| 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 |
| 1764.1-a1 |
1764.1-a |
$2$ |
$2$ |
\(\Q(\sqrt{53}) \) |
$2$ |
$[2, 0]$ |
1764.1 |
\( 2^{2} \cdot 3^{2} \cdot 7^{2} \) |
\( - 2^{4} \cdot 3^{4} \cdot 7^{5} \) |
$4.21601$ |
$(-a-2), (-a+3), (2), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.338549963$ |
$14.44384594$ |
2.686752586 |
\( -\frac{91622224}{21609} a + \frac{1517875393}{86436} \) |
\( \bigl[a + 1\) , \( -1\) , \( 1\) , \( 3 a + 10\) , \( 51 a + 160\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}-{x}^{2}+\left(3a+10\right){x}+51a+160$ |
| 1764.1-a2 |
1764.1-a |
$2$ |
$2$ |
\(\Q(\sqrt{53}) \) |
$2$ |
$[2, 0]$ |
1764.1 |
\( 2^{2} \cdot 3^{2} \cdot 7^{2} \) |
\( 2^{2} \cdot 3^{8} \cdot 7^{4} \) |
$4.21601$ |
$(-a-2), (-a+3), (2), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$0.169274981$ |
$14.44384594$ |
2.686752586 |
\( -\frac{70673424880}{567} a + \frac{4096513272853}{7938} \) |
\( \bigl[a + 1\) , \( -1\) , \( 1\) , \( -87 a - 280\) , \( 679 a + 2140\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}-{x}^{2}+\left(-87a-280\right){x}+679a+2140$ |
| 1764.1-b1 |
1764.1-b |
$2$ |
$2$ |
\(\Q(\sqrt{53}) \) |
$2$ |
$[2, 0]$ |
1764.1 |
\( 2^{2} \cdot 3^{2} \cdot 7^{2} \) |
\( - 2^{8} \cdot 3^{4} \cdot 7^{5} \) |
$4.21601$ |
$(-a-2), (-a+3), (2), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \cdot 3 \) |
$0.287189618$ |
$7.904092697$ |
3.741657855 |
\( \frac{2027999}{49392} a + \frac{91653739}{49392} \) |
\( \bigl[a\) , \( -a\) , \( 1\) , \( -12 a - 25\) , \( 11 a + 42\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}-a{x}^{2}+\left(-12a-25\right){x}+11a+42$ |
| 1764.1-b2 |
1764.1-b |
$2$ |
$2$ |
\(\Q(\sqrt{53}) \) |
$2$ |
$[2, 0]$ |
1764.1 |
\( 2^{2} \cdot 3^{2} \cdot 7^{2} \) |
\( 2^{4} \cdot 3^{8} \cdot 7^{7} \) |
$4.21601$ |
$(-a-2), (-a+3), (2), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{4} \cdot 3 \) |
$0.143594809$ |
$7.904092697$ |
3.741657855 |
\( \frac{6104872236083}{38118276} a + \frac{4808887949291}{9529569} \) |
\( \bigl[a\) , \( -a\) , \( 1\) , \( -132 a - 405\) , \( 1539 a + 4834\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}-a{x}^{2}+\left(-132a-405\right){x}+1539a+4834$ |
| 1764.1-c1 |
1764.1-c |
$6$ |
$8$ |
\(\Q(\sqrt{53}) \) |
$2$ |
$[2, 0]$ |
1764.1 |
\( 2^{2} \cdot 3^{2} \cdot 7^{2} \) |
\( 2^{16} \cdot 3^{4} \cdot 7^{2} \) |
$4.21601$ |
$(-a-2), (-a+3), (2), (3)$ |
0 |
$\Z/8\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$4$ |
\( 2^{4} \) |
$1$ |
$12.07873502$ |
1.659141855 |
\( -\frac{7189057}{16128} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -4\) , \( 5\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-4{x}+5$ |
| 1764.1-c2 |
1764.1-c |
$6$ |
$8$ |
\(\Q(\sqrt{53}) \) |
$2$ |
$[2, 0]$ |
1764.1 |
\( 2^{2} \cdot 3^{2} \cdot 7^{2} \) |
\( 2^{2} \cdot 3^{32} \cdot 7^{4} \) |
$4.21601$ |
$(-a-2), (-a+3), (2), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{6} \) |
