$8$ |
$12$ |
4.4.11324.1 |
$4$ |
$[4, 0]$ |
10.1 |
\( 2 \cdot 5 \) |
\( 2 \cdot 5^{36} \) |
$12.68056$ |
$(a^3-5a), (a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$9$ |
\( 2 \) |
$4.435002603$ |
$4.420382005$ |
3.316089596 |
\( \frac{7856676960299175668001817761}{29103830456733703613281250} a^{3} - \frac{27631448782715195011362669607}{29103830456733703613281250} a^{2} + \frac{71561916707521519718706567697}{29103830456733703613281250} a + \frac{14685953958821655498210937026}{14551915228366851806640625} \) |
\( \bigl[a + 1\) , \( -a^{2} + a + 3\) , \( a^{2} - 3\) , \( 4 a^{3} - 82 a^{2} + 60 a + 35\) , \( 73 a^{3} - 606 a^{2} + 424 a + 227\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{2}-3\right){y}={x}^{3}+\left(-a^{2}+a+3\right){x}^{2}+\left(4a^{3}-82a^{2}+60a+35\right){x}+73a^{3}-606a^{2}+424a+227$ |
| 10.1-b8 |
10.1-b |
$8$ |
$12$ |
4.4.11324.1 |
$4$ |
$[4, 0]$ |
10.1 |
\( 2 \cdot 5 \) |
\( 2^{2} \cdot 5^{18} \) |
$12.68056$ |
$(a^3-5a), (a+1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2Cs, 3B.1.2 |
$9$ |
\( 2^{2} \) |
$2.217501301$ |
$17.68152802$ |
3.316089596 |
\( -\frac{15164333906399358528}{3814697265625} a^{3} + \frac{138181750293129166897}{7629394531250} a^{2} - \frac{81423039235754101037}{7629394531250} a - \frac{47447665542168389867}{7629394531250} \) |
\( \bigl[a + 1\) , \( -a^{2} + a + 3\) , \( a^{2} - 3\) , \( 4 a^{3} - 82 a^{2} + 65 a + 35\) , \( 56 a^{3} - 593 a^{2} + 430 a + 227\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{2}-3\right){y}={x}^{3}+\left(-a^{2}+a+3\right){x}^{2}+\left(4a^{3}-82a^{2}+65a+35\right){x}+56a^{3}-593a^{2}+430a+227$ |
| 10.1-c1 |
10.1-c |
$4$ |
$4$ |
4.4.11324.1 |
$4$ |
$[4, 0]$ |
10.1 |
\( 2 \cdot 5 \) |
\( - 2^{4} \cdot 5 \) |
$12.68056$ |
$(a^3-5a), (a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.195098330$ |
$411.6522212$ |
1.509433839 |
\( -\frac{142152661}{20} a^{3} + \frac{110986533}{5} a^{2} - \frac{111025351}{10} a - \frac{124866677}{20} \) |
\( \bigl[a^{3} + a^{2} - 4 a - 3\) , \( -a^{2} + 2\) , \( a^{3} - 3 a + 1\) , \( -4 a^{3} - 4 a^{2} + 13 a + 7\) , \( -a^{3} + a^{2} + 7 a\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-4a-3\right){x}{y}+\left(a^{3}-3a+1\right){y}={x}^{3}+\left(-a^{2}+2\right){x}^{2}+\left(-4a^{3}-4a^{2}+13a+7\right){x}-a^{3}+a^{2}+7a$ |
| 10.1-c2 |
10.1-c |
$4$ |
$4$ |
4.4.11324.1 |
$4$ |
$[4, 0]$ |
10.1 |
\( 2 \cdot 5 \) |
\( - 2 \cdot 5^{4} \) |
$12.68056$ |
$(a^3-5a), (a+1)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.195098330$ |
