| 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-a1 |
1083.2-a |
$1$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
1083.2 |
\( 3 \cdot 19^{2} \) |
\( 3^{4} \cdot 19^{2} \) |
$0.88788$ |
$(-2a+1), (-5a+3), (-5a+2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
|
|
$1$ |
\( 2 \) |
$0.037574592$ |
$5.328644115$ |
0.924784107 |
\( -\frac{1404928}{171} \) |
\( \bigl[0\) , \( a\) , \( 1\) , \( -2 a + 2\) , \( 2\bigr] \) |
${y}^2+{y}={x}^{3}+a{x}^{2}+\left(-2a+2\right){x}+2$ |
| 1083.2-b1 |
1083.2-b |
$6$ |
$8$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
1083.2 |
\( 3 \cdot 19^{2} \) |
\( 3 \cdot 19^{10} \) |
$0.88788$ |
$(-2a+1), (-5a+3), (-5a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$0.816172249$ |
0.942434535 |
\( -\frac{7240152655469734}{50950689123} a + \frac{1727319988870667}{50950689123} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( 130 a + 63\) , \( -464 a + 999\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(130a+63\right){x}-464a+999$ |
| 1083.2-b2 |
1083.2-b |
$6$ |
$8$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
1083.2 |
\( 3 \cdot 19^{2} \) |
\( 3 \cdot 19^{10} \) |
$0.88788$ |
$(-2a+1), (-5a+3), (-5a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$0.816172249$ |
0.942434535 |
\( \frac{7240152655469734}{50950689123} a - \frac{5512832666599067}{50950689123} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -130 a + 193\) , \( 464 a + 535\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(-130a+193\right){x}+464a+535$ |
| 1083.2-b3 |
1083.2-b |
$6$ |
$8$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
1083.2 |
\( 3 \cdot 19^{2} \) |
\( 3^{2} \cdot 19^{8} \) |
$0.88788$ |
$(-2a+1), (-5a+3), (-5a+2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1$ |
$1.632344499$ |
0.942434535 |
\( \frac{67419143}{390963} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( 8\) , \( 29\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+8{x}+29$ |
| 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 |
\( \frac{389017}{57} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -2\) , \( -1\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-2{x}-1$ |
| 1083.2-b5 |
1083.2-b |
$6$ |
$8$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
1083.2 |
\( 3 \cdot 19^{2} \) |
\( 3^{4} \cdot 19^{4} \) |
$0.88788$ |
$(-2a+1), (-5a+3), (-5a+2)$ |
0 |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$1$ |
$3.264688998$ |
0.942434535 |
\( \frac{30664297}{3249} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -7\) , \( 5\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-7{x}+5$ |
| 1083.2-b6 |
1083.2-b |
$6$ |
$8$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
1083.2 |
\( 3 \cdot 19^{2} \) |
\( 3^{8} \cdot 19^{2} \) |
$0.88788$ |
$(-2a+1), (-5a+3), (-5a+2)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$1.632344499$ |
0.942434535 |
\( \frac{115714886617}{1539} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -102\) , \( 385\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-102{x}+385$ |
| 1083.2-c1 |
1083.2-c |
$2$ |
$5$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
1083.2 |
\( 3 \cdot 19^{2} \) |
\( 3^{4} \cdot 19^{10} \) |
$0.88788$ |
$(-2a+1), (-5a+3), (-5a+2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$5$ |
5B.1.2 |
$1$ |
\( 2^{2} \) |
$1$ |
$0.271765830$ |
1.255232601 |
\( -\frac{9358714467168256}{22284891} \) |
\( \bigl[0\) , \( -a\) , \( 1\) , \( -4390 a + 4390\) , \( -113432\bigr] \) |
${y}^2+{y}={x}^{3}-a{x}^{2}+\left(-4390a+4390\right){x}-113432$ |
| 1083.2-c2 |
1083.2-c |
$2$ |
$5$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
1083.2 |
\( 3 \cdot 19^{2} \) |
\( 3^{20} \cdot 19^{2} \) |
$0.88788$ |
$(-2a+1), (-5a+3), (-5a+2)$ |
0 |
$\Z/5\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$5$ |
5B.1.1 |
$1$ |
\( 2^{2} \cdot 5 \) |
$1$ |
$1.358829150$ |
1.255232601 |
\( \frac{841232384}{1121931} \) |
\( \bigl[0\) , \( -a\) , \( 1\) , \( 20 a - 20\) , \( -32\bigr] \) |
${y}^2+{y}={x}^{3}-a{x}^{2}+\left(20a-20\right){x}-32$ |
*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.
