| 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 |
$4$ |
$10$ |
4.4.16400.1 |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$11.44354$ |
$\textsf{none}$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-20$ |
$N(\mathrm{U}(1))$ |
✓ |
|
✓ |
✓ |
|
|
$1$ |
\( 1 \) |
$1$ |
$932.9796544$ |
1.821336779 |
\( 565760 a^{2} - 3045440 \) |
\( \bigl[a^{3} - 6 a + 1\) , \( -a - 1\) , \( a^{2} + a - 6\) , \( -15 a^{3} - 43 a^{2} + 74 a + 222\) , \( -107 a^{3} - 297 a^{2} + 556 a + 1551\bigr] \) |
${y}^2+\left(a^{3}-6a+1\right){x}{y}+\left(a^{2}+a-6\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-15a^{3}-43a^{2}+74a+222\right){x}-107a^{3}-297a^{2}+556a+1551$ |
| 1.1-a2 |
1.1-a |
$4$ |
$10$ |
4.4.16400.1 |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$11.44354$ |
$\textsf{none}$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-20$ |
$N(\mathrm{U}(1))$ |
✓ |
|
✓ |
✓ |
|
|
$1$ |
\( 1 \) |
$1$ |
$932.9796544$ |
1.821336779 |
\( 565760 a^{2} - 3045440 \) |
\( \bigl[a^{3} - 6 a + 1\) , \( -a^{3} + 7 a - 1\) , \( a^{2} + a - 6\) , \( 14 a^{3} - 43 a^{2} - 70 a + 222\) , \( 106 a^{3} - 297 a^{2} - 550 a + 1551\bigr] \) |
${y}^2+\left(a^{3}-6a+1\right){x}{y}+\left(a^{2}+a-6\right){y}={x}^{3}+\left(-a^{3}+7a-1\right){x}^{2}+\left(14a^{3}-43a^{2}-70a+222\right){x}+106a^{3}-297a^{2}-550a+1551$ |
| 1.1-a3 |
1.1-a |
$4$ |
$10$ |
4.4.16400.1 |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$11.44354$ |
$\textsf{none}$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-20$ |
$N(\mathrm{U}(1))$ |
✓ |
|
✓ |
✓ |
|
|
$1$ |
\( 1 \) |
$1$ |
$932.9796544$ |
1.821336779 |
\( -565760 a^{2} + 4309440 \) |
\( \bigl[a^{3} - 6 a + 1\) , \( a + 1\) , \( a^{2} + a - 6\) , \( 10 a^{3} + 21 a^{2} - 70 a - 147\) , \( 36 a^{3} + 87 a^{2} - 266 a - 638\bigr] \) |
${y}^2+\left(a^{3}-6a+1\right){x}{y}+\left(a^{2}+a-6\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(10a^{3}+21a^{2}-70a-147\right){x}+36a^{3}+87a^{2}-266a-638$ |
| 1.1-a4 |
1.1-a |
$4$ |
$10$ |
4.4.16400.1 |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$11.44354$ |
$\textsf{none}$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-20$ |
$N(\mathrm{U}(1))$ |
✓ |
|
✓ |
✓ |
|
|
$1$ |
\( 1 \) |
$1$ |
$932.9796544$ |
1.821336779 |
\( -565760 a^{2} + 4309440 \) |
\( \bigl[a^{3} - 6 a + 1\) , \( -a^{3} + 8 a + 1\) , \( 1\) , \( -7 a^{3} + 19 a^{2} + 57 a - 130\) , \( -15 a^{3} + 40 a^{2} + 119 a - 291\bigr] \) |
${y}^2+\left(a^{3}-6a+1\right){x}{y}+{y}={x}^{3}+\left(-a^{3}+8a+1\right){x}^{2}+\left(-7a^{3}+19a^{2}+57a-130\right){x}-15a^{3}+40a^{2}+119a-291$ |
| 11.1-a1 |
11.1-a |
$1$ |
$1$ |
4.4.16400.1 |
$4$ |
$[4, 0]$ |
11.1 |
\( 11 \) |
\( 11^{4} \) |
$15.44310$ |
$(-a^3-2a^2+6a+10)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2^{2} \) |
$0.041213486$ |
$682.8329739$ |
3.516024563 |
\( \frac{5069967360}{14641} a^{3} - \frac{13979684864}{14641} a^{2} - \frac{27289116672}{14641} a + \frac{75231780864}{14641} \) |
\( \bigl[0\) , \( a\) , \( a^{3} - 7 a\) , \( 2 a^{3} + 5 a^{2} - 15 a - 35\) , \( -4 a^{3} - 8 a^{2} + 31 a + 61\bigr] \) |
${y}^2+\left(a^{3}-7a\right){y}={x}^{3}+a{x}^{2}+\left(2a^{3}+5a^{2}-15a-35\right){x}-4a^{3}-8a^{2}+31a+61$ |
| 11.1-b1 |
11.1-b |
$1$ |
$1$ |
4.4.16400.1 |
$4$ |
$[4, 0]$ |
11.1 |
\( 11 \) |
\( 11^{4} \) |
$15.44310$ |
$(-a^3-2a^2+6a+10)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \) |
$1$ |
$94.11149161$ |
1.469774568 |
\( \frac{5069967360}{14641} a^{3} - \frac{13979684864}{14641} a^{2} - \frac{27289116672}{14641} a + \frac{75231780864}{14641} \) |
\( \bigl[0\) , \( -a\) , \( a^{2} - 6\) , \( 2 a^{3} + 5 a^{2} - 15 a - 35\) , \( 4 a^{3} + 9 a^{2} - 31 a - 70\bigr] \) |
${y}^2+\left(a^{2}-6\right){y}={x}^{3}-a{x}^{2}+\left(2a^{3}+5a^{2}-15a-35\right){x}+4a^{3}+9a^{2}-31a-70$ |
| 11.2-a1 |
11.2-a |
$1$ |
$1$ |
4.4.16400.1 |
$4$ |
$[4, 0]$ |
11.2 |
\( 11 \) |
\( 11^{4} \) |
$15.44310$ |
$(-a^3+7a+2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2^{2} \) |
$0.041213486$ |
$682.8329739$ |
3.516024563 |
\( -\frac{5069967360}{14641} a^{3} - \frac{13979684864}{14641} a^{2} + \frac{27289116672}{14641} a + \frac{75231780864}{14641} \) |
\( \bigl[0\) , \( -a\) , \( a^{3} - 7 a\) , \( -2 a^{3} + 5 a^{2} + 15 a - 35\) , \( 4 a^{3} - 8 a^{2} - 31 a + 61\bigr] \) |
${y}^2+\left(a^{3}-7a\right){y}={x}^{3}-a{x}^{2}+\left(-2a^{3}+5a^{2}+15a-35\right){x}+4a^{3}-8a^{2}-31a+61$ |