$823.3044425$ |
1.509433839 |
\( -\frac{37440829549}{1250} a^{3} - \frac{7119488387}{1250} a^{2} + \frac{178723471327}{1250} a + \frac{31462654066}{625} \) |
\( \bigl[a^{3} + a^{2} - 3 a - 3\) , \( a^{3} - a^{2} - 5 a + 3\) , \( 0\) , \( 5 a^{3} + a^{2} - 17 a + 7\) , \( 4 a^{3} + a^{2} - 11 a + 7\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-3a-3\right){x}{y}={x}^{3}+\left(a^{3}-a^{2}-5a+3\right){x}^{2}+\left(5a^{3}+a^{2}-17a+7\right){x}+4a^{3}+a^{2}-11a+7$ |
| 10.1-c3 |
10.1-c |
$4$ |
$4$ |
4.4.11324.1 |
$4$ |
$[4, 0]$ |
10.1 |
\( 2 \cdot 5 \) |
\( 2 \cdot 5 \) |
$12.68056$ |
$(a^3-5a), (a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$0.195098330$ |
$823.3044425$ |
1.509433839 |
\( \frac{18832953773724794693}{10} a^{3} + \frac{23657763477810708539}{10} a^{2} - \frac{40788365420862504299}{10} a - \frac{8347238427245277262}{5} \) |
\( \bigl[a + 1\) , \( a^{2} - 4\) , \( a^{3} + a^{2} - 4 a - 3\) , \( 36 a^{3} - a^{2} - 165 a - 52\) , \( 138 a^{3} + 36 a^{2} - 677 a - 242\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{3}+a^{2}-4a-3\right){y}={x}^{3}+\left(a^{2}-4\right){x}^{2}+\left(36a^{3}-a^{2}-165a-52\right){x}+138a^{3}+36a^{2}-677a-242$ |
| 10.1-c4 |
10.1-c |
$4$ |
$4$ |
4.4.11324.1 |
$4$ |
$[4, 0]$ |
10.1 |
\( 2 \cdot 5 \) |
\( 2^{2} \cdot 5^{2} \) |
$12.68056$ |
$(a^3-5a), (a+1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$0.097549165$ |
$1646.608885$ |
1.509433839 |
\( \frac{9860231737}{25} a^{3} + \frac{24772865687}{50} a^{2} - \frac{42710342177}{50} a - \frac{17481075207}{50} \) |
\( \bigl[a + 1\) , \( a^{2} - 4\) , \( a^{3} + a^{2} - 4 a - 3\) , \( 11 a^{3} - a^{2} - 50 a - 12\) , \( -35 a^{3} - 9 a^{2} + 171 a + 58\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{3}+a^{2}-4a-3\right){y}={x}^{3}+\left(a^{2}-4\right){x}^{2}+\left(11a^{3}-a^{2}-50a-12\right){x}-35a^{3}-9a^{2}+171a+58$ |
| 13.1-a1 |
13.1-a |
$2$ |
$2$ |
4.4.11324.1 |
$4$ |
$[4, 0]$ |
13.1 |
\( 13 \) |
\( 13^{3} \) |
$13.10332$ |
$(a^2-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$724.6166066$ |
1.702348064 |
\( \frac{1287439}{2197} a^{3} - \frac{4538712}{2197} a^{2} - \frac{5523890}{2197} a + \frac{20788412}{2197} \) |
\( \bigl[a^{2} + a - 2\) , \( a + 1\) , \( a^{2} + a - 3\) , \( 5 a^{2} + 4 a - 10\) , \( 3 a^{3} + 4 a^{2} - 7 a - 2\bigr] \) |
${y}^2+\left(a^{2}+a-2\right){x}{y}+\left(a^{2}+a-3\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(5a^{2}+4a-10\right){x}+3a^{3}+4a^{2}-7a-2$ |
