| 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 |
| 28224.1-a1 |
28224.1-a |
$2$ |
$2$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
28224.1 |
\( 2^{6} \cdot 3^{2} \cdot 7^{2} \) |
\( 2^{12} \cdot 3^{10} \cdot 7^{12} \) |
$2.31645$ |
$(a+1), (3), (7)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \cdot 3 \cdot 5 \) |
$0.139949265$ |
$0.396863609$ |
1.666223116 |
\( \frac{15926924096}{28588707} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( 210\) , \( 1764\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+210{x}+1764$ |
| 28224.1-a2 |
28224.1-a |
$2$ |
$2$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
28224.1 |
\( 2^{6} \cdot 3^{2} \cdot 7^{2} \) |
\( 2^{12} \cdot 3^{20} \cdot 7^{6} \) |
$2.31645$ |
$(a+1), (3), (7)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \cdot 3 \cdot 5 \) |
$0.069974632$ |
$0.396863609$ |
1.666223116 |
\( \frac{92100460096}{20253807} \) |
\( \bigl[0\) , \( -i\) , \( 0\) , \( 376\) , \( -2338 i\bigr] \) |
${y}^2={x}^{3}-i{x}^{2}+376{x}-2338i$ |
| 28224.1-b1 |
28224.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
28224.1 |
\( 2^{6} \cdot 3^{2} \cdot 7^{2} \) |
\( 2^{6} \cdot 3^{2} \cdot 7^{8} \) |
$2.31645$ |
$(a+1), (3), (7)$ |
$2$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1.779146940$ |
$2.248837995$ |
4.001013241 |
\( \frac{830584}{7203} \) |
\( \bigl[i + 1\) , \( -i\) , \( i + 1\) , \( -i - 4\) , \( -11 i\bigr] \) |
${y}^2+\left(i+1\right){x}{y}+\left(i+1\right){y}={x}^{3}-i{x}^{2}+\left(-i-4\right){x}-11i$ |
| 28224.1-b2 |
28224.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
28224.1 |
\( 2^{6} \cdot 3^{2} \cdot 7^{2} \) |
\( 2^{12} \cdot 3^{8} \cdot 7^{2} \) |
$2.31645$ |
$(a+1), (3), (7)$ |
$2$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$0.444786735$ |
$2.248837995$ |
4.001013241 |
\( \frac{3241792}{567} \) |
\( \bigl[0\) , \( -i\) , \( 0\) , \( 12\) , \( -18 i\bigr] \) |
${y}^2={x}^{3}-i{x}^{2}+12{x}-18i$ |
| 28224.1-b3 |
28224.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
28224.1 |
\( 2^{6} \cdot 3^{2} \cdot 7^{2} \) |
\( 2^{12} \cdot 3^{4} \cdot 7^{4} \) |
$2.31645$ |
$(a+1), (3), (7)$ |
$2$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$0.444786735$ |
$2.248837995$ |
4.001013241 |
\( \frac{5088448}{441} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -14\) , \( -24\bigr] \) |
${y}^2={x}^{3}+{x}^{2}-14{x}-24$ |
| 28224.1-b4 |
28224.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
28224.1 |
\( 2^{6} \cdot 3^{2} \cdot 7^{2} \) |
\( 2^{6} \cdot 3^{2} \cdot 7^{2} \) |
$2.31645$ |
$(a+1), (3), (7)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1.779146940$ |
$2.248837995$ |
4.001013241 |
\( \frac{2438569736}{21} \) |
\( \bigl[i + 1\) , \( -i\) , \( 0\) , \( 56\) , \( -171 i\bigr] \) |
${y}^2+\left(i+1\right){x}{y}={x}^{3}-i{x}^{2}+56{x}-171i$ |
| 28224.1-c1 |
28224.1-c |
$2$ |
$2$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
28224.1 |
\( 2^{6} \cdot 3^{2} \cdot 7^{2} \) |
\( 2^{12} \cdot 3^{2} \cdot 7^{4} \) |
$2.31645$ |
$(a+1), (3), (7)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.614371403$ |
$3.047233106$ |
3.744265762 |
\( \frac{8000}{147} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( 2\) , \( -4\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+2{x}-4$ |
| 28224.1-c2 |
28224.1-c |
$2$ |
$2$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
28224.1 |
\( 2^{6} \cdot 3^{2} \cdot 7^{2} \) |
\( 2^{12} \cdot 3^{4} \cdot 7^{2} \) |
$2.31645$ |
$(a+1), (3), (7)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.307185701$ |
$3.047233106$ |
3.744265762 |
\( \frac{1000000}{63} \) |
\( \bigl[0\) , \( -i\) , \( 0\) , \( 8\) , \( 6 i\bigr] \) |
${y}^2={x}^{3}-i{x}^{2}+8{x}+6i$ |
| 28224.1-d1 |
28224.1-d |
$4$ |
$4$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
28224.1 |
\( 2^{6} \cdot 3^{2} \cdot 7^{2} \) |
\( 2^{6} \cdot 3^{16} \cdot 7^{2} \) |
$2.31645$ |
$(a+1), (3), (7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$1.640914345$ |
3.281828691 |
\( \frac{23393656}{45927} \) |
\( \bigl[i + 1\) , \( -i\) , \( i + 1\) , \( -i - 12\) , \( -23 i\bigr] \) |
${y}^2+\left(i+1\right){x}{y}+\left(i+1\right){y}={x}^{3}-i{x}^{2}+\left(-i-12\right){x}-23i$ |
| 28224.1-d2 |
28224.1-d |
$4$ |
$4$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
28224.1 |
\( 2^{6} \cdot 3^{2} \cdot 7^{2} \) |
\( 2^{12} \cdot 3^{8} \cdot 7^{4} \) |
$2.31645$ |
$(a+1), (3), (7)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$1$ |
$1.640914345$ |
3.281828691 |
\( \frac{19248832}{3969} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -22\) , \( -40\bigr] \) |
${y}^2={x}^{3}+{x}^{2}-22{x}-40$ |
| 28224.1-d3 |
28224.1-d |
$4$ |
$4$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
28224.1 |
\( 2^{6} \cdot 3^{2} \cdot 7^{2} \) |
\( 2^{6} \cdot 3^{4} \cdot 7^{8} \) |
$2.31645$ |
$(a+1), (3), (7)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$4$ |
\( 2^{3} \) |
$1$ |
$1.640914345$ |
3.281828691 |
\( \frac{306182024}{21609} \) |
\( \bigl[i + 1\) , \( -i\) , \( 0\) , \( 28\) , \( 49 i\bigr] \) |
${y}^2+\left(i+1\right){x}{y}={x}^{3}-i{x}^{2}+28{x}+49i$ |
| 28224.1-d4 |
28224.1-d |
$4$ |
$4$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
28224.1 |
\( 2^{6} \cdot 3^{2} \cdot 7^{2} \) |
\( 2^{12} \cdot 3^{4} \cdot 7^{2} \) |
$2.31645$ |
$(a+1), (3), (7)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$4$ |
\( 2^{3} \) |
$1$ |
$1.640914345$ |
3.281828691 |
\( \frac{1036433728}{63} \) |
\( \bigl[0\) , \( -i\) , \( 0\) , \( 84\) , \( 270 i\bigr] \) |
${y}^2={x}^{3}-i{x}^{2}+84{x}+270i$ |
*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.
