| 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 |
| 1536.1-a2 |
1536.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
1536.1 |
\( 2^{9} \cdot 3 \) |
\( 2^{10} \cdot 3^{2} \) |
$1.58227$ |
$(a), (-a-1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$0.904956275$ |
$6.501062528$ |
2.080017293 |
\( \frac{1408}{9} a + \frac{128}{9} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -a\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}-a{x}$ |
| 1536.1-b2 |
1536.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
1536.1 |
\( 2^{9} \cdot 3 \) |
\( 2^{10} \cdot 3^{2} \) |
$1.58227$ |
$(a), (-a-1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$1.207282053$ |
$6.501062528$ |
2.774904841 |
\( \frac{1408}{9} a + \frac{128}{9} \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( -a\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}-a{x}$ |
| 3072.1-b2 |
3072.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
3072.1 |
\( 2^{10} \cdot 3 \) |
\( 2^{16} \cdot 3^{2} \) |
$1.88165$ |
$(a), (-a-1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1$ |
$4.596945398$ |
1.625265632 |
\( \frac{1408}{9} a + \frac{128}{9} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -1\) , \( a - 1\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}-{x}+a-1$ |
| 3072.1-c2 |
3072.1-c |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
3072.1 |
\( 2^{10} \cdot 3 \) |
\( 2^{16} \cdot 3^{2} \) |
$1.88165$ |
$(a), (-a-1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1$ |
$4.596945398$ |
1.625265632 |
\( \frac{1408}{9} a + \frac{128}{9} \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( -1\) , \( -a + 1\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}-{x}-a+1$ |
| 4608.1-a2 |
4608.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
4608.1 |
\( 2^{9} \cdot 3^{2} \) |
\( 2^{10} \cdot 3^{8} \) |
$2.08239$ |
$(a), (-a-1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1$ |
$3.753390200$ |
1.327023831 |
\( \frac{1408}{9} a + \frac{128}{9} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( a + 1\) , \( a + 2\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}+a+2$ |
| 4608.1-b2 |
4608.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
4608.1 |
\( 2^{9} \cdot 3^{2} \) |
\( 2^{10} \cdot 3^{8} \) |
$2.08239$ |
$(a), (-a-1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1$ |
$3.753390200$ |
1.327023831 |
\( \frac{1408}{9} a + \frac{128}{9} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( a + 1\) , \( -a - 2\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}-a-2$ |
| 9216.1-b2 |
9216.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
9216.1 |
\( 2^{10} \cdot 3^{2} \) |
\( 2^{16} \cdot 3^{8} \) |
$2.47639$ |
$(a), (-a-1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$0.898616527$ |
$2.654047663$ |
3.372858468 |
\( \frac{1408}{9} a + \frac{128}{9} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -2 a - 2\) , \( 4 a - 4\bigr] \) |
${y}^2={x}^{3}+\left(-2a-2\right){x}+4a-4$ |
| 9216.1-f2 |
9216.1-f |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
9216.1 |
\( 2^{10} \cdot 3^{2} \) |
\( 2^{16} \cdot 3^{8} \) |
$2.47639$ |
$(a), (-a-1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$1$ |
$2.654047663$ |
1.876695100 |
\( \frac{1408}{9} a + \frac{128}{9} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -2 a - 2\) , \( -4 a + 4\bigr] \) |
${y}^2={x}^{3}+\left(-2a-2\right){x}-4a+4$ |
| 13824.3-d2 |
13824.3-d |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
13824.3 |
\( 2^{9} \cdot 3^{3} \) |
\( 2^{10} \cdot 3^{8} \) |
$2.74058$ |
$(a), (-a-1), (a-1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$0.700977202$ |
$3.753390200$ |
3.720853813 |
\( \frac{1408}{9} a + \frac{128}{9} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -a - 2\) , \( 2 a\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(-a-2\right){x}+2a$ |
| 13824.3-s2 |
13824.3-s |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
13824.3 |
\( 2^{9} \cdot 3^{3} \) |
\( 2^{10} \cdot 3^{8} \) |
$2.74058$ |
$(a), (-a-1), (a-1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$1$ |
$3.753390200$ |
2.654047663 |
\( \frac{1408}{9} a + \frac{128}{9} \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( -a - 2\) , \( -2 a\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(-a-2\right){x}-2a$ |
| 27648.3-c2 |
27648.3-c |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
27648.3 |
\( 2^{10} \cdot 3^{3} \) |
\( 2^{16} \cdot 3^{8} \) |
$3.25911$ |
$(a), (-a-1), (a-1)$ |
$2$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$0.397516128$ |
$2.654047663$ |
5.968132565 |
\( \frac{1408}{9} a + \frac{128}{9} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 3\) , \( a - 5\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+3{x}+a-5$ |
| 27648.3-bu2 |
27648.3-bu |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
27648.3 |
\( 2^{10} \cdot 3^{3} \) |
\( 2^{16} \cdot 3^{8} \) |
$3.25911$ |
$(a), (-a-1), (a-1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$1$ |
$2.654047663$ |
3.753390200 |
\( \frac{1408}{9} a + \frac{128}{9} \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( 3\) , \( -a + 5\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+3{x}-a+5$ |
| 41472.3-f2 |
41472.3-f |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
41472.3 |
\( 2^{9} \cdot 3^{4} \) |
\( 2^{10} \cdot 3^{14} \) |
$3.60680$ |
$(a), (-a-1), (a-1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$1$ |
$2.167020842$ |
3.064630265 |
\( \frac{1408}{9} a + \frac{128}{9} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -3 a + 3\) , \( -7 a - 8\bigr] \) |
${y}^2={x}^{3}+\left(-3a+3\right){x}-7a-8$ |
| 41472.3-z2 |
41472.3-z |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
41472.3 |
\( 2^{9} \cdot 3^{4} \) |
\( 2^{10} \cdot 3^{14} \) |
$3.60680$ |
$(a), (-a-1), (a-1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$0.879584223$ |
$2.167020842$ |
5.391200862 |
\( \frac{1408}{9} a + \frac{128}{9} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -3 a + 3\) , \( 7 a + 8\bigr] \) |
${y}^2={x}^{3}+\left(-3a+3\right){x}+7a+8$ |
*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.
