| 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 |
| 5.1-a1 |
5.1-a |
$2$ |
$5$ |
3.3.785.1 |
$3$ |
$[3, 0]$ |
5.1 |
\( 5 \) |
\( - 5^{5} \) |
$3.27392$ |
$(a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.4.1 |
$1$ |
\( 1 \) |
$0.220764971$ |
$72.68301432$ |
1.718104287 |
\( -\frac{15313823739}{3125} a^{2} + \frac{51891754119}{3125} a - \frac{32058425671}{3125} \) |
\( \bigl[a^{2} - 4\) , \( a^{2} - a - 4\) , \( a^{2} + a - 4\) , \( 3 a^{2} - 3 a - 16\) , \( 31 a^{2} - 8 a - 192\bigr] \) |
${y}^2+\left(a^{2}-4\right){x}{y}+\left(a^{2}+a-4\right){y}={x}^{3}+\left(a^{2}-a-4\right){x}^{2}+\left(3a^{2}-3a-16\right){x}+31a^{2}-8a-192$ |
| 5.1-a2 |
5.1-a |
$2$ |
$5$ |
3.3.785.1 |
$3$ |
$[3, 0]$ |
5.1 |
\( 5 \) |
\( -5 \) |
$3.27392$ |
$(a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.4.2 |
$1$ |
\( 1 \) |
$0.044152994$ |
$363.4150716$ |
1.718104287 |
\( -\frac{88704}{5} a^{2} - \frac{147291}{5} a + \frac{160574}{5} \) |
\( \bigl[a^{2} - 3\) , \( -a - 1\) , \( 0\) , \( -a^{2} - 3 a + 2\) , \( 2 a^{2} + 3 a - 3\bigr] \) |
${y}^2+\left(a^{2}-3\right){x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-a^{2}-3a+2\right){x}+2a^{2}+3a-3$ |
| 9.1-a1 |
9.1-a |
$2$ |
$5$ |
3.3.785.1 |
$3$ |
$[3, 0]$ |
9.1 |
\( 3^{2} \) |
\( - 3^{10} \) |
$3.61089$ |
$(a^2+a-4)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.4.1 |
$1$ |
\( 5 \) |
$1$ |
$7.639278082$ |
1.363287633 |
\( -\frac{1123861}{81} a^{2} - \frac{77064587}{243} a - \frac{164467013}{243} \) |
\( \bigl[a^{2} - 3\) , \( -a^{2} + 4\) , \( 0\) , \( 666 a^{2} - 125 a - 4098\) , \( 16829 a^{2} - 3152 a - 103536\bigr] \) |
${y}^2+\left(a^{2}-3\right){x}{y}={x}^{3}+\left(-a^{2}+4\right){x}^{2}+\left(666a^{2}-125a-4098\right){x}+16829a^{2}-3152a-103536$ |
| 9.1-a2 |
9.1-a |
$2$ |
$5$ |
3.3.785.1 |
$3$ |
$[3, 0]$ |
9.1 |
\( 3^{2} \) |
\( - 3^{2} \) |
$3.61089$ |
$(a^2+a-4)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.4.2 |
$1$ |
\( 1 \) |
$1$ |
$38.19639041$ |
1.363287633 |
\( -2064866 a^{2} + \frac{20990633}{3} a - \frac{12963838}{3} \) |
\( \bigl[a^{2} + a - 3\) , \( -a^{2} - a + 4\) , \( 0\) , \( -3 a^{2} + 2 a + 22\) , \( -6 a^{2} + 2 a + 39\bigr] \) |
${y}^2+\left(a^{2}+a-3\right){x}{y}={x}^{3}+\left(-a^{2}-a+4\right){x}^{2}+\left(-3a^{2}+2a+22\right){x}-6a^{2}+2a+39$ |
| 9.1-b1 |
9.1-b |
$2$ |
$5$ |
3.3.785.1 |
$3$ |
$[3, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{2} \) |
$3.61089$ |
$(a^2+a-4)$ |
$0 \le r \le 1$ |
$\Z/5\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.1.1 |
|
\( 1 \) |
$1$ |
$207.8896130$ |
1.923260399 |
\( \frac{4630}{3} a^{2} - \frac{15565}{3} a + \frac{9292}{3} \) |
\( \bigl[a^{2} - 4\) , \( -a^{2} - a + 5\) , \( a^{2} + a - 3\) , \( -3 a^{2} - 2 a + 14\) , \( -6 a^{2} - 7 a + 18\bigr] \) |
${y}^2+\left(a^{2}-4\right){x}{y}+\left(a^{2}+a-3\right){y}={x}^{3}+\left(-a^{2}-a+5\right){x}^{2}+\left(-3a^{2}-2a+14\right){x}-6a^{2}-7a+18$ |
| 9.1-b2 |
9.1-b |
$2$ |
$5$ |
3.3.785.1 |
$3$ |
$[3, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{10} \) |
$3.61089$ |
$(a^2+a-4)$ |
$0 \le r \le 1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.1.2 |
|
\( 1 \) |
$1$ |
$1.663116904$ |
1.923260399 |
\( -\frac{290516873758889}{243} a^{2} - \frac{457813686972118}{243} a + \frac{563961278557702}{243} \) |
\( \bigl[a^{2} - 4\) , \( -a^{2} - a + 5\) , \( a^{2} + a - 3\) , \( -843 a^{2} - 1332 a + 1629\) , \( -27220 a^{2} - 42920 a + 52773\bigr] \) |
${y}^2+\left(a^{2}-4\right){x}{y}+\left(a^{2}+a-3\right){y}={x}^{3}+\left(-a^{2}-a+5\right){x}^{2}+\left(-843a^{2}-1332a+1629\right){x}-27220a^{2}-42920a+52773$ |