| 11.2-b1 |
11.2-b |
$1$ |
$1$ |
4.4.16400.1 |
$4$ |
$[4, 0]$ |
11.2 |
\( 11 \) |
\( 11^{4} \) |
$15.44310$ |
$(-a^3+7a+2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \) |
$1$ |
$94.11149161$ |
1.469774568 |
\( -\frac{5069967360}{14641} a^{3} - \frac{13979684864}{14641} a^{2} + \frac{27289116672}{14641} a + \frac{75231780864}{14641} \) |
\( \bigl[0\) , \( a\) , \( a^{2} - 6\) , \( -2 a^{3} + 5 a^{2} + 15 a - 35\) , \( -4 a^{3} + 9 a^{2} + 31 a - 70\bigr] \) |
${y}^2+\left(a^{2}-6\right){y}={x}^{3}+a{x}^{2}+\left(-2a^{3}+5a^{2}+15a-35\right){x}-4a^{3}+9a^{2}+31a-70$ |
| 19.1-a1 |
19.1-a |
$2$ |
$3$ |
4.4.16400.1 |
$4$ |
$[4, 0]$ |
19.1 |
\( 19 \) |
\( 19^{12} \) |
$16.53502$ |
$(a^2+a-4)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.2 |
$1$ |
\( 2^{2} \cdot 3 \) |
$1.403755163$ |
$5.505102201$ |
2.896516895 |
\( -\frac{260081870579892941420531712}{2213314919066161} a^{3} - \frac{717846408960670827499892736}{2213314919066161} a^{2} + \frac{1399751787087143777899143168}{2213314919066161} a + \frac{3863424973120559478115966976}{2213314919066161} \) |
\( \bigl[0\) , \( a^{2} - 8\) , \( a^{3} + a^{2} - 6 a - 7\) , \( -189 a^{3} + 430 a^{2} + 1431 a - 3272\) , \( -77400 a^{3} + 179546 a^{2} + 589627 a - 1367803\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-6a-7\right){y}={x}^{3}+\left(a^{2}-8\right){x}^{2}+\left(-189a^{3}+430a^{2}+1431a-3272\right){x}-77400a^{3}+179546a^{2}+589627a-1367803$ |
| 19.1-a2 |
19.1-a |
$2$ |
$3$ |
4.4.16400.1 |
$4$ |
$[4, 0]$ |
19.1 |
\( 19 \) |
\( 19^{4} \) |
$16.53502$ |
$(a^2+a-4)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1 |
$1$ |
\( 2^{2} \) |
$0.467918387$ |
$445.9132782$ |
2.896516895 |
\( \frac{64098067009536}{130321} a^{3} + \frac{148700151410688}{130321} a^{2} - \frac{488300922445824}{130321} a - \frac{1132805100666880}{130321} \) |
\( \bigl[0\) , \( a^{2} - 8\) , \( a^{3} + a^{2} - 6 a - 7\) , \( 21 a^{3} - 50 a^{2} - 159 a + 378\) , \( 2850 a^{3} - 6613 a^{2} - 21713 a + 50376\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-6a-7\right){y}={x}^{3}+\left(a^{2}-8\right){x}^{2}+\left(21a^{3}-50a^{2}-159a+378\right){x}+2850a^{3}-6613a^{2}-21713a+50376$ |
| 19.1-b1 |
19.1-b |
$4$ |
$15$ |
4.4.16400.1 |
$4$ |
$[4, 0]$ |
19.1 |
\( 19 \) |
\( - 19^{3} \) |
$16.53502$ |
$(a^2+a-4)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3, 5$ |
3B.1.2, 5B[2] |
$1$ |
\( 3 \) |
$5.459177605$ |
$6.388084289$ |
3.267812905 |
\( \frac{6630368958622669095}{6859} a^{3} - \frac{15410236864329038175}{6859} a^{2} - \frac{50366099200344265580}{6859} a + \frac{116997492663148095175}{6859} \) |
\( \bigl[a^{3} + a^{2} - 7 a - 7\) , \( -a^{3} - a^{2} + 8 a + 6\) , \( a^{3} - 6 a\) , \( -817 a^{3} - 2237 a^{2} + 4498 a + 12277\) , \( 37692 a^{3} + 105138 a^{2} - 197236 a - 552811\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-7a-7\right){x}{y}+\left(a^{3}-6a\right){y}={x}^{3}+\left(-a^{3}-a^{2}+8a+6\right){x}^{2}+\left(-817a^{3}-2237a^{2}+4498a+12277\right){x}+37692a^{3}+105138a^{2}-197236a-552811$ |
| 19.1-b2 |
19.1-b |
$4$ |
$15$ |
4.4.16400.1 |
$4$ |
$[4, 0]$ |
19.1 |
\( 19 \) |
\( - 19^{15} \) |
$16.53502$ |
$(a^2+a-4)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3, 5$ |
3B.1.2, 5B[2] |
$1$ |
\( 3 \cdot 5 \) |
$1.091835521$ |
$6.388084289$ |
3.267812905 |
\( \frac{35837154163366394281545}{15181127029874798299} a^{3} + \frac{65378672019532107253000}{15181127029874798299} a^{2} - \frac{272832802000467030921805}{15181127029874798299} a - \frac{500017660482708507945475}{15181127029874798299} \) |
\( \bigl[a^{3} - 6 a\) , \( a + 1\) , \( a^{3} + a^{2} - 7 a - 6\) , \( -50 a^{3} + 117 a^{2} + 413 a - 962\) , \( -92 a^{3} + 120 a^{2} + 1231 a - 2356\bigr] \) |
${y}^2+\left(a^{3}-6a\right){x}{y}+\left(a^{3}+a^{2}-7a-6\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-50a^{3}+117a^{2}+413a-962\right){x}-92a^{3}+120a^{2}+1231a-2356$ |
| 19.1-b3 |
19.1-b |
$4$ |
$15$ |
4.4.16400.1 |
$4$ |
$[4, 0]$ |
19.1 |
\( 19 \) |
\( - 19^{5} \) |
$16.53502$ |
$(a^2+a-4)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3, 5$ |
3B.1.1, 5B[2] |
$1$ |
\( 5 \) |
$0.363945173$ |
$517.4348274$ |
3.267812905 |
\( \frac{2289565641755}{2476099} a^{3} - \frac{5313278941225}{2476099} a^{2} - \frac{17442014714520}{2476099} a + \frac{40477042159125}{2476099} \) |