$1$ |
$0.754920939$ |
1.659141855 |
\( \frac{6359387729183}{4218578658} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( 386\) , \( 1277\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}+386{x}+1277$ |
| 1764.1-c3 |
1764.1-c |
$6$ |
$8$ |
\(\Q(\sqrt{53}) \) |
$2$ |
$[2, 0]$ |
1764.1 |
\( 2^{2} \cdot 3^{2} \cdot 7^{2} \) |
\( 2^{4} \cdot 3^{16} \cdot 7^{8} \) |
$4.21601$ |
$(-a-2), (-a+3), (2), (3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{6} \) |
$1$ |
$3.019683757$ |
1.659141855 |
\( \frac{124475734657}{63011844} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -104\) , \( 101\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-104{x}+101$ |
| 1764.1-c4 |
1764.1-c |
$6$ |
$8$ |
\(\Q(\sqrt{53}) \) |
$2$ |
$[2, 0]$ |
1764.1 |
\( 2^{2} \cdot 3^{2} \cdot 7^{2} \) |
\( 2^{2} \cdot 3^{8} \cdot 7^{16} \) |
$4.21601$ |
$(-a-2), (-a+3), (2), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$4$ |
\( 2^{4} \) |
$1$ |
$0.754920939$ |
1.659141855 |
\( \frac{84448510979617}{933897762} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -914\) , \( -10915\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-914{x}-10915$ |
| 1764.1-c5 |
1764.1-c |
$6$ |
$8$ |
\(\Q(\sqrt{53}) \) |
$2$ |
$[2, 0]$ |
1764.1 |
\( 2^{2} \cdot 3^{2} \cdot 7^{2} \) |
\( 2^{8} \cdot 3^{8} \cdot 7^{4} \) |
$4.21601$ |
$(-a-2), (-a+3), (2), (3)$ |
0 |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{6} \) |
$1$ |
$12.07873502$ |
1.659141855 |
\( \frac{65597103937}{63504} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -84\) , \( 261\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-84{x}+261$ |
| 1764.1-c6 |
1764.1-c |
$6$ |
$8$ |
\(\Q(\sqrt{53}) \) |
$2$ |
$[2, 0]$ |
1764.1 |
\( 2^{2} \cdot 3^{2} \cdot 7^{2} \) |
\( 2^{4} \cdot 3^{4} \cdot 7^{2} \) |
$4.21601$ |
$(-a-2), (-a+3), (2), (3)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$4$ |
\( 2^{2} \) |
$1$ |
$12.07873502$ |
1.659141855 |
\( \frac{268498407453697}{252} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -1344\) , \( 18405\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-1344{x}+18405$ |
| 1764.1-d1 |
1764.1-d |
$2$ |
$2$ |
\(\Q(\sqrt{53}) \) |
$2$ |
$[2, 0]$ |
1764.1 |
\( 2^{2} \cdot 3^{2} \cdot 7^{2} \) |
\( 2^{12} \cdot 3^{2} \cdot 7^{4} \) |
$4.21601$ |
$(-a-2), (-a+3), (2), (3)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.962791028$ |
$8.267390006$ |
8.746866795 |
\( \frac{2758535}{168} a - \frac{638849177}{9408} \) |
\( \bigl[a + 1\) , \( -a + 1\) , \( 1\) , \( 2 a - 5\) , \( -a + 3\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(2a-5\right){x}-a+3$ |
| 1764.1-d2 |
1764.1-d |
$2$ |
$2$ |
\(\Q(\sqrt{53}) \) |
$2$ |
$[2, 0]$ |
1764.1 |
\( 2^{2} \cdot 3^{2} \cdot 7^{2} \) |
\( 2^{6} \cdot 3^{4} \cdot 7^{5} \) |
$4.21601$ |
$(-a-2), (-a+3), (2), (3)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.962791028$ |
$8.267390006$ |
8.746866795 |