| 9.1-c1 |
9.1-c |
$2$ |
$2$ |
3.3.785.1 |
$3$ |
$[3, 0]$ |
9.1 |
\( 3^{2} \) |
\( - 3^{4} \) |
$3.61089$ |
$(a^2+a-4)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$70.14942175$ |
1.251870113 |
\( \frac{8640495615640}{9} a^{2} - \frac{29278230938230}{9} a + \frac{18087780752677}{9} \) |
\( \bigl[a^{2} + a - 4\) , \( a^{2} - a - 5\) , \( a + 1\) , \( -17 a^{2} + 64 a - 50\) , \( 109 a^{2} - 363 a + 216\bigr] \) |
${y}^2+\left(a^{2}+a-4\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a^{2}-a-5\right){x}^{2}+\left(-17a^{2}+64a-50\right){x}+109a^{2}-363a+216$ |
| 9.1-c2 |
9.1-c |
$2$ |
$2$ |
3.3.785.1 |
$3$ |
$[3, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{2} \) |
$3.61089$ |
$(a^2+a-4)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$140.2988435$ |
1.251870113 |
\( -230860 a^{2} + \frac{2568460}{3} a - \frac{1629941}{3} \) |
\( \bigl[a^{2} + a - 4\) , \( a^{2} - a - 5\) , \( a + 1\) , \( -2 a^{2} + 4 a + 5\) , \( 2 a^{2} - 2 a - 4\bigr] \) |
${y}^2+\left(a^{2}+a-4\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a^{2}-a-5\right){x}^{2}+\left(-2a^{2}+4a+5\right){x}+2a^{2}-2a-4$ |
| 15.1-a1 |
15.1-a |
$2$ |
$2$ |
3.3.785.1 |
$3$ |
$[3, 0]$ |
15.1 |
\( 3 \cdot 5 \) |
\( - 3^{3} \cdot 5^{5} \) |
$3.93177$ |
$(a-2), (a^2+a-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$0.416240354$ |
$140.8455589$ |
1.569328185 |
\( \frac{6933767}{3375} a^{2} + \frac{1156904}{3375} a - \frac{1146424}{675} \) |
\( \bigl[a\) , \( -a^{2} + a + 3\) , \( a^{2} + a - 4\) , \( -4 a^{2} - 6 a + 12\) , \( -6 a^{2} - 9 a + 11\bigr] \) |
${y}^2+a{x}{y}+\left(a^{2}+a-4\right){y}={x}^{3}+\left(-a^{2}+a+3\right){x}^{2}+\left(-4a^{2}-6a+12\right){x}-6a^{2}-9a+11$ |
| 15.1-a2 |
15.1-a |
$2$ |
$2$ |
3.3.785.1 |
$3$ |
$[3, 0]$ |
15.1 |
\( 3 \cdot 5 \) |
\( - 3^{6} \cdot 5^{10} \) |
$3.93177$ |
$(a-2), (a^2+a-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.208120177$ |
$70.42277947$ |
1.569328185 |
\( -\frac{93891589196}{2278125} a^{2} + \frac{19908802549}{2278125} a + \frac{116720890996}{455625} \) |
\( \bigl[a\) , \( -a^{2} + a + 3\) , \( a^{2} + a - 4\) , \( -9 a^{2} - 16 a + 17\) , \( 22 a^{2} + 35 a - 44\bigr] \) |
${y}^2+a{x}{y}+\left(a^{2}+a-4\right){y}={x}^{3}+\left(-a^{2}+a+3\right){x}^{2}+\left(-9a^{2}-16a+17\right){x}+22a^{2}+35a-44$ |
| 15.2-a1 |
15.2-a |
$4$ |
$10$ |
3.3.785.1 |
$3$ |
$[3, 0]$ |
15.2 |
\( 3 \cdot 5 \) |
\( - 3^{10} \cdot 5^{10} \) |
$3.93177$ |
$(a-2), (a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B.4.1 |
$1$ |
\( 2^{2} \) |
$0.839847852$ |
$18.99910249$ |
1.708520240 |
\( \frac{805058590861631339}{576650390625} a^{2} + \frac{1268977584604502531}{576650390625} a - \frac{1562043547410087929}{576650390625} \) |
\( \bigl[a^{2} - 3\) , \( 1\) , \( a^{2} + a - 3\) , \( 75 a^{2} - 12 a - 472\) , \( 161 a^{2} - 42 a - 967\bigr] \) |
${y}^2+\left(a^{2}-3\right){x}{y}+\left(a^{2}+a-3\right){y}={x}^{3}+{x}^{2}+\left(75a^{2}-12a-472\right){x}+161a^{2}-42a-967$ |
| 15.2-a2 |
15.2-a |
$4$ |
$10$ |
3.3.785.1 |
$3$ |
$[3, 0]$ |
15.2 |
\( 3 \cdot 5 \) |
\( - 3^{5} \cdot 5^{5} \) |
$3.93177$ |
$(a-2), (a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B.4.1 |
$1$ |
\( 1 \) |
$1.679695705$ |
$37.99820499$ |
1.708520240 |
\( -\frac{25089380164}{759375} a^{2} - \frac{129708562831}{759375} a + \frac{498426941254}{759375} \) |
\( \bigl[a^{2} - 3\) , \( 1\) , \( a^{2} + a - 3\) , \( 55 a^{2} - 7 a - 352\) , \( 438 a^{2} - 88 a - 2686\bigr] \) |
${y}^2+\left(a^{2}-3\right){x}{y}+\left(a^{2}+a-3\right){y}={x}^{3}+{x}^{2}+\left(55a^{2}-7a-352\right){x}+438a^{2}-88a-2686$ |