\( \bigl[a^{3} - 6 a\) , \( a + 1\) , \( a^{3} + a^{2} - 7 a - 6\) , \( -30 a^{3} + 77 a^{2} + 228 a - 567\) , \( 198 a^{3} - 445 a^{2} - 1525 a + 3458\bigr] \) |
${y}^2+\left(a^{3}-6a\right){x}{y}+\left(a^{3}+a^{2}-7a-6\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-30a^{3}+77a^{2}+228a-567\right){x}+198a^{3}-445a^{2}-1525a+3458$ |
| 19.1-b4 |
19.1-b |
$4$ |
$15$ |
4.4.16400.1 |
$4$ |
$[4, 0]$ |
19.1 |
\( 19 \) |
\( -19 \) |
$16.53502$ |
$(a^2+a-4)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3, 5$ |
3B.1.1, 5B[2] |
$1$ |
\( 1 \) |
$1.819725868$ |
$517.4348274$ |
3.267812905 |
\( -\frac{24005877695}{19} a^{3} - \frac{66262595100}{19} a^{2} + \frac{129187416855}{19} a + \frac{356600683675}{19} \) |
\( \bigl[a^{3} - 6 a\) , \( -a^{2} - a + 6\) , \( a^{2} - 6\) , \( -12 a^{3} + 24 a^{2} + 102 a - 216\) , \( -73 a^{3} + 154 a^{2} + 633 a - 1386\bigr] \) |
${y}^2+\left(a^{3}-6a\right){x}{y}+\left(a^{2}-6\right){y}={x}^{3}+\left(-a^{2}-a+6\right){x}^{2}+\left(-12a^{3}+24a^{2}+102a-216\right){x}-73a^{3}+154a^{2}+633a-1386$ |
| 19.1-c1 |
19.1-c |
$4$ |
$15$ |
4.4.16400.1 |
$4$ |
$[4, 0]$ |
19.1 |
\( 19 \) |
\( - 19^{3} \) |
$16.53502$ |
$(a^2+a-4)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3, 5$ |
3B, 5B[2] |
$1$ |
\( 1 \) |
$1$ |
$98.99387271$ |
0.773012275 |
\( \frac{6630368958622669095}{6859} a^{3} - \frac{15410236864329038175}{6859} a^{2} - \frac{50366099200344265580}{6859} a + \frac{116997492663148095175}{6859} \) |
\( \bigl[a^{2} + a - 6\) , \( a^{3} - a^{2} - 6 a + 7\) , \( 0\) , \( -809 a^{3} - 2216 a^{2} + 4441 a + 12136\) , \( -40319 a^{3} - 112303 a^{2} + 211833 a + 592438\bigr] \) |
${y}^2+\left(a^{2}+a-6\right){x}{y}={x}^{3}+\left(a^{3}-a^{2}-6a+7\right){x}^{2}+\left(-809a^{3}-2216a^{2}+4441a+12136\right){x}-40319a^{3}-112303a^{2}+211833a+592438$ |
| 19.1-c2 |
19.1-c |
$4$ |
$15$ |
4.4.16400.1 |
$4$ |
$[4, 0]$ |
19.1 |
\( 19 \) |
\( - 19^{15} \) |
$16.53502$ |
$(a^2+a-4)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3, 5$ |
3B, 5B[2] |
$1$ |
\( 1 \) |
$1$ |
$98.99387271$ |
0.773012275 |
\( \frac{35837154163366394281545}{15181127029874798299} a^{3} + \frac{65378672019532107253000}{15181127029874798299} a^{2} - \frac{272832802000467030921805}{15181127029874798299} a - \frac{500017660482708507945475}{15181127029874798299} \) |
\( \bigl[1\) , \( a^{2} - a - 6\) , \( a^{3} - 7 a + 1\) , \( -52 a^{3} + 113 a^{2} + 424 a - 939\) , \( 103 a^{3} - 150 a^{2} - 1235 a + 2384\bigr] \) |
${y}^2+{x}{y}+\left(a^{3}-7a+1\right){y}={x}^{3}+\left(a^{2}-a-6\right){x}^{2}+\left(-52a^{3}+113a^{2}+424a-939\right){x}+103a^{3}-150a^{2}-1235a+2384$ |
| 19.1-c3 |
19.1-c |
$4$ |
$15$ |
4.4.16400.1 |
$4$ |
$[4, 0]$ |
19.1 |
\( 19 \) |
\( - 19^{5} \) |
$16.53502$ |
$(a^2+a-4)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3, 5$ |
3B, 5B[2] |
$1$ |
\( 1 \) |
$1$ |
$98.99387271$ |
0.773012275 |
\( \frac{2289565641755}{2476099} a^{3} - \frac{5313278941225}{2476099} a^{2} - \frac{17442014714520}{2476099} a + \frac{40477042159125}{2476099} \) |
\( \bigl[1\) , \( a^{2} - a - 6\) , \( a^{3} - 7 a + 1\) , \( -32 a^{3} + 73 a^{2} + 239 a - 544\) , \( -212 a^{3} + 490 a^{2} + 1626 a - 3765\bigr] \) |
${y}^2+{x}{y}+\left(a^{3}-7a+1\right){y}={x}^{3}+\left(a^{2}-a-6\right){x}^{2}+\left(-32a^{3}+73a^{2}+239a-544\right){x}-212a^{3}+490a^{2}+1626a-3765$ |
| 19.1-c4 |
19.1-c |
$4$ |
$15$ |
4.4.16400.1 |
$4$ |
$[4, 0]$ |
19.1 |
\( 19 \) |
\( -19 \) |
$16.53502$ |
$(a^2+a-4)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3, 5$ |
3B, 5B[2] |
$1$ |
\( 1 \) |
$1$ |
$98.99387271$ |
0.773012275 |
\( -\frac{24005877695}{19} a^{3} - \frac{66262595100}{19} a^{2} + \frac{129187416855}{19} a + \frac{356600683675}{19} \) |
\( \bigl[1\) , \( -a^{2} + a + 7\) , \( a^{3} - 7 a + 1\) , \( -12 a^{3} + 22 a^{2} + 105 a - 205\) , \( 61 a^{3} - 130 a^{2} - 529 a + 1166\bigr] \) |
${y}^2+{x}{y}+\left(a^{3}-7a+1\right){y}={x}^{3}+\left(-a^{2}+a+7\right){x}^{2}+\left(-12a^{3}+22a^{2}+105a-205\right){x}+61a^{3}-130a^{2}-529a+1166$ |
| 19.1-d1 |
19.1-d |
$2$ |
$3$ |
4.4.16400.1 |
$4$ |
$[4, 0]$ |
19.1 |
\( 19 \) |
\( 19^{12} \) |
$16.53502$ |
$(a^2+a-4)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 2 \) |
$1$ |
$34.85936199$ |
0.544411769 |
\( -\frac{260081870579892941420531712}{2213314919066161} a^{3} - \frac{717846408960670827499892736}{2213314919066161} a^{2} + \frac{1399751787087143777899143168}{2213314919066161} a + \frac{3863424973120559478115966976}{2213314919066161} \) |
