| 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-a6 |
192.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
192.1 |
\( 2^{6} \cdot 3 \) |
\( 2^{20} \cdot 3^{8} \) |
$0.57614$ |
$(-2a+1), (2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$1$ |
$1.817673508$ |
0.524717144 |
\( \frac{1556068}{81} \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( -24 a + 24\) , \( -36\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(-24a+24\right){x}-36$ |
| 768.1-a6 |
768.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
768.1 |
\( 2^{8} \cdot 3 \) |
\( 2^{20} \cdot 3^{8} \) |
$0.81478$ |
$(-2a+1), (2)$ |
0 |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$1$ |
$1.817673508$ |
1.049434289 |
\( \frac{1556068}{81} \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( -24 a + 24\) , \( 36\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(-24a+24\right){x}+36$ |
| 2304.1-a6 |
2304.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
2304.1 |
\( 2^{8} \cdot 3^{2} \) |
\( 2^{20} \cdot 3^{14} \) |
$1.07231$ |
$(-2a+1), (2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$1$ |
$1.049434289$ |
1.211782339 |
\( \frac{1556068}{81} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( a + 73\) , \( 289 a - 108\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(a+73\right){x}+289a-108$ |
| 2304.1-b6 |
2304.1-b |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
2304.1 |
\( 2^{8} \cdot 3^{2} \) |
\( 2^{20} \cdot 3^{14} \) |
$1.07231$ |
$(-2a+1), (2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$1$ |
$1.049434289$ |
1.211782339 |
\( \frac{1556068}{81} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( a + 73\) , \( -289 a + 108\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(a+73\right){x}-289a+108$ |
| 12288.1-b6 |
12288.1-b |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
12288.1 |
\( 2^{12} \cdot 3 \) |
\( 2^{32} \cdot 3^{8} \) |
$1.62956$ |
$(-2a+1), (2)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$2.158547729$ |
$0.908836754$ |
2.265254003 |
\( \frac{1556068}{81} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 97 a\) , \( 385\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+97a{x}+385$ |
| 12288.1-g6 |
12288.1-g |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
12288.1 |
\( 2^{12} \cdot 3 \) |
\( 2^{32} \cdot 3^{8} \) |
$1.62956$ |
$(-2a+1), (2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$1$ |
$0.908836754$ |
2.098868579 |
\( \frac{1556068}{81} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -97\) , \( -385\bigr] \) |
${y}^2={x}^{3}+{x}^{2}-97{x}-385$ |
| 28224.1-c6 |
28224.1-c |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
28224.1 |
\( 2^{6} \cdot 3^{2} \cdot 7^{2} \) |
\( 2^{20} \cdot 3^{14} \cdot 7^{6} \) |
$2.00611$ |
$(-2a+1), (-3a+1), (2)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$1.765770104$ |
$0.396648878$ |
3.234966217 |
\( \frac{1556068}{81} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 220 a - 584\) , \( -2596 a + 5160\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(220a-584\right){x}-2596a+5160$ |
| 28224.3-c6 |
28224.3-c |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
28224.3 |
\( 2^{6} \cdot 3^{2} \cdot 7^{2} \) |
\( 2^{20} \cdot 3^{14} \cdot 7^{6} \) |
$2.00611$ |
$(-2a+1), (3a-2), (2)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$1.765770104$ |
$0.396648878$ |
3.234966217 |
\( \frac{1556068}{81} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 585 a - 219\) , \( 2961 a + 1980\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(585a-219\right){x}+2961a+1980$ |
| 32448.1-e6 |
32448.1-e |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
32448.1 |
\( 2^{6} \cdot 3 \cdot 13^{2} \) |
\( 2^{20} \cdot 3^{8} \cdot 13^{6} \) |
$2.07729$ |
$(-2a+1), (-4a+1), (2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{6} \) |
$1$ |
$0.504131926$ |
2.328485625 |
\( \frac{1556068}{81} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( 365 a - 170\) , \( -1465 a - 806\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+\left(365a-170\right){x}-1465a-806$ |
| 32448.3-e6 |
32448.3-e |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
32448.3 |
\( 2^{6} \cdot 3 \cdot 13^{2} \) |
\( 2^{20} \cdot 3^{8} \cdot 13^{6} \) |
$2.07729$ |
$(-2a+1), (4a-3), (2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{6} \) |
$1$ |
$0.504131926$ |
2.328485625 |
\( \frac{1556068}{81} \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( 170 a - 365\) , \( 1465 a - 2271\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(170a-365\right){x}+1465a-2271$ |
| 36864.1-l6 |
36864.1-l |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
36864.1 |
\( 2^{12} \cdot 3^{2} \) |
\( 2^{32} \cdot 3^{14} \) |
$2.14462$ |
$(-2a+1), (2)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$2.786181258$ |
$0.524717144$ |
3.376245242 |
\( \frac{1556068}{81} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 293 a - 292\) , \( -2018 a + 863\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(293a-292\right){x}-2018a+863$ |
