| 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 |
| 28322.2-a1 |
28322.2-a |
$2$ |
$2$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
28322.2 |
\( 2 \cdot 7^{2} \cdot 17^{2} \) |
\( 2^{4} \cdot 7^{2} \cdot 17^{2} \) |
$2.31846$ |
$(a+1), (a+4), (a-4), (7)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.295638994$ |
$4.931797341$ |
2.916063213 |
\( \frac{658503}{476} \) |
\( \bigl[i\) , \( 1\) , \( 0\) , \( 2\) , \( 0\bigr] \) |
${y}^2+i{x}{y}={x}^{3}+{x}^{2}+2{x}$ |
| 28322.2-a2 |
28322.2-a |
$2$ |
$2$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
28322.2 |
\( 2 \cdot 7^{2} \cdot 17^{2} \) |
\( 2^{2} \cdot 7^{4} \cdot 17^{4} \) |
$2.31846$ |
$(a+1), (a+4), (a-4), (7)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$0.073909748$ |
$2.465898670$ |
2.916063213 |
\( \frac{60698457}{28322} \) |
\( \bigl[i\) , \( 1\) , \( 0\) , \( -8\) , \( -6\bigr] \) |
${y}^2+i{x}{y}={x}^{3}+{x}^{2}-8{x}-6$ |
| 28322.2-b1 |
28322.2-b |
$2$ |
$2$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
28322.2 |
\( 2 \cdot 7^{2} \cdot 17^{2} \) |
\( 2^{20} \cdot 7^{2} \cdot 17^{4} \) |
$2.31846$ |
$(a+1), (a+4), (a-4), (7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$1.218326690$ |
2.436653380 |
\( \frac{3449795831}{2071552} \) |
\( \bigl[i\) , \( -1\) , \( 0\) , \( 32\) , \( 0\bigr] \) |
${y}^2+i{x}{y}={x}^{3}-{x}^{2}+32{x}$ |
| 28322.2-b2 |
28322.2-b |
$2$ |
$2$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
28322.2 |
\( 2 \cdot 7^{2} \cdot 17^{2} \) |
\( 2^{10} \cdot 7^{4} \cdot 17^{8} \) |
$2.31846$ |
$(a+1), (a+4), (a-4), (7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$0.609163345$ |
2.436653380 |
\( \frac{234770924809}{130960928} \) |
\( \bigl[i\) , \( -1\) , \( 0\) , \( -128\) , \( 160\bigr] \) |
${y}^2+i{x}{y}={x}^{3}-{x}^{2}-128{x}+160$ |
| 28322.2-c1 |
28322.2-c |
$2$ |
$2$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
28322.2 |
\( 2 \cdot 7^{2} \cdot 17^{2} \) |
\( 2^{28} \cdot 7^{4} \cdot 17^{2} \) |
$2.31846$ |
$(a+1), (a+4), (a-4), (7)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \cdot 7 \) |
$0.106740737$ |
$0.888923806$ |
2.656762721 |
\( \frac{23912763841}{13647872} \) |
\( \bigl[i\) , \( 0\) , \( 0\) , \( -60\) , \( -16\bigr] \) |
${y}^2+i{x}{y}={x}^{3}-60{x}-16$ |
| 28322.2-c2 |
28322.2-c |
$2$ |
$2$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
28322.2 |
\( 2 \cdot 7^{2} \cdot 17^{2} \) |
\( 2^{14} \cdot 7^{8} \cdot 17^{4} \) |
$2.31846$ |
$(a+1), (a+4), (a-4), (7)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{5} \cdot 7 \) |
$0.053370368$ |
$0.444461903$ |
2.656762721 |
\( \frac{37936442980801}{88817792} \) |
\( \bigl[i\) , \( 0\) , \( 0\) , \( -700\) , \( -7056\bigr] \) |
${y}^2+i{x}{y}={x}^{3}-700{x}-7056$ |
| 28322.2-d1 |
28322.2-d |
$2$ |
$2$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
28322.2 |
\( 2 \cdot 7^{2} \cdot 17^{2} \) |
\( 2^{13} \cdot 7^{2} \cdot 17^{12} \) |
$2.31846$ |
$(a+1), (a+4), (a-4), (7)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \cdot 5 \cdot 13 \) |
$0.193578519$ |
$0.195268638$ |
4.913975804 |
\( \frac{236075253124625298367}{1806330534802304} a - \frac{456074453096252547169}{1806330534802304} \) |
\( \bigl[1\) , \( i + 1\) , \( i + 1\) , \( -2474 i + 2332\) , \( 25970 i + 73686\bigr] \) |
${y}^2+{x}{y}+\left(i+1\right){y}={x}^{3}+\left(i+1\right){x}^{2}+\left(-2474i+2332\right){x}+25970i+73686$ |
| 28322.2-d2 |
28322.2-d |
$2$ |
$2$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
28322.2 |
\( 2 \cdot 7^{2} \cdot 17^{2} \) |
\( 2^{26} \cdot 7^{4} \cdot 17^{6} \) |
$2.31846$ |
$(a+1), (a+4), (a-4), (7)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \cdot 5 \cdot 13 \) |
$0.096789259$ |
$0.390537276$ |
4.913975804 |
\( \frac{74231456780721}{569941958656} a + \frac{2255357609047}{2544383744} \) |
\( \bigl[i\) , \( -i - 1\) , \( i + 1\) , \( -234 i + 93\) , \( -1331 i - 662\bigr] \) |
${y}^2+i{x}{y}+\left(i+1\right){y}={x}^{3}+\left(-i-1\right){x}^{2}+\left(-234i+93\right){x}-1331i-662$ |
| 28322.2-e1 |
28322.2-e |
$2$ |