\( -\frac{19062050559161}{9604} a + \frac{1420525285468939}{172872} \) |
\( \bigl[a + 1\) , \( -a + 1\) , \( 1\) , \( 42 a - 205\) , \( -273 a + 1027\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(42a-205\right){x}-273a+1027$ |
| 1764.1-e1 |
1764.1-e |
$2$ |
$2$ |
\(\Q(\sqrt{53}) \) |
$2$ |
$[2, 0]$ |
1764.1 |
\( 2^{2} \cdot 3^{2} \cdot 7^{2} \) |
\( - 2^{12} \cdot 3^{4} \cdot 7^{3} \) |
$4.21601$ |
$(-a-2), (-a+3), (2), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.947575064$ |
$9.725999907$ |
5.063723010 |
\( -\frac{21517469}{28224} a + \frac{43997491}{14112} \) |
\( \bigl[1\) , \( a + 1\) , \( 0\) , \( -7 a - 21\) , \( 151 a + 474\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-7a-21\right){x}+151a+474$ |
| 1764.1-e2 |
1764.1-e |
$2$ |
$2$ |
\(\Q(\sqrt{53}) \) |
$2$ |
$[2, 0]$ |
1764.1 |
\( 2^{2} \cdot 3^{2} \cdot 7^{2} \) |
\( 2^{6} \cdot 3^{8} \cdot 7^{6} \) |
$4.21601$ |
$(-a-2), (-a+3), (2), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$0.473787532$ |
$9.725999907$ |
5.063723010 |
\( \frac{37388356465}{1555848} a + \frac{136162407853}{1555848} \) |
\( \bigl[1\) , \( a + 1\) , \( 0\) , \( -287 a - 901\) , \( 4543 a + 14266\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-287a-901\right){x}+4543a+14266$ |
| 1764.1-f1 |
1764.1-f |
$2$ |
$2$ |
\(\Q(\sqrt{53}) \) |
$2$ |
$[2, 0]$ |
1764.1 |
\( 2^{2} \cdot 3^{2} \cdot 7^{2} \) |
\( 2^{4} \cdot 3^{2} \cdot 7^{4} \) |
$4.21601$ |
$(-a-2), (-a+3), (2), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \cdot 3 \) |
$0.536938799$ |
$22.57486383$ |
4.994974170 |
\( -\frac{97336677}{1372} a + \frac{1216052125}{4116} \) |
\( \bigl[a\) , \( a + 1\) , \( a + 1\) , \( 7 a - 11\) , \( -5 a + 42\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(7a-11\right){x}-5a+42$ |
| 1764.1-f2 |
1764.1-f |
$2$ |
$2$ |
\(\Q(\sqrt{53}) \) |
$2$ |
$[2, 0]$ |
1764.1 |
\( 2^{2} \cdot 3^{2} \cdot 7^{2} \) |
\( 2^{2} \cdot 3^{4} \cdot 7^{8} \) |
$4.21601$ |
$(-a-2), (-a+3), (2), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \cdot 3 \) |
$0.268469399$ |
$11.28743191$ |
4.994974170 |
\( \frac{9779590643}{235298} a + \frac{140073814519}{1058841} \) |
\( \bigl[a\) , \( a + 1\) , \( a + 1\) , \( 7 a - 21\) , \( -a + 8\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(7a-21\right){x}-a+8$ |
| 1764.1-g1 |
1764.1-g |
$2$ |
$2$ |
\(\Q(\sqrt{53}) \) |
$2$ |
$[2, 0]$ |
1764.1 |
\( 2^{2} \cdot 3^{2} \cdot 7^{2} \) |
\( - 2^{4} \cdot 3^{10} \cdot 7^{17} \) |
$4.21601$ |
$(-a-2), (-a+3), (2), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \cdot 5 \) |
$1$ |
$1.391806930$ |
0.955896924 |
\( -\frac{166704776095313452543}{13453731159372} a + \frac{344964795939153500633}{6726865579686} \) |
\( \bigl[a\) , \( 0\) , \( 1\) , \( 5984 a - 25461\) , \( -486338 a + 2019807\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+\left(5984a-25461\right){x}-486338a+2019807$ |
| 1764.1-g2 |
1764.1-g |
$2$ |
