| 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-b2 |
1536.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1536.1 |
\( 2^{9} \cdot 3 \) |
\( 2^{10} \cdot 3^{2} \) |
$1.93788$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$1$ |
$24.28254506$ |
1.752441741 |
\( \frac{16000}{3} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -a - 2\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(-a-2\right){x}$ |
| 1536.1-k2 |
1536.1-k |
$4$ |
$4$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1536.1 |
\( 2^{9} \cdot 3 \) |
\( 2^{10} \cdot 3^{2} \) |
$1.93788$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$1$ |
$24.28254506$ |
1.752441741 |
\( \frac{16000}{3} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( a - 2\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(a-2\right){x}$ |
| 1536.1-n2 |
1536.1-n |
$4$ |
$4$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1536.1 |
\( 2^{9} \cdot 3 \) |
\( 2^{10} \cdot 3^{2} \) |
$1.93788$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$1$ |
$24.28254506$ |
1.752441741 |
\( \frac{16000}{3} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -a - 2\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(-a-2\right){x}$ |
| 1536.1-w2 |
1536.1-w |
$4$ |
$4$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1536.1 |
\( 2^{9} \cdot 3 \) |
\( 2^{10} \cdot 3^{2} \) |
$1.93788$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$1$ |
$24.28254506$ |
1.752441741 |
\( \frac{16000}{3} \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( a - 2\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(a-2\right){x}$ |
| 3072.1-d2 |
3072.1-d |
$4$ |
$4$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
3072.1 |
\( 2^{10} \cdot 3 \) |
\( 2^{16} \cdot 3^{2} \) |
$2.30454$ |
$(a+1), (a)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1.207525233$ |
$12.81018584$ |
4.465406728 |
\( \frac{16000}{3} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -3\) , \( -3\bigr] \) |
${y}^2={x}^{3}+{x}^{2}-3{x}-3$ |
| 3072.1-bb2 |
3072.1-bb |
$4$ |
$4$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
3072.1 |
\( 2^{10} \cdot 3 \) |
\( 2^{16} \cdot 3^{2} \) |
$2.30454$ |
$(a+1), (a)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$0.848371993$ |
$12.81018584$ |
3.137264466 |
\( \frac{16000}{3} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 14 a - 22\) , \( 32 a - 56\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(14a-22\right){x}+32a-56$ |
| 3072.1-bn2 |
3072.1-bn |
$4$ |
$4$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
3072.1 |
\( 2^{10} \cdot 3 \) |
\( 2^{16} \cdot 3^{2} \) |
$2.30454$ |
$(a+1), (a)$ |
$2$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$0.298069290$ |
$23.01457612$ |
3.960587271 |
\( \frac{16000}{3} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -3\) , \( 3\bigr] \) |
${y}^2={x}^{3}-{x}^{2}-3{x}+3$ |
| 3072.1-bu2 |
3072.1-bu |
$4$ |
$4$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
3072.1 |
\( 2^{10} \cdot 3 \) |
\( 2^{16} \cdot 3^{2} \) |
$2.30454$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1$ |
$23.01457612$ |
3.321867930 |
\( \frac{16000}{3} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 14 a - 22\) , \( -32 a + 56\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(14a-22\right){x}-32a+56$ |
| 4608.1-g2 |
4608.1-g |
$4$ |
$4$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
4608.1 |
\( 2^{9} \cdot 3^{2} \) |
\( 2^{10} \cdot 3^{8} \) |
$2.55039$ |
$(a+1), (a)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$0.747740990$ |
$18.79132271$ |
4.056186517 |
\( \frac{16000}{3} \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( 5 a - 9\) , \( -4 a + 8\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(5a-9\right){x}-4a+8$ |
| 4608.1-j2 |
4608.1-j |
$4$ |
$4$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
4608.1 |
\( 2^{9} \cdot 3^{2} \) |
\( 2^{10} \cdot 3^{8} \) |
$2.55039$ |
$(a+1), (a)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$0.747740990$ |
$18.79132271$ |
4.056186517 |
\( \frac{16000}{3} \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( -5 a - 9\) , \( 4 a + 8\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(-5a-9\right){x}+4a+8$ |
| 4608.1-r2 |
4608.1-r |
$4$ |
$4$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
4608.1 |
\( 2^{9} \cdot 3^{2} \) |
\( 2^{10} \cdot 3^{8} \) |
$2.55039$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1$ |
$10.45947294$ |
1.509694880 |
\( \frac{16000}{3} \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( 5 a - 9\) , \( 4 a - 8\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(5a-9\right){x}+4a-8$ |
| 4608.1-bd2 |
4608.1-bd |
$4$ |
$4$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
4608.1 |
\( 2^{9} \cdot 3^{2} \) |
\( 2^{10} \cdot 3^{8} \) |
$2.55039$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1$ |
$10.45947294$ |
1.509694880 |
\( \frac{16000}{3} \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( -5 a - 9\) , \( -4 a - 8\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(-5a-9\right){x}-4a-8$ |
*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.
