| 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 |
| 18.1-a6 |
18.1-a |
$6$ |
$8$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
18.1 |
\( 2 \cdot 3^{2} \) |
\( - 2 \cdot 3^{4} \) |
$0.75889$ |
$(-a+2), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 2 \) |
$1$ |
$1.680639832$ |
0.815230064 |
\( \frac{35465918197138001}{18} a + \frac{55381904319590417}{18} \) |
\( \bigl[1\) , \( a\) , \( a\) , \( -26 a + 41\) , \( 269 a - 769\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+a{x}^{2}+\left(-26a+41\right){x}+269a-769$ |
| 144.4-d6 |
144.4-d |
$6$ |
$8$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
144.4 |
\( 2^{4} \cdot 3^{2} \) |
\( - 2^{13} \cdot 3^{4} \) |
$1.27630$ |
$(-a+2), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$3.670672990$ |
$1.255153815$ |
2.234848983 |
\( \frac{35465918197138001}{18} a + \frac{55381904319590417}{18} \) |
\( \bigl[a\) , \( a\) , \( 0\) , \( -89 a + 57\) , \( -1329 a + 2254\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+a{x}^{2}+\left(-89a+57\right){x}-1329a+2254$ |
| 162.1-a6 |
162.1-a |
$6$ |
$8$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
162.1 |
\( 2 \cdot 3^{4} \) |
\( - 2 \cdot 3^{16} \) |
$1.31444$ |
$(-a+2), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$4.878712504$ |
1.183261586 |
\( \frac{35465918197138001}{18} a + \frac{55381904319590417}{18} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -234 a + 357\) , \( -7141 a + 19807\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}+\left(-234a+357\right){x}-7141a+19807$ |
| 288.3-c6 |
288.3-c |
$6$ |
$8$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
288.3 |
\( 2^{5} \cdot 3^{2} \) |
\( - 2^{13} \cdot 3^{4} \) |
$1.51779$ |
$(-a+2), (-a-1), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.740113010$ |
$4.899414597$ |
1.758926798 |
\( \frac{35465918197138001}{18} a + \frac{55381904319590417}{18} \) |
\( \bigl[a + 1\) , \( -a + 1\) , \( 0\) , \( -144 a + 304\) , \( 4630 a - 11690\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-144a+304\right){x}+4630a-11690$ |
| 576.7-h6 |
576.7-h |
$6$ |
$8$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
576.7 |
\( 2^{6} \cdot 3^{2} \) |
\( - 2^{19} \cdot 3^{4} \) |
$1.80496$ |
$(-a+2), (3)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$4$ |
\( 2^{3} \) |
$1$ |
$3.464409285$ |
1.680485342 |
\( \frac{35465918197138001}{18} a + \frac{55381904319590417}{18} \) |
\( \bigl[a\) , \( a + 1\) , \( a\) , \( -900 a - 1369\) , \( 19384 a + 29899\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-900a-1369\right){x}+19384a+29899$ |
| 576.7-k6 |
576.7-k |
$6$ |
$8$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
576.7 |
\( 2^{6} \cdot 3^{2} \) |
\( - 2^{19} \cdot 3^{4} \) |
$1.80496$ |
$(-a+2), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$5.174656042$ |
1.255038437 |
\( \frac{35465918197138001}{18} a + \frac{55381904319590417}{18} \) |
\( \bigl[a\) , \( -1\) , \( a\) , \( -616 a + 1519\) , \( -48003 a + 123109\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(-616a+1519\right){x}-48003a+123109$ |
*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.
