| 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 |
| 4.3-a1 |
4.3-a |
$2$ |
$2$ |
\(\Q(\sqrt{2}, \sqrt{17})\) |
$4$ |
$[4, 0]$ |
4.3 |
\( 2^{2} \) |
\( 2^{8} \) |
$14.45223$ |
$(4/9a^3-2/3a^2-47/9a+29/9)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 3 \) |
$0.068789810$ |
$942.8701559$ |
1.430732181 |
\( 128 a^{3} - 192 a^{2} - 1792 a + 2496 \) |
\( \bigl[-\frac{1}{9} a^{3} + \frac{2}{3} a^{2} + \frac{5}{9} a - \frac{32}{9}\) , \( -\frac{1}{9} a^{3} - \frac{1}{3} a^{2} + \frac{14}{9} a + \frac{22}{9}\) , \( -\frac{1}{3} a^{3} + a^{2} + \frac{11}{3} a - \frac{11}{3}\) , \( -\frac{1}{3} a^{3} - a^{2} + \frac{23}{3} a + \frac{7}{3}\) , \( -\frac{1}{9} a^{3} - \frac{4}{3} a^{2} + \frac{41}{9} a + \frac{4}{9}\bigr] \) |
${y}^2+\left(-\frac{1}{9}a^{3}+\frac{2}{3}a^{2}+\frac{5}{9}a-\frac{32}{9}\right){x}{y}+\left(-\frac{1}{3}a^{3}+a^{2}+\frac{11}{3}a-\frac{11}{3}\right){y}={x}^{3}+\left(-\frac{1}{9}a^{3}-\frac{1}{3}a^{2}+\frac{14}{9}a+\frac{22}{9}\right){x}^{2}+\left(-\frac{1}{3}a^{3}-a^{2}+\frac{23}{3}a+\frac{7}{3}\right){x}-\frac{1}{9}a^{3}-\frac{4}{3}a^{2}+\frac{41}{9}a+\frac{4}{9}$ |
| 4.3-b1 |
4.3-b |
$2$ |
$2$ |
\(\Q(\sqrt{2}, \sqrt{17})\) |
$4$ |
$[4, 0]$ |
4.3 |
\( 2^{2} \) |
\( 2^{8} \) |
$14.45223$ |
$(4/9a^3-2/3a^2-47/9a+29/9)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 3 \) |
$0.068789810$ |
$942.8701559$ |
1.430732181 |
\( 128 a^{3} - 192 a^{2} - 1792 a + 2496 \) |
\( \bigl[-\frac{1}{9} a^{3} + \frac{2}{3} a^{2} + \frac{5}{9} a - \frac{32}{9}\) , \( \frac{1}{9} a^{3} + \frac{1}{3} a^{2} - \frac{14}{9} a - \frac{22}{9}\) , \( -\frac{1}{3} a^{3} + a^{2} + \frac{11}{3} a - \frac{11}{3}\) , \( -\frac{16}{9} a^{3} + \frac{11}{3} a^{2} + \frac{170}{9} a - \frac{179}{9}\) , \( -\frac{14}{9} a^{3} + \frac{10}{3} a^{2} + \frac{142}{9} a - \frac{196}{9}\bigr] \) |
${y}^2+\left(-\frac{1}{9}a^{3}+\frac{2}{3}a^{2}+\frac{5}{9}a-\frac{32}{9}\right){x}{y}+\left(-\frac{1}{3}a^{3}+a^{2}+\frac{11}{3}a-\frac{11}{3}\right){y}={x}^{3}+\left(\frac{1}{9}a^{3}+\frac{1}{3}a^{2}-\frac{14}{9}a-\frac{22}{9}\right){x}^{2}+\left(-\frac{16}{9}a^{3}+\frac{11}{3}a^{2}+\frac{170}{9}a-\frac{179}{9}\right){x}-\frac{14}{9}a^{3}+\frac{10}{3}a^{2}+\frac{142}{9}a-\frac{196}{9}$ |
| 16.4-a1 |
16.4-a |
$2$ |
$2$ |
\(\Q(\sqrt{2}, \sqrt{17})\) |
$4$ |
$[4, 0]$ |
16.4 |
\( 2^{4} \) |
\( 2^{8} \) |
$17.18670$ |
$(4/9a^3-2/3a^2-47/9a+29/9)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$942.8701559$ |
3.466434397 |
\( 128 a^{3} - 192 a^{2} - 1792 a + 2496 \) |
\( \bigl[-\frac{1}{9} a^{3} + \frac{2}{3} a^{2} + \frac{5}{9} a - \frac{32}{9}\) , \( \frac{1}{9} a^{3} + \frac{1}{3} a^{2} - \frac{5}{9} a - \frac{22}{9}\) , \( -\frac{1}{3} a^{3} + a^{2} + \frac{11}{3} a - \frac{11}{3}\) , \( -\frac{23}{9} a^{3} + \frac{10}{3} a^{2} + \frac{295}{9} a - \frac{25}{9}\) , \( -\frac{25}{3} a^{3} + 8 a^{2} + \frac{305}{3} a + \frac{31}{3}\bigr] \) |
