| 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 |
| 28322.1-a1 |
28322.1-a |
$6$ |
$18$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
28322.1 |
\( 2 \cdot 7^{2} \cdot 17^{2} \) |
\( 2^{36} \cdot 7^{2} \cdot 17^{6} \) |
$2.31846$ |
$(a+1), (a+4), (7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \cdot 3^{2} \) |
$1$ |
$0.212319842$ |
3.821757156 |
\( -\frac{548347731625}{1835008} \) |
\( \bigl[1\) , \( -i\) , \( 1\) , \( 1364 i + 2557\) , \( -45435 i + 41066\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-i{x}^{2}+\left(1364i+2557\right){x}-45435i+41066$ |
| 28322.1-a2 |
28322.1-a |
$6$ |
$18$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
28322.1 |
\( 2 \cdot 7^{2} \cdot 17^{2} \) |
\( 2^{4} \cdot 7^{2} \cdot 17^{6} \) |
$2.31846$ |
$(a+1), (a+4), (7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \) |
$1$ |
$1.910878578$ |
3.821757156 |
\( -\frac{15625}{28} \) |
\( \bigl[1\) , \( -i\) , \( 1\) , \( 4 i + 7\) , \( 13 i - 12\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-i{x}^{2}+\left(4i+7\right){x}+13i-12$ |
| 28322.1-a3 |
28322.1-a |
$6$ |
$18$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
28322.1 |
\( 2 \cdot 7^{2} \cdot 17^{2} \) |
\( 2^{12} \cdot 7^{6} \cdot 17^{6} \) |
$2.31846$ |
$(a+1), (a+4), (7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3Cs |
$1$ |
\( 2^{3} \cdot 3 \) |
$1$ |
$0.636959526$ |
3.821757156 |
\( \frac{9938375}{21952} \) |
\( \bigl[1\) , \( -i\) , \( 1\) , \( -36 i - 68\) , \( -299 i + 270\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-i{x}^{2}+\left(-36i-68\right){x}-299i+270$ |
| 28322.1-a4 |
28322.1-a |
$6$ |
$18$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
28322.1 |
\( 2 \cdot 7^{2} \cdot 17^{2} \) |
\( 2^{6} \cdot 7^{12} \cdot 17^{6} \) |
$2.31846$ |
$(a+1), (a+4), (7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3Cs |
$1$ |
\( 2^{4} \cdot 3 \) |
$1$ |
$0.318479763$ |
3.821757156 |
\( \frac{4956477625}{941192} \) |
\( \bigl[1\) , \( -i\) , \( 1\) , \( 284 i + 532\) , \( -3627 i + 3278\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-i{x}^{2}+\left(284i+532\right){x}-3627i+3278$ |
| 28322.1-a5 |
28322.1-a |
$6$ |
$18$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
28322.1 |
\( 2 \cdot 7^{2} \cdot 17^{2} \) |
\( 2^{2} \cdot 7^{4} \cdot 17^{6} \) |
$2.31846$ |
$(a+1), (a+4), (7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{4} \) |
$1$ |
$0.955439289$ |
3.821757156 |
\( \frac{128787625}{98} \) |
\( \bigl[1\) , \( -i\) , \( 1\) , \( 84 i + 157\) , \( 637 i - 576\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-i{x}^{2}+\left(84i+157\right){x}+637i-576$ |
| 28322.1-a6 |
28322.1-a |
$6$ |
$18$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
28322.1 |
\( 2 \cdot 7^{2} \cdot 17^{2} \) |
\( 2^{18} \cdot 7^{4} \cdot 17^{6} \) |
$2.31846$ |
$(a+1), (a+4), (7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{4} \cdot 3^{2} \) |
$1$ |
$0.106159921$ |
3.821757156 |
\( \frac{2251439055699625}{25088} \) |
\( \bigl[1\) , \( -i\) , \( 1\) , \( 21844 i + 40957\) , \( -2867579 i + 2591850\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-i{x}^{2}+\left(21844i+40957\right){x}-2867579i+2591850$ |
*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.
