| 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 |
| 1083.1-a1 |
1083.1-a |
$1$ |
$1$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1083.1 |
\( 3 \cdot 19^{2} \) |
\( 3^{4} \cdot 19^{2} \) |
$1.77577$ |
$(a), (19)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
|
|
$1$ |
\( 2 \) |
$0.037574592$ |
$30.86363048$ |
1.339092757 |
\( -\frac{1404928}{171} \) |
\( \bigl[0\) , \( -1\) , \( 1\) , \( -2\) , \( 2\bigr] \) |
${y}^2+{y}={x}^{3}-{x}^{2}-2{x}+2$ |
| 1083.1-b1 |
1083.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1083.1 |
\( 3 \cdot 19^{2} \) |
\( 3^{2} \cdot 19^{8} \) |
$1.77577$ |
$(a), (19)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$2.601893913$ |
$2.262154252$ |
1.699108754 |
\( \frac{67419143}{390963} \) |
\( \bigl[a\) , \( -1\) , \( a\) , \( 7\) , \( -30\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}-{x}^{2}+7{x}-30$ |
| 1083.1-b2 |
1083.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1083.1 |
\( 3 \cdot 19^{2} \) |
\( 3^{2} \cdot 19^{2} \) |
$1.77577$ |
$(a), (19)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.650473478$ |
$36.19446804$ |
1.699108754 |
\( \frac{389017}{57} \) |
\( \bigl[1\) , \( a + 1\) , \( 0\) , \( 86 a - 146\) , \( -500 a + 867\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(86a-146\right){x}-500a+867$ |
| 1083.1-b3 |
1083.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1083.1 |
\( 3 \cdot 19^{2} \) |
\( 3^{4} \cdot 19^{4} \) |
$1.77577$ |
$(a), (19)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$1.300946956$ |
$9.048617011$ |
1.699108754 |
\( \frac{30664297}{3249} \) |
\( \bigl[a\) , \( -1\) , \( a\) , \( -8\) , \( -6\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}-{x}^{2}-8{x}-6$ |
| 1083.1-b4 |
1083.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1083.1 |
\( 3 \cdot 19^{2} \) |
\( 3^{8} \cdot 19^{2} \) |
$1.77577$ |
$(a), (19)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$2.601893913$ |
$2.262154252$ |
1.699108754 |
\( \frac{115714886617}{1539} \) |
\( \bigl[a\) , \( -1\) , \( a\) , \( -103\) , \( -386\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}-{x}^{2}-103{x}-386$ |
| 1083.1-c1 |
1083.1-c |
$2$ |
$5$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1083.1 |
\( 3 \cdot 19^{2} \) |
\( 3^{4} \cdot 19^{10} \) |
$1.77577$ |
$(a), (19)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$5$ |
5B.1.2 |
$1$ |
\( 2^{2} \cdot 5 \) |
$1$ |
$0.085998375$ |
0.496511851 |
\( -\frac{9358714467168256}{22284891} \) |
\( \bigl[0\) , \( -a + 1\) , \( a\) , \( 245858 a - 425861\) , \( 87559214 a - 151657044\bigr] \) |
${y}^2+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(245858a-425861\right){x}+87559214a-151657044$ |
| 1083.1-c2 |
1083.1-c |
$2$ |
$5$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1083.1 |
\( 3 \cdot 19^{2} \) |
\( 3^{20} \cdot 19^{2} \) |
$1.77577$ |
$(a), (19)$ |
0 |
$\Z/5\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$5$ |
5B.1.1 |
$1$ |
\( 2^{2} \cdot 5 \) |
$1$ |
$2.149959381$ |
0.496511851 |
\( \frac{841232384}{1121931} \) |
\( \bigl[0\) , \( 1\) , \( 1\) , \( 20\) , \( -32\bigr] \) |
${y}^2+{y}={x}^{3}+{x}^{2}+20{x}-32$ |
| 1083.1-d1 |
1083.1-d |
$2$ |
$5$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1083.1 |
\( 3 \cdot 19^{2} \) |
\( 3^{4} \cdot 19^{10} \) |
$1.77577$ |
$(a), (19)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$5$ |
5B.4.2 |
$1$ |
\( 2 \cdot 5 \) |
$0.226284916$ |
$3.435258684$ |
4.488016288 |
\( -\frac{9358714467168256}{22284891} \) |
\( \bigl[0\) , \( a - 1\) , \( 1\) , \( 245858 a - 425861\) , \( -87559214 a + 151657043\bigr] \) |
${y}^2+{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(245858a-425861\right){x}-87559214a+151657043$ |
| 1083.1-d2 |
1083.1-d |
$2$ |
$5$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1083.1 |
\( 3 \cdot 19^{2} \) |
\( 3^{20} \cdot 19^{2} \) |
$1.77577$ |
$(a), (19)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$5$ |
5B.4.1 |
$1$ |
\( 2 \) |
$1.131424581$ |
$3.435258684$ |
4.488016288 |
\( \frac{841232384}{1121931} \) |
\( \bigl[0\) , \( -1\) , \( a\) , \( 20\) , \( 31\bigr] \) |
${y}^2+a{y}={x}^{3}-{x}^{2}+20{x}+31$ |
| 1083.1-e1 |
1083.1-e |
$4$ |
$4$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1083.1 |
\( 3 \cdot 19^{2} \) |
\( 3^{2} \cdot 19^{8} \) |
$1.77577$ |
$(a), (19)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$4$ |
\( 2^{3} \) |
$1$ |
$4.711524088$ |
2.720199700 |
\( \frac{67419143}{390963} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( 8\) , \( 29\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+8{x}+29$ |
| 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-e3 |
1083.1-e |
$4$ |
$4$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1083.1 |
\( 3 \cdot 19^{2} \) |
\( 3^{4} \cdot 19^{4} \) |
$1.77577$ |
$(a), (19)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1$ |
$18.84609635$ |
2.720199700 |
\( \frac{30664297}{3249} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -7\) , \( 5\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-7{x}+5$ |
| 1083.1-e4 |
1083.1-e |
$4$ |
$4$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1083.1 |
\( 3 \cdot 19^{2} \) |
\( 3^{8} \cdot 19^{2} \) |
$1.77577$ |
$(a), (19)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$18.84609635$ |
2.720199700 |
\( \frac{115714886617}{1539} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -102\) , \( 385\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-102{x}+385$ |
| 1083.1-f1 |
1083.1-f |
$1$ |
$1$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1083.1 |
\( 3 \cdot 19^{2} \) |
\( 3^{4} \cdot 19^{2} \) |
$1.77577$ |
$(a), (19)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
|
|
$1$ |
\( 2^{2} \) |
$1$ |
$3.679988085$ |
4.249284223 |
\( -\frac{1404928}{171} \) |
\( \bigl[0\) , \( 1\) , \( a\) , \( -2\) , \( -3\bigr] \) |
${y}^2+a{y}={x}^{3}+{x}^{2}-2{x}-3$ |
*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.
