| 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 |
| 2178.1-a1 |
2178.1-a |
$4$ |
$6$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
2178.1 |
\( 2 \cdot 3^{2} \cdot 11^{2} \) |
\( 2^{6} \cdot 3^{4} \cdot 11^{12} \) |
$1.22091$ |
$(a+1), (3), (11)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2^{3} \cdot 3 \) |
$0.183632440$ |
$0.623134288$ |
1.373132044 |
\( -\frac{7357983625}{127552392} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -41\) , \( -556\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-41{x}-556$ |
| 2178.1-a2 |
2178.1-a |
$4$ |
$6$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
2178.1 |
\( 2 \cdot 3^{2} \cdot 11^{2} \) |
\( 2^{2} \cdot 3^{12} \cdot 11^{4} \) |
$1.22091$ |
$(a+1), (3), (11)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{3} \cdot 3 \) |
$0.550897322$ |
$1.869402865$ |
1.373132044 |
\( \frac{9938375}{176418} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( 4\) , \( 20\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+4{x}+20$ |
| 2178.1-a3 |
2178.1-a |
$4$ |
$6$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
2178.1 |
\( 2 \cdot 3^{2} \cdot 11^{2} \) |
\( 2^{4} \cdot 3^{6} \cdot 11^{2} \) |
$1.22091$ |
$(a+1), (3), (11)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2 \cdot 3 \) |
$1.101794645$ |
$3.738805730$ |
1.373132044 |
\( \frac{18609625}{1188} \) |
\( \bigl[i\) , \( 0\) , \( i\) , \( -5\) , \( -4\bigr] \) |
${y}^2+i{x}{y}+i{y}={x}^{3}-5{x}-4$ |
| 2178.1-a4 |
2178.1-a |
$4$ |
$6$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
2178.1 |
\( 2 \cdot 3^{2} \cdot 11^{2} \) |
\( 2^{12} \cdot 3^{2} \cdot 11^{6} \) |
$1.22091$ |
$(a+1), (3), (11)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2 \cdot 3 \) |
$0.367264881$ |
$1.246268576$ |
1.373132044 |
\( \frac{57736239625}{255552} \) |
\( \bigl[i\) , \( 0\) , \( i\) , \( -80\) , \( 284\bigr] \) |
${y}^2+i{x}{y}+i{y}={x}^{3}-80{x}+284$ |
| 2178.1-b1 |
2178.1-b |
$4$ |
$10$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
2178.1 |
\( 2 \cdot 3^{2} \cdot 11^{2} \) |
\( 2^{2} \cdot 3^{4} \cdot 11^{20} \) |
$1.22091$ |
$(a+1), (3), (11)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 5$ |
2B, 5B.1.2 |
$1$ |
\( 2^{3} \cdot 5 \) |
$1$ |
$0.112045110$ |
1.120451108 |
\( -\frac{112427521449300721}{466873642818} \) |
\( \bigl[i\) , \( 0\) , \( 0\) , \( -10055\) , \( 390309\bigr] \) |
${y}^2+i{x}{y}={x}^{3}-10055{x}+390309$ |
| 2178.1-b2 |
2178.1-b |
$4$ |
$10$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
2178.1 |
\( 2 \cdot 3^{2} \cdot 11^{2} \) |
\( 2^{10} \cdot 3^{20} \cdot 11^{4} \) |
$1.22091$ |
$(a+1), (3), (11)$ |
0 |
$\Z/10\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 5$ |
2B, 5B.1.1 |
$1$ |
\( 2^{3} \cdot 5^{2} \) |
$1$ |
$0.560225554$ |
1.120451108 |
\( \frac{168105213359}{228637728} \) |
\( \bigl[i\) , \( 0\) , \( 0\) , \( 115\) , \( -561\bigr] \) |
${y}^2+i{x}{y}={x}^{3}+115{x}-561$ |
| 2178.1-b3 |
2178.1-b |
$4$ |
$10$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
2178.1 |
\( 2 \cdot 3^{2} \cdot 11^{2} \) |
\( 2^{20} \cdot 3^{10} \cdot 11^{2} \) |
$1.22091$ |
$(a+1), (3), (11)$ |
0 |
$\Z/10\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 5$ |
2B, 5B.1.1 |
$1$ |
\( 2^{2} \cdot 5^{2} \) |
$1$ |
$1.120451108$ |
1.120451108 |
\( \frac{10091699281}{2737152} \) |
\( \bigl[1\) , \( 0\) , \( 0\) , \( -45\) , \( 81\bigr] \) |
${y}^2+{x}{y}={x}^{3}-45{x}+81$ |
| 2178.1-b4 |
2178.1-b |
$4$ |
$10$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
2178.1 |
\( 2 \cdot 3^{2} \cdot 11^{2} \) |
\( 2^{4} \cdot 3^{2} \cdot 11^{10} \) |
$1.22091$ |
$(a+1), (3), (11)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 5$ |
2B, 5B.1.2 |
$1$ |
\( 2^{2} \cdot 5 \) |
$1$ |
$0.224090221$ |
1.120451108 |
\( \frac{112763292123580561}{1932612} \) |
\( \bigl[1\) , \( 0\) , \( 0\) , \( -10065\) , \( -389499\bigr] \) |
${y}^2+{x}{y}={x}^{3}-10065{x}-389499$ |
| 2178.1-c1 |
2178.1-c |
$4$ |
$4$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
2178.1 |
\( 2 \cdot 3^{2} \cdot 11^{2} \) |
\( 2^{2} \cdot 3^{8} \cdot 11^{8} \) |
$1.22091$ |
$(a+1), (3), (11)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$1$ |
$1.209138112$ |
2.418276224 |
\( -\frac{192100033}{2371842} \) |
\( \bigl[i\) , \( -1\) , \( i\) , \( -11\) , \( 81\bigr] \) |
${y}^2+i{x}{y}+i{y}={x}^{3}-{x}^{2}-11{x}+81$ |
| 2178.1-c2 |
2178.1-c |
$4$ |
$4$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
2178.1 |
\( 2 \cdot 3^{2} \cdot 11^{2} \) |
\( 2^{8} \cdot 3^{2} \cdot 11^{2} \) |
$1.22091$ |
$(a+1), (3), (11)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$4.836552448$ |
2.418276224 |
\( \frac{912673}{528} \) |
\( \bigl[i\) , \( -1\) , \( i\) , \( -1\) , \( 1\bigr] \) |
${y}^2+i{x}{y}+i{y}={x}^{3}-{x}^{2}-{x}+1$ |
| 2178.1-c3 |
2178.1-c |
$4$ |
$4$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
2178.1 |
\( 2 \cdot 3^{2} \cdot 11^{2} \) |
\( 2^{4} \cdot 3^{4} \cdot 11^{4} \) |
$1.22091$ |
$(a+1), (3), (11)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$1$ |
$2.418276224$ |
2.418276224 |
\( \frac{1180932193}{4356} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -22\) , \( -49\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-22{x}-49$ |
| 2178.1-c4 |
2178.1-c |
$4$ |
$4$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
2178.1 |
\( 2 \cdot 3^{2} \cdot 11^{2} \) |
\( 2^{2} \cdot 3^{2} \cdot 11^{2} \) |
$1.22091$ |
$(a+1), (3), (11)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$4$ |
\( 2 \) |
$1$ |
$1.209138112$ |
2.418276224 |
\( \frac{4824238966273}{66} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -352\) , \( -2689\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-352{x}-2689$ |
*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.