$2$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
28322.2 |
\( 2 \cdot 7^{2} \cdot 17^{2} \) |
\( 2^{13} \cdot 7^{2} \cdot 17^{12} \) |
$2.31846$ |
$(a+1), (a+4), (a-4), (7)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \cdot 5 \cdot 13 \) |
$0.193578519$ |
$0.195268638$ |
4.913975804 |
\( -\frac{236075253124625298367}{1806330534802304} a - \frac{456074453096252547169}{1806330534802304} \) |
\( \bigl[1\) , \( -i + 1\) , \( i + 1\) , \( 2473 i + 2332\) , \( -25971 i + 73686\bigr] \) |
${y}^2+{x}{y}+\left(i+1\right){y}={x}^{3}+\left(-i+1\right){x}^{2}+\left(2473i+2332\right){x}-25971i+73686$ |
| 28322.2-e2 |
28322.2-e |
$2$ |
$2$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
28322.2 |
\( 2 \cdot 7^{2} \cdot 17^{2} \) |
\( 2^{26} \cdot 7^{4} \cdot 17^{6} \) |
$2.31846$ |
$(a+1), (a+4), (a-4), (7)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \cdot 5 \cdot 13 \) |
$0.096789259$ |
$0.390537276$ |
4.913975804 |
\( -\frac{74231456780721}{569941958656} a + \frac{2255357609047}{2544383744} \) |
\( \bigl[i\) , \( i - 1\) , \( i + 1\) , \( 233 i + 93\) , \( 1330 i - 662\bigr] \) |
${y}^2+i{x}{y}+\left(i+1\right){y}={x}^{3}+\left(i-1\right){x}^{2}+\left(233i+93\right){x}+1330i-662$ |
| 28322.2-f1 |
28322.2-f |
$2$ |
$2$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
28322.2 |
\( 2 \cdot 7^{2} \cdot 17^{2} \) |
\( 2^{2} \cdot 7^{8} \cdot 17^{4} \) |
$2.31846$ |
$(a+1), (a+4), (a-4), (7)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$0.248073574$ |
$1.301095723$ |
5.164279471 |
\( \frac{2433138625}{1387778} \) |
\( \bigl[i\) , \( -1\) , \( i\) , \( -27\) , \( 5\bigr] \) |
${y}^2+i{x}{y}+i{y}={x}^{3}-{x}^{2}-27{x}+5$ |
| 28322.2-f2 |
28322.2-f |
$2$ |
$2$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
28322.2 |
\( 2 \cdot 7^{2} \cdot 17^{2} \) |
\( 2^{4} \cdot 7^{4} \cdot 17^{2} \) |
$2.31846$ |
$(a+1), (a+4), (a-4), (7)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.496147148$ |
$2.602191447$ |
5.164279471 |
\( \frac{647214625}{3332} \) |
\( \bigl[i\) , \( -1\) , \( i\) , \( -17\) , \( 37\bigr] \) |
${y}^2+i{x}{y}+i{y}={x}^{3}-{x}^{2}-17{x}+37$ |
| 28322.2-g1 |
28322.2-g |
$4$ |
$4$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
28322.2 |
\( 2 \cdot 7^{2} \cdot 17^{2} \) |
\( 2^{2} \cdot 7^{16} \cdot 17^{2} \) |
$2.31846$ |
$(a+1), (a+4), (a-4), (7)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1.352861604$ |
$0.572204849$ |
6.192911767 |
\( \frac{250404380127}{196003234} \) |
\( \bigl[i\) , \( 1\) , \( i\) , \( 132\) , \( 377\bigr] \) |
${y}^2+i{x}{y}+i{y}={x}^{3}+{x}^{2}+132{x}+377$ |
| 28322.2-g2 |
28322.2-g |
$4$ |
$4$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
28322.2 |
\( 2 \cdot 7^{2} \cdot 17^{2} \) |
\( 2^{4} \cdot 7^{8} \cdot 17^{4} \) |
$2.31846$ |
$(a+1), (a+4), (a-4), (7)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{6} \) |
$0.676430802$ |
$1.144409698$ |
6.192911767 |
\( \frac{6403769793}{2775556} \) |
\( \bigl[i\) , \( 1\) , \( i\) , \( -38\) , \( 37\bigr] \) |
${y}^2+i{x}{y}+i{y}={x}^{3}+{x}^{2}-38{x}+37$ |
| 28322.2-g3 |
28322.2-g |
$4$ |
$4$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
28322.2 |
\( 2 \cdot 7^{2} \cdot 17^{2} \) |
\( 2^{8} \cdot 7^{4} \cdot 17^{2} \) |
$2.31846$ |
$(a+1), (a+4), (a-4), (7)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1.352861604$ |
$2.288819397$ |
6.192911767 |
\( \frac{721734273}{13328} \) |
\( \bigl[i\) , \( 1\) , \( i\) , \( -18\) , \( -35\bigr] \) |
${y}^2+i{x}{y}+i{y}={x}^{3}+{x}^{2}-18{x}-35$ |
| 28322.2-g4 |
28322.2-g |
$4$ |
$4$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
28322.2 |
\( 2 \cdot 7^{2} \cdot 17^{2} \) |
\( 2^{2} \cdot 7^{4} \cdot 17^{8} \) |
$2.31846$ |
$(a+1), (a+4), (a-4), (7)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{6} \) |
$1.352861604$ |
$0.572204849$ |
6.192911767 |
\( \frac{16342588257633}{8185058} \) |
\( \bigl[i\) , \( 1\) , \( i\) , \( -528\) , \( 4545\bigr] \) |
${y}^2+i{x}{y}+i{y}={x}^{3}+{x}^{2}-528{x}+4545$ |
*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.
