| 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 |
$2$ |
$2$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
192.1 |
\( 2^{6} \cdot 3 \) |
\( - 2^{18} \cdot 3^{7} \) |
$2.51132$ |
$(a-4), (a+3), (4a+13)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \cdot 7 \) |
$1$ |
$2.366795926$ |
2.194428451 |
\( -\frac{3312124708}{81} a + \frac{14159196572}{81} \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( 63 a - 257\) , \( 580 a - 2492\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(63a-257\right){x}+580a-2492$ |
| 192.1-a2 |
192.1-a |
$2$ |
$2$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
192.1 |
\( 2^{6} \cdot 3 \) |
\( - 2^{15} \cdot 3^{14} \) |
$2.51132$ |
$(a-4), (a+3), (4a+13)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \cdot 7 \) |
$1$ |
$2.366795926$ |
2.194428451 |
\( \frac{5386438}{2187} a - \frac{19183426}{2187} \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( 10678 a - 45644\) , \( 1210209 a - 5173542\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(10678a-45644\right){x}+1210209a-5173542$ |
| 192.1-b1 |
192.1-b |
$2$ |
$2$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
192.1 |
\( 2^{6} \cdot 3 \) |
\( - 2^{15} \cdot 3^{14} \) |
$2.51132$ |
$(a-4), (a+3), (4a+13)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1.521708516$ |
$7.619769145$ |
3.071608443 |
\( -\frac{5386438}{2187} a - \frac{4598996}{729} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 108 a - 459\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(108a-459\right){x}$ |
| 192.1-b2 |
192.1-b |
$2$ |
$2$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
192.1 |
\( 2^{6} \cdot 3 \) |
\( - 2^{18} \cdot 3^{7} \) |
$2.51132$ |
$(a-4), (a+3), (4a+13)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.760854258$ |
$7.619769145$ |
3.071608443 |
\( \frac{3312124708}{81} a + \frac{10847071864}{81} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -75236 a + 321628\) , \( -2819016 a + 12051060\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+\left(-75236a+321628\right){x}-2819016a+12051060$ |
| 192.1-c1 |
192.1-c |
$2$ |
$2$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
192.1 |
\( 2^{6} \cdot 3 \) |
\( - 2^{15} \cdot 3^{6} \) |
$2.51132$ |
$(a-4), (a+3), (4a+13)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$7.166267540$ |
0.949195323 |
\( -\frac{1107766}{27} a + \frac{1566988}{9} \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( -1046 a - 3422\) , \( -56325 a - 184461\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(-1046a-3422\right){x}-56325a-184461$ |
| 192.1-c2 |
192.1-c |
$2$ |
$2$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
192.1 |
\( 2^{6} \cdot 3 \) |
\( - 2^{18} \cdot 3^{3} \) |
$2.51132$ |
$(a-4), (a+3), (4a+13)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$7.166267540$ |
0.949195323 |
\( \frac{4444996}{9} a + \frac{14556088}{9} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -7 a - 18\) , \( -12 a - 36\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(-7a-18\right){x}-12a-36$ |
| 192.1-d1 |
192.1-d |
$2$ |
$2$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
192.1 |
\( 2^{6} \cdot 3 \) |
\( - 2^{15} \cdot 3^{14} \) |
$2.51132$ |
$(a-4), (a+3), (4a+13)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \cdot 7 \) |
$1$ |
$2.366795926$ |
2.194428451 |
\( -\frac{5386438}{2187} a - \frac{4598996}{729} \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( -10678 a - 34966\) , \( -1210209 a - 3963333\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(-10678a-34966\right){x}-1210209a-3963333$ |
| 192.1-d2 |
192.1-d |
$2$ |
$2$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
192.1 |
\( 2^{6} \cdot 3 \) |
\( - 2^{18} \cdot 3^{7} \) |
$2.51132$ |
$(a-4), (a+3), (4a+13)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \cdot 7 \) |
$1$ |
$2.366795926$ |
2.194428451 |
\( \frac{3312124708}{81} a + \frac{10847071864}{81} \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( -63 a - 194\) , \( -580 a - 1912\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(-63a-194\right){x}-580a-1912$ |
| 192.1-e1 |
192.1-e |
$4$ |
$4$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
192.1 |
\( 2^{6} \cdot 3 \) |
\( - 2^{21} \cdot 3^{4} \) |
$2.51132$ |
$(a-4), (a+3), (4a+13)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$8.216077211$ |
$1.771343648$ |
