| 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 |
| 19881.1-a1 |
19881.1-a |
$1$ |
$1$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
19881.1 |
\( 3^{2} \cdot 47^{2} \) |
\( 3^{14} \cdot 47^{2} \) |
$2.12216$ |
$(3), (47)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
|
|
$1$ |
\( 7 \) |
$0.034486775$ |
$1.994769578$ |
0.963104375 |
\( \frac{207474688}{102789} \) |
\( \bigl[0\) , \( -1\) , \( i\) , \( -12\) , \( -2\bigr] \) |
${y}^2+i{y}={x}^{3}-{x}^{2}-12{x}-2$ |
| 19881.1-b1 |
19881.1-b |
$2$ |
$2$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
19881.1 |
\( 3^{2} \cdot 47^{2} \) |
\( 3^{12} \cdot 47^{2} \) |
$2.12216$ |
$(3), (47)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \cdot 3 \) |
$0.332125862$ |
$2.351838609$ |
2.343319276 |
\( -\frac{57066625}{34263} \) |
\( \bigl[i\) , \( -1\) , \( i\) , \( -7\) , \( 16\bigr] \) |
${y}^2+i{x}{y}+i{y}={x}^{3}-{x}^{2}-7{x}+16$ |
| 19881.1-b2 |
19881.1-b |
$2$ |
$2$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
19881.1 |
\( 3^{2} \cdot 47^{2} \) |
\( 3^{6} \cdot 47^{4} \) |
$2.12216$ |
$(3), (47)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \cdot 3 \) |
$0.664251724$ |
$1.175919304$ |
2.343319276 |
\( \frac{323535264625}{59643} \) |
\( \bigl[i\) , \( -1\) , \( i\) , \( -142\) , \( 718\bigr] \) |
${y}^2+i{x}{y}+i{y}={x}^{3}-{x}^{2}-142{x}+718$ |
| 19881.1-c1 |
19881.1-c |
$4$ |
$4$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
19881.1 |
\( 3^{2} \cdot 47^{2} \) |
\( 3^{8} \cdot 47^{2} \) |
$2.12216$ |
$(3), (47)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1.604386698$ |
$3.509884905$ |
2.815606327 |
\( -\frac{912673}{3807} \) |
\( \bigl[i\) , \( 0\) , \( 0\) , \( -2\) , \( -3\bigr] \) |
${y}^2+i{x}{y}={x}^{3}-2{x}-3$ |
| 19881.1-c2 |
19881.1-c |
$4$ |
$4$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
19881.1 |
\( 3^{2} \cdot 47^{2} \) |
\( 3^{2} \cdot 47^{8} \) |
$2.12216$ |
$(3), (47)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$6.417546794$ |
$0.877471226$ |
2.815606327 |
\( \frac{26383748833}{14639043} \) |
\( \bigl[i\) , \( 0\) , \( 0\) , \( -62\) , \( -33\bigr] \) |
${y}^2+i{x}{y}={x}^{3}-62{x}-33$ |
| 19881.1-c3 |
19881.1-c |
$4$ |
$4$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
19881.1 |
\( 3^{2} \cdot 47^{2} \) |
\( 3^{4} \cdot 47^{4} \) |
$2.12216$ |
$(3), (47)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$3.208773397$ |
$1.754942452$ |
2.815606327 |
\( \frac{11497268593}{19881} \) |
\( \bigl[i\) , \( 0\) , \( 0\) , \( -47\) , \( -120\bigr] \) |
${y}^2+i{x}{y}={x}^{3}-47{x}-120$ |
| 19881.1-c4 |
19881.1-c |
$4$ |
$4$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
19881.1 |
\( 3^{2} \cdot 47^{2} \) |
\( 3^{2} \cdot 47^{2} \) |
$2.12216$ |
$(3), (47)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$6.417546794$ |
$0.877471226$ |
2.815606327 |
\( \frac{47034153084673}{141} \) |
\( \bigl[i\) , \( 0\) , \( 0\) , \( -752\) , \( -7875\bigr] \) |
${y}^2+i{x}{y}={x}^{3}-752{x}-7875$ |
| 19881.1-d1 |
19881.1-d |
$1$ |
$1$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
19881.1 |
\( 3^{2} \cdot 47^{2} \) |
\( 3^{2} \cdot 47^{2} \) |
$2.12216$ |
$(3), (47)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
|
|
$1$ |
\( 1 \) |
$0.198495236$ |
$6.007099121$ |
2.384761121 |
\( \frac{262144}{141} \) |
\( \bigl[0\) , \( 1\) , \( i\) , \( -1\) , \( 0\bigr] \) |
${y}^2+i{y}={x}^{3}+{x}^{2}-{x}$ |
| 19881.1-e1 |
19881.1-e |
$1$ |
$1$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
19881.1 |
\( 3^{2} \cdot 47^{2} \) |
\( 3^{2} \cdot 47^{2} \) |
$2.12216$ |
$(3), (47)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
|
|
$1$ |
\( 1 \) |
$0.980698281$ |
$2.912030795$ |
5.711647194 |
\( \frac{2019487744}{141} \) |
\( \bigl[0\) , \( -1\) , \( i\) , \( -26\) , \( 61\bigr] \) |
${y}^2+i{y}={x}^{3}-{x}^{2}-26{x}+61$ |
*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.