| 15.2-a3 |
15.2-a |
$4$ |
$10$ |
3.3.785.1 |
$3$ |
$[3, 0]$ |
15.2 |
\( 3 \cdot 5 \) |
\( - 3^{2} \cdot 5^{2} \) |
$3.93177$ |
$(a-2), (a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B.4.2 |
$1$ |
\( 2^{2} \) |
$0.167969570$ |
$94.99551247$ |
1.708520240 |
\( -\frac{474614682832216}{225} a^{2} + \frac{88887613981061}{225} a + \frac{2919928520246476}{225} \) |
\( \bigl[a^{2} + a - 3\) , \( -1\) , \( a^{2} + a - 3\) , \( 20 a^{2} + 3 a - 135\) , \( -95 a^{2} + 40 a + 541\bigr] \) |
${y}^2+\left(a^{2}+a-3\right){x}{y}+\left(a^{2}+a-3\right){y}={x}^{3}-{x}^{2}+\left(20a^{2}+3a-135\right){x}-95a^{2}+40a+541$ |
| 15.2-a4 |
15.2-a |
$4$ |
$10$ |
3.3.785.1 |
$3$ |
$[3, 0]$ |
15.2 |
\( 3 \cdot 5 \) |
\( - 3 \cdot 5 \) |
$3.93177$ |
$(a-2), (a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B.4.2 |
$1$ |
\( 1 \) |
$0.335939141$ |
$189.9910249$ |
1.708520240 |
\( -\frac{7431769}{15} a^{2} - \frac{4179976}{15} a + \frac{60073024}{15} \) |
\( \bigl[a^{2} + a - 3\) , \( -1\) , \( a^{2} + a - 3\) , \( 8 a - 15\) , \( -4 a^{2} + 17 a - 3\bigr] \) |
${y}^2+\left(a^{2}+a-3\right){x}{y}+\left(a^{2}+a-3\right){y}={x}^{3}-{x}^{2}+\left(8a-15\right){x}-4a^{2}+17a-3$ |
| 15.2-b1 |
15.2-b |
$6$ |
$8$ |
3.3.785.1 |
$3$ |
$[3, 0]$ |
15.2 |
\( 3 \cdot 5 \) |
\( 3^{2} \cdot 5^{8} \) |
$3.93177$ |
$(a-2), (a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 2^{4} \) |
$1$ |
$1.677329918$ |
0.957863551 |
\( -\frac{2762421153954670601047049}{3515625} a^{2} + \frac{517356524035998674755129}{3515625} a + \frac{16994990990732196688324364}{3515625} \) |
\( \bigl[a^{2} + a - 4\) , \( -a^{2} + a + 3\) , \( 1\) , \( 255 a^{2} - 30 a - 1607\) , \( 4253 a^{2} - 756 a - 26252\bigr] \) |
${y}^2+\left(a^{2}+a-4\right){x}{y}+{y}={x}^{3}+\left(-a^{2}+a+3\right){x}^{2}+\left(255a^{2}-30a-1607\right){x}+4253a^{2}-756a-26252$ |
| 15.2-b2 |
15.2-b |
$6$ |
$8$ |
3.3.785.1 |
$3$ |
$[3, 0]$ |
15.2 |
\( 3 \cdot 5 \) |
\( - 3^{8} \cdot 5^{2} \) |
$3.93177$ |
$(a-2), (a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$16$ |
\( 2^{2} \) |
$1$ |
$1.677329918$ |
0.957863551 |
\( \frac{2154621983559594094227929}{164025} a^{2} - \frac{7300914501119667671929609}{164025} a + \frac{4510427532245375321396356}{164025} \) |
\( \bigl[a^{2} + a - 4\) , \( -a^{2} + a + 3\) , \( 1\) , \( -75 a^{2} + 300 a - 277\) , \( -1077 a^{2} + 3914 a - 2954\bigr] \) |
${y}^2+\left(a^{2}+a-4\right){x}{y}+{y}={x}^{3}+\left(-a^{2}+a+3\right){x}^{2}+\left(-75a^{2}+300a-277\right){x}-1077a^{2}+3914a-2954$ |
| 15.2-b3 |
15.2-b |
$6$ |
$8$ |
3.3.785.1 |
$3$ |
$[3, 0]$ |
15.2 |
\( 3 \cdot 5 \) |
\( 3^{4} \cdot 5^{4} \) |
$3.93177$ |
$(a-2), (a)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$4$ |
\( 2^{3} \) |
$1$ |
$13.41863935$ |
0.957863551 |
\( \frac{27137864062334}{50625} a^{2} - \frac{152423185980739}{50625} a + \frac{212562263704501}{50625} \) |
\( \bigl[a^{2} + a - 4\) , \( -a^{2} + a + 3\) , \( 1\) , \( 10 a^{2} + 15 a - 102\) , \( 74 a^{2} + 23 a - 549\bigr] \) |
${y}^2+\left(a^{2}+a-4\right){x}{y}+{y}={x}^{3}+\left(-a^{2}+a+3\right){x}^{2}+\left(10a^{2}+15a-102\right){x}+74a^{2}+23a-549$ |
| 15.2-b4 |
15.2-b |
$6$ |
$8$ |
3.3.785.1 |
$3$ |
$[3, 0]$ |
15.2 |
\( 3 \cdot 5 \) |
\( 3^{2} \cdot 5^{2} \) |
$3.93177$ |
$(a-2), (a)$ |
0 |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$4$ |
\( 2^{2} \) |
$1$ |
$107.3491148$ |
0.957863551 |
\( \frac{140568755549}{225} a^{2} + \frac{221499293246}{225} a - \frac{272852338439}{225} \) |
\( \bigl[a^{2} + a - 4\) , \( -a^{2} + a + 3\) , \( 1\) , \( 3\) , \( 2 a^{2} - 12\bigr] \) |