3.855315319 |
\( -\frac{958972498}{9} a + \frac{1366509176}{3} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -19 a - 62\) , \( -484 a - 1596\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(-19a-62\right){x}-484a-1596$ |
| 192.1-e2 |
192.1-e |
$4$ |
$4$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
192.1 |
\( 2^{6} \cdot 3 \) |
\( - 2^{12} \cdot 3 \) |
$2.51132$ |
$(a-4), (a+3), (4a+13)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$2.054019302$ |
$14.17074918$ |
3.855315319 |
\( \frac{688}{3} a + \frac{2272}{3} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -4 a - 7\) , \( 4 a + 16\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(-4a-7\right){x}+4a+16$ |
| 192.1-e3 |
192.1-e |
$4$ |
$4$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
192.1 |
\( 2^{6} \cdot 3 \) |
\( 2^{18} \cdot 3^{2} \) |
$2.51132$ |
$(a-4), (a+3), (4a+13)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$4.108038605$ |
$7.085374592$ |
3.855315319 |
\( \frac{77836}{3} a + \frac{342248}{3} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -39 a - 122\) , \( -212 a - 692\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(-39a-122\right){x}-212a-692$ |
| 192.1-e4 |
192.1-e |
$4$ |
$4$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
192.1 |
\( 2^{6} \cdot 3 \) |
\( 2^{21} \cdot 3 \) |
$2.51132$ |
$(a-4), (a+3), (4a+13)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$8.216077211$ |
$3.542687296$ |
3.855315319 |
\( \frac{19982794694}{3} a + \frac{65442007544}{3} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -619 a - 2022\) , \( -15604 a - 51100\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(-619a-2022\right){x}-15604a-51100$ |
| 192.1-f1 |
192.1-f |
$2$ |
$2$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
192.1 |
\( 2^{6} \cdot 3 \) |
\( - 2^{18} \cdot 3^{3} \) |
$2.51132$ |
$(a-4), (a+3), (4a+13)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \cdot 3 \) |
$0.325874447$ |
$8.580802466$ |
4.444490997 |
\( -\frac{4444996}{9} a + \frac{19001084}{9} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -14100 a - 46176\) , \( -7551888 a - 24731808\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+\left(-14100a-46176\right){x}-7551888a-24731808$ |
| 192.1-f2 |
192.1-f |
$2$ |
$2$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
192.1 |
\( 2^{6} \cdot 3 \) |
\( - 2^{15} \cdot 3^{6} \) |
$2.51132$ |
$(a-4), (a+3), (4a+13)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \cdot 3 \) |
$0.651748895$ |
$8.580802466$ |
4.444490997 |
\( \frac{1107766}{27} a + \frac{3593198}{27} \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( -140 a - 455\) , \( -1554 a - 5088\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(-140a-455\right){x}-1554a-5088$ |
| 192.1-g1 |
192.1-g |
$6$ |
$8$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
192.1 |
\( 2^{6} \cdot 3 \) |
\( 2^{22} \cdot 3^{16} \) |
$2.51132$ |
$(a-4), (a+3), (4a+13)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$16$ |
\( 2 \) |
$1$ |
$1.162639934$ |
1.231963370 |
\( \frac{207646}{6561} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( 16\) , \( -180\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+16{x}-180$ |
| 192.1-g2 |
192.1-g |
$6$ |
$8$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
192.1 |
\( 2^{6} \cdot 3 \) |
\( 2^{8} \cdot 3^{2} \) |
$2.51132$ |
$(a-4), (a+3), (4a+13)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$18.60223895$ |
1.231963370 |
\( \frac{2048}{3} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( 1\) , \( 0\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+{x}$ |
| 192.1-g3 |
192.1-g |
$6$ |
$8$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
192.1 |
\( 2^{6} \cdot 3 \) |
\( 2^{16} \cdot 3^{4} \) |
$2.51132$ |
$(a-4), (a+3), (4a+13)$ |
0 |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$1$ |
$18.60223895$ |
1.231963370 |
\( \frac{35152}{9} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -4\) , \( 4\bigr] \) |
${y}^2={x}^{3}-{x}^{2}-4{x}+4$ |
| 192.1-g4 |
192.1-g |
$6$ |
$8$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
192.1 |
\( 2^{6} \cdot 3 \) |
\( 2^{20} \cdot 3^{8} \) |
$2.51132$ |
$(a-4), (a+3), (4a+13)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$4$ |
\( 2^{3} \) |
$1$ |
$4.650559737$ |
1.231963370 |
\( \frac{1556068}{81} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -24\) , \( -36\bigr] \) |