${y}^2+\left(-\frac{1}{9}a^{3}+\frac{2}{3}a^{2}+\frac{5}{9}a-\frac{32}{9}\right){x}{y}+\left(-\frac{1}{3}a^{3}+a^{2}+\frac{11}{3}a-\frac{11}{3}\right){y}={x}^{3}+\left(\frac{1}{9}a^{3}+\frac{1}{3}a^{2}-\frac{5}{9}a-\frac{22}{9}\right){x}^{2}+\left(-\frac{23}{9}a^{3}+\frac{10}{3}a^{2}+\frac{295}{9}a-\frac{25}{9}\right){x}-\frac{25}{3}a^{3}+8a^{2}+\frac{305}{3}a+\frac{31}{3}$ |
| 16.4-d1 |
16.4-d |
$2$ |
$2$ |
\(\Q(\sqrt{2}, \sqrt{17})\) |
$4$ |
$[4, 0]$ |
16.4 |
\( 2^{4} \) |
\( 2^{8} \) |
$17.18670$ |
$(4/9a^3-2/3a^2-47/9a+29/9)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$942.8701559$ |
3.466434397 |
\( 128 a^{3} - 192 a^{2} - 1792 a + 2496 \) |
\( \bigl[-\frac{1}{9} a^{3} + \frac{2}{3} a^{2} + \frac{5}{9} a - \frac{32}{9}\) , \( -\frac{5}{9} a^{3} + \frac{1}{3} a^{2} + \frac{61}{9} a + \frac{2}{9}\) , \( -\frac{1}{3} a^{3} + a^{2} + \frac{11}{3} a - \frac{11}{3}\) , \( -\frac{16}{9} a^{3} + \frac{8}{3} a^{2} + \frac{224}{9} a - \frac{17}{9}\) , \( -\frac{4}{9} a^{3} + \frac{14}{3} a^{2} + \frac{164}{9} a - \frac{11}{9}\bigr] \) |
${y}^2+\left(-\frac{1}{9}a^{3}+\frac{2}{3}a^{2}+\frac{5}{9}a-\frac{32}{9}\right){x}{y}+\left(-\frac{1}{3}a^{3}+a^{2}+\frac{11}{3}a-\frac{11}{3}\right){y}={x}^{3}+\left(-\frac{5}{9}a^{3}+\frac{1}{3}a^{2}+\frac{61}{9}a+\frac{2}{9}\right){x}^{2}+\left(-\frac{16}{9}a^{3}+\frac{8}{3}a^{2}+\frac{224}{9}a-\frac{17}{9}\right){x}-\frac{4}{9}a^{3}+\frac{14}{3}a^{2}+\frac{164}{9}a-\frac{11}{9}$ |
| 64.1-a2 |
64.1-a |
$2$ |
$2$ |
\(\Q(\sqrt{2}, \sqrt{17})\) |
$4$ |
$[4, 0]$ |
64.1 |
\( 2^{6} \) |
\( 2^{20} \) |
$20.43854$ |
$(7/9a^3-5/3a^2-71/9a+80/9), (4/9a^3-2/3a^2-47/9a+29/9)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 1 \) |
$1.396569388$ |
$471.4350779$ |
4.841116167 |
\( 128 a^{3} - 192 a^{2} - 1792 a + 2496 \) |
\( \bigl[0\) , \( -\frac{1}{3} a^{3} + \frac{14}{3} a + \frac{7}{3}\) , \( 0\) , \( \frac{22}{3} a^{3} + 18 a^{2} - \frac{38}{3} a - \frac{4}{3}\) , \( 162 a^{3} + 323 a^{2} - 500 a - 80\bigr] \) |
${y}^2={x}^{3}+\left(-\frac{1}{3}a^{3}+\frac{14}{3}a+\frac{7}{3}\right){x}^{2}+\left(\frac{22}{3}a^{3}+18a^{2}-\frac{38}{3}a-\frac{4}{3}\right){x}+162a^{3}+323a^{2}-500a-80$ |
| 64.1-d2 |
64.1-d |
$2$ |
$2$ |
\(\Q(\sqrt{2}, \sqrt{17})\) |
$4$ |
$[4, 0]$ |
64.1 |
\( 2^{6} \) |
\( 2^{20} \) |
$20.43854$ |
$(7/9a^3-5/3a^2-71/9a+80/9), (4/9a^3-2/3a^2-47/9a+29/9)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 1 \) |
$1.396569388$ |
$471.4350779$ |
4.841116167 |
\( 128 a^{3} - 192 a^{2} - 1792 a + 2496 \) |
\( \bigl[0\) , \( -\frac{1}{9} a^{3} + \frac{2}{3} a^{2} + \frac{14}{9} a - \frac{23}{9}\) , \( 0\) , \( -\frac{410}{9} a^{3} + \frac{118}{3} a^{2} + \frac{4930}{9} a + \frac{740}{9}\) , \( -\frac{2626}{3} a^{3} + 747 a^{2} + \frac{31460}{3} a + \frac{4576}{3}\bigr] \) |
${y}^2={x}^{3}+\left(-\frac{1}{9}a^{3}+\frac{2}{3}a^{2}+\frac{14}{9}a-\frac{23}{9}\right){x}^{2}+\left(-\frac{410}{9}a^{3}+\frac{118}{3}a^{2}+\frac{4930}{9}a+\frac{740}{9}\right){x}-\frac{2626}{3}a^{3}+747a^{2}+\frac{31460}{3}a+\frac{4576}{3}$ |
*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.