${y}^2+\left(a^{2}+a-4\right){x}{y}+{y}={x}^{3}+\left(-a^{2}+a+3\right){x}^{2}+3{x}+2a^{2}-12$ |
| 15.2-b5 |
15.2-b |
$6$ |
$8$ |
3.3.785.1 |
$3$ |
$[3, 0]$ |
15.2 |
\( 3 \cdot 5 \) |
\( - 3 \cdot 5 \) |
$3.93177$ |
$(a-2), (a)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$429.3964592$ |
0.957863551 |
\( -\frac{130201}{15} a^{2} - \frac{202429}{15} a + \frac{287176}{15} \) |
\( \bigl[a^{2} + a - 4\) , \( -a^{2} + a + 3\) , \( 1\) , \( 8\) , \( 2 a + 1\bigr] \) |
${y}^2+\left(a^{2}+a-4\right){x}{y}+{y}={x}^{3}+\left(-a^{2}+a+3\right){x}^{2}+8{x}+2a+1$ |
| 15.2-b6 |
15.2-b |
$6$ |
$8$ |
3.3.785.1 |
$3$ |
$[3, 0]$ |
15.2 |
\( 3 \cdot 5 \) |
\( 3 \cdot 5 \) |
$3.93177$ |
$(a-2), (a)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$16$ |
\( 1 \) |
$1$ |
$26.83727870$ |
0.957863551 |
\( \frac{51241969707324211486}{15} a^{2} + \frac{80745736551235585069}{15} a - \frac{99469092005530821931}{15} \) |
\( \bigl[a^{2} + a - 4\) , \( -a^{2} + a + 3\) , \( 1\) , \( -10 a^{2} - 15 a + 28\) , \( 18 a^{2} + 29 a - 47\bigr] \) |
${y}^2+\left(a^{2}+a-4\right){x}{y}+{y}={x}^{3}+\left(-a^{2}+a+3\right){x}^{2}+\left(-10a^{2}-15a+28\right){x}+18a^{2}+29a-47$ |
| 15.2-c1 |
15.2-c |
$2$ |
$2$ |
3.3.785.1 |
$3$ |
$[3, 0]$ |
15.2 |
\( 3 \cdot 5 \) |
\( - 3^{2} \cdot 5^{10} \) |
$3.93177$ |
$(a-2), (a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \cdot 5 \) |
$0.057798737$ |
$89.22615774$ |
2.761003606 |
\( \frac{1802836380554}{87890625} a^{2} - \frac{3740144876359}{87890625} a + \frac{2000168056831}{87890625} \) |
\( \bigl[1\) , \( -a^{2} + 4\) , \( a\) , \( -17 a^{2} + 55 a - 29\) , \( 108 a^{2} - 368 a + 230\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a^{2}+4\right){x}^{2}+\left(-17a^{2}+55a-29\right){x}+108a^{2}-368a+230$ |
| 15.2-c2 |
15.2-c |
$2$ |
$2$ |
3.3.785.1 |
$3$ |
$[3, 0]$ |
15.2 |
\( 3 \cdot 5 \) |
\( - 3 \cdot 5^{5} \) |
$3.93177$ |
$(a-2), (a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 5 \) |
$0.115597474$ |
$178.4523154$ |
2.761003606 |
\( -\frac{1859341}{9375} a^{2} - \frac{2924314}{9375} a + \frac{19868551}{9375} \) |
\( \bigl[1\) , \( -a^{2} + 4\) , \( a\) , \( -2 a^{2} + 5 a + 1\) , \( -2 a + 3\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a^{2}+4\right){x}^{2}+\left(-2a^{2}+5a+1\right){x}-2a+3$ |
| 17.1-a1 |
17.1-a |
$2$ |
$5$ |
3.3.785.1 |
$3$ |
$[3, 0]$ |
17.1 |
\( 17 \) |
\( - 17^{5} \) |
$4.01465$ |
$(a^2-a-3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.4.1 |
$1$ |
\( 5 \) |
$1$ |
$17.91414766$ |
3.196916740 |
\( \frac{3608563662}{1419857} a^{2} - \frac{1068856785}{1419857} a - \frac{21597573604}{1419857} \) |
\( \bigl[a^{2} + a - 3\) , \( a^{2} - 3\) , \( a^{2} + a - 4\) , \( 224 a^{2} - 34 a - 1356\) , \( 3016 a^{2} - 549 a - 18516\bigr] \) |
${y}^2+\left(a^{2}+a-3\right){x}{y}+\left(a^{2}+a-4\right){y}={x}^{3}+\left(a^{2}-3\right){x}^{2}+\left(224a^{2}-34a-1356\right){x}+3016a^{2}-549a-18516$ |
| 17.1-a2 |
17.1-a |
$2$ |
$5$ |
3.3.785.1 |
$3$ |
$[3, 0]$ |
17.1 |
\( 17 \) |
\( -17 \) |
$4.01465$ |
$(a^2-a-3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.4.2 |
$1$ |
\( 1 \) |
$1$ |
$89.57073832$ |
3.196916740 |
\( -\frac{555597}{17} a^{2} + \frac{1873602}{17} a - \frac{1155634}{17} \) |
\( \bigl[a + 1\) , \( -a^{2} + 5\) , \( a^{2} - 4\) , \( -3 a^{2} + 16\) , \( -5 a^{2} + a + 29\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{2}-4\right){y}={x}^{3}+\left(-a^{2}+5\right){x}^{2}+\left(-3a^{2}+16\right){x}-5a^{2}+a+29$ |
| 25.1-a1 |
25.1-a |
$1$ |
$1$ |
3.3.785.1 |
$3$ |
$[3, 0]$ |
25.1 |
\( 5^{2} \) |
\( - 5^{15} \) |
$4.28118$ |
$(a), (a^2+a-2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \) |
