| 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 |
| 58482.1-a1 |
58482.1-a |
$2$ |
$2$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
58482.1 |
\( 2 \cdot 3^{4} \cdot 19^{2} \) |
\( 2^{4} \cdot 3^{6} \cdot 19^{2} \) |
$2.77923$ |
$(a+1), (3), (19)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.237879944$ |
$3.855564791$ |
3.668646161 |
\( \frac{132651}{76} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -3\) , \( 1\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}-3{x}+1$ |
| 58482.1-a2 |
58482.1-a |
$2$ |
$2$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
58482.1 |
\( 2 \cdot 3^{4} \cdot 19^{2} \) |
\( 2^{2} \cdot 3^{6} \cdot 19^{4} \) |
$2.77923$ |
$(a+1), (3), (19)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.237879944$ |
$1.927782395$ |
3.668646161 |
\( \frac{149721291}{722} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -33\) , \( -65\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}-33{x}-65$ |
| 58482.1-b1 |
58482.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
58482.1 |
\( 2 \cdot 3^{4} \cdot 19^{2} \) |
\( 2^{10} \cdot 3^{36} \cdot 19^{8} \) |
$2.77923$ |
$(a+1), (3), (19)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$4$ |
\( 2^{5} \) |
$1$ |
$0.036828220$ |
1.178503068 |
\( -\frac{16576888679672833}{2216253521952} \) |
\( \bigl[i\) , \( 1\) , \( 0\) , \( -47808\) , \( -4476064\bigr] \) |
${y}^2+i{x}{y}={x}^{3}+{x}^{2}-47808{x}-4476064$ |
| 58482.1-b2 |
58482.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
58482.1 |
\( 2 \cdot 3^{4} \cdot 19^{2} \) |
\( 2^{40} \cdot 3^{18} \cdot 19^{2} \) |
$2.77923$ |
$(a+1), (3), (19)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$4$ |
\( 2^{3} \) |
$1$ |
$0.147312883$ |
1.178503068 |
\( \frac{4824238966273}{537919488} \) |
\( \bigl[i\) , \( 1\) , \( 0\) , \( -3168\) , \( -62464\bigr] \) |
${y}^2+i{x}{y}={x}^{3}+{x}^{2}-3168{x}-62464$ |
| 58482.1-b3 |
58482.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
58482.1 |
\( 2 \cdot 3^{4} \cdot 19^{2} \) |
\( 2^{20} \cdot 3^{24} \cdot 19^{4} \) |
$2.77923$ |
$(a+1), (3), (19)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$16$ |
\( 2^{4} \) |
$1$ |
$0.073656441$ |
1.178503068 |
\( \frac{18120364883707393}{269485056} \) |
\( \bigl[i\) , \( 1\) , \( 0\) , \( -49248\) , \( -4218880\bigr] \) |
${y}^2+i{x}{y}={x}^{3}+{x}^{2}-49248{x}-4218880$ |
| 58482.1-b4 |
58482.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
58482.1 |
\( 2 \cdot 3^{4} \cdot 19^{2} \) |
\( 2^{10} \cdot 3^{18} \cdot 19^{2} \) |
$2.77923$ |
$(a+1), (3), (19)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$16$ |
\( 2^{3} \) |
$1$ |
$0.036828220$ |
1.178503068 |
\( \frac{74220219816682217473}{16416} \) |
\( \bigl[i\) , \( 1\) , \( 0\) , \( -787968\) , \( -269419360\bigr] \) |
${y}^2+i{x}{y}={x}^{3}+{x}^{2}-787968{x}-269419360$ |
| 58482.1-c1 |
58482.1-c |
$4$ |
$6$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
58482.1 |
\( 2 \cdot 3^{4} \cdot 19^{2} \) |
\( 2^{2} \cdot 3^{16} \cdot 19^{12} \) |
