| 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 |
| 1083.2-b4 |
1083.2-b |
$6$ |
$8$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
1083.2 |
\( 3 \cdot 19^{2} \) |
\( 3^{2} \cdot 19^{2} \) |
$0.88788$ |
$(-2a+1), (-5a+3), (-5a+2)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$6.529377996$ |
0.942434535 |
\( \frac{389017}{57} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -2\) , \( -1\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-2{x}-1$ |
| 3249.1-c2 |
3249.1-c |
$4$ |
$4$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
3249.1 |
\( 3^{2} \cdot 19^{2} \) |
\( 3^{2} \cdot 19^{2} \) |
$1.34929$ |
$(3), (19)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$0.650473478$ |
$6.529377996$ |
2.123593608 |
\( \frac{389017}{57} \) |
\( \bigl[i\) , \( 0\) , \( i\) , \( -1\) , \( 1\bigr] \) |
${y}^2+i{x}{y}+i{y}={x}^{3}-{x}+1$ |
| 3249.1-c2 |
3249.1-c |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
3249.1 |
\( 3^{2} \cdot 19^{2} \) |
\( 3^{2} \cdot 19^{2} \) |
$1.78495$ |
$(3), (19)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1.637562893$ |
$6.529377996$ |
4.041297109 |
\( \frac{389017}{57} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -2\) , \( -1\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-2{x}-1$ |
| 3249.5-c2 |
3249.5-c |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
3249.5 |
\( 3^{2} \cdot 19^{2} \) |
\( 3^{2} \cdot 19^{2} \) |
$1.90819$ |
$(-a-1), (a-1), (-3a+1), (3a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$2.106375061$ |
$6.529377996$ |
4.862532555 |
\( \frac{389017}{57} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -2\) , \( -1\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-2{x}-1$ |
| 3249.2-b2 |
3249.2-b |
$4$ |
$4$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
3249.2 |
\( 3^{2} \cdot 19^{2} \) |
\( 3^{2} \cdot 19^{2} \) |
$2.23755$ |
$(-a), (a-1), (19)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$6.529377996$ |
0.984340769 |
\( \frac{389017}{57} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -2\) , \( -1\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-2{x}-1$ |
| 171.1-a2 |
171.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{-19}) \) |
$2$ |
$[0, 1]$ |
171.1 |
\( 3^{2} \cdot 19 \) |
\( 3^{2} \cdot 19^{2} \) |
$1.40852$ |
$(-2a+1), (3)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$6.529377996$ |
0.374485511 |
\( \frac{389017}{57} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -2\) , \( -1\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3-2{x}-1$ |
| 3249.2-c2 |
3249.2-c |
$4$ |
$4$ |
\(\Q(\sqrt{-31}) \) |
$2$ |
$[0, 1]$ |
3249.2 |
\( 3^{2} \cdot 19^{2} \) |
\( 3^{2} \cdot 19^{2} \) |
$3.75627$ |
$(19,a+5), (19,a+13), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$6.529377996$ |
0.586355453 |
\( \frac{389017}{57} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -2\) , \( -1\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3-2{x}-1$ |
| 3249.1-a2 |
3249.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{-43}) \) |
$2$ |
$[0, 1]$ |
3249.1 |
\( 3^{2} \cdot 19^{2} \) |
\( 3^{2} \cdot 19^{2} \) |
$4.42395$ |
$(3), (19)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$4.908045001$ |
$6.529377996$ |
4.887042542 |
\( \frac{389017}{57} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -2\) , \( -1\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3-2{x}-1$ |
| 3249.2-a2 |
3249.2-a |
$4$ |
$4$ |
\(\Q(\sqrt{-67}) \) |
$2$ |
$[0, 1]$ |
3249.2 |
\( 3^{2} \cdot 19^{2} \) |
\( 3^{2} \cdot 19^{2} \) |
$5.52222$ |
$(a+1), (a-2), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$6.529377996$ |
0.398845240 |
\( \frac{389017}{57} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -2\) , \( -1\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3-2{x}-1$ |
| 171.2-d2 |
171.2-d |
$4$ |
$4$ |
\(\Q(\sqrt{-95}) \) |
$2$ |
$[0, 1]$ |
171.2 |
\( 3^{2} \cdot 19 \) |
\( 3^{2} \cdot 19^{2} \) |
$3.14956$ |
$(3,a), (3,a+2), (19,a+9)$ |
$0 \le r \le 1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
|
\( 2 \) |
$1$ |
$6.529377996$ |
9.068341580 |
\( \frac{389017}{57} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -2\) , \( -1\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3-2{x}-1$ |
| 3249.1-a2 |
3249.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{-163}) \) |
$2$ |
$[0, 1]$ |
3249.1 |
\( 3^{2} \cdot 19^{2} \) |
\( 3^{2} \cdot 19^{2} \) |
$8.61330$ |
$(3), (19)$ |
$0 \le r \le 1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
|
\( 1 \) |
$1$ |
$6.529377996$ |
5.006658911 |
\( \frac{389017}{57} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -2\) , \( -1\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3-2{x}-1$ |