$2$ |
\(\Q(\sqrt{53}) \) |
$2$ |
$[2, 0]$ |
1764.1 |
\( 2^{2} \cdot 3^{2} \cdot 7^{2} \) |
\( 2^{2} \cdot 3^{20} \cdot 7^{16} \) |
$4.21601$ |
$(-a-2), (-a+3), (2), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \cdot 5 \) |
$1$ |
$0.695903465$ |
0.955896924 |
\( \frac{1547065413108055008433}{33359761956402} a + \frac{4858212730393530287365}{33359761956402} \) |
\( \bigl[a\) , \( 0\) , \( 1\) , \( 4694 a - 30631\) , \( -400390 a + 2097959\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+\left(4694a-30631\right){x}-400390a+2097959$ |
| 1764.1-h1 |
1764.1-h |
$2$ |
$2$ |
\(\Q(\sqrt{53}) \) |
$2$ |
$[2, 0]$ |
1764.1 |
\( 2^{2} \cdot 3^{2} \cdot 7^{2} \) |
\( - 2^{20} \cdot 3^{2} \cdot 7^{13} \) |
$4.21601$ |
$(-a-2), (-a+3), (2), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \cdot 5 \) |
$1.970870035$ |
$2.046085904$ |
5.539160067 |
\( \frac{1540934276805361}{17709468672} a - \frac{3174321151420247}{8854734336} \) |
\( \bigl[a + 1\) , \( a + 1\) , \( a\) , \( -155 a - 787\) , \( -1360 a - 2199\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-155a-787\right){x}-1360a-2199$ |
| 1764.1-h2 |
1764.1-h |
$2$ |
$2$ |
\(\Q(\sqrt{53}) \) |
$2$ |
$[2, 0]$ |
1764.1 |
\( 2^{2} \cdot 3^{2} \cdot 7^{2} \) |
\( 2^{10} \cdot 3^{4} \cdot 7^{14} \) |
$4.21601$ |
$(-a-2), (-a+3), (2), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \cdot 5 \) |
$0.985435017$ |
$2.046085904$ |
5.539160067 |
\( -\frac{4469851863496388334143}{81352871712} a + \frac{18505449179239697900773}{81352871712} \) |
\( \bigl[a + 1\) , \( a + 1\) , \( a\) , \( -1435 a - 9267\) , \( 73328 a + 358153\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-1435a-9267\right){x}+73328a+358153$ |
| 1764.1-i1 |
1764.1-i |
$2$ |
$2$ |
\(\Q(\sqrt{53}) \) |
$2$ |
$[2, 0]$ |
1764.1 |
\( 2^{2} \cdot 3^{2} \cdot 7^{2} \) |
\( - 2^{4} \cdot 3^{4} \cdot 7^{5} \) |
$4.21601$ |
$(-a-2), (-a+3), (2), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.338549963$ |
$14.44384594$ |
2.686752586 |
\( \frac{91622224}{21609} a + \frac{127931833}{9604} \) |
\( \bigl[a\) , \( -a\) , \( 1\) , \( -4 a + 14\) , \( -51 a + 211\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}-a{x}^{2}+\left(-4a+14\right){x}-51a+211$ |
| 1764.1-i2 |
1764.1-i |
$2$ |
$2$ |
\(\Q(\sqrt{53}) \) |
$2$ |
$[2, 0]$ |
1764.1 |
\( 2^{2} \cdot 3^{2} \cdot 7^{2} \) |
\( 2^{2} \cdot 3^{8} \cdot 7^{4} \) |
$4.21601$ |
$(-a-2), (-a+3), (2), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$0.169274981$ |
$14.44384594$ |
2.686752586 |
\( \frac{70673424880}{567} a + \frac{3107085324533}{7938} \) |
\( \bigl[a\) , \( -a\) , \( 1\) , \( 86 a - 366\) , \( -679 a + 2819\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}-a{x}^{2}+\left(86a-366\right){x}-679a+2819$ |
| 1764.1-j1 |
1764.1-j |
$4$ |
$10$ |
\(\Q(\sqrt{53}) \) |
$2$ |
$[2, 0]$ |
1764.1 |
\( 2^{2} \cdot 3^{2} \cdot 7^{2} \) |
\( 2^{6} \cdot 3^{4} \cdot 7^{20} \) |
$4.21601$ |