\( \bigl[0\) , \( -a^{2} + 8\) , \( a + 1\) , \( -189 a^{3} + 430 a^{2} + 1431 a - 3272\) , \( 77400 a^{3} - 179548 a^{2} - 589628 a + 1367811\bigr] \) |
${y}^2+\left(a+1\right){y}={x}^{3}+\left(-a^{2}+8\right){x}^{2}+\left(-189a^{3}+430a^{2}+1431a-3272\right){x}+77400a^{3}-179548a^{2}-589628a+1367811$ |
| 19.1-d2 |
19.1-d |
$2$ |
$3$ |
4.4.16400.1 |
$4$ |
$[4, 0]$ |
19.1 |
\( 19 \) |
\( 19^{4} \) |
$16.53502$ |
$(a^2+a-4)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 2 \) |
$1$ |
$34.85936199$ |
0.544411769 |
\( \frac{64098067009536}{130321} a^{3} + \frac{148700151410688}{130321} a^{2} - \frac{488300922445824}{130321} a - \frac{1132805100666880}{130321} \) |
\( \bigl[0\) , \( -a^{2} + 8\) , \( a + 1\) , \( 21 a^{3} - 50 a^{2} - 159 a + 378\) , \( -2850 a^{3} + 6611 a^{2} + 21712 a - 50368\bigr] \) |
${y}^2+\left(a+1\right){y}={x}^{3}+\left(-a^{2}+8\right){x}^{2}+\left(21a^{3}-50a^{2}-159a+378\right){x}-2850a^{3}+6611a^{2}+21712a-50368$ |
| 19.2-a1 |
19.2-a |
$2$ |
$3$ |
4.4.16400.1 |
$4$ |
$[4, 0]$ |
19.2 |
\( 19 \) |
\( 19^{12} \) |
$16.53502$ |
$(a^3-2a^2-7a+13)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.2 |
$1$ |
\( 2^{2} \cdot 3 \) |
$1.403755163$ |
$5.505102201$ |
2.896516895 |
\( \frac{260081870579892941420531712}{2213314919066161} a^{3} - \frac{717846408960670827499892736}{2213314919066161} a^{2} - \frac{1399751787087143777899143168}{2213314919066161} a + \frac{3863424973120559478115966976}{2213314919066161} \) |
\( \bigl[0\) , \( a^{2} - 8\) , \( a^{3} + a^{2} - 6 a - 7\) , \( 189 a^{3} + 430 a^{2} - 1431 a - 3272\) , \( 77400 a^{3} + 179546 a^{2} - 589628 a - 1367803\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-6a-7\right){y}={x}^{3}+\left(a^{2}-8\right){x}^{2}+\left(189a^{3}+430a^{2}-1431a-3272\right){x}+77400a^{3}+179546a^{2}-589628a-1367803$ |
| 19.2-a2 |
19.2-a |
$2$ |
$3$ |
4.4.16400.1 |
$4$ |
$[4, 0]$ |
19.2 |
\( 19 \) |
\( 19^{4} \) |
$16.53502$ |
$(a^3-2a^2-7a+13)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1 |
$1$ |
\( 2^{2} \) |
$0.467918387$ |
$445.9132782$ |
2.896516895 |
\( -\frac{64098067009536}{130321} a^{3} + \frac{148700151410688}{130321} a^{2} + \frac{488300922445824}{130321} a - \frac{1132805100666880}{130321} \) |
\( \bigl[0\) , \( a^{2} - 8\) , \( a^{3} + a^{2} - 6 a - 7\) , \( -21 a^{3} - 50 a^{2} + 159 a + 378\) , \( -2850 a^{3} - 6613 a^{2} + 21712 a + 50376\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-6a-7\right){y}={x}^{3}+\left(a^{2}-8\right){x}^{2}+\left(-21a^{3}-50a^{2}+159a+378\right){x}-2850a^{3}-6613a^{2}+21712a+50376$ |
| 19.2-b1 |
19.2-b |
$4$ |
$15$ |
4.4.16400.1 |
$4$ |
$[4, 0]$ |
19.2 |
\( 19 \) |
\( - 19^{3} \) |
$16.53502$ |
$(a^3-2a^2-7a+13)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3, 5$ |
3B.1.2, 5B[2] |
$1$ |
\( 3 \) |
$5.459177605$ |
$6.388084289$ |
3.267812905 |
\( -\frac{6630368958622669095}{6859} a^{3} - \frac{15410236864329038175}{6859} a^{2} + \frac{50366099200344265580}{6859} a + \frac{116997492663148095175}{6859} \) |
\( \bigl[a^{3} + a^{2} - 7 a - 7\) , \( -a^{3} - a^{2} + 8 a + 6\) , \( a^{3} + a^{2} - 7 a - 6\) , \( 806 a^{3} - 2234 a^{2} - 4416 a + 12256\) , \( -38765 a^{3} + 107946 a^{2} + 203591 a - 569179\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-7a-7\right){x}{y}+\left(a^{3}+a^{2}-7a-6\right){y}={x}^{3}+\left(-a^{3}-a^{2}+8a+6\right){x}^{2}+\left(806a^{3}-2234a^{2}-4416a+12256\right){x}-38765a^{3}+107946a^{2}+203591a-569179$ |
| 19.2-b2 |
19.2-b |
$4$ |
$15$ |
4.4.16400.1 |
$4$ |
$[4, 0]$ |
19.2 |
\( 19 \) |
\( - 19^{15} \) |
$16.53502$ |
$(a^3-2a^2-7a+13)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3, 5$ |
3B.1.2, 5B[2] |
$1$ |
\( 3 \cdot 5 \) |
$1.091835521$ |
$6.388084289$ |
3.267812905 |
\( -\frac{35837154163366394281545}{15181127029874798299} a^{3} + \frac{65378672019532107253000}{15181127029874798299} a^{2} + \frac{272832802000467030921805}{15181127029874798299} a - \frac{500017660482708507945475}{15181127029874798299} \) |
\( \bigl[a^{3} - 6 a\) , \( -a + 1\) , \( a^{3} + a^{2} - 7 a - 6\) , \( 49 a^{3} + 117 a^{2} - 408 a - 962\) , \( 92 a^{3} + 120 a^{2} - 1232 a - 2356\bigr] \) |
${y}^2+\left(a^{3}-6a\right){x}{y}+\left(a^{3}+a^{2}-7a-6\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(49a^{3}+117a^{2}-408a-962\right){x}+92a^{3}+120a^{2}-1232a-2356$ |
| 19.2-b3 |
19.2-b |
$4$ |