| 57.1-a2 |
57.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{-57}) \) |
$2$ |
$[0, 1]$ |
57.1 |
\( 3 \cdot 19 \) |
\( 3^{2} \cdot 19^{2} \) |
$3.70744$ |
$(3,a), (19,a)$ |
$0 \le r \le 2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$4$ |
\( 2^{2} \) |
$1$ |
$6.529377996$ |
3.459348971 |
\( \frac{389017}{57} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -2\) , \( -1\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3-2{x}-1$ |
| 57.1-h2 |
57.1-h |
$4$ |
$4$ |
\(\Q(\sqrt{-399}) \) |
$2$ |
$[0, 1]$ |
57.1 |
\( 3 \cdot 19 \) |
\( 3^{2} \cdot 19^{2} \) |
$4.90449$ |
$(3,a+1), (19,a+9)$ |
$0 \le r \le 2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$4$ |
\( 2^{2} \) |
$1$ |
$6.529377996$ |
2.615022021 |
\( \frac{389017}{57} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -2\) , \( -1\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3-2{x}-1$ |
| 57.1-g2 |
57.1-g |
$4$ |
$4$ |
\(\Q(\sqrt{-114}) \) |
$2$ |
$[0, 1]$ |
57.1 |
\( 3 \cdot 19 \) |
\( 3^{2} \cdot 19^{2} \) |
$5.24312$ |
$(3,a), (19,a)$ |
$0 \le r \le 2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$4$ |
\( 2^{2} \) |
$1$ |
$6.529377996$ |
2.446129115 |
\( \frac{389017}{57} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -2\) , \( -1\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3-2{x}-1$ |
| 57.1-h2 |
57.1-h |
$4$ |
$4$ |
\(\Q(\sqrt{-627}) \) |
$2$ |
$[0, 1]$ |
57.1 |
\( 3 \cdot 19 \) |
\( 3^{2} \cdot 19^{2} \) |
$6.14810$ |
$(3,a+1), (19,a+9)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$1$ |
$13.05875599$ |
0.521516479 |
\( \frac{389017}{57} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -2\) , \( -1\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3-2{x}-1$ |
| 3249.1-f2 |
3249.1-f |
$4$ |
$4$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
3249.1 |
\( 3^{2} \cdot 19^{2} \) |
\( 3^{2} \cdot 19^{2} \) |
$1.50855$ |
$(4a-3), (-4a+1), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$0.390921292$ |
$18.84609635$ |
1.647387382 |
\( \frac{389017}{57} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -2\) , \( -1\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-2{x}-1$ |
| 3249.1-b2 |
3249.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
3249.1 |
\( 3^{2} \cdot 19^{2} \) |
\( 3^{2} \cdot 19^{2} \) |
$1.90819$ |
$(3), (19)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$18.84609635$ |
1.665775316 |
\( \frac{389017}{57} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -2\) , \( -1\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-2{x}-1$ |
| 1083.1-e2 |
1083.1-e |
$4$ |
$4$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1083.1 |
\( 3 \cdot 19^{2} \) |
\( 3^{2} \cdot 19^{2} \) |
$1.77577$ |
$(a), (19)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$18.84609635$ |
2.720199700 |
\( \frac{389017}{57} \) |
\( \bigl[a\) , \( -a + 1\) , \( a\) , \( 84 a - 147\) , \( 585 a - 1014\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(84a-147\right){x}+585a-1014$ |
| 1083.1-f2 |
1083.1-f |
$4$ |
$4$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
1083.1 |
\( 3 \cdot 19^{2} \) |
\( 3^{2} \cdot 19^{2} \) |
$2.34912$ |
$(-a+2), (19)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.460486004$ |
$18.84609635$ |
3.787548392 |
\( \frac{389017}{57} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -2\) , \( -1\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-2{x}-1$ |
| 57.1-g3 |
57.1-g |
$6$ |
$8$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
57.1 |
\( 3 \cdot 19 \) |
\( 3^{2} \cdot 19^{2} \) |
$1.85372$ |
$(4a+13), (10a-43)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$3.892773922$ |
$18.84609635$ |
4.858622600 |
\( \frac{389017}{57} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -2\) , \( -1\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-2{x}-1$ |
| 171.1-i3 |
171.1-i |
$6$ |
$8$ |
\(\Q(\sqrt{19}) \) |
$2$ |
$[2, 0]$ |
171.1 |
\( 3^{2} \cdot 19 \) |
\( 3^{2} \cdot 19^{2} \) |
$2.81705$ |
$(-a-4), (-a+4), (a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$18.84609635$ |
1.080897756 |
\( \frac{389017}{57} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -2\) , \( -1\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-2{x}-1$ |
| 513.1-c3 |
513.1-c |
$4$ |
$4$ |
3.3.361.1 |
$3$ |
$[3, 0]$ |
513.1 |
\( 3^{3} \cdot 19 \) |
\( 3^{3} \cdot 19^{3} \) |
$4.80373$ |
$(a^2-a-4), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$81.81484478$ |
1.076511115 |
\( \frac{389017}{57} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -2\) , \( -1\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-2{x}-1$ |
*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.
