| 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 |
| 16562.2-a1 |
16562.2-a |
$1$ |
$1$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
16562.2 |
\( 2 \cdot 7^{2} \cdot 13^{2} \) |
\( 2^{14} \cdot 7^{2} \cdot 13^{10} \) |
$2.02743$ |
$(a+1), (-3a-2), (2a+3), (7)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
|
|
$1$ |
\( 2 \) |
$1$ |
$0.533192753$ |
1.066385507 |
\( -\frac{1207949625}{332678528} \) |
\( \bigl[i\) , \( 1\) , \( 0\) , \( -22\) , \( -884\bigr] \) |
${y}^2+i{x}{y}={x}^{3}+{x}^{2}-22{x}-884$ |
| 16562.2-b1 |
16562.2-b |
$1$ |
$1$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
16562.2 |
\( 2 \cdot 7^{2} \cdot 13^{2} \) |
\( 2^{22} \cdot 7^{14} \cdot 13^{2} \) |
$2.02743$ |
$(a+1), (-3a-2), (2a+3), (7)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
|
|
$1$ |
\( 2 \cdot 7 \) |
$1$ |
$0.175111233$ |
2.451557275 |
\( -\frac{10824513276632329}{21926008832} \) |
\( \bigl[i\) , \( 0\) , \( i\) , \( -4608\) , \( -120244\bigr] \) |
${y}^2+i{x}{y}+i{y}={x}^{3}-4608{x}-120244$ |
| 16562.2-c1 |
16562.2-c |
$1$ |
$1$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
16562.2 |
\( 2 \cdot 7^{2} \cdot 13^{2} \) |
\( 2^{2} \cdot 7^{6} \cdot 13^{2} \) |
$2.02743$ |
$(a+1), (-3a-2), (2a+3), (7)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
|
|
$1$ |
\( 2 \cdot 3 \) |
$0.080276374$ |
$3.051746300$ |
2.939797548 |
\( \frac{4019679}{8918} \) |
\( \bigl[i\) , \( 1\) , \( i\) , \( 4\) , \( 5\bigr] \) |
${y}^2+i{x}{y}+i{y}={x}^{3}+{x}^{2}+4{x}+5$ |
| 16562.2-d1 |
16562.2-d |
$3$ |
$9$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
16562.2 |
\( 2 \cdot 7^{2} \cdot 13^{2} \) |
\( 2^{2} \cdot 7^{2} \cdot 13^{2} \) |
$2.02743$ |
$(a+1), (-3a-2), (2a+3), (7)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3$ |
3B.1.2 |
$9$ |
\( 2 \) |
$0.486052662$ |
$0.256426207$ |
4.486919069 |
\( -\frac{424962187484640625}{182} \) |
\( \bigl[i\) , \( 0\) , \( 0\) , \( -15663\) , \( 755809\bigr] \) |
${y}^2+i{x}{y}={x}^{3}-15663{x}+755809$ |
| 16562.2-d2 |
16562.2-d |
$3$ |
$9$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
16562.2 |
\( 2 \cdot 7^{2} \cdot 13^{2} \) |
\( 2^{6} \cdot 7^{6} \cdot 13^{6} \) |
$2.02743$ |
$(a+1), (-3a-2), (2a+3), (7)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3$ |
3Cs.1.1 |
$1$ |
\( 2 \cdot 3^{4} \) |
$0.162017554$ |
$0.769278622$ |
4.486919069 |
\( -\frac{795309684625}{6028568} \) |
\( \bigl[i\) , \( 0\) , \( 0\) , \( -193\) , \( 1055\bigr] \) |
${y}^2+i{x}{y}={x}^{3}-193{x}+1055$ |
| 16562.2-d3 |
16562.2-d |
$3$ |
$9$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
16562.2 |
\( 2 \cdot 7^{2} \cdot 13^{2} \) |
\( 2^{18} \cdot 7^{2} \cdot 13^{2} \) |
$2.02743$ |
$(a+1), (-3a-2), (2a+3), (7)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3$ |
3B.1.1 |
$1$ |
\( 2 \cdot 3^{2} \) |
$0.486052662$ |
$2.307835866$ |
4.486919069 |
\( \frac{37595375}{46592} \) |
\( \bigl[i\) , \( 0\) , \( 0\) , \( 7\) , \( 7\bigr] \) |
${y}^2+i{x}{y}={x}^{3}+7{x}+7$ |
| 16562.2-e1 |
16562.2-e |
$4$ |
$4$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
16562.2 |
\( 2 \cdot 7^{2} \cdot 13^{2} \) |
\( 2^{40} \cdot 7^{6} \cdot 13^{4} \) |
$2.02743$ |
$(a+1), (-3a-2), (2a+3), (7)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{5} \cdot 3 \cdot 5 \) |
$0.397337202$ |
$0.220089901$ |
5.246994338 |
\( \frac{71903073502287}{60782804992} \) |
\( \bigl[i\) , \( 1\) , \( i\) , \( 867\) , \( -6445\bigr] \) |
${y}^2+i{x}{y}+i{y}={x}^{3}+{x}^{2}+867{x}-6445$ |
| 16562.2-e2 |
16562.2-e |
$4$ |
$4$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
16562.2 |
\( 2 \cdot 7^{2} \cdot 13^{2} \) |
\( 2^{20} \cdot 7^{12} \cdot 13^{8} \) |
$2.02743$ |
$(a+1), (-3a-2), (2a+3), (7)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \cdot 3 \cdot 5 \) |
$0.794674404$ |
$0.110044950$ |
5.246994338 |
\( \frac{8511781274893233}{3440817243136} \) |
\( \bigl[i\) , \( 1\) , \( i\) , \( -4253\) , \( -59693\bigr] \) |
${y}^2+i{x}{y}+i{y}={x}^{3}+{x}^{2}-4253{x}-59693$ |
| 16562.2-e3 |
16562.2-e |
$4$ |
$4$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
16562.2 |
\( 2 \cdot 7^{2} \cdot 13^{2} \) |
\( 2^{10} \cdot 7^{24} \cdot 13^{4} \) |
$2.02743$ |
$(a+1), (-3a-2), (2a+3), (7)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{5} \cdot 3 \cdot 5 \) |
$1.589348808$ |
$0.055022475$ |
5.246994338 |
\( \frac{3389174547561866673}{74853681183008} \) |
\( \bigl[i\) , \( 1\) , \( i\) , \( -31293\) , \( 2081875\bigr] \) |
${y}^2+i{x}{y}+i{y}={x}^{3}+{x}^{2}-31293{x}+2081875$ |
| 16562.2-e4 |
16562.2-e |
$4$ |
$4$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
16562.2 |
\( 2 \cdot 7^{2} \cdot 13^{2} \) |
\( 2^{10} \cdot 7^{6} \cdot 13^{16} \) |
$2.02743$ |
$(a+1), (-3a-2), (2a+3), (7)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \cdot 3 \cdot 5 \) |
$1.589348808$ |
$0.055022475$ |
5.246994338 |
\( \frac{22868021811807457713}{8953460393696} \) |
\( \bigl[i\) , \( 1\) , \( i\) , \( -59133\) , \( -5547693\bigr] \) |
${y}^2+i{x}{y}+i{y}={x}^{3}+{x}^{2}-59133{x}-5547693$ |
*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.