| 36864.1-m6 |
36864.1-m |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
36864.1 |
\( 2^{12} \cdot 3^{2} \) |
\( 2^{32} \cdot 3^{14} \) |
$2.14462$ |
$(-2a+1), (2)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$2.786181258$ |
$0.524717144$ |
3.376245242 |
\( \frac{1556068}{81} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 293 a - 292\) , \( 2018 a - 863\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(293a-292\right){x}+2018a-863$ |
| 37632.1-e6 |
37632.1-e |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
37632.1 |
\( 2^{8} \cdot 3 \cdot 7^{2} \) |
\( 2^{20} \cdot 3^{8} \cdot 7^{6} \) |
$2.15570$ |
$(-2a+1), (-3a+1), (2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$1$ |
$0.687016009$ |
1.586595513 |
\( \frac{1556068}{81} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -73 a + 195\) , \( -769 a - 109\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+\left(-73a+195\right){x}-769a-109$ |
| 37632.1-k6 |
37632.1-k |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
37632.1 |
\( 2^{8} \cdot 3 \cdot 7^{2} \) |
\( 2^{20} \cdot 3^{8} \cdot 7^{6} \) |
$2.15570$ |
$(-2a+1), (-3a+1), (2)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{7} \) |
$0.321540817$ |
$0.687016009$ |
4.081241752 |
\( \frac{1556068}{81} \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( -122 a - 73\) , \( 769 a + 109\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(-122a-73\right){x}+769a+109$ |
| 37632.3-e6 |
37632.3-e |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
37632.3 |
\( 2^{8} \cdot 3 \cdot 7^{2} \) |
\( 2^{20} \cdot 3^{8} \cdot 7^{6} \) |
$2.15570$ |
$(-2a+1), (3a-2), (2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$1$ |
$0.687016009$ |
1.586595513 |
\( \frac{1556068}{81} \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( 122 a - 195\) , \( 769 a - 878\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(122a-195\right){x}+769a-878$ |
| 37632.3-k6 |
37632.3-k |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
37632.3 |
\( 2^{8} \cdot 3 \cdot 7^{2} \) |
\( 2^{20} \cdot 3^{8} \cdot 7^{6} \) |
$2.15570$ |
$(-2a+1), (3a-2), (2)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{7} \) |
$0.321540817$ |
$0.687016009$ |
4.081241752 |
\( \frac{1556068}{81} \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( 122 a - 195\) , \( -769 a + 878\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(122a-195\right){x}-769a+878$ |
| 112896.1-p6 |
112896.1-p |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
112896.1 |
\( 2^{8} \cdot 3^{2} \cdot 7^{2} \) |
\( 2^{20} \cdot 3^{14} \cdot 7^{6} \) |
$2.83706$ |
$(-2a+1), (-3a+1), (2)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{6} \) |
$1.182551022$ |
$0.396648878$ |
4.332967921 |
\( \frac{1556068}{81} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 220 a - 584\) , \( 2596 a - 5160\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(220a-584\right){x}+2596a-5160$ |
| 112896.3-p6 |
112896.3-p |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
112896.3 |
\( 2^{8} \cdot 3^{2} \cdot 7^{2} \) |
\( 2^{20} \cdot 3^{14} \cdot 7^{6} \) |
$2.83706$ |
$(-2a+1), (3a-2), (2)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{6} \) |
$1.182551022$ |
$0.396648878$ |
4.332967921 |
\( \frac{1556068}{81} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 585 a - 219\) , \( -2961 a - 1980\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(585a-219\right){x}-2961a-1980$ |
| 120000.1-h6 |
120000.1-h |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
120000.1 |
\( 2^{6} \cdot 3 \cdot 5^{4} \) |
\( 2^{20} \cdot 3^{8} \cdot 5^{12} \) |
$2.88068$ |
$(-2a+1), (2), (5)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{6} \) |
$1.665930347$ |
$0.363534701$ |
5.594510179 |
\( \frac{1556068}{81} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -608\) , \( -5712\bigr] \) |
${y}^2={x}^{3}+{x}^{2}-608{x}-5712$ |
| 129792.1-d6 |
129792.1-d |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
129792.1 |
\( 2^{8} \cdot 3 \cdot 13^{2} \) |
\( 2^{20} \cdot 3^{8} \cdot 13^{6} \) |
$2.93773$ |
$(-2a+1), (-4a+1), (2)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$1.695770643$ |
$0.504131926$ |
3.948577566 |
\( \frac{1556068}{81} \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( -170 a - 195\) , \( 1465 a + 806\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(-170a-195\right){x}+1465a+806$ |
| 129792.3-d6 |
129792.3-d |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
129792.3 |
\( 2^{8} \cdot 3 \cdot 13^{2} \) |
\( 2^{20} \cdot 3^{8} \cdot 13^{6} \) |
$2.93773$ |
$(-2a+1), (4a-3), (2)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$1.695770643$ |
$0.504131926$ |
3.948577566 |
\( \frac{1556068}{81} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -365 a + 195\) , \( -1465 a + 2271\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+\left(-365a+195\right){x}-1465a+2271$ |
*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.
