| 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-d4 |
1536.1-d |
$4$ |
$4$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1536.1 |
\( 2^{9} \cdot 3 \) |
\( 2^{17} \cdot 3^{3} \) |
$1.93788$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$4$ |
\( 1 \) |
$1$ |
$2.905995327$ |
0.838888592 |
\( \frac{1291466278840}{9} a + 248542803096 \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 4758 a - 8239\) , \( -59237 a + 102601\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(4758a-8239\right){x}-59237a+102601$ |
| 1536.1-g4 |
1536.1-g |
$4$ |
$4$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1536.1 |
\( 2^{9} \cdot 3 \) |
\( 2^{17} \cdot 3^{3} \) |
$1.93788$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$2.905995327$ |
2.516665776 |
\( \frac{1291466278840}{9} a + 248542803096 \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( 340 a - 594\) , \( -1050 a + 1812\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+\left(340a-594\right){x}-1050a+1812$ |
| 1536.1-r4 |
1536.1-r |
$4$ |
$4$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1536.1 |
\( 2^{9} \cdot 3 \) |
\( 2^{17} \cdot 3^{3} \) |
$1.93788$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 3 \) |
$1$ |
$11.62398130$ |
2.516665776 |
\( \frac{1291466278840}{9} a + 248542803096 \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 4758 a - 8239\) , \( 59237 a - 102601\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(4758a-8239\right){x}+59237a-102601$ |
| 1536.1-u4 |
1536.1-u |
$4$ |
$4$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1536.1 |
\( 2^{9} \cdot 3 \) |
\( 2^{17} \cdot 3^{3} \) |
$1.93788$ |
$(a+1), (a)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$11.62398130$ |
0.838888592 |
\( \frac{1291466278840}{9} a + 248542803096 \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( 340 a - 594\) , \( 1050 a - 1812\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+\left(340a-594\right){x}+1050a-1812$ |
| 3072.1-l4 |
3072.1-l |
$4$ |
$4$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
3072.1 |
\( 2^{10} \cdot 3 \) |
\( 2^{23} \cdot 3^{3} \) |
$2.30454$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$4$ |
\( 2^{2} \) |
$1$ |
$1.917567739$ |
2.214216501 |
\( \frac{1291466278840}{9} a + 248542803096 \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -150 a - 305\) , \( -1434 a - 2499\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+\left(-150a-305\right){x}-1434a-2499$ |
| 3072.1-n4 |
3072.1-n |
$4$ |
$4$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
3072.1 |
\( 2^{10} \cdot 3 \) |
\( 2^{23} \cdot 3^{3} \) |
$2.30454$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$1.917567739$ |
1.660662376 |
\( \frac{1291466278840}{9} a + 248542803096 \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 172 a - 336\) , \( 372 a - 780\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(172a-336\right){x}+372a-780$ |
| 3072.1-bj4 |
3072.1-bj |
$4$ |
$4$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
3072.1 |
\( 2^{10} \cdot 3 \) |
\( 2^{23} \cdot 3^{3} \) |
$2.30454$ |
$(a+1), (a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1.327571650$ |
$8.807833659$ |
3.375487085 |
\( \frac{1291466278840}{9} a + 248542803096 \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 172 a - 336\) , \( -372 a + 780\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(172a-336\right){x}-372a+780$ |
| 3072.1-bw4 |
3072.1-bw |
$4$ |
$4$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
3072.1 |
\( 2^{10} \cdot 3 \) |
\( 2^{23} \cdot 3^{3} \) |
$2.30454$ |
$(a+1), (a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2 \cdot 3 \) |
$0.543379137$ |
$8.807833659$ |
4.144791566 |
\( \frac{1291466278840}{9} a + 248542803096 \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -150 a - 305\) , \( 1434 a + 2499\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+\left(-150a-305\right){x}+1434a+2499$ |
| 4608.1-d4 |
4608.1-d |
$4$ |
$4$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
4608.1 |
\( 2^{9} \cdot 3^{2} \) |
\( 2^{17} \cdot 3^{9} \) |
$2.55039$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$7.191566068$ |
2.076026302 |
\( \frac{1291466278840}{9} a + 248542803096 \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( 1020 a - 1782\) , \( -5436 a + 9450\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(1020a-1782\right){x}-5436a+9450$ |
| 4608.1-l4 |
4608.1-l |
$4$ |
$4$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
4608.1 |
\( 2^{9} \cdot 3^{2} \) |
\( 2^{17} \cdot 3^{9} \) |
$2.55039$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$7.191566068$ |
2.076026302 |
\( \frac{1291466278840}{9} a + 248542803096 \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( 14272 a - 24720\) , \( -322076 a + 557852\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(14272a-24720\right){x}-322076a+557852$ |
| 4608.1-x4 |
4608.1-x |
$4$ |
$4$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
4608.1 |
\( 2^{9} \cdot 3^{2} \) |
\( 2^{17} \cdot 3^{9} \) |
$2.55039$ |
$(a+1), (a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$2.230598773$ |
$1.565687503$ |
4.032699974 |
\( \frac{1291466278840}{9} a + 248542803096 \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( 14272 a - 24720\) , \( 322076 a - 557852\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(14272a-24720\right){x}+322076a-557852$ |
| 4608.1-z4 |
4608.1-z |
$4$ |
$4$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
4608.1 |
\( 2^{9} \cdot 3^{2} \) |
\( 2^{17} \cdot 3^{9} \) |
$2.55039$ |
$(a+1), (a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$8.922395092$ |
$1.565687503$ |
4.032699974 |
\( \frac{1291466278840}{9} a + 248542803096 \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( 1020 a - 1782\) , \( 5436 a - 9450\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(1020a-1782\right){x}+5436a-9450$ |
*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.