$(-a-2), (-a+3), (2), (3)$ |
0 |
$\Z/10\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 5$ |
2B, 5B.1.1 |
$9$ |
\( 2^{3} \cdot 5^{2} \) |
$1$ |
$1.362921264$ |
3.369809402 |
\( \frac{144446945077709}{20338217928} \) |
\( \bigl[a\) , \( 1\) , \( 0\) , \( -7651 a - 24042\) , \( 591532 a + 1857453\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+{x}^{2}+\left(-7651a-24042\right){x}+591532a+1857453$ |
| 1764.1-j2 |
1764.1-j |
$4$ |
$10$ |
\(\Q(\sqrt{53}) \) |
$2$ |
$[2, 0]$ |
1764.1 |
\( 2^{2} \cdot 3^{2} \cdot 7^{2} \) |
\( 2^{60} \cdot 3^{10} \cdot 7^{2} \) |
$4.21601$ |
$(-a-2), (-a+3), (2), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 5$ |
2B, 5B.1.2 |
$225$ |
\( 2 \) |
$1$ |
$0.218067402$ |
3.369809402 |
\( \frac{145522445882936669}{1826434842624} \) |
\( \bigl[a\) , \( 1\) , \( 0\) , \( -76706 a - 241072\) , \( -21970160 a - 68988956\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+{x}^{2}+\left(-76706a-241072\right){x}-21970160a-68988956$ |
| 1764.1-j3 |
1764.1-j |
$4$ |
$10$ |
\(\Q(\sqrt{53}) \) |
$2$ |
$[2, 0]$ |
1764.1 |
\( 2^{2} \cdot 3^{2} \cdot 7^{2} \) |
\( 2^{12} \cdot 3^{2} \cdot 7^{10} \) |
$4.21601$ |
$(-a-2), (-a+3), (2), (3)$ |
0 |
$\Z/10\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 5$ |
2B, 5B.1.1 |
$9$ |
\( 2 \cdot 5^{2} \) |
$1$ |
$5.451685056$ |
3.369809402 |
\( \frac{129162875619149}{3226944} \) |
\( \bigl[a + 1\) , \( -a + 1\) , \( 0\) , \( 7371 a - 30533\) , \( -644684 a + 2669041\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(7371a-30533\right){x}-644684a+2669041$ |
| 1764.1-j4 |
1764.1-j |
$4$ |
$10$ |
\(\Q(\sqrt{53}) \) |
$2$ |
$[2, 0]$ |
1764.1 |
\( 2^{2} \cdot 3^{2} \cdot 7^{2} \) |
\( 2^{30} \cdot 3^{20} \cdot 7^{4} \) |
$4.21601$ |
$(-a-2), (-a+3), (2), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 5$ |
2B, 5B.1.2 |
$225$ |
\( 2^{3} \) |
$1$ |
$0.054516850$ |
3.369809402 |
\( \frac{590654974879986273629}{94810963968} \) |
\( \bigl[a + 1\) , \( -a + 1\) , \( 0\) , \( 1223586 a - 5069138\) , \( 1408580848 a - 5831683340\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(1223586a-5069138\right){x}+1408580848a-5831683340$ |
| 1764.1-k1 |
1764.1-k |
$2$ |
$2$ |
\(\Q(\sqrt{53}) \) |
$2$ |
$[2, 0]$ |
1764.1 |
\( 2^{2} \cdot 3^{2} \cdot 7^{2} \) |
\( - 2^{8} \cdot 3^{4} \cdot 7^{5} \) |
$4.21601$ |
$(-a-2), (-a+3), (2), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \cdot 3 \) |
$0.287189618$ |
$7.904092697$ |
3.741657855 |
\( -\frac{2027999}{49392} a + \frac{5204541}{2744} \) |
\( \bigl[a + 1\) , \( -1\) , \( 1\) , \( 11 a - 37\) , \( -11 a + 53\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}-{x}^{2}+\left(11a-37\right){x}-11a+53$ |
| 1764.1-k2 |
1764.1-k |
$2$ |
$2$ |
\(\Q(\sqrt{53}) \) |
$2$ |
$[2, 0]$ |
1764.1 |
\( 2^{2} \cdot 3^{2} \cdot 7^{2} \) |
\( 2^{4} \cdot 3^{8} \cdot 7^{7} \) |
$4.21601$ |
$(-a-2), (-a+3), (2), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{4} \cdot 3 \) |