${y}^2={x}^{3}-{x}^{2}-24{x}-36$ |
| 192.1-g5 |
192.1-g |
$6$ |
$8$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
192.1 |
\( 2^{6} \cdot 3 \) |
\( 2^{20} \cdot 3^{2} \) |
$2.51132$ |
$(a-4), (a+3), (4a+13)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$18.60223895$ |
1.231963370 |
\( \frac{28756228}{3} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -64\) , \( 220\bigr] \) |
${y}^2={x}^{3}-{x}^{2}-64{x}+220$ |
| 192.1-g6 |
192.1-g |
$6$ |
$8$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
192.1 |
\( 2^{6} \cdot 3 \) |
\( 2^{22} \cdot 3^{4} \) |
$2.51132$ |
$(a-4), (a+3), (4a+13)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$16$ |
\( 2 \) |
$1$ |
$1.162639934$ |
1.231963370 |
\( \frac{3065617154}{9} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -384\) , \( -2772\bigr] \) |
${y}^2={x}^{3}-{x}^{2}-384{x}-2772$ |
| 192.1-h1 |
192.1-h |
$2$ |
$2$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
192.1 |
\( 2^{6} \cdot 3 \) |
\( - 2^{18} \cdot 3^{7} \) |
$2.51132$ |
$(a-4), (a+3), (4a+13)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.760854258$ |
$7.619769145$ |
3.071608443 |
\( -\frac{3312124708}{81} a + \frac{14159196572}{81} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( 75236 a + 246392\) , \( 2819016 a + 9232044\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+\left(75236a+246392\right){x}+2819016a+9232044$ |
| 192.1-h2 |
192.1-h |
$2$ |
$2$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
192.1 |
\( 2^{6} \cdot 3 \) |
\( - 2^{15} \cdot 3^{14} \) |
$2.51132$ |
$(a-4), (a+3), (4a+13)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1.521708516$ |
$7.619769145$ |
3.071608443 |
\( \frac{5386438}{2187} a - \frac{19183426}{2187} \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( -108 a - 351\) , \( 0\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(-108a-351\right){x}$ |
| 192.1-i1 |
192.1-i |
$2$ |
$2$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
192.1 |
\( 2^{6} \cdot 3 \) |
\( - 2^{18} \cdot 3^{3} \) |
$2.51132$ |
$(a-4), (a+3), (4a+13)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$7.166267540$ |
0.949195323 |
\( -\frac{4444996}{9} a + \frac{19001084}{9} \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( 7 a - 25\) , \( 12 a - 48\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(7a-25\right){x}+12a-48$ |
| 192.1-i2 |
192.1-i |
$2$ |
$2$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
192.1 |
\( 2^{6} \cdot 3 \) |
\( - 2^{15} \cdot 3^{6} \) |
$2.51132$ |
$(a-4), (a+3), (4a+13)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$7.166267540$ |
0.949195323 |
\( \frac{1107766}{27} a + \frac{3593198}{27} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 1046 a - 4468\) , \( 56325 a - 240786\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(1046a-4468\right){x}+56325a-240786$ |
| 192.1-j1 |
192.1-j |
$4$ |
$4$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
192.1 |
\( 2^{6} \cdot 3 \) |
\( - 2^{12} \cdot 3 \) |
$2.51132$ |
$(a-4), (a+3), (4a+13)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$2.054019302$ |
$14.17074918$ |
3.855315319 |
\( -\frac{688}{3} a + \frac{2960}{3} \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( 4 a - 11\) , \( -4 a + 20\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(4a-11\right){x}-4a+20$ |
| 192.1-j2 |
192.1-j |
$4$ |
$4$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
192.1 |
\( 2^{6} \cdot 3 \) |
\( 2^{21} \cdot 3 \) |
$2.51132$ |
$(a-4), (a+3), (4a+13)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$8.216077211$ |
$3.542687296$ |
3.855315319 |
\( -\frac{19982794694}{3} a + \frac{85424802238}{3} \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( 619 a - 2641\) , \( 15604 a - 66704\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(619a-2641\right){x}+15604a-66704$ |
| 192.1-j3 |
192.1-j |
$4$ |
$4$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
192.1 |
\( 2^{6} \cdot 3 \) |
\( 2^{18} \cdot 3^{2} \) |
$2.51132$ |
$(a-4), (a+3), (4a+13)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$4.108038605$ |
$7.085374592$ |
3.855315319 |
\( -\frac{77836}{3} a + 140028 \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( 39 a - 161\) , \( 212 a - 904\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(39a-161\right){x}+212a-904$ |
| 192.1-j4 |