$15$ |
4.4.16400.1 |
$4$ |
$[4, 0]$ |
19.2 |
\( 19 \) |
\( - 19^{5} \) |
$16.53502$ |
$(a^3-2a^2-7a+13)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3, 5$ |
3B.1.1, 5B[2] |
$1$ |
\( 5 \) |
$0.363945173$ |
$517.4348274$ |
3.267812905 |
\( -\frac{2289565641755}{2476099} a^{3} - \frac{5313278941225}{2476099} a^{2} + \frac{17442014714520}{2476099} a + \frac{40477042159125}{2476099} \) |
\( \bigl[a^{3} - 6 a\) , \( -a + 1\) , \( a^{3} + a^{2} - 7 a - 6\) , \( 29 a^{3} + 77 a^{2} - 223 a - 567\) , \( -198 a^{3} - 445 a^{2} + 1524 a + 3458\bigr] \) |
${y}^2+\left(a^{3}-6a\right){x}{y}+\left(a^{3}+a^{2}-7a-6\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(29a^{3}+77a^{2}-223a-567\right){x}-198a^{3}-445a^{2}+1524a+3458$ |
| 19.2-b4 |
19.2-b |
$4$ |
$15$ |
4.4.16400.1 |
$4$ |
$[4, 0]$ |
19.2 |
\( 19 \) |
\( -19 \) |
$16.53502$ |
$(a^3-2a^2-7a+13)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3, 5$ |
3B.1.1, 5B[2] |
$1$ |
\( 1 \) |
$1.819725868$ |
$517.4348274$ |
3.267812905 |
\( \frac{24005877695}{19} a^{3} - \frac{66262595100}{19} a^{2} - \frac{129187416855}{19} a + \frac{356600683675}{19} \) |
\( \bigl[a^{3} - 6 a\) , \( -a^{2} + a + 6\) , \( a^{2} - 6\) , \( 11 a^{3} + 24 a^{2} - 97 a - 216\) , \( 73 a^{3} + 154 a^{2} - 633 a - 1386\bigr] \) |
${y}^2+\left(a^{3}-6a\right){x}{y}+\left(a^{2}-6\right){y}={x}^{3}+\left(-a^{2}+a+6\right){x}^{2}+\left(11a^{3}+24a^{2}-97a-216\right){x}+73a^{3}+154a^{2}-633a-1386$ |
| 19.2-c1 |
19.2-c |
$4$ |
$15$ |
4.4.16400.1 |
$4$ |
$[4, 0]$ |
19.2 |
\( 19 \) |
\( - 19^{3} \) |
$16.53502$ |
$(a^3-2a^2-7a+13)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3, 5$ |
3B, 5B[2] |
$1$ |
\( 1 \) |
$1$ |
$98.99387271$ |
0.773012275 |
\( -\frac{6630368958622669095}{6859} a^{3} - \frac{15410236864329038175}{6859} a^{2} + \frac{50366099200344265580}{6859} a + \frac{116997492663148095175}{6859} \) |
\( \bigl[a^{2} + a - 6\) , \( a^{3} - a^{2} - 6 a + 7\) , \( a^{3} + a^{2} - 7 a - 7\) , \( 813 a^{3} - 2219 a^{2} - 4466 a + 12156\) , \( 36936 a^{3} - 102924 a^{2} - 193756 a + 542252\bigr] \) |
${y}^2+\left(a^{2}+a-6\right){x}{y}+\left(a^{3}+a^{2}-7a-7\right){y}={x}^{3}+\left(a^{3}-a^{2}-6a+7\right){x}^{2}+\left(813a^{3}-2219a^{2}-4466a+12156\right){x}+36936a^{3}-102924a^{2}-193756a+542252$ |
| 19.2-c2 |
19.2-c |
$4$ |
$15$ |
4.4.16400.1 |
$4$ |
$[4, 0]$ |
19.2 |
\( 19 \) |
\( - 19^{15} \) |
$16.53502$ |
$(a^3-2a^2-7a+13)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3, 5$ |
3B, 5B[2] |
$1$ |
\( 1 \) |
$1$ |
$98.99387271$ |
0.773012275 |
\( -\frac{35837154163366394281545}{15181127029874798299} a^{3} + \frac{65378672019532107253000}{15181127029874798299} a^{2} + \frac{272832802000467030921805}{15181127029874798299} a - \frac{500017660482708507945475}{15181127029874798299} \) |
\( \bigl[1\) , \( a^{2} + a - 6\) , \( a^{3} - 7 a + 1\) , \( 51 a^{3} + 113 a^{2} - 417 a - 939\) , \( -104 a^{3} - 150 a^{2} + 1242 a + 2384\bigr] \) |
${y}^2+{x}{y}+\left(a^{3}-7a+1\right){y}={x}^{3}+\left(a^{2}+a-6\right){x}^{2}+\left(51a^{3}+113a^{2}-417a-939\right){x}-104a^{3}-150a^{2}+1242a+2384$ |
| 19.2-c3 |
19.2-c |
$4$ |
$15$ |
4.4.16400.1 |
$4$ |
$[4, 0]$ |
19.2 |
\( 19 \) |
\( - 19^{5} \) |
$16.53502$ |
$(a^3-2a^2-7a+13)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3, 5$ |
3B, 5B[2] |
$1$ |
\( 1 \) |
$1$ |
$98.99387271$ |
0.773012275 |
\( -\frac{2289565641755}{2476099} a^{3} - \frac{5313278941225}{2476099} a^{2} + \frac{17442014714520}{2476099} a + \frac{40477042159125}{2476099} \) |
\( \bigl[1\) , \( a^{2} + a - 6\) , \( a^{3} - 7 a + 1\) , \( 31 a^{3} + 73 a^{2} - 232 a - 544\) , \( 211 a^{3} + 490 a^{2} - 1619 a - 3765\bigr] \) |
${y}^2+{x}{y}+\left(a^{3}-7a+1\right){y}={x}^{3}+\left(a^{2}+a-6\right){x}^{2}+\left(31a^{3}+73a^{2}-232a-544\right){x}+211a^{3}+490a^{2}-1619a-3765$ |
| 19.2-c4 |
19.2-c |
$4$ |
$15$ |
4.4.16400.1 |
$4$ |
$[4, 0]$ |
19.2 |
\( 19 \) |
\( -19 \) |
$16.53502$ |
$(a^3-2a^2-7a+13)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3, 5$ |
3B, 5B[2] |
$1$ |
\( 1 \) |
$1$ |
$98.99387271$ |
0.773012275 |
\( \frac{24005877695}{19} a^{3} - \frac{66262595100}{19} a^{2} - \frac{129187416855}{19} a + \frac{356600683675}{19} \) |
\( \bigl[1\) , \( -a^{2} - a + 7\) , \( a^{3} - 7 a + 1\) , \( 11 a^{3} + 22 a^{2} - 98 a - 205\) , \( -62 a^{3} - 130 a^{2} + 536 a + 1166\bigr] \) |
