| 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 |
| 192.1-a1 |
192.1-a |
$2$ |
$2$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
192.1 |
\( 2^{6} \cdot 3 \) |
\( 2^{16} \cdot 3^{14} \) |
$1.52431$ |
$(-a+2), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$5.062045892$ |
2.209257949 |
\( -\frac{11855696}{2187} a + \frac{117012512}{2187} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -31 a - 77\) , \( -157 a - 258\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(-31a-77\right){x}-157a-258$ |
| 192.1-a2 |
192.1-a |
$2$ |
$2$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
192.1 |
\( 2^{6} \cdot 3 \) |
\( - 2^{8} \cdot 3^{7} \) |
$1.52431$ |
$(-a+2), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$4$ |
\( 2 \) |
$1$ |
$5.062045892$ |
2.209257949 |
\( \frac{25019564800}{81} a + \frac{44817242368}{81} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -36 a - 62\) , \( -155 a - 275\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(-36a-62\right){x}-155a-275$ |
| 192.1-b1 |
192.1-b |
$2$ |
$2$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
192.1 |
\( 2^{6} \cdot 3 \) |
\( - 2^{8} \cdot 3^{7} \) |
$1.52431$ |
$(-a+2), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$4$ |
\( 2 \) |
$1$ |
$5.062045892$ |
2.209257949 |
\( -\frac{25019564800}{81} a + \frac{69836807168}{81} \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( 36 a - 98\) , \( 155 a - 430\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(36a-98\right){x}+155a-430$ |
| 192.1-b2 |
192.1-b |
$2$ |
$2$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
192.1 |
\( 2^{6} \cdot 3 \) |
\( 2^{16} \cdot 3^{14} \) |
$1.52431$ |
$(-a+2), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$5.062045892$ |
2.209257949 |
\( \frac{11855696}{2187} a + \frac{35052272}{729} \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( 31 a - 108\) , \( 157 a - 415\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(31a-108\right){x}+157a-415$ |
| 192.1-c1 |
192.1-c |
$2$ |
$2$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
192.1 |
\( 2^{6} \cdot 3 \) |
\( - 2^{8} \cdot 3 \) |
$1.52431$ |
$(-a+2), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$21.95917113$ |
2.395941998 |
\( \frac{256}{3} a + \frac{4864}{3} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -a + 3\) , \( 0\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+\left(-a+3\right){x}$ |
| 192.1-c2 |
192.1-c |
$2$ |
$2$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
192.1 |
\( 2^{6} \cdot 3 \) |
\( 2^{16} \cdot 3^{2} \) |
$1.52431$ |
$(-a+2), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$10.97958556$ |
2.395941998 |
\( \frac{77872}{3} a + \frac{145568}{3} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( 4 a - 12\) , \( 4 a - 12\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+\left(4a-12\right){x}+4a-12$ |
| 192.1-d1 |
192.1-d |
$4$ |
$4$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
192.1 |
\( 2^{6} \cdot 3 \) |
\( - 2^{8} \cdot 3 \) |
$1.52431$ |
$(-a+2), (2)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$34.67048791$ |
0.945715090 |
\( -\frac{4864}{3} a + \frac{13568}{3} \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( 1\) , \( 4 a + 7\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+{x}+4a+7$ |
| 192.1-d2 |
192.1-d |
$4$ |
$4$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
192.1 |
\( 2^{6} \cdot 3 \) |
\( 2^{20} \cdot 3^{4} \) |
$1.52431$ |
$(-a+2), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$4.333810989$ |
0.945715090 |
\( -\frac{121322980}{9} a + \frac{112888388}{3} \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( -45 a - 84\) , \( -135 a - 243\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(-45a-84\right){x}-135a-243$ |
| 192.1-d3 |
192.1-d |
$4$ |
$4$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
192.1 |
\( 2^{6} \cdot 3 \) |
\( 2^{16} \cdot 3^{2} \) |
$1.52431$ |
$(-a+2), (2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$1$ |
$17.33524395$ |
0.945715090 |
