| 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 |
| 868.2-b5 |
868.2-b |
$5$ |
$9$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
868.2 |
\( 2^{2} \cdot 7 \cdot 31 \) |
\( 2^{2} \cdot 7^{2} \cdot 31^{9} \) |
$0.84010$ |
$(-3a+1), (6a-5), (2)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1[2] |
$1$ |
\( 2 \cdot 3^{2} \) |
$1$ |
$0.497046915$ |
1.147880680 |
\( \frac{406635051366709052855}{2591082971745758} a + \frac{44028606239712586643}{1295541485872879} \) |
\( \bigl[a + 1\) , \( 1\) , \( a\) , \( -499 a + 27\) , \( -5019 a + 2806\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+{x}^{2}+\left(-499a+27\right){x}-5019a+2806$ |
| 54684.2-a4 |
54684.2-a |
$5$ |
$9$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
54684.2 |
\( 2^{2} \cdot 3^{2} \cdot 7^{2} \cdot 31 \) |
\( 2^{2} \cdot 3^{6} \cdot 7^{8} \cdot 31^{9} \) |
$2.36681$ |
$(-2a+1), (-3a+1), (6a-5), (2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B[2] |
$1$ |
\( 2 \cdot 3^{2} \) |
$1$ |
$0.108464529$ |
2.254392903 |
\( \frac{406635051366709052855}{2591082971745758} a + \frac{44028606239712586643}{1295541485872879} \) |
\( \bigl[1\) , \( a\) , \( 0\) , \( -7717 a - 3856\) , \( 397303 a - 10303\bigr] \) |
${y}^2+{x}{y}={x}^{3}+a{x}^{2}+\left(-7717a-3856\right){x}+397303a-10303$ |
| 55552.2-e4 |
55552.2-e |
$5$ |
$9$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
55552.2 |
\( 2^{8} \cdot 7 \cdot 31 \) |
\( 2^{26} \cdot 7^{2} \cdot 31^{9} \) |
$2.37615$ |
$(-3a+1), (6a-5), (2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B[2] |
$1$ |
\( 2^{2} \) |
$2.657384984$ |
$0.124261728$ |
3.050360885 |
\( \frac{406635051366709052855}{2591082971745758} a + \frac{44028606239712586643}{1295541485872879} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -7979 a + 422\) , \( 305673 a - 171170\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+\left(-7979a+422\right){x}+305673a-171170$ |
| 146692.2-b4 |
146692.2-b |
$5$ |
$9$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
146692.2 |
\( 2^{2} \cdot 7 \cdot 13^{2} \cdot 31 \) |
\( 2^{2} \cdot 7^{2} \cdot 13^{6} \cdot 31^{9} \) |
$3.02901$ |
$(-3a+1), (-4a+1), (6a-5), (2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B[2] |
$1$ |
\( 2^{2} \cdot 3^{2} \) |
$0.252641283$ |
$0.137856010$ |
2.895555473 |
\( \frac{406635051366709052855}{2591082971745758} a + \frac{44028606239712586643}{1295541485872879} \) |
\( \bigl[1\) , \( a - 1\) , \( 1\) , \( -7296 a + 3701\) , \( -154103 a + 217381\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-7296a+3701\right){x}-154103a+217381$ |
| 146692.6-b4 |
146692.6-b |
$5$ |
$9$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
146692.6 |
\( 2^{2} \cdot 7 \cdot 13^{2} \cdot 31 \) |
\( 2^{2} \cdot 7^{2} \cdot 13^{6} \cdot 31^{9} \) |
$3.02901$ |
$(-3a+1), (4a-3), (6a-5), (2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B[2] |
$1$ |
\( 2 \) |
$4.988945552$ |
$0.137856010$ |
3.176609500 |
\( \frac{406635051366709052855}{2591082971745758} a + \frac{44028606239712586643}{1295541485872879} \) |
\( \bigl[a\) , \( a - 1\) , \( a\) , \( -4175 a - 3095\) , \( -177982 a - 25782\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-4175a-3095\right){x}-177982a-25782$ |
*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.