${y}^2+{x}{y}+\left(a^{3}-7a+1\right){y}={x}^{3}+\left(-a^{2}-a+7\right){x}^{2}+\left(11a^{3}+22a^{2}-98a-205\right){x}-62a^{3}-130a^{2}+536a+1166$ |
| 19.2-d1 |
19.2-d |
$2$ |
$3$ |
4.4.16400.1 |
$4$ |
$[4, 0]$ |
19.2 |
\( 19 \) |
\( 19^{12} \) |
$16.53502$ |
$(a^3-2a^2-7a+13)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 2 \) |
$1$ |
$34.85936199$ |
0.544411769 |
\( \frac{260081870579892941420531712}{2213314919066161} a^{3} - \frac{717846408960670827499892736}{2213314919066161} a^{2} - \frac{1399751787087143777899143168}{2213314919066161} a + \frac{3863424973120559478115966976}{2213314919066161} \) |
\( \bigl[0\) , \( -a^{2} + 8\) , \( a + 1\) , \( 189 a^{3} + 430 a^{2} - 1431 a - 3272\) , \( -77400 a^{3} - 179548 a^{2} + 589627 a + 1367811\bigr] \) |
${y}^2+\left(a+1\right){y}={x}^{3}+\left(-a^{2}+8\right){x}^{2}+\left(189a^{3}+430a^{2}-1431a-3272\right){x}-77400a^{3}-179548a^{2}+589627a+1367811$ |
| 19.2-d2 |
19.2-d |
$2$ |
$3$ |
4.4.16400.1 |
$4$ |
$[4, 0]$ |
19.2 |
\( 19 \) |
\( 19^{4} \) |
$16.53502$ |
$(a^3-2a^2-7a+13)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 2 \) |
$1$ |
$34.85936199$ |
0.544411769 |
\( -\frac{64098067009536}{130321} a^{3} + \frac{148700151410688}{130321} a^{2} + \frac{488300922445824}{130321} a - \frac{1132805100666880}{130321} \) |
\( \bigl[0\) , \( -a^{2} + 8\) , \( a + 1\) , \( -21 a^{3} - 50 a^{2} + 159 a + 378\) , \( 2850 a^{3} + 6611 a^{2} - 21713 a - 50368\bigr] \) |
${y}^2+\left(a+1\right){y}={x}^{3}+\left(-a^{2}+8\right){x}^{2}+\left(-21a^{3}-50a^{2}+159a+378\right){x}+2850a^{3}+6611a^{2}-21713a-50368$ |
| 25.1-a1 |
25.1-a |
$2$ |
$2$ |
4.4.16400.1 |
$4$ |
$[4, 0]$ |
25.1 |
\( 5^{2} \) |
\( 5^{9} \) |
$17.11209$ |
$(-2a^3-5a^2+11a+26), (3a^2-a-20)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1.311494435$ |
$210.9323391$ |
4.320337679 |
\( -\frac{88066307653507}{625} a^{3} + \frac{1944559550551}{5} a^{2} + \frac{473969873974344}{625} a - \frac{1308194173159092}{625} \) |
\( \bigl[a^{3} - 6 a\) , \( a^{3} - 8 a - 1\) , \( a^{2} + a - 6\) , \( -17 a^{3} + 23 a^{2} + 162 a - 272\) , \( 238 a^{3} - 597 a^{2} - 1570 a + 3873\bigr] \) |
${y}^2+\left(a^{3}-6a\right){x}{y}+\left(a^{2}+a-6\right){y}={x}^{3}+\left(a^{3}-8a-1\right){x}^{2}+\left(-17a^{3}+23a^{2}+162a-272\right){x}+238a^{3}-597a^{2}-1570a+3873$ |
| 25.1-a2 |
25.1-a |
$2$ |
$2$ |
4.4.16400.1 |
$4$ |
$[4, 0]$ |
25.1 |
\( 5^{2} \) |
\( 5^{6} \) |
$17.11209$ |
$(-2a^3-5a^2+11a+26), (3a^2-a-20)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.655747217$ |
$210.9323391$ |
4.320337679 |
\( \frac{2667502}{25} a^{3} - \frac{1475327}{5} a^{2} - \frac{14351774}{25} a + \frac{39719602}{25} \) |
\( \bigl[a^{3} - 6 a\) , \( a^{3} - 8 a - 1\) , \( a^{2} + a - 6\) , \( 3 a^{3} - 17 a^{2} - 23 a + 123\) , \( 26 a^{3} - 58 a^{2} - 193 a + 424\bigr] \) |
${y}^2+\left(a^{3}-6a\right){x}{y}+\left(a^{2}+a-6\right){y}={x}^{3}+\left(a^{3}-8a-1\right){x}^{2}+\left(3a^{3}-17a^{2}-23a+123\right){x}+26a^{3}-58a^{2}-193a+424$ |
| 25.1-b1 |
25.1-b |
$2$ |
$2$ |
4.4.16400.1 |
$4$ |
$[4, 0]$ |
25.1 |
\( 5^{2} \) |
\( 5^{9} \) |
$17.11209$ |
$(-2a^3-5a^2+11a+26), (3a^2-a-20)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.786108838$ |
$346.0788290$ |
4.248795061 |
\( -\frac{88066307653507}{625} a^{3} + \frac{1944559550551}{5} a^{2} + \frac{473969873974344}{625} a - \frac{1308194173159092}{625} \) |
\( \bigl[1\) , \( -a^{3} + a^{2} + 8 a - 7\) , \( a^{3} - 7 a + 1\) , \( -15 a^{3} + 24 a^{2} + 149 a - 279\) , \( -195 a^{3} + 488 a^{2} + 1297 a - 3199\bigr] \) |
${y}^2+{x}{y}+\left(a^{3}-7a+1\right){y}={x}^{3}+\left(-a^{3}+a^{2}+8a-7\right){x}^{2}+\left(-15a^{3}+24a^{2}+149a-279\right){x}-195a^{3}+488a^{2}+1297a-3199$ |
| 25.1-b2 |
25.1-b |
$2$ |
$2$ |
4.4.16400.1 |
$4$ |
$[4, 0]$ |
25.1 |
\( 5^{2} \) |
\( 5^{6} \) |
$17.11209$ |
$(-2a^3-5a^2+11a+26), (3a^2-a-20)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.393054419$ |
$346.0788290$ |
4.248795061 |
\( \frac{2667502}{25} a^{3} - \frac{1475327}{5} a^{2} - \frac{14351774}{25} a + \frac{39719602}{25} \) |
\( \bigl[1\) , \( -a^{3} + a^{2} + 8 a - 7\) , \( a^{3} - 7 a + 1\) , \( 5 a^{3} - 16 a^{2} - 36 a + 116\) , \( -28 a^{3} + 64 a^{2} + 210 a - 480\bigr] \) |
${y}^2+{x}{y}+\left(a^{3}-7a+1\right){y}={x}^{3}+\left(-a^{3}+a^{2}+8a-7\right){x}^{2}+\left(5a^{3}-16a^{2}-36a+116\right){x}-28a^{3}+64a^{2}+210a-480$ |
| 25.1-c1 |
25.1-c |
$2$ |
$2$ |
4.4.16400.1 |
$4$ |