$0.386692331$ |
$20.03090018$ |
1.658755777 |
\( -\frac{1529977764}{48828125} a^{2} + \frac{7727748644}{48828125} a - \frac{4508889521}{48828125} \) |
\( \bigl[a^{2} - 4\) , \( a^{2} - 5\) , \( a^{2} + a - 4\) , \( a - 4\) , \( -a^{2} + 4 a - 4\bigr] \) |
${y}^2+\left(a^{2}-4\right){x}{y}+\left(a^{2}+a-4\right){y}={x}^{3}+\left(a^{2}-5\right){x}^{2}+\left(a-4\right){x}-a^{2}+4a-4$ |
| 25.2-a1 |
25.2-a |
$2$ |
$5$ |
3.3.785.1 |
$3$ |
$[3, 0]$ |
25.2 |
\( 5^{2} \) |
\( 5^{4} \) |
$4.28118$ |
$(a^2+a-2)$ |
0 |
$\Z/5\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$5$ |
5B.1.1 |
$1$ |
\( 3 \) |
$1$ |
$272.5665943$ |
1.167398270 |
\( 17001 a^{2} + 36564 a - 40406 \) |
\( \bigl[a^{2} + a - 3\) , \( -a + 1\) , \( a^{2} - 3\) , \( -a^{2} + 7 a - 1\) , \( 2 a^{2} - 2 a + 8\bigr] \) |
${y}^2+\left(a^{2}+a-3\right){x}{y}+\left(a^{2}-3\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-a^{2}+7a-1\right){x}+2a^{2}-2a+8$ |
| 25.2-a2 |
25.2-a |
$2$ |
$5$ |
3.3.785.1 |
$3$ |
$[3, 0]$ |
25.2 |
\( 5^{2} \) |
\( 5^{8} \) |
$4.28118$ |
$(a^2+a-2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$5$ |
5B.1.2 |
$1$ |
\( 3 \) |
$1$ |
$10.90266377$ |
1.167398270 |
\( 1578501 a^{2} + 2439129 a - 3179261 \) |
\( \bigl[a + 1\) , \( a\) , \( a\) , \( 1163 a^{2} - 225 a - 7130\) , \( 36908 a^{2} - 6799 a - 227352\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+a{x}^{2}+\left(1163a^{2}-225a-7130\right){x}+36908a^{2}-6799a-227352$ |
| 25.2-b1 |
25.2-b |
$2$ |
$5$ |
3.3.785.1 |
$3$ |
$[3, 0]$ |
25.2 |
\( 5^{2} \) |
\( 5^{2} \) |
$4.28118$ |
$(a^2+a-2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$5$ |
5B.4.2 |
$1$ |
\( 1 \) |
$0.123226833$ |
$242.4310857$ |
3.198747945 |
\( 1578501 a^{2} + 2439129 a - 3179261 \) |
\( \bigl[a^{2} - 3\) , \( -a^{2} + a + 5\) , \( a + 1\) , \( 119140 a^{2} - 22314 a - 732972\) , \( -37555418 a^{2} + 7033520 a + 231048759\bigr] \) |
${y}^2+\left(a^{2}-3\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a^{2}+a+5\right){x}^{2}+\left(119140a^{2}-22314a-732972\right){x}-37555418a^{2}+7033520a+231048759$ |
| 25.2-b2 |
25.2-b |
$2$ |
$5$ |
3.3.785.1 |
$3$ |
$[3, 0]$ |
25.2 |
\( 5^{2} \) |
\( 5^{10} \) |
$4.28118$ |
$(a^2+a-2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$5$ |
5B.4.1 |
$1$ |
\( 1 \) |
$0.616134165$ |
$48.48621715$ |
3.198747945 |
\( 17001 a^{2} + 36564 a - 40406 \) |
\( \bigl[a\) , \( -a^{2} - a + 3\) , \( a^{2} - 3\) , \( -8 a^{2} + 2 a + 50\) , \( 25 a^{2} - 6 a - 157\bigr] \) |
${y}^2+a{x}{y}+\left(a^{2}-3\right){y}={x}^{3}+\left(-a^{2}-a+3\right){x}^{2}+\left(-8a^{2}+2a+50\right){x}+25a^{2}-6a-157$ |
| 25.3-a1 |
25.3-a |
$2$ |
$5$ |
3.3.785.1 |
$3$ |
$[3, 0]$ |
25.3 |
\( 5^{2} \) |
\( - 5^{7} \) |
$4.28118$ |
$(a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$5$ |
5B.4.2 |
$1$ |
\( 2 \) |
$0.065278729$ |
$162.5241608$ |
2.271988084 |
\( -\frac{88704}{5} a^{2} - \frac{147291}{5} a + \frac{160574}{5} \) |
\( \bigl[a^{2} - 4\) , \( a^{2} + a - 4\) , \( a^{2} - 4\) , \( 3 a^{2} - 8\) , \( 2 a^{2} - 4\bigr] \) |
${y}^2+\left(a^{2}-4\right){x}{y}+\left(a^{2}-4\right){y}={x}^{3}+\left(a^{2}+a-4\right){x}^{2}+\left(3a^{2}-8\right){x}+2a^{2}-4$ |
| 25.3-a2 |
25.3-a |
$2$ |
$5$ |
3.3.785.1 |
$3$ |
$[3, 0]$ |
25.3 |
\( 5^{2} \) |
\( - 5^{11} \) |
$4.28118$ |
$(a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$5$ |
5B.4.1 |
$1$ |
\( 2 \) |
$0.326393648$ |
$32.50483216$ |
2.271988084 |
\( -\frac{15313823739}{3125} a^{2} + \frac{51891754119}{3125} a - \frac{32058425671}{3125} \) |
