| 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 |
| 192.1-a3 |
192.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
192.1 |
\( 2^{6} \cdot 3 \) |
\( 2^{22} \cdot 3^{16} \) |
$0.57614$ |
$(-2a+1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$0.908836754$ |
0.524717144 |
\( \frac{207646}{6561} \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( 16 a - 16\) , \( -180\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(16a-16\right){x}-180$ |
| 768.1-a3 |
768.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
768.1 |
\( 2^{8} \cdot 3 \) |
\( 2^{22} \cdot 3^{16} \) |
$0.81478$ |
$(-2a+1), (2)$ |
0 |
$\Z/8\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{6} \) |
$1$ |
$0.908836754$ |
1.049434289 |
\( \frac{207646}{6561} \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( 16 a - 16\) , \( 180\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(16a-16\right){x}+180$ |
| 2304.1-a3 |
2304.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
2304.1 |
\( 2^{8} \cdot 3^{2} \) |
\( 2^{22} \cdot 3^{22} \) |
$1.07231$ |
$(-2a+1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$0.524717144$ |
1.211782339 |
\( \frac{207646}{6561} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( a - 47\) , \( 1033 a - 540\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(a-47\right){x}+1033a-540$ |
| 2304.1-b3 |
2304.1-b |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
2304.1 |
\( 2^{8} \cdot 3^{2} \) |
\( 2^{22} \cdot 3^{22} \) |
$1.07231$ |
$(-2a+1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$0.524717144$ |
1.211782339 |
\( \frac{207646}{6561} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( a - 47\) , \( -1033 a + 540\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(a-47\right){x}-1033a+540$ |
| 12288.1-b3 |
12288.1-b |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
12288.1 |
\( 2^{12} \cdot 3 \) |
\( 2^{34} \cdot 3^{16} \) |
$1.62956$ |
$(-2a+1), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1.079273864$ |
$0.454418377$ |
2.265254003 |
\( \frac{207646}{6561} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -63 a\) , \( 1377\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}-63a{x}+1377$ |
| 12288.1-g3 |
12288.1-g |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
12288.1 |
\( 2^{12} \cdot 3 \) |
\( 2^{34} \cdot 3^{16} \) |
$1.62956$ |
$(-2a+1), (2)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{6} \) |
$1$ |
$0.454418377$ |
2.098868579 |
\( \frac{207646}{6561} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( 63\) , \( -1377\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+63{x}-1377$ |
| 28224.1-c3 |
28224.1-c |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
28224.1 |
\( 2^{6} \cdot 3^{2} \cdot 7^{2} \) |
\( 2^{22} \cdot 3^{22} \cdot 7^{6} \) |
$2.00611$ |
$(-2a+1), (-3a+1), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$3.531540208$ |
$0.198324439$ |
3.234966217 |
\( \frac{207646}{6561} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -140 a + 376\) , \( -10516 a + 19224\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(-140a+376\right){x}-10516a+19224$ |
| 28224.3-c3 |
28224.3-c |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
28224.3 |
\( 2^{6} \cdot 3^{2} \cdot 7^{2} \) |
\( 2^{22} \cdot 3^{22} \cdot 7^{6} \) |
$2.00611$ |
$(-2a+1), (3a-2), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$3.531540208$ |
$0.198324439$ |
3.234966217 |
\( \frac{207646}{6561} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -375 a + 141\) , \( 10281 a + 9084\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(-375a+141\right){x}+10281a+9084$ |
| 32448.1-e3 |
32448.1-e |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
32448.1 |
\( 2^{6} \cdot 3 \cdot 13^{2} \) |
\( 2^{22} \cdot 3^{16} \cdot 13^{6} \) |
$2.07729$ |
$(-2a+1), (-4a+1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$1$ |
$0.252065963$ |
2.328485625 |
\( \frac{207646}{6561} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -235 a + 110\) , \( -6369 a - 2934\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+\left(-235a+110\right){x}-6369a-2934$ |
| 32448.3-e3 |
32448.3-e |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
32448.3 |
\( 2^{6} \cdot 3 \cdot 13^{2} \) |
\( 2^{22} \cdot 3^{16} \cdot 13^{6} \) |
$2.07729$ |
$(-2a+1), (4a-3), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$1$ |
$0.252065963$ |
2.328485625 |
\( \frac{207646}{6561} \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( -110 a + 235\) , \( 6369 a - 9303\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(-110a+235\right){x}+6369a-9303$ |
| 36864.1-l3 |
36864.1-l |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
36864.1 |
\( 2^{12} \cdot 3^{2} \) |
\( 2^{34} \cdot 3^{22} \) |
$2.14462$ |
$(-2a+1), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1.393090629$ |
$0.262358572$ |
3.376245242 |
\( \frac{207646}{6561} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -187 a + 188\) , \( -8450 a + 4319\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(-187a+188\right){x}-8450a+4319$ |