192.1-j |
$4$ |
$4$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
192.1 |
\( 2^{6} \cdot 3 \) |
\( - 2^{21} \cdot 3^{4} \) |
$2.51132$ |
$(a-4), (a+3), (4a+13)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$8.216077211$ |
$1.771343648$ |
3.855315319 |
\( \frac{958972498}{9} a + \frac{3140555030}{9} \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( 19 a - 81\) , \( 484 a - 2080\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(19a-81\right){x}+484a-2080$ |
| 192.1-k1 |
192.1-k |
$4$ |
$4$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
192.1 |
\( 2^{6} \cdot 3 \) |
\( - 2^{12} \cdot 3 \) |
$2.51132$ |
$(a-4), (a+3), (4a+13)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$22.67129565$ |
3.002886467 |
\( -\frac{688}{3} a + \frac{2960}{3} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( 97 a + 318\) , \( 16754 a + 54868\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+\left(97a+318\right){x}+16754a+54868$ |
| 192.1-k2 |
192.1-k |
$4$ |
$4$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
192.1 |
\( 2^{6} \cdot 3 \) |
\( 2^{21} \cdot 3 \) |
$2.51132$ |
$(a-4), (a+3), (4a+13)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$4$ |
\( 2 \) |
$1$ |
$11.33564782$ |
3.002886467 |
\( -\frac{19982794694}{3} a + \frac{85424802238}{3} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -11088 a - 36312\) , \( -816304 a - 2673328\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+\left(-11088a-36312\right){x}-816304a-2673328$ |
| 192.1-k3 |
192.1-k |
$4$ |
$4$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
192.1 |
\( 2^{6} \cdot 3 \) |
\( 2^{18} \cdot 3^{2} \) |
$2.51132$ |
$(a-4), (a+3), (4a+13)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$1$ |
$22.67129565$ |
3.002886467 |
\( -\frac{77836}{3} a + 140028 \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -4468 a - 14632\) , \( 304848 a + 998352\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+\left(-4468a-14632\right){x}+304848a+998352$ |
| 192.1-k4 |
192.1-k |
$4$ |
$4$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
192.1 |
\( 2^{6} \cdot 3 \) |
\( - 2^{21} \cdot 3^{4} \) |
$2.51132$ |
$(a-4), (a+3), (4a+13)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$11.33564782$ |
3.002886467 |
\( \frac{958972498}{9} a + \frac{3140555030}{9} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -70888 a - 232152\) , \( 19937056 a + 65292208\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+\left(-70888a-232152\right){x}+19937056a+65292208$ |
| 192.1-l1 |
192.1-l |
$4$ |
$4$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
192.1 |
\( 2^{6} \cdot 3 \) |
\( - 2^{21} \cdot 3^{4} \) |
$2.51132$ |
$(a-4), (a+3), (4a+13)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$11.33564782$ |
3.002886467 |
\( -\frac{958972498}{9} a + \frac{1366509176}{3} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( 70888 a - 303040\) , \( -19937056 a + 85229264\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+\left(70888a-303040\right){x}-19937056a+85229264$ |
| 192.1-l2 |
192.1-l |
$4$ |
$4$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
192.1 |
\( 2^{6} \cdot 3 \) |
\( - 2^{12} \cdot 3 \) |
$2.51132$ |
$(a-4), (a+3), (4a+13)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$22.67129565$ |
3.002886467 |
\( \frac{688}{3} a + \frac{2272}{3} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -97 a + 415\) , \( -16754 a + 71622\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+\left(-97a+415\right){x}-16754a+71622$ |
| 192.1-l3 |
192.1-l |
$4$ |
$4$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
192.1 |
\( 2^{6} \cdot 3 \) |
\( 2^{18} \cdot 3^{2} \) |
$2.51132$ |
$(a-4), (a+3), (4a+13)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$1$ |
$22.67129565$ |
3.002886467 |
\( \frac{77836}{3} a + \frac{342248}{3} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( 4468 a - 19100\) , \( -304848 a + 1303200\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+\left(4468a-19100\right){x}-304848a+1303200$ |
| 192.1-l4 |
192.1-l |
$4$ |
$4$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
192.1 |
\( 2^{6} \cdot 3 \) |
\( 2^{21} \cdot 3 \) |
$2.51132$ |
$(a-4), (a+3), (4a+13)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$4$ |
\( 2 \) |
$1$ |
$11.33564782$ |
3.002886467 |