\( \frac{53200}{3} a + \frac{121184}{3} \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( -25 a - 44\) , \( 81 a + 145\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(-25a-44\right){x}+81a+145$ |
| 192.1-d4 |
192.1-d |
$4$ |
$4$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
192.1 |
\( 2^{6} \cdot 3 \) |
\( - 2^{20} \cdot 3 \) |
$1.52431$ |
$(-a+2), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$8.667621979$ |
0.945715090 |
\( \frac{5202690124}{3} a + \frac{9319516204}{3} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -47 a + 128\) , \( 725 a - 2020\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+\left(-47a+128\right){x}+725a-2020$ |
| 192.1-e1 |
192.1-e |
$6$ |
$8$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
192.1 |
\( 2^{6} \cdot 3 \) |
\( 2^{22} \cdot 3^{16} \) |
$1.52431$ |
$(-a+2), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$2.841754258$ |
2.480486475 |
\( \frac{207646}{6561} \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( -78 a + 221\) , \( -4241 a + 11838\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(-78a+221\right){x}-4241a+11838$ |
| 192.1-e2 |
192.1-e |
$6$ |
$8$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
192.1 |
\( 2^{6} \cdot 3 \) |
\( 2^{8} \cdot 3^{2} \) |
$1.52431$ |
$(-a+2), (2)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$4$ |
\( 2^{2} \) |
$1$ |
$11.36701703$ |
2.480486475 |
\( \frac{2048}{3} \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( -3 a + 11\) , \( 4 a - 12\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(-3a+11\right){x}+4a-12$ |
| 192.1-e3 |
192.1-e |
$6$ |
$8$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
192.1 |
\( 2^{6} \cdot 3 \) |
\( 2^{16} \cdot 3^{4} \) |
$1.52431$ |
$(-a+2), (2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$1$ |
$11.36701703$ |
2.480486475 |
\( \frac{35152}{9} \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( 22 a - 59\) , \( 75 a - 210\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(22a-59\right){x}+75a-210$ |
| 192.1-e4 |
192.1-e |
$6$ |
$8$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
192.1 |
\( 2^{6} \cdot 3 \) |
\( 2^{20} \cdot 3^{8} \) |
$1.52431$ |
$(-a+2), (2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$1$ |
$11.36701703$ |
2.480486475 |
\( \frac{1556068}{81} \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( -122 a - 217\) , \( 985 a + 1765\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(-122a-217\right){x}+985a+1765$ |
| 192.1-e5 |
192.1-e |
$6$ |
$8$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
192.1 |
\( 2^{6} \cdot 3 \) |
\( 2^{20} \cdot 3^{2} \) |
$1.52431$ |
$(-a+2), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$4$ |
\( 2^{2} \) |
$1$ |
$2.841754258$ |
2.480486475 |
\( \frac{28756228}{3} \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( 322 a - 899\) , \( 4959 a - 13842\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(322a-899\right){x}+4959a-13842$ |
| 192.1-e6 |
192.1-e |
$6$ |
$8$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
192.1 |
\( 2^{6} \cdot 3 \) |
\( 2^{22} \cdot 3^{4} \) |
$1.52431$ |
$(-a+2), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$11.36701703$ |
2.480486475 |
\( \frac{3065617154}{9} \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( 1922 a - 5379\) , \( -68449 a + 191102\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(1922a-5379\right){x}-68449a+191102$ |
| 192.1-f1 |
192.1-f |
$4$ |
$4$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
192.1 |
\( 2^{6} \cdot 3 \) |
\( - 2^{20} \cdot 3 \) |
$1.52431$ |
$(-a+2), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$3.411050126$ |
$3.410424115$ |
2.538556564 |
\( -\frac{5202690124}{3} a + \frac{14522206328}{3} \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( 20 a - 44\) , \( 76 a - 192\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(20a-44\right){x}+76a-192$ |
| 192.1-f2 |
192.1-f |
$4$ |
$4$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
192.1 |
\( 2^{6} \cdot 3 \) |