| 36864.1-m3 |
36864.1-m |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
36864.1 |
\( 2^{12} \cdot 3^{2} \) |
\( 2^{34} \cdot 3^{22} \) |
$2.14462$ |
$(-2a+1), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1.393090629$ |
$0.262358572$ |
3.376245242 |
\( \frac{207646}{6561} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -187 a + 188\) , \( 8450 a - 4319\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(-187a+188\right){x}+8450a-4319$ |
| 37632.1-e3 |
37632.1-e |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
37632.1 |
\( 2^{8} \cdot 3 \cdot 7^{2} \) |
\( 2^{22} \cdot 3^{16} \cdot 7^{6} \) |
$2.15570$ |
$(-2a+1), (-3a+1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$0.343508004$ |
1.586595513 |
\( \frac{207646}{6561} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( 47 a - 125\) , \( -3161 a - 133\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+\left(47a-125\right){x}-3161a-133$ |
| 37632.1-k3 |
37632.1-k |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
37632.1 |
\( 2^{8} \cdot 3 \cdot 7^{2} \) |
\( 2^{22} \cdot 3^{16} \cdot 7^{6} \) |
$2.15570$ |
$(-2a+1), (-3a+1), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{7} \) |
$0.160770408$ |
$0.343508004$ |
4.081241752 |
\( \frac{207646}{6561} \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( 78 a + 47\) , \( 3161 a + 133\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(78a+47\right){x}+3161a+133$ |
| 37632.3-e3 |
37632.3-e |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
37632.3 |
\( 2^{8} \cdot 3 \cdot 7^{2} \) |
\( 2^{22} \cdot 3^{16} \cdot 7^{6} \) |
$2.15570$ |
$(-2a+1), (3a-2), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$0.343508004$ |
1.586595513 |
\( \frac{207646}{6561} \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( -78 a + 125\) , \( 3161 a - 3294\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(-78a+125\right){x}+3161a-3294$ |
| 37632.3-k3 |
37632.3-k |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
37632.3 |
\( 2^{8} \cdot 3 \cdot 7^{2} \) |
\( 2^{22} \cdot 3^{16} \cdot 7^{6} \) |
$2.15570$ |
$(-2a+1), (3a-2), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{7} \) |
$0.160770408$ |
$0.343508004$ |
4.081241752 |
\( \frac{207646}{6561} \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( -78 a + 125\) , \( -3161 a + 3294\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(-78a+125\right){x}-3161a+3294$ |
| 112896.1-p3 |
112896.1-p |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
112896.1 |
\( 2^{8} \cdot 3^{2} \cdot 7^{2} \) |
\( 2^{22} \cdot 3^{22} \cdot 7^{6} \) |
$2.83706$ |
$(-2a+1), (-3a+1), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$2.365102045$ |
$0.198324439$ |
4.332967921 |
\( \frac{207646}{6561} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -140 a + 376\) , \( 10516 a - 19224\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(-140a+376\right){x}+10516a-19224$ |
| 112896.3-p3 |
112896.3-p |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
112896.3 |
\( 2^{8} \cdot 3^{2} \cdot 7^{2} \) |
\( 2^{22} \cdot 3^{22} \cdot 7^{6} \) |
$2.83706$ |
$(-2a+1), (3a-2), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$2.365102045$ |
$0.198324439$ |
4.332967921 |
\( \frac{207646}{6561} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -375 a + 141\) , \( -10281 a - 9084\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(-375a+141\right){x}-10281a-9084$ |
| 120000.1-h3 |
120000.1-h |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
120000.1 |
\( 2^{6} \cdot 3 \cdot 5^{4} \) |
\( 2^{22} \cdot 3^{16} \cdot 5^{12} \) |
$2.88068$ |
$(-2a+1), (2), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{6} \) |
$0.832965173$ |
$0.181767350$ |
5.594510179 |
\( \frac{207646}{6561} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( 392\) , \( -21712\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+392{x}-21712$ |
| 129792.1-d3 |
129792.1-d |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
129792.1 |
\( 2^{8} \cdot 3 \cdot 13^{2} \) |
\( 2^{22} \cdot 3^{16} \cdot 13^{6} \) |
$2.93773$ |
$(-2a+1), (-4a+1), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$3.391541286$ |
$0.252065963$ |
3.948577566 |
\( \frac{207646}{6561} \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( 110 a + 125\) , \( 6369 a + 2934\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(110a+125\right){x}+6369a+2934$ |
| 129792.3-d3 |
129792.3-d |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
129792.3 |
\( 2^{8} \cdot 3 \cdot 13^{2} \) |
\( 2^{22} \cdot 3^{16} \cdot 13^{6} \) |
$2.93773$ |
$(-2a+1), (4a-3), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$3.391541286$ |
$0.252065963$ |
3.948577566 |
\( \frac{207646}{6561} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( 235 a - 125\) , \( -6369 a + 9303\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+\left(235a-125\right){x}-6369a+9303$ |
*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.