$[4, 0]$ |
25.1 |
\( 5^{2} \) |
\( 5^{9} \) |
$17.11209$ |
$(-2a^3-5a^2+11a+26), (3a^2-a-20)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.786108838$ |
$346.0788290$ |
4.248795061 |
\( \frac{88066307653507}{625} a^{3} + \frac{1944559550551}{5} a^{2} - \frac{473969873974344}{625} a - \frac{1308194173159092}{625} \) |
\( \bigl[1\) , \( a^{3} + a^{2} - 8 a - 7\) , \( a^{3} - 7 a + 1\) , \( 14 a^{3} + 24 a^{2} - 142 a - 279\) , \( 194 a^{3} + 488 a^{2} - 1290 a - 3199\bigr] \) |
${y}^2+{x}{y}+\left(a^{3}-7a+1\right){y}={x}^{3}+\left(a^{3}+a^{2}-8a-7\right){x}^{2}+\left(14a^{3}+24a^{2}-142a-279\right){x}+194a^{3}+488a^{2}-1290a-3199$ |
| 25.1-c2 |
25.1-c |
$2$ |
$2$ |
4.4.16400.1 |
$4$ |
$[4, 0]$ |
25.1 |
\( 5^{2} \) |
\( 5^{6} \) |
$17.11209$ |
$(-2a^3-5a^2+11a+26), (3a^2-a-20)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.393054419$ |
$346.0788290$ |
4.248795061 |
\( -\frac{2667502}{25} a^{3} - \frac{1475327}{5} a^{2} + \frac{14351774}{25} a + \frac{39719602}{25} \) |
\( \bigl[1\) , \( a^{3} + a^{2} - 8 a - 7\) , \( a^{3} - 7 a + 1\) , \( -6 a^{3} - 16 a^{2} + 43 a + 116\) , \( 27 a^{3} + 64 a^{2} - 203 a - 480\bigr] \) |
${y}^2+{x}{y}+\left(a^{3}-7a+1\right){y}={x}^{3}+\left(a^{3}+a^{2}-8a-7\right){x}^{2}+\left(-6a^{3}-16a^{2}+43a+116\right){x}+27a^{3}+64a^{2}-203a-480$ |
| 25.1-d1 |
25.1-d |
$2$ |
$2$ |
4.4.16400.1 |
$4$ |
$[4, 0]$ |
25.1 |
\( 5^{2} \) |
\( 5^{9} \) |
$17.11209$ |
$(-2a^3-5a^2+11a+26), (3a^2-a-20)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1.311494435$ |
$210.9323391$ |
4.320337679 |
\( \frac{88066307653507}{625} a^{3} + \frac{1944559550551}{5} a^{2} - \frac{473969873974344}{625} a - \frac{1308194173159092}{625} \) |
\( \bigl[a^{3} - 6 a\) , \( -a^{3} + 8 a - 1\) , \( a^{2} + a - 6\) , \( 16 a^{3} + 23 a^{2} - 157 a - 272\) , \( -239 a^{3} - 597 a^{2} + 1576 a + 3873\bigr] \) |
${y}^2+\left(a^{3}-6a\right){x}{y}+\left(a^{2}+a-6\right){y}={x}^{3}+\left(-a^{3}+8a-1\right){x}^{2}+\left(16a^{3}+23a^{2}-157a-272\right){x}-239a^{3}-597a^{2}+1576a+3873$ |
| 25.1-d2 |
25.1-d |
$2$ |
$2$ |
4.4.16400.1 |
$4$ |
$[4, 0]$ |
25.1 |
\( 5^{2} \) |
\( 5^{6} \) |
$17.11209$ |
$(-2a^3-5a^2+11a+26), (3a^2-a-20)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.655747217$ |
$210.9323391$ |
4.320337679 |
\( -\frac{2667502}{25} a^{3} - \frac{1475327}{5} a^{2} + \frac{14351774}{25} a + \frac{39719602}{25} \) |
\( \bigl[a^{3} - 6 a\) , \( -a^{3} + 8 a - 1\) , \( a^{2} + a - 6\) , \( -4 a^{3} - 17 a^{2} + 28 a + 123\) , \( -27 a^{3} - 58 a^{2} + 199 a + 424\bigr] \) |
${y}^2+\left(a^{3}-6a\right){x}{y}+\left(a^{2}+a-6\right){y}={x}^{3}+\left(-a^{3}+8a-1\right){x}^{2}+\left(-4a^{3}-17a^{2}+28a+123\right){x}-27a^{3}-58a^{2}+199a+424$ |
| 25.2-a1 |
25.2-a |
$2$ |
$5$ |
4.4.16400.1 |
$4$ |
$[4, 0]$ |
25.2 |
\( 5^{2} \) |
\( 5^{2} \) |
$17.11209$ |
$(3a^2-a-20)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$5$ |
5B[2] |
$1$ |
\( 1 \) |
$1$ |
$140.4230409$ |
1.096519727 |
\( 592548095748 a^{3} + 1374656144746 a^{2} - 4514051526737 a - 10472177250734 \) |
\( \bigl[a^{3} - 6 a\) , \( a^{3} + a^{2} - 7 a - 8\) , \( a^{3} - 7 a + 1\) , \( a^{3} + 5 a^{2} - 3 a - 25\) , \( 2 a^{3} + 8 a^{2} - 11 a - 49\bigr] \) |
${y}^2+\left(a^{3}-6a\right){x}{y}+\left(a^{3}-7a+1\right){y}={x}^{3}+\left(a^{3}+a^{2}-7a-8\right){x}^{2}+\left(a^{3}+5a^{2}-3a-25\right){x}+2a^{3}+8a^{2}-11a-49$ |
| 25.2-a2 |
25.2-a |
$2$ |
$5$ |
4.4.16400.1 |
$4$ |
$[4, 0]$ |
25.2 |
\( 5^{2} \) |
\( 5^{10} \) |
$17.11209$ |
$(3a^2-a-20)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$5$ |
5B[2] |
$1$ |
\( 1 \) |
$1$ |
$140.4230409$ |
1.096519727 |
\( -44565 a^{3} - 122870 a^{2} + 239885 a + 661180 \) |
\( \bigl[a\) , \( a^{3} + a^{2} - 6 a - 7\) , \( a\) , \( 2 a^{2} + a - 15\) , \( -a^{3} + 3 a^{2} + 8 a - 24\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(a^{3}+a^{2}-6a-7\right){x}^{2}+\left(2a^{2}+a-15\right){x}-a^{3}+3a^{2}+8a-24$ |
| 25.2-b1 |
25.2-b |
$2$ |
$2$ |
4.4.16400.1 |
$4$ |
$[4, 0]$ |
25.2 |
\( 5^{2} \) |
\( 5^{6} \) |
$17.11209$ |
$(3a^2-a-20)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$5$ |
5Ns.2.1[2] |
$1$ |
\( 2 \) |
$1$ |
$676.4471278$ |
2.641082316 |
\( 1728 \) |
\( \bigl[a^{3} - 6 a + 1\) , \( a^{3} + a^{2} - 6 a - 8\) , \( a^{3} + a^{2} - 7 a - 7\) , \( 4 a^{3} + 12 a^{2} - 21 a - 66\) , \( 9 a^{3} + 25 a^{2} - 49 a - 137\bigr] \) |