\( - 2^{8} \cdot 3 \) |
$1.52431$ |
$(-a+2), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.852762531$ |
$13.64169646$ |
2.538556564 |
\( \frac{4864}{3} a + \frac{8704}{3} \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( 1\) , \( 0\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+{x}$ |
| 192.1-f3 |
192.1-f |
$4$ |
$4$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
192.1 |
\( 2^{6} \cdot 3 \) |
\( 2^{16} \cdot 3^{2} \) |
$1.52431$ |
$(-a+2), (2)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$1.705525063$ |
$13.64169646$ |
2.538556564 |
\( -\frac{53200}{3} a + 58128 \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( -4\) , \( 4 a\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}-4{x}+4a$ |
| 192.1-f4 |
192.1-f |
$4$ |
$4$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
192.1 |
\( 2^{6} \cdot 3 \) |
\( 2^{20} \cdot 3^{4} \) |
$1.52431$ |
$(-a+2), (2)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.852762531$ |
$13.64169646$ |
2.538556564 |
\( \frac{121322980}{9} a + \frac{217342184}{9} \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( -20 a - 44\) , \( 108 a + 192\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(-20a-44\right){x}+108a+192$ |
| 192.1-g1 |
192.1-g |
$2$ |
$2$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
192.1 |
\( 2^{6} \cdot 3 \) |
\( - 2^{8} \cdot 3 \) |
$1.52431$ |
$(-a+2), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$21.95917113$ |
2.395941998 |
\( -\frac{256}{3} a + \frac{5120}{3} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( a + 2\) , \( 0\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+\left(a+2\right){x}$ |
| 192.1-g2 |
192.1-g |
$2$ |
$2$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
192.1 |
\( 2^{6} \cdot 3 \) |
\( 2^{16} \cdot 3^{2} \) |
$1.52431$ |
$(-a+2), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$10.97958556$ |
2.395941998 |
\( -\frac{77872}{3} a + 74480 \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -4 a - 8\) , \( -4 a - 8\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+\left(-4a-8\right){x}-4a-8$ |
| 192.1-h1 |
192.1-h |
$2$ |
$2$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
192.1 |
\( 2^{6} \cdot 3 \) |
\( - 2^{8} \cdot 3 \) |
$1.52431$ |
$(-a+2), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.393259272$ |
$22.72318029$ |
1.950017184 |
\( -\frac{256}{3} a + \frac{5120}{3} \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( a\) , \( 1\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+a{x}+1$ |
| 192.1-h2 |
192.1-h |
$2$ |
$2$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
192.1 |
\( 2^{6} \cdot 3 \) |
\( 2^{16} \cdot 3^{2} \) |
$1.52431$ |
$(-a+2), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.196629636$ |
$22.72318029$ |
1.950017184 |
\( -\frac{77872}{3} a + 74480 \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( 6 a - 15\) , \( -15 a + 42\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(6a-15\right){x}-15a+42$ |
| 192.1-i1 |
192.1-i |
$4$ |
$4$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
192.1 |
\( 2^{6} \cdot 3 \) |
\( - 2^{20} \cdot 3 \) |
$1.52431$ |
$(-a+2), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$8.667621979$ |
0.945715090 |
\( -\frac{5202690124}{3} a + \frac{14522206328}{3} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( 47 a + 81\) , \( -725 a - 1295\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+\left(47a+81\right){x}-725a-1295$ |
| 192.1-i2 |
192.1-i |
$4$ |
$4$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
192.1 |
\( 2^{6} \cdot 3 \) |
\( - 2^{8} \cdot 3 \) |
$1.52431$ |
$(-a+2), (2)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$34.67048791$ |
0.945715090 |
\( \frac{4864}{3} a + \frac{8704}{3} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 1\) , \( -4 a + 11\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+{x}-4a+11$ |
| 192.1-i3 |
192.1-i |
$4$ |
$4$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
192.1 |
\( 2^{6} \cdot 3 \) |
\( 2^{16} \cdot 3^{2} \) |
