| 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 |
| 18144.2-a1 |
18144.2-a |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
18144.2 |
\( 2^{5} \cdot 3^{4} \cdot 7 \) |
\( 2^{13} \cdot 3^{12} \cdot 7 \) |
$2.74392$ |
$(a), (-a+1), (-2a+1), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$0.765787282$ |
$0.652280894$ |
3.020742951 |
\( \frac{4096655365}{28} a - \frac{2878658051}{14} \) |
\( \bigl[a\) , \( -a - 1\) , \( a\) , \( -191 a + 769\) , \( 4751 a + 933\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-191a+769\right){x}+4751a+933$ |
| 18144.2-a2 |
18144.2-a |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
18144.2 |
\( 2^{5} \cdot 3^{4} \cdot 7 \) |
\( 2^{5} \cdot 3^{12} \cdot 7^{2} \) |
$2.74392$ |
$(a), (-a+1), (-2a+1), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1.531574565$ |
$1.304561789$ |
3.020742951 |
\( -\frac{13647889}{14} a - \frac{40536829}{7} \) |
\( \bigl[a\) , \( -a - 1\) , \( a\) , \( -20 a - 104\) , \( -86 a - 362\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-20a-104\right){x}-86a-362$ |
| 18144.2-a3 |
18144.2-a |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
18144.2 |
\( 2^{5} \cdot 3^{4} \cdot 7 \) |
\( 2^{14} \cdot 3^{12} \cdot 7^{2} \) |
$2.74392$ |
$(a), (-a+1), (-2a+1), (3)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{6} \) |
$0.382893641$ |
$1.304561789$ |
3.020742951 |
\( -\frac{1145925}{112} a - \frac{72257}{56} \) |
\( \bigl[a\) , \( -a - 1\) , \( a\) , \( -11 a + 49\) , \( 71 a - 3\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-11a+49\right){x}+71a-3$ |
| 18144.2-a4 |
18144.2-a |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
18144.2 |
\( 2^{5} \cdot 3^{4} \cdot 7 \) |
\( 2^{10} \cdot 3^{12} \cdot 7^{4} \) |
$2.74392$ |
$(a), (-a+1), (-2a+1), (3)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$0.765787282$ |
$1.304561789$ |
3.020742951 |
\( \frac{361845}{196} a - \frac{43727}{98} \) |
\( \bigl[a\) , \( -a - 1\) , \( a\) , \( 22 a - 17\) , \( -61 a + 41\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(22a-17\right){x}-61a+41$ |
| 18144.2-a5 |
18144.2-a |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
18144.2 |
\( 2^{5} \cdot 3^{4} \cdot 7 \) |
\( 2^{19} \cdot 3^{12} \cdot 7 \) |
$2.74392$ |
$(a), (-a+1), (-2a+1), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.765787282$ |
$1.304561789$ |
3.020742951 |
\( -\frac{138325}{1792} a - \frac{317937}{896} \) |
\( \bigl[a\) , \( -a - 1\) , \( a\) , \( 4 a - 17\) , \( 25 a - 55\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(4a-17\right){x}+25a-55$ |
| 18144.2-a6 |
18144.2-a |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
18144.2 |
\( 2^{5} \cdot 3^{4} \cdot 7 \) |
\( 2^{11} \cdot 3^{12} \cdot 7^{8} \) |
$2.74392$ |
$(a), (-a+1), (-2a+1), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1.531574565$ |
$0.652280894$ |
3.020742951 |
\( -\frac{5786513}{4802} a + \frac{263001}{343} \) |
\( \bigl[a\) , \( -a - 1\) , \( a\) , \( -68 a - 17\) , \( -277 a - 67\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-68a-17\right){x}-277a-67$ |
*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.