${y}^2+\left(a^{3}-6a+1\right){x}{y}+\left(a^{3}+a^{2}-7a-7\right){y}={x}^{3}+\left(a^{3}+a^{2}-6a-8\right){x}^{2}+\left(4a^{3}+12a^{2}-21a-66\right){x}+9a^{3}+25a^{2}-49a-137$ |
| 25.2-b2 |
25.2-b |
$2$ |
$2$ |
4.4.16400.1 |
$4$ |
$[4, 0]$ |
25.2 |
\( 5^{2} \) |
\( 5^{6} \) |
$17.11209$ |
$(3a^2-a-20)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$5$ |
5Ns.2.1[2] |
$1$ |
\( 2 \) |
$1$ |
$676.4471278$ |
2.641082316 |
\( 1728 \) |
\( \bigl[a^{3} - 6 a + 1\) , \( a^{3} + a^{2} - 6 a - 8\) , \( a^{2} + a - 6\) , \( 5 a^{3} - 3 a^{2} - 26 a + 22\) , \( 3 a^{3} + 18 a^{2} - 17 a - 101\bigr] \) |
${y}^2+\left(a^{3}-6a+1\right){x}{y}+\left(a^{2}+a-6\right){y}={x}^{3}+\left(a^{3}+a^{2}-6a-8\right){x}^{2}+\left(5a^{3}-3a^{2}-26a+22\right){x}+3a^{3}+18a^{2}-17a-101$ |
| 25.2-c1 |
25.2-c |
$2$ |
$5$ |
4.4.16400.1 |
$4$ |
$[4, 0]$ |
25.2 |
\( 5^{2} \) |
\( 5^{10} \) |
$17.11209$ |
$(3a^2-a-20)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$5$ |
5B[2] |
$1$ |
\( 1 \) |
$1$ |
$194.8128145$ |
1.521232505 |
\( -44565 a^{3} - 122870 a^{2} + 239885 a + 661180 \) |
\( \bigl[a^{2} - 7\) , \( -a^{3} - a^{2} + 6 a + 8\) , \( 0\) , \( -2 a^{3} + 13 a + 2\) , \( -2 a^{2} - a + 17\bigr] \) |
${y}^2+\left(a^{2}-7\right){x}{y}={x}^{3}+\left(-a^{3}-a^{2}+6a+8\right){x}^{2}+\left(-2a^{3}+13a+2\right){x}-2a^{2}-a+17$ |
| 25.2-c2 |
25.2-c |
$2$ |
$5$ |
4.4.16400.1 |
$4$ |
$[4, 0]$ |
25.2 |
\( 5^{2} \) |
\( 5^{2} \) |
$17.11209$ |
$(3a^2-a-20)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$5$ |
5B[2] |
$1$ |
\( 1 \) |
$1$ |
$194.8128145$ |
1.521232505 |
\( 592548095748 a^{3} + 1374656144746 a^{2} - 4514051526737 a - 10472177250734 \) |
\( \bigl[1\) , \( -a^{3} + 7 a\) , \( a^{3} - 6 a\) , \( a^{3} + 3 a^{2} - 5 a - 13\) , \( a^{3} + a^{2} - 5 a - 6\bigr] \) |
${y}^2+{x}{y}+\left(a^{3}-6a\right){y}={x}^{3}+\left(-a^{3}+7a\right){x}^{2}+\left(a^{3}+3a^{2}-5a-13\right){x}+a^{3}+a^{2}-5a-6$ |
| 25.3-a1 |
25.3-a |
$2$ |
$5$ |
4.4.16400.1 |
$4$ |
$[4, 0]$ |
25.3 |
\( 5^{2} \) |
\( 5^{2} \) |
$17.11209$ |
$(-2a^3-5a^2+11a+26)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$5$ |
5B[2] |
$1$ |
\( 1 \) |
$1$ |
$140.4230409$ |
1.096519727 |
\( -592548095748 a^{3} + 1374656144746 a^{2} + 4514051526737 a - 10472177250734 \) |
\( \bigl[a^{3} - 6 a\) , \( -a^{3} + a^{2} + 7 a - 8\) , \( a^{3} - 7 a + 1\) , \( -2 a^{3} + 5 a^{2} + 9 a - 25\) , \( -3 a^{3} + 8 a^{2} + 18 a - 49\bigr] \) |
${y}^2+\left(a^{3}-6a\right){x}{y}+\left(a^{3}-7a+1\right){y}={x}^{3}+\left(-a^{3}+a^{2}+7a-8\right){x}^{2}+\left(-2a^{3}+5a^{2}+9a-25\right){x}-3a^{3}+8a^{2}+18a-49$ |
| 25.3-a2 |
25.3-a |
$2$ |
$5$ |
4.4.16400.1 |
$4$ |
$[4, 0]$ |
25.3 |
\( 5^{2} \) |
\( 5^{10} \) |
$17.11209$ |
$(-2a^3-5a^2+11a+26)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$5$ |
5B[2] |
$1$ |
\( 1 \) |
$1$ |
$140.4230409$ |
1.096519727 |
\( 44565 a^{3} - 122870 a^{2} - 239885 a + 661180 \) |
\( \bigl[a\) , \( -a^{3} + a^{2} + 6 a - 7\) , \( a\) , \( 2 a^{2} - a - 15\) , \( a^{3} + 3 a^{2} - 8 a - 24\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a^{3}+a^{2}+6a-7\right){x}^{2}+\left(2a^{2}-a-15\right){x}+a^{3}+3a^{2}-8a-24$ |
| 25.3-b1 |
25.3-b |
$2$ |
$2$ |
4.4.16400.1 |
$4$ |
$[4, 0]$ |
25.3 |
\( 5^{2} \) |
\( 5^{6} \) |
$17.11209$ |
$(-2a^3-5a^2+11a+26)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$5$ |
5Ns.2.1[2] |
$1$ |
\( 2 \) |
$1$ |
$676.4471278$ |
2.641082316 |
\( 1728 \) |
\( \bigl[a^{3} - 6 a + 1\) , \( a^{3} + a^{2} - 6 a - 8\) , \( a^{3} + a^{2} - 7 a - 7\) , \( a + 2\) , \( -5 a^{3} - 14 a^{2} + 25 a + 70\bigr] \) |
${y}^2+\left(a^{3}-6a+1\right){x}{y}+\left(a^{3}+a^{2}-7a-7\right){y}={x}^{3}+\left(a^{3}+a^{2}-6a-8\right){x}^{2}+\left(a+2\right){x}-5a^{3}-14a^{2}+25a+70$ |
| 25.3-b2 |
25.3-b |
$2$ |
$2$ |
4.4.16400.1 |
$4$ |
$[4, 0]$ |
25.3 |
\( 5^{2} \) |
\( 5^{6} \) |
$17.11209$ |
$(-2a^3-5a^2+11a+26)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$5$ |
5Ns.2.1[2] |
$1$ |
\( 2 \) |
$1$ |
$676.4471278$ |
2.641082316 |
\( 1728 \) |
\( \bigl[a^{3} - 6 a + 1\) , \( a^{3} + a^{2} - 6 a - 8\) , \( a^{2} + a - 6\) , \( a^{3} + 9 a^{2} - 4 a - 46\) , \( 5 a^{3} + 11 a^{2} - 27 a - 62\bigr] \) |
${y}^2+\left(a^{3}-6a+1\right){x}{y}+\left(a^{2}+a-6\right){y}={x}^{3}+\left(a^{3}+a^{2}-6a-8\right){x}^{2}+\left(a^{3}+9a^{2}-4a-46\right){x}+5a^{3}+11a^{2}-27a-62$ |
*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.