$0.143594809$ |
$7.904092697$ |
3.741657855 |
\( -\frac{6104872236083}{38118276} a + \frac{25340424033247}{38118276} \) |
\( \bigl[a + 1\) , \( -1\) , \( 1\) , \( 131 a - 537\) , \( -1539 a + 6373\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}-{x}^{2}+\left(131a-537\right){x}-1539a+6373$ |
| 1764.1-l1 |
1764.1-l |
$2$ |
$2$ |
\(\Q(\sqrt{53}) \) |
$2$ |
$[2, 0]$ |
1764.1 |
\( 2^{2} \cdot 3^{2} \cdot 7^{2} \) |
\( 2^{2} \cdot 3^{4} \cdot 7^{8} \) |
$4.21601$ |
$(-a-2), (-a+3), (2), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \cdot 3 \) |
$0.268469399$ |
$11.28743191$ |
4.994974170 |
\( -\frac{9779590643}{235298} a + \frac{368163944825}{2117682} \) |
\( \bigl[a + 1\) , \( a - 1\) , \( 0\) , \( -8\) , \( -14 a - 20\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a-1\right){x}^{2}-8{x}-14a-20$ |
| 1764.1-l2 |
1764.1-l |
$2$ |
$2$ |
\(\Q(\sqrt{53}) \) |
$2$ |
$[2, 0]$ |
1764.1 |
\( 2^{2} \cdot 3^{2} \cdot 7^{2} \) |
\( 2^{4} \cdot 3^{2} \cdot 7^{4} \) |
$4.21601$ |
$(-a-2), (-a+3), (2), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \cdot 3 \) |
$0.536938799$ |
$22.57486383$ |
4.994974170 |
\( \frac{97336677}{1372} a + \frac{462021047}{2058} \) |
\( \bigl[a + 1\) , \( a - 1\) , \( 0\) , \( 2\) , \( 0\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a-1\right){x}^{2}+2{x}$ |
| 1764.1-m1 |
1764.1-m |
$2$ |
$2$ |
\(\Q(\sqrt{53}) \) |
$2$ |
$[2, 0]$ |
1764.1 |
\( 2^{2} \cdot 3^{2} \cdot 7^{2} \) |
\( - 2^{12} \cdot 3^{4} \cdot 7^{3} \) |
$4.21601$ |
$(-a-2), (-a+3), (2), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.947575064$ |
$9.725999907$ |
5.063723010 |
\( \frac{21517469}{28224} a + \frac{22159171}{9408} \) |
\( \bigl[1\) , \( -a - 1\) , \( 1\) , \( 9 a - 30\) , \( -159 a + 654\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(9a-30\right){x}-159a+654$ |
| 1764.1-m2 |
1764.1-m |
$2$ |
$2$ |
\(\Q(\sqrt{53}) \) |
$2$ |
$[2, 0]$ |
1764.1 |
\( 2^{2} \cdot 3^{2} \cdot 7^{2} \) |
\( 2^{6} \cdot 3^{8} \cdot 7^{6} \) |
$4.21601$ |
$(-a-2), (-a+3), (2), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$0.473787532$ |
$9.725999907$ |
5.063723010 |
\( -\frac{37388356465}{1555848} a + \frac{86775382159}{777924} \) |
\( \bigl[1\) , \( -a - 1\) , \( 1\) , \( 289 a - 1190\) , \( -4831 a + 19998\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(289a-1190\right){x}-4831a+19998$ |
| 1764.1-n1 |
1764.1-n |
$2$ |
$2$ |
\(\Q(\sqrt{53}) \) |
$2$ |
$[2, 0]$ |
1764.1 |
\( 2^{2} \cdot 3^{2} \cdot 7^{2} \) |
\( 2^{12} \cdot 3^{2} \cdot 7^{4} \) |
$4.21601$ |
$(-a-2), (-a+3), (2), (3)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.962791028$ |
$8.267390006$ |
8.746866795 |
\( -\frac{2758535}{168} a - \frac{484371217}{9408} \) |
\( \bigl[a\) , \( 1\) , \( 1\) , \( -3 a - 2\) , \( a + 2\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+{x}^{2}+\left(-3a-2\right){x}+a+2$ |
| 1764.1-n2 |
1764.1-n |