\( \bigl[a\) , \( a^{2} - a - 4\) , \( a^{2} - 4\) , \( -3 a^{2} + 8 a - 3\) , \( 11 a^{2} - 13 a - 41\bigr] \) |
${y}^2+a{x}{y}+\left(a^{2}-4\right){y}={x}^{3}+\left(a^{2}-a-4\right){x}^{2}+\left(-3a^{2}+8a-3\right){x}+11a^{2}-13a-41$ |
| 27.1-a1 |
27.1-a |
$2$ |
$5$ |
3.3.785.1 |
$3$ |
$[3, 0]$ |
27.1 |
\( 3^{3} \) |
\( - 3^{13} \) |
$4.33645$ |
$(a-2), (a^2+a-4)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.4.2 |
$1$ |
\( 1 \) |
$0.492598209$ |
$46.31985532$ |
2.443129286 |
\( \frac{323584}{243} a^{2} + \frac{4096}{243} a - \frac{622592}{81} \) |
\( \bigl[0\) , \( a^{2} - a - 3\) , \( a^{2} + a - 3\) , \( 10 a^{2} + 14 a - 15\) , \( -21 a^{2} - 35 a + 41\bigr] \) |
${y}^2+\left(a^{2}+a-3\right){y}={x}^{3}+\left(a^{2}-a-3\right){x}^{2}+\left(10a^{2}+14a-15\right){x}-21a^{2}-35a+41$ |
| 27.1-a2 |
27.1-a |
$2$ |
$5$ |
3.3.785.1 |
$3$ |
$[3, 0]$ |
27.1 |
\( 3^{3} \) |
\( - 3^{17} \) |
$4.33645$ |
$(a-2), (a^2+a-4)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.4.1 |
$1$ |
\( 1 \) |
$2.462991048$ |
$9.263971064$ |
2.443129286 |
\( -\frac{162593563258880}{14348907} a^{2} - \frac{256203590094848}{14348907} a + \frac{315615133147136}{14348907} \) |
\( \bigl[0\) , \( -a^{2} + a + 4\) , \( a\) , \( -38 a^{2} - 60 a + 79\) , \( -257 a^{2} - 410 a + 483\bigr] \) |
${y}^2+a{y}={x}^{3}+\left(-a^{2}+a+4\right){x}^{2}+\left(-38a^{2}-60a+79\right){x}-257a^{2}-410a+483$ |
| 27.2-a1 |
27.2-a |
$2$ |
$3$ |
3.3.785.1 |
$3$ |
$[3, 0]$ |
27.2 |
\( 3^{3} \) |
\( - 3^{11} \) |
$4.33645$ |
$(a-2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$3$ |
3B |
$1$ |
\( 1 \) |
$0.554829487$ |
$51.62114733$ |
3.066716385 |
\( -295 a^{2} + 60 a + 1825 \) |
\( \bigl[a^{2} + a - 3\) , \( -a^{2} + 4\) , \( a^{2} + a - 3\) , \( -826 a^{2} + 2795 a - 1722\) , \( -1351964 a^{2} + 4581117 a - 2830164\bigr] \) |
${y}^2+\left(a^{2}+a-3\right){x}{y}+\left(a^{2}+a-3\right){y}={x}^{3}+\left(-a^{2}+4\right){x}^{2}+\left(-826a^{2}+2795a-1722\right){x}-1351964a^{2}+4581117a-2830164$ |
| 27.2-a2 |
27.2-a |
$2$ |
$3$ |
3.3.785.1 |
$3$ |
$[3, 0]$ |
27.2 |
\( 3^{3} \) |
\( - 3^{9} \) |
$4.33645$ |
$(a-2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$3$ |
3B |
$1$ |
\( 1 \) |
$1.664488462$ |
$17.20704911$ |
3.066716385 |
\( -1715280 a^{2} + 4135265 a - 2235325 \) |
\( \bigl[a + 1\) , \( a + 1\) , \( 1\) , \( -7 a^{2} + 29 a - 18\) , \( -32 a^{2} + 112 a - 70\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-7a^{2}+29a-18\right){x}-32a^{2}+112a-70$ |
| 27.2-b1 |
27.2-b |
$2$ |
$3$ |
3.3.785.1 |
$3$ |
$[3, 0]$ |
27.2 |
\( 3^{3} \) |
\( - 3^{3} \) |
$4.33645$ |
$(a-2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$3$ |
3B.1.2 |
$1$ |
\( 1 \) |
$3.921181316$ |
$6.282944941$ |
2.637950275 |
\( -1715280 a^{2} + 4135265 a - 2235325 \) |
\( \bigl[a\) , \( a^{2} + a - 4\) , \( a^{2} + a - 3\) , \( -a^{2} + a + 2\) , \( -4 a^{2} - 4 a + 5\bigr] \) |
${y}^2+a{x}{y}+\left(a^{2}+a-3\right){y}={x}^{3}+\left(a^{2}+a-4\right){x}^{2}+\left(-a^{2}+a+2\right){x}-4a^{2}-4a+5$ |
| 27.2-b2 |
27.2-b |
$2$ |
$3$ |
3.3.785.1 |
$3$ |
$[3, 0]$ |
27.2 |
\( 3^{3} \) |
\( - 3^{5} \) |
$4.33645$ |
$(a-2)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$3$ |
3B.1.1 |
$1$ |
\( 3 \) |
$1.307060438$ |
$56.54650447$ |
2.637950275 |
\( -295 a^{2} + 60 a + 1825 \) |
\( \bigl[1\) , \( -a^{2} - a + 5\) , \( 1\) , \( -43 a^{2} + 146 a - 86\) , \( -16030 a^{2} + 54315 a - 33553\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(-a^{2}-a+5\right){x}^{2}+\left(-43a^{2}+146a-86\right){x}-16030a^{2}+54315a-33553$ |
| 37.1-a1 |
37.1-a |
$1$ |
$1$ |
3.3.785.1 |
$3$ |
$[3, 0]$ |
37.1 |
\( 37 \) |
\( -37 \) |