| 13.1-a2 |
13.1-a |
$2$ |
$2$ |
4.4.11324.1 |
$4$ |
$[4, 0]$ |
13.1 |
\( 13 \) |
\( 13^{6} \) |
$13.10332$ |
$(a^2-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$362.3083033$ |
1.702348064 |
\( \frac{11278122311}{4826809} a^{3} + \frac{19746711156}{4826809} a^{2} - \frac{27804512170}{4826809} a - \frac{11176284828}{4826809} \) |
\( \bigl[a^{3} - 3 a\) , \( a^{3} - a^{2} - 4 a + 4\) , \( a^{3} + a^{2} - 4 a - 3\) , \( -24 a^{3} - 35 a^{2} + 46 a + 31\) , \( -240 a^{3} - 305 a^{2} + 515 a + 218\bigr] \) |
${y}^2+\left(a^{3}-3a\right){x}{y}+\left(a^{3}+a^{2}-4a-3\right){y}={x}^{3}+\left(a^{3}-a^{2}-4a+4\right){x}^{2}+\left(-24a^{3}-35a^{2}+46a+31\right){x}-240a^{3}-305a^{2}+515a+218$ |
| 16.1-a1 |
16.1-a |
$1$ |
$1$ |
4.4.11324.1 |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{12} \) |
$13.44787$ |
$(a^3-5a), (-a^2+a+3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2 \cdot 3 \) |
$0.005621324$ |
$1900.808235$ |
2.409840373 |
\( \frac{379267}{16} a^{3} + \frac{17211}{16} a^{2} - \frac{426585}{4} a - \frac{296785}{8} \) |
\( \bigl[a^{3} - 4 a\) , \( -a^{2} + 4\) , \( a^{2} + a - 2\) , \( -a^{3} - 3 a^{2} + 5 a + 9\) , \( -a^{3} - a^{2} + 2 a + 5\bigr] \) |
${y}^2+\left(a^{3}-4a\right){x}{y}+\left(a^{2}+a-2\right){y}={x}^{3}+\left(-a^{2}+4\right){x}^{2}+\left(-a^{3}-3a^{2}+5a+9\right){x}-a^{3}-a^{2}+2a+5$ |
| 16.2-a1 |
16.2-a |
$6$ |
$8$ |
4.4.11324.1 |
$4$ |
$[4, 0]$ |
16.2 |
\( 2^{4} \) |
\( 2^{12} \) |
$13.44787$ |
$(a^3-5a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$614.9707027$ |
2.889511986 |
\( -2155689 a^{3} + 6662753 a^{2} - 3147109 a - 2057725 \) |
\( \bigl[a^{2} + a - 2\) , \( a^{3} + a^{2} - 5 a - 2\) , \( a^{3} + a^{2} - 4 a - 2\) , \( 6 a^{3} + 2 a^{2} - 22 a - 8\) , \( 19 a^{3} + 7 a^{2} - 84 a - 30\bigr] \) |
${y}^2+\left(a^{2}+a-2\right){x}{y}+\left(a^{3}+a^{2}-4a-2\right){y}={x}^{3}+\left(a^{3}+a^{2}-5a-2\right){x}^{2}+\left(6a^{3}+2a^{2}-22a-8\right){x}+19a^{3}+7a^{2}-84a-30$ |
| 16.2-a2 |
16.2-a |
$6$ |
$8$ |
4.4.11324.1 |
$4$ |
$[4, 0]$ |
16.2 |
\( 2^{4} \) |
\( 2^{12} \) |
$13.44787$ |
$(a^3-5a)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$1$ |
$1229.941405$ |
2.889511986 |
\( -224626 a^{3} - 29044 a^{2} + 1105288 a + 394939 \) |
\( \bigl[a^{2} + a - 2\) , \( -a\) , \( a^{2} + a - 2\) , \( -4 a^{3} - 4 a^{2} + 9 a + 1\) , \( 2 a^{3} + 3 a^{2} - 4 a - 3\bigr] \) |
${y}^2+\left(a^{2}+a-2\right){x}{y}+\left(a^{2}+a-2\right){y}={x}^{3}-a{x}^{2}+\left(-4a^{3}-4a^{2}+9a+1\right){x}+2a^{3}+3a^{2}-4a-3$ |