$2.77923$ |
$(a+1), (3), (19)$ |
$2$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{4} \cdot 3 \) |
$6.214136413$ |
$0.134961792$ |
4.472911933 |
\( -\frac{8078253774625}{846825858} \) |
\( \bigl[i\) , \( 1\) , \( 0\) , \( -3762\) , \( -97470\bigr] \) |
${y}^2+i{x}{y}={x}^{3}+{x}^{2}-3762{x}-97470$ |
| 58482.1-c2 |
58482.1-c |
$4$ |
$6$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
58482.1 |
\( 2 \cdot 3^{4} \cdot 19^{2} \) |
\( 2^{6} \cdot 3^{24} \cdot 19^{4} \) |
$2.77923$ |
$(a+1), (3), (19)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2^{4} \) |
$0.690459601$ |
$0.404885376$ |
4.472911933 |
\( \frac{3616805375}{2105352} \) |
\( \bigl[i\) , \( 1\) , \( 0\) , \( 288\) , \( 216\bigr] \) |
${y}^2+i{x}{y}={x}^{3}+{x}^{2}+288{x}+216$ |
| 58482.1-c3 |
58482.1-c |
$4$ |
$6$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
58482.1 |
\( 2 \cdot 3^{4} \cdot 19^{2} \) |
\( 2^{12} \cdot 3^{18} \cdot 19^{2} \) |
$2.77923$ |
$(a+1), (3), (19)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2^{3} \) |
$0.690459601$ |
$0.809770753$ |
4.472911933 |
\( \frac{57066625}{32832} \) |
\( \bigl[i\) , \( 1\) , \( 0\) , \( -72\) , \( 0\bigr] \) |
${y}^2+i{x}{y}={x}^{3}+{x}^{2}-72{x}$ |
| 58482.1-c4 |
58482.1-c |
$4$ |
$6$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
58482.1 |
\( 2 \cdot 3^{4} \cdot 19^{2} \) |
\( 2^{4} \cdot 3^{14} \cdot 19^{6} \) |
$2.77923$ |
$(a+1), (3), (19)$ |
$2$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{3} \cdot 3 \) |
$6.214136413$ |
$0.269923584$ |
4.472911933 |
\( \frac{8671983378625}{82308} \) |
\( \bigl[i\) , \( 1\) , \( 0\) , \( -3852\) , \( -92988\bigr] \) |
${y}^2+i{x}{y}={x}^{3}+{x}^{2}-3852{x}-92988$ |
| 58482.1-d1 |
58482.1-d |
$2$ |
$5$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
58482.1 |
\( 2 \cdot 3^{4} \cdot 19^{2} \) |
\( 2^{2} \cdot 3^{12} \cdot 19^{10} \) |
$2.77923$ |
$(a+1), (3), (19)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$5$ |
5B.4.2 |
$1$ |
\( 2 \cdot 5 \) |
$1$ |
$0.321685320$ |
3.216853208 |
\( -\frac{37966934881}{4952198} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -630\) , \( 6898\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}-630{x}+6898$ |
| 58482.1-d2 |
58482.1-d |
$2$ |
$5$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
58482.1 |
\( 2 \cdot 3^{4} \cdot 19^{2} \) |
\( 2^{10} \cdot 3^{12} \cdot 19^{2} \) |
$2.77923$ |
$(a+1), (3), (19)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$5$ |
5B.4.1 |
$1$ |
\( 2 \) |
$1$ |
$1.608426604$ |
3.216853208 |
\( -\frac{1}{608} \) |
\( \bigl[i\) , \( 1\) , \( 0\) , \( 0\) , \( 32\bigr] \) |
${y}^2+i{x}{y}={x}^{3}+{x}^{2}+32$ |
| 58482.1-e1 |
58482.1-e |
$2$ |
$2$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
58482.1 |
\( 2 \cdot 3^{4} \cdot 19^{2} \) |
\( 2^{2} \cdot 3^{32} \cdot 19^{4} \) |
$2.77923$ |
$(a+1), (3), (19)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$3.495490644$ |
$0.239218432$ |
6.689486356 |
\( -\frac{69173457625}{42633378} \) |