$4.57025$ |
$(a^2+a-8)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$1.752300088$ |
$19.06044436$ |
3.576250491 |
\( -\frac{249471809}{37} a^{2} + \frac{703016444}{37} a - \frac{415557170}{37} \) |
\( \bigl[a^{2} - 4\) , \( a^{2} - 4\) , \( a^{2} + a - 4\) , \( 8 a^{2} - 4 a - 53\) , \( 20 a^{2} - 5 a - 126\bigr] \) |
${y}^2+\left(a^{2}-4\right){x}{y}+\left(a^{2}+a-4\right){y}={x}^{3}+\left(a^{2}-4\right){x}^{2}+\left(8a^{2}-4a-53\right){x}+20a^{2}-5a-126$ |
| 37.1-b1 |
37.1-b |
$2$ |
$3$ |
3.3.785.1 |
$3$ |
$[3, 0]$ |
37.1 |
\( 37 \) |
\( 37 \) |
$4.57025$ |
$(a^2+a-8)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1 |
$1$ |
\( 1 \) |
$1$ |
$138.7607401$ |
0.550287021 |
\( \frac{21295}{37} a^{2} - \frac{270435}{37} a + \frac{203800}{37} \) |
\( \bigl[a\) , \( 0\) , \( a^{2} - 4\) , \( -a\) , \( -a^{2} + 5\bigr] \) |
${y}^2+a{x}{y}+\left(a^{2}-4\right){y}={x}^{3}-a{x}-a^{2}+5$ |
| 37.1-b2 |
37.1-b |
$2$ |
$3$ |
3.3.785.1 |
$3$ |
$[3, 0]$ |
37.1 |
\( 37 \) |
\( 37^{3} \) |
$4.57025$ |
$(a^2+a-8)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.2 |
$1$ |
\( 3 \) |
$1$ |
$5.139286672$ |
0.550287021 |
\( -\frac{6186588748383405}{50653} a^{2} - \frac{9748664303378360}{50653} a + \frac{12009187914343425}{50653} \) |
\( \bigl[a\) , \( 0\) , \( a^{2} - 4\) , \( -5 a^{2} - a + 25\) , \( 32 a^{2} - 8 a - 207\bigr] \) |
${y}^2+a{x}{y}+\left(a^{2}-4\right){y}={x}^{3}+\left(-5a^{2}-a+25\right){x}+32a^{2}-8a-207$ |
| 37.1-c1 |
37.1-c |
$1$ |
$1$ |
3.3.785.1 |
$3$ |
$[3, 0]$ |
37.1 |
\( 37 \) |
\( 37 \) |
$4.57025$ |
$(a^2+a-8)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$0.246208246$ |
$108.4491517$ |
2.859006754 |
\( -\frac{19873776550239}{37} a^{2} + \frac{3722034904318}{37} a + \frac{122267617644160}{37} \) |
\( \bigl[a^{2} - 4\) , \( a + 1\) , \( a^{2} + a - 3\) , \( a^{2} + 2 a - 1\) , \( -21 a^{2} - 33 a + 41\bigr] \) |
${y}^2+\left(a^{2}-4\right){x}{y}+\left(a^{2}+a-3\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(a^{2}+2a-1\right){x}-21a^{2}-33a+41$ |
| 37.1-d1 |
37.1-d |
$1$ |
$1$ |
3.3.785.1 |
$3$ |
$[3, 0]$ |
37.1 |
\( 37 \) |
\( 37 \) |
$4.57025$ |
$(a^2+a-8)$ |
$2$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$0.018802010$ |
$376.1974450$ |
2.272101914 |
\( -\frac{140360}{37} a^{2} - \frac{11901}{37} a + \frac{772312}{37} \) |
\( \bigl[a^{2} + a - 3\) , \( -a^{2} - a + 4\) , \( a + 1\) , \( -a - 2\) , \( 0\bigr] \) |
${y}^2+\left(a^{2}+a-3\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a^{2}-a+4\right){x}^{2}+\left(-a-2\right){x}$ |
| 37.1-e1 |
37.1-e |
$1$ |
$1$ |
3.3.785.1 |
$3$ |
$[3, 0]$ |
37.1 |
\( 37 \) |
\( -37 \) |
$4.57025$ |
$(a^2+a-8)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$0.080584111$ |
$92.27590986$ |
0.796203684 |
\( -\frac{4700}{37} a^{2} + \frac{11755}{37} a + \frac{57261}{37} \) |
\( \bigl[a\) , \( -a + 1\) , \( a^{2} + a - 4\) , \( -4 a^{2} - 2 a + 25\) , \( -a^{2} - 2 a + 5\bigr] \) |
${y}^2+a{x}{y}+\left(a^{2}+a-4\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-4a^{2}-2a+25\right){x}-a^{2}-2a+5$ |
| 40.2-a1 |
40.2-a |
$2$ |
$3$ |
3.3.785.1 |
$3$ |
$[3, 0]$ |
40.2 |
\( 2^{3} \cdot 5 \) |
\( - 2^{3} \cdot 5^{3} \) |
$4.63003$ |
$(a^2+a-2), (2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 1 \) |
$1$ |
$47.71378695$ |
1.702978083 |
\( \frac{419563813214}{25} a^{2} - \frac{157154970739}{50} a - \frac{1032497638971}{10} \) |
\( \bigl[a^{2} + a - 4\) , \( a^{2} - a - 4\) , \( a^{2} + a - 4\) , \( 16 a^{2} - 4 a - 94\) , \( -66 a^{2} + 13 a + 409\bigr] \) |