| 16.2-a3 |
16.2-a |
$6$ |
$8$ |
4.4.11324.1 |
$4$ |
$[4, 0]$ |
16.2 |
\( 2^{4} \) |
\( 2^{12} \) |
$13.44787$ |
$(a^3-5a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$4$ |
\( 2 \) |
$1$ |
$153.7426756$ |
2.889511986 |
\( -305523916811 a^{3} - 55768842233 a^{2} + 1464100257869 a + 515196650157 \) |
\( \bigl[a^{2} + a - 2\) , \( -a\) , \( a^{2} + a - 2\) , \( -49 a^{3} - 64 a^{2} + 99 a + 41\) , \( 408 a^{3} + 509 a^{2} - 892 a - 363\bigr] \) |
${y}^2+\left(a^{2}+a-2\right){x}{y}+\left(a^{2}+a-2\right){y}={x}^{3}-a{x}^{2}+\left(-49a^{3}-64a^{2}+99a+41\right){x}+408a^{3}+509a^{2}-892a-363$ |
| 16.2-a4 |
16.2-a |
$6$ |
$8$ |
4.4.11324.1 |
$4$ |
$[4, 0]$ |
16.2 |
\( 2^{4} \) |
\( - 2^{12} \) |
$13.44787$ |
$(a^3-5a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$307.4853513$ |
2.889511986 |
\( 273577301639170 a^{3} - 371107593060366 a^{2} - 1235586673541100 a + 1534795780915977 \) |
\( \bigl[a^{3} - 3 a\) , \( a^{2} - 2\) , \( a^{3} + a^{2} - 3 a - 2\) , \( 13 a^{3} - 15 a^{2} - 108 a - 35\) , \( -288 a^{3} - 212 a^{2} + 988 a + 366\bigr] \) |
${y}^2+\left(a^{3}-3a\right){x}{y}+\left(a^{3}+a^{2}-3a-2\right){y}={x}^{3}+\left(a^{2}-2\right){x}^{2}+\left(13a^{3}-15a^{2}-108a-35\right){x}-288a^{3}-212a^{2}+988a+366$ |
| 16.2-a5 |
16.2-a |
$6$ |
$8$ |
4.4.11324.1 |
$4$ |
$[4, 0]$ |
16.2 |
\( 2^{4} \) |
\( 2^{12} \) |
$13.44787$ |
$(a^3-5a)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$1$ |
$1229.941405$ |
2.889511986 |
\( 6250036 a^{3} - 8477824 a^{2} - 28229184 a + 35066649 \) |
\( \bigl[a^{3} - 3 a\) , \( a^{2} - 2\) , \( a^{3} + a^{2} - 3 a - 2\) , \( 3 a^{3} - 18 a - 5\) , \( -a^{3} - 4 a^{2} - 6 a - 2\bigr] \) |
${y}^2+\left(a^{3}-3a\right){x}{y}+\left(a^{3}+a^{2}-3a-2\right){y}={x}^{3}+\left(a^{2}-2\right){x}^{2}+\left(3a^{3}-18a-5\right){x}-a^{3}-4a^{2}-6a-2$ |
| 16.2-a6 |
16.2-a |
$6$ |
$8$ |
4.4.11324.1 |
$4$ |
$[4, 0]$ |
16.2 |
\( 2^{4} \) |
\( - 2^{12} \) |
$13.44787$ |
$(a^3-5a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$307.4853513$ |
2.889511986 |
\( -2075320 a^{3} + 6410242 a^{2} - 3015868 a - 1989779 \) |
\( \bigl[a^{3} - 3 a\) , \( -a^{3} + a^{2} + 5 a - 2\) , \( a\) , \( -32 a^{3} + 45 a^{2} + 149 a - 179\) , \( 254 a^{3} - 341 a^{2} - 1142 a + 1417\bigr] \) |
${y}^2+\left(a^{3}-3a\right){x}{y}+a{y}={x}^{3}+\left(-a^{3}+a^{2}+5a-2\right){x}^{2}+\left(-32a^{3}+45a^{2}+149a-179\right){x}+254a^{3}-341a^{2}-1142a+1417$ |
*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.