\( \bigl[i\) , \( 1\) , \( i\) , \( -769\) , \( -12003\bigr] \) |
${y}^2+i{x}{y}+i{y}={x}^{3}+{x}^{2}-769{x}-12003$ |
| 58482.1-e2 |
58482.1-e |
$2$ |
$2$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
58482.1 |
\( 2 \cdot 3^{4} \cdot 19^{2} \) |
\( 2^{4} \cdot 3^{22} \cdot 19^{2} \) |
$2.77923$ |
$(a+1), (3), (19)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1.747745322$ |
$0.478436865$ |
6.689486356 |
\( \frac{96386901625}{18468} \) |
\( \bigl[i\) , \( 1\) , \( i\) , \( -859\) , \( -9915\bigr] \) |
${y}^2+i{x}{y}+i{y}={x}^{3}+{x}^{2}-859{x}-9915$ |
| 58482.1-f1 |
58482.1-f |
$3$ |
$9$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
58482.1 |
\( 2 \cdot 3^{4} \cdot 19^{2} \) |
\( 2^{6} \cdot 3^{12} \cdot 19^{2} \) |
$2.77923$ |
$(a+1), (3), (19)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$3$ |
3B.1.2 |
$1$ |
\( 2 \cdot 3 \) |
$0.504387587$ |
$1.136863399$ |
6.881037449 |
\( -\frac{413493625}{152} \) |
\( \bigl[i\) , \( 1\) , \( i\) , \( -139\) , \( 601\bigr] \) |
${y}^2+i{x}{y}+i{y}={x}^{3}+{x}^{2}-139{x}+601$ |
| 58482.1-f2 |
58482.1-f |
$3$ |
$9$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
58482.1 |
\( 2 \cdot 3^{4} \cdot 19^{2} \) |
\( 2^{54} \cdot 3^{12} \cdot 19^{2} \) |
$2.77923$ |
$(a+1), (3), (19)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$3$ |
3B.1.1 |
$1$ |
\( 2 \cdot 3^{3} \) |
$4.539488286$ |
$0.126318155$ |
6.881037449 |
\( -\frac{69173457625}{2550136832} \) |
\( \bigl[i\) , \( 1\) , \( i\) , \( -769\) , \( -66305\bigr] \) |
${y}^2+i{x}{y}+i{y}={x}^{3}+{x}^{2}-769{x}-66305$ |
| 58482.1-f3 |
58482.1-f |
$3$ |
$9$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
58482.1 |
\( 2 \cdot 3^{4} \cdot 19^{2} \) |
\( 2^{18} \cdot 3^{12} \cdot 19^{6} \) |
$2.77923$ |
$(a+1), (3), (19)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$3$ |
3Cs.1.1 |
$1$ |
\( 2 \cdot 3^{3} \) |
$1.513162762$ |
$0.378954466$ |
6.881037449 |
\( \frac{94196375}{3511808} \) |
\( \bigl[i\) , \( 1\) , \( i\) , \( 86\) , \( 2437\bigr] \) |
${y}^2+i{x}{y}+i{y}={x}^{3}+{x}^{2}+86{x}+2437$ |
| 58482.1-g1 |
58482.1-g |
$2$ |
$2$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
58482.1 |
\( 2 \cdot 3^{4} \cdot 19^{2} \) |
\( 2^{4} \cdot 3^{18} \cdot 19^{2} \) |
$2.77923$ |
$(a+1), (3), (19)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1.551718204$ |
$1.285188263$ |
7.977000101 |
\( \frac{132651}{76} \) |
\( \bigl[i\) , \( 1\) , \( i\) , \( -28\) , \( -1\bigr] \) |
${y}^2+i{x}{y}+i{y}={x}^{3}+{x}^{2}-28{x}-1$ |
| 58482.1-g2 |
58482.1-g |
$2$ |
$2$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
58482.1 |
\( 2 \cdot 3^{4} \cdot 19^{2} \) |
\( 2^{2} \cdot 3^{18} \cdot 19^{4} \) |
$2.77923$ |
$(a+1), (3), (19)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$3.103436408$ |
$0.642594131$ |
7.977000101 |
\( \frac{149721291}{722} \) |
\( \bigl[i\) , \( 1\) , \( i\) , \( -298\) , \( -2053\bigr] \) |
${y}^2+i{x}{y}+i{y}={x}^{3}+{x}^{2}-298{x}-2053$ |
*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.