\( \frac{19982794694}{3} a + \frac{65442007544}{3} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( 11088 a - 47400\) , \( 816304 a - 3489632\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+\left(11088a-47400\right){x}+816304a-3489632$ |
| 192.1-m1 |
192.1-m |
$6$ |
$8$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
192.1 |
\( 2^{6} \cdot 3 \) |
\( 2^{22} \cdot 3^{16} \) |
$2.51132$ |
$(a-4), (a+3), (4a+13)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1.562595083$ |
$2.841754258$ |
4.705280649 |
\( \frac{207646}{6561} \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( 189253 a + 619794\) , \( 637681788 a + 2088355064\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(189253a+619794\right){x}+637681788a+2088355064$ |
| 192.1-m2 |
192.1-m |
$6$ |
$8$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
192.1 |
\( 2^{6} \cdot 3 \) |
\( 2^{8} \cdot 3^{2} \) |
$2.51132$ |
$(a-4), (a+3), (4a+13)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$3.125190167$ |
$11.36701703$ |
4.705280649 |
\( \frac{2048}{3} \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( 8053 a + 26379\) , \( -937017 a - 3068656\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(8053a+26379\right){x}-937017a-3068656$ |
| 192.1-m3 |
192.1-m |
$6$ |
$8$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
192.1 |
\( 2^{6} \cdot 3 \) |
\( 2^{16} \cdot 3^{4} \) |
$2.51132$ |
$(a-4), (a+3), (4a+13)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$1.562595083$ |
$11.36701703$ |
4.705280649 |
\( \frac{35152}{9} \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( -52347 a - 171426\) , \( -9515232 a - 31161600\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(-52347a-171426\right){x}-9515232a-31161600$ |
| 192.1-m4 |
192.1-m |
$6$ |
$8$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
192.1 |
\( 2^{6} \cdot 3 \) |
\( 2^{20} \cdot 3^{8} \) |
$2.51132$ |
$(a-4), (a+3), (4a+13)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$0.781297541$ |
$11.36701703$ |
4.705280649 |
\( \frac{1556068}{81} \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( -293947 a - 962646\) , \( 160466628 a + 525514920\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(-293947a-962646\right){x}+160466628a+525514920$ |
| 192.1-m5 |
192.1-m |
$6$ |
$8$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
192.1 |
\( 2^{6} \cdot 3 \) |
\( 2^{20} \cdot 3^{2} \) |
$2.51132$ |
$(a-4), (a+3), (4a+13)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$3.125190167$ |
$2.841754258$ |
4.705280649 |
\( \frac{28756228}{3} \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( -777147 a - 2545086\) , \( -725337972 a - 2375421816\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(-777147a-2545086\right){x}-725337972a-2375421816$ |
| 192.1-m6 |
192.1-m |
$6$ |
$8$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
192.1 |
\( 2^{6} \cdot 3 \) |
\( 2^{22} \cdot 3^{4} \) |
$2.51132$ |
$(a-4), (a+3), (4a+13)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1.562595083$ |
$11.36701703$ |
4.705280649 |
\( \frac{3065617154}{9} \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( -4642747 a - 15204606\) , \( 10574750028 a + 34631430936\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(-4642747a-15204606\right){x}+10574750028a+34631430936$ |
| 192.1-n1 |
192.1-n |
$2$ |
$2$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
192.1 |
\( 2^{6} \cdot 3 \) |
\( - 2^{15} \cdot 3^{6} \) |
$2.51132$ |
$(a-4), (a+3), (4a+13)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \cdot 3 \) |
$0.651748895$ |
$8.580802466$ |
4.444490997 |
\( -\frac{1107766}{27} a + \frac{1566988}{9} \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( 140 a - 595\) , \( 1554 a - 6642\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(140a-595\right){x}+1554a-6642$ |
| 192.1-n2 |
192.1-n |
$2$ |
$2$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
192.1 |
\( 2^{6} \cdot 3 \) |
\( - 2^{18} \cdot 3^{3} \) |
$2.51132$ |
$(a-4), (a+3), (4a+13)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \cdot 3 \) |
$0.325874447$ |
$8.580802466$ |
4.444490997 |
\( \frac{4444996}{9} a + \frac{14556088}{9} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( 14100 a - 60276\) , \( 7551888 a - 32283696\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+\left(14100a-60276\right){x}+7551888a-32283696$ |
*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.