${y}^2+\left(a^{2}+a-4\right){x}{y}+\left(a^{2}+a-4\right){y}={x}^{3}+\left(a^{2}-a-4\right){x}^{2}+\left(16a^{2}-4a-94\right){x}-66a^{2}+13a+409$ |
| 40.2-a2 |
40.2-a |
$2$ |
$3$ |
3.3.785.1 |
$3$ |
$[3, 0]$ |
40.2 |
\( 2^{3} \cdot 5 \) |
\( - 2^{9} \cdot 5^{9} \) |
$4.63003$ |
$(a^2+a-2), (2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 3 \) |
$1$ |
$15.90459565$ |
1.702978083 |
\( -\frac{392255812}{3125} a^{2} + \frac{10704190133}{25000} a - \frac{336158987}{1250} \) |
\( \bigl[a\) , \( a^{2} + a - 5\) , \( a^{2} + a - 3\) , \( 21619 a^{2} + 34033 a - 42046\) , \( 2614427 a^{2} + 4119954 a - 5074533\bigr] \) |
${y}^2+a{x}{y}+\left(a^{2}+a-3\right){y}={x}^{3}+\left(a^{2}+a-5\right){x}^{2}+\left(21619a^{2}+34033a-42046\right){x}+2614427a^{2}+4119954a-5074533$ |
| 40.2-b1 |
40.2-b |
$1$ |
$1$ |
3.3.785.1 |
$3$ |
$[3, 0]$ |
40.2 |
\( 2^{3} \cdot 5 \) |
\( 2^{3} \cdot 5 \) |
$4.63003$ |
$(a^2+a-2), (2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$0.149376401$ |
$135.3587688$ |
2.164984617 |
\( \frac{137023}{10} a^{2} + \frac{231108}{5} a - \frac{158203}{2} \) |
\( \bigl[a^{2} - 3\) , \( a^{2} - a - 5\) , \( a^{2} + a - 3\) , \( -3 a^{2} - 7 a + 8\) , \( a^{2} + a + 1\bigr] \) |
${y}^2+\left(a^{2}-3\right){x}{y}+\left(a^{2}+a-3\right){y}={x}^{3}+\left(a^{2}-a-5\right){x}^{2}+\left(-3a^{2}-7a+8\right){x}+a^{2}+a+1$ |
| 40.2-c1 |
40.2-c |
$2$ |
$3$ |
3.3.785.1 |
$3$ |
$[3, 0]$ |
40.2 |
\( 2^{3} \cdot 5 \) |
\( 2^{3} \cdot 5^{3} \) |
$4.63003$ |
$(a^2+a-2), (2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 1 \) |
$0.513259656$ |
$80.94141421$ |
4.448302807 |
\( \frac{6126145327}{25} a^{2} + \frac{19306820083}{50} a - \frac{4756739703}{10} \) |
\( \bigl[a\) , \( -a^{2} + a + 3\) , \( 0\) , \( -4 a + 7\) , \( -2 a^{2} + 7 a - 3\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-a^{2}+a+3\right){x}^{2}+\left(-4a+7\right){x}-2a^{2}+7a-3$ |
| 40.2-c2 |
40.2-c |
$2$ |
$3$ |
3.3.785.1 |
$3$ |
$[3, 0]$ |
40.2 |
\( 2^{3} \cdot 5 \) |
\( 2^{9} \cdot 5 \) |
$4.63003$ |
$(a^2+a-2), (2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 1 \) |
$0.171086552$ |
$242.8242426$ |
4.448302807 |
\( \frac{3109}{20} a^{2} + \frac{29401}{40} a - 725 \) |
\( \bigl[1\) , \( a^{2} - 3\) , \( a\) , \( -4614 a^{2} + 15636 a - 9659\) , \( 689824 a^{2} - 2337461 a + 1444058\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(a^{2}-3\right){x}^{2}+\left(-4614a^{2}+15636a-9659\right){x}+689824a^{2}-2337461a+1444058$ |
| 40.2-d1 |
40.2-d |
$1$ |
$1$ |
3.3.785.1 |
$3$ |
$[3, 0]$ |
40.2 |
\( 2^{3} \cdot 5 \) |
\( 2^{3} \cdot 5^{3} \) |
$4.63003$ |
$(a^2+a-2), (2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 3 \) |
$0.077070165$ |
$124.0344794$ |
3.070693029 |
\( -\frac{5940621}{50} a^{2} + \frac{21896973}{50} a - \frac{2758023}{10} \) |
\( \bigl[1\) , \( -1\) , \( a\) , \( -a^{2} + 2 a\) , \( a^{2} - 4 a + 2\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(-a^{2}+2a\right){x}+a^{2}-4a+2$ |
| 45.1-a1 |
45.1-a |
$4$ |
$6$ |
3.3.785.1 |
$3$ |
$[3, 0]$ |
45.1 |
\( 3^{2} \cdot 5 \) |
\( 3^{12} \cdot 5 \) |
$4.72181$ |
$(a), (a^2+a-4)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$1$ |
$180.9782256$ |
3.229694931 |
\( -\frac{36670995751}{3645} a^{2} + \frac{6936027346}{3645} a + \frac{225874239161}{3645} \) |
\( \bigl[a^{2} + a - 3\) , \( -a + 1\) , \( a^{2} - 3\) , \( -1959 a^{2} + 6646 a - 4111\) , \( 126916 a^{2} - 430044 a + 265674\bigr] \) |
${y}^2+\left(a^{2}+a-3\right){x}{y}+\left(a^{2}-3\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-1959a^{2}+6646a-4111\right){x}+126916a^{2}-430044a+265674$ |
*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.