$1.52431$ |
$(-a+2), (2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$1$ |
$17.33524395$ |
0.945715090 |
\( -\frac{53200}{3} a + 58128 \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 25 a - 69\) , \( -81 a + 226\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(25a-69\right){x}-81a+226$ |
| 192.1-i4 |
192.1-i |
$4$ |
$4$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
192.1 |
\( 2^{6} \cdot 3 \) |
\( 2^{20} \cdot 3^{4} \) |
$1.52431$ |
$(-a+2), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$4.333810989$ |
0.945715090 |
\( \frac{121322980}{9} a + \frac{217342184}{9} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 45 a - 129\) , \( 135 a - 378\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(45a-129\right){x}+135a-378$ |
| 192.1-j1 |
192.1-j |
$6$ |
$8$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
192.1 |
\( 2^{6} \cdot 3 \) |
\( 2^{22} \cdot 3^{16} \) |
$1.52431$ |
$(-a+2), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$6.551017245$ |
$1.162639934$ |
1.662050944 |
\( \frac{207646}{6561} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( 16\) , \( -180\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+16{x}-180$ |
| 192.1-j2 |
192.1-j |
$6$ |
$8$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
192.1 |
\( 2^{6} \cdot 3 \) |
\( 2^{8} \cdot 3^{2} \) |
$1.52431$ |
$(-a+2), (2)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.818877155$ |
$18.60223895$ |
1.662050944 |
\( \frac{2048}{3} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( 1\) , \( 0\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+{x}$ |
| 192.1-j3 |
192.1-j |
$6$ |
$8$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
192.1 |
\( 2^{6} \cdot 3 \) |
\( 2^{16} \cdot 3^{4} \) |
$1.52431$ |
$(-a+2), (2)$ |
$1$ |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1.637754311$ |
$18.60223895$ |
1.662050944 |
\( \frac{35152}{9} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -4\) , \( 4\bigr] \) |
${y}^2={x}^{3}-{x}^{2}-4{x}+4$ |
| 192.1-j4 |
192.1-j |
$6$ |
$8$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
192.1 |
\( 2^{6} \cdot 3 \) |
\( 2^{20} \cdot 3^{8} \) |
$1.52431$ |
$(-a+2), (2)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$3.275508622$ |
$4.650559737$ |
1.662050944 |
\( \frac{1556068}{81} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -24\) , \( -36\bigr] \) |
${y}^2={x}^{3}-{x}^{2}-24{x}-36$ |
| 192.1-j5 |
192.1-j |
$6$ |
$8$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
192.1 |
\( 2^{6} \cdot 3 \) |
\( 2^{20} \cdot 3^{2} \) |
$1.52431$ |
$(-a+2), (2)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.818877155$ |
$18.60223895$ |
1.662050944 |
\( \frac{28756228}{3} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -64\) , \( 220\bigr] \) |
${y}^2={x}^{3}-{x}^{2}-64{x}+220$ |
| 192.1-j6 |
192.1-j |
$6$ |
$8$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
192.1 |
\( 2^{6} \cdot 3 \) |
\( 2^{22} \cdot 3^{4} \) |
$1.52431$ |
$(-a+2), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$6.551017245$ |
$1.162639934$ |
1.662050944 |
\( \frac{3065617154}{9} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -384\) , \( -2772\bigr] \) |
${y}^2={x}^{3}-{x}^{2}-384{x}-2772$ |
| 192.1-k1 |
192.1-k |
$4$ |
$4$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
192.1 |
\( 2^{6} \cdot 3 \) |
\( - 2^{8} \cdot 3 \) |
$1.52431$ |
$(-a+2), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.852762531$ |
$13.64169646$ |
2.538556564 |
\( -\frac{4864}{3} a + \frac{13568}{3} \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( 1\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+{x}$ |
| 192.1-k2 |
192.1-k |
$4$ |
$4$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
192.1 |
\( 2^{6} \cdot 3 \) |
\( 2^{20} \cdot 3^{4} \) |
$1.52431$ |
$(-a+2), (2)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.852762531$ |
$13.64169646$ |
2.538556564 |