$2$ |
$2$ |
\(\Q(\sqrt{53}) \) |
$2$ |
$[2, 0]$ |
1764.1 |
\( 2^{2} \cdot 3^{2} \cdot 7^{2} \) |
\( 2^{6} \cdot 3^{4} \cdot 7^{5} \) |
$4.21601$ |
$(-a-2), (-a+3), (2), (3)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.962791028$ |
$8.267390006$ |
8.746866795 |
\( \frac{19062050559161}{9604} a + \frac{1077408375404041}{172872} \) |
\( \bigl[a\) , \( 1\) , \( 1\) , \( -43 a - 162\) , \( 273 a + 754\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+{x}^{2}+\left(-43a-162\right){x}+273a+754$ |
| 1764.1-o1 |
1764.1-o |
$2$ |
$2$ |
\(\Q(\sqrt{53}) \) |
$2$ |
$[2, 0]$ |
1764.1 |
\( 2^{2} \cdot 3^{2} \cdot 7^{2} \) |
\( - 2^{20} \cdot 3^{2} \cdot 7^{13} \) |
$4.21601$ |
$(-a-2), (-a+3), (2), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \cdot 5 \) |
$1.970870035$ |
$2.046085904$ |
5.539160067 |
\( -\frac{1540934276805361}{17709468672} a - \frac{1602569342011711}{5903156224} \) |
\( \bigl[a\) , \( a\) , \( a\) , \( 163 a - 957\) , \( 410 a - 539\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+a{x}^{2}+\left(163a-957\right){x}+410a-539$ |
| 1764.1-o2 |
1764.1-o |
$2$ |
$2$ |
\(\Q(\sqrt{53}) \) |
$2$ |
$[2, 0]$ |
1764.1 |
\( 2^{2} \cdot 3^{2} \cdot 7^{2} \) |
\( 2^{10} \cdot 3^{4} \cdot 7^{14} \) |
$4.21601$ |
$(-a-2), (-a+3), (2), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \cdot 5 \) |
$0.985435017$ |
$2.046085904$ |
5.539160067 |
\( \frac{4469851863496388334143}{81352871712} a + \frac{7017798657871654783315}{40676435856} \) |
\( \bigl[a\) , \( a\) , \( a\) , \( 1443 a - 10717\) , \( -84038 a + 460901\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+a{x}^{2}+\left(1443a-10717\right){x}-84038a+460901$ |
| 1764.1-p1 |
1764.1-p |
$2$ |
$2$ |
\(\Q(\sqrt{53}) \) |
$2$ |
$[2, 0]$ |
1764.1 |
\( 2^{2} \cdot 3^{2} \cdot 7^{2} \) |
\( 2^{2} \cdot 3^{20} \cdot 7^{16} \) |
$4.21601$ |
$(-a-2), (-a+3), (2), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \cdot 5 \) |
$1$ |
$0.695903465$ |
0.955896924 |
\( -\frac{1547065413108055008433}{33359761956402} a + \frac{3202639071750792647899}{16679880978201} \) |
\( \bigl[a + 1\) , \( -a\) , \( 1\) , \( -4695 a - 25937\) , \( 400390 a + 1697569\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}-a{x}^{2}+\left(-4695a-25937\right){x}+400390a+1697569$ |
| 1764.1-p2 |
1764.1-p |
$2$ |
$2$ |
\(\Q(\sqrt{53}) \) |
$2$ |
$[2, 0]$ |
1764.1 |
\( 2^{2} \cdot 3^{2} \cdot 7^{2} \) |
\( - 2^{4} \cdot 3^{10} \cdot 7^{17} \) |
$4.21601$ |
$(-a-2), (-a+3), (2), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \cdot 5 \) |
$1$ |
$1.391806930$ |
0.955896924 |
\( \frac{166704776095313452543}{13453731159372} a + \frac{58136090642554838747}{1494859017708} \) |
\( \bigl[a + 1\) , \( -a\) , \( 1\) , \( -5985 a - 19477\) , \( 486338 a + 1533469\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}-a{x}^{2}+\left(-5985a-19477\right){x}+486338a+1533469$ |
*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.