\( -\frac{121322980}{9} a + \frac{112888388}{3} \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( 20 a - 64\) , \( -108 a + 300\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(20a-64\right){x}-108a+300$ |
| 192.1-k3 |
192.1-k |
$4$ |
$4$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
192.1 |
\( 2^{6} \cdot 3 \) |
\( 2^{16} \cdot 3^{2} \) |
$1.52431$ |
$(-a+2), (2)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$1.705525063$ |
$13.64169646$ |
2.538556564 |
\( \frac{53200}{3} a + \frac{121184}{3} \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( -4\) , \( -4 a + 4\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}-4{x}-4a+4$ |
| 192.1-k4 |
192.1-k |
$4$ |
$4$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
192.1 |
\( 2^{6} \cdot 3 \) |
\( - 2^{20} \cdot 3 \) |
$1.52431$ |
$(-a+2), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$3.411050126$ |
$3.410424115$ |
2.538556564 |
\( \frac{5202690124}{3} a + \frac{9319516204}{3} \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( -20 a - 24\) , \( -76 a - 116\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(-20a-24\right){x}-76a-116$ |
| 192.1-l1 |
192.1-l |
$2$ |
$2$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
192.1 |
\( 2^{6} \cdot 3 \) |
\( - 2^{8} \cdot 3 \) |
$1.52431$ |
$(-a+2), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.393259272$ |
$22.72318029$ |
1.950017184 |
\( \frac{256}{3} a + \frac{4864}{3} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -a + 1\) , \( 1\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(-a+1\right){x}+1$ |
| 192.1-l2 |
192.1-l |
$2$ |
$2$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
192.1 |
\( 2^{6} \cdot 3 \) |
\( 2^{16} \cdot 3^{2} \) |
$1.52431$ |
$(-a+2), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.196629636$ |
$22.72318029$ |
1.950017184 |
\( \frac{77872}{3} a + \frac{145568}{3} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -6 a - 9\) , \( 15 a + 27\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(-6a-9\right){x}+15a+27$ |
| 192.1-m1 |
192.1-m |
$2$ |
$2$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
192.1 |
\( 2^{6} \cdot 3 \) |
\( - 2^{8} \cdot 3^{7} \) |
$1.52431$ |
$(-a+2), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \cdot 7 \) |
$0.146347611$ |
$9.659230135$ |
2.159317701 |
\( -\frac{25019564800}{81} a + \frac{69836807168}{81} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( a - 5\) , \( -48 a - 81\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+\left(a-5\right){x}-48a-81$ |
| 192.1-m2 |
192.1-m |
$2$ |
$2$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
192.1 |
\( 2^{6} \cdot 3 \) |
\( 2^{16} \cdot 3^{14} \) |
$1.52431$ |
$(-a+2), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \cdot 7 \) |
$0.073173805$ |
$4.829615067$ |
2.159317701 |
\( \frac{11855696}{2187} a + \frac{35052272}{729} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -119 a - 220\) , \( -1117 a - 1996\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+\left(-119a-220\right){x}-1117a-1996$ |
| 192.1-n1 |
192.1-n |
$2$ |
$2$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
192.1 |
\( 2^{6} \cdot 3 \) |
\( 2^{16} \cdot 3^{14} \) |
$1.52431$ |
$(-a+2), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \cdot 7 \) |
$0.073173805$ |
$4.829615067$ |
2.159317701 |
\( -\frac{11855696}{2187} a + \frac{117012512}{2187} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( 119 a - 339\) , \( 1117 a - 3113\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+\left(119a-339\right){x}+1117a-3113$ |
| 192.1-n2 |
192.1-n |
$2$ |
$2$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
192.1 |
\( 2^{6} \cdot 3 \) |
\( - 2^{8} \cdot 3^{7} \) |
$1.52431$ |
$(-a+2), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \cdot 7 \) |
$0.146347611$ |
$9.659230135$ |
2.159317701 |
\( \frac{25019564800}{81} a + \frac{44817242368}{81} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -a - 4\) , \( 48 a - 129\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+\left(-a-4\right){x}+48a-129$ |
*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.
