| 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 |
| 171.1-a4 |
171.1-a |
$4$ |
$6$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
171.1 |
\( 3^{2} \cdot 19 \) |
\( 3^{3} \cdot 19^{2} \) |
$0.55969$ |
$(-2a+1), (-5a+3)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B.1.1[2] |
$1$ |
\( 2^{2} \) |
$1$ |
$4.069706291$ |
0.522143560 |
\( -\frac{363527109}{361} a + \frac{287391186}{361} \) |
\( \bigl[1\) , \( -1\) , \( a + 1\) , \( 5 a + 5\) , \( -11 a + 11\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(5a+5\right){x}-11a+11$ |
| 3249.1-a4 |
3249.1-a |
$4$ |
$6$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
3249.1 |
\( 3^{2} \cdot 19^{2} \) |
\( 3^{9} \cdot 19^{8} \) |
$1.16852$ |
$(-2a+1), (-5a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B[2] |
$1$ |
\( 2^{3} \) |
$1$ |
$0.539045766$ |
1.244872874 |
\( -\frac{363527109}{361} a + \frac{287391186}{361} \) |
\( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( -600 a + 426\) , \( -2310 a + 5603\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-600a+426\right){x}-2310a+5603$ |
| 8379.1-a4 |
8379.1-a |
$4$ |
$6$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
8379.1 |
\( 3^{2} \cdot 7^{2} \cdot 19 \) |
\( 3^{9} \cdot 7^{6} \cdot 19^{2} \) |
$1.48080$ |
$(-2a+1), (-3a+1), (-5a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B[2] |
$1$ |
\( 2^{4} \) |
$0.286427186$ |
$0.888082720$ |
2.349778965 |
\( -\frac{363527109}{361} a + \frac{287391186}{361} \) |
\( \bigl[a + 1\) , \( 0\) , \( 1\) , \( -212 a + 34\) , \( 1149 a - 785\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(-212a+34\right){x}+1149a-785$ |
| 8379.5-d4 |
8379.5-d |
$4$ |
$6$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
8379.5 |
\( 3^{2} \cdot 7^{2} \cdot 19 \) |
\( 3^{9} \cdot 7^{6} \cdot 19^{2} \) |
$1.48080$ |
$(-2a+1), (3a-2), (-5a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B[2] |
$1$ |
\( 2^{3} \) |
$1$ |
$0.888082720$ |
2.050939191 |
\( -\frac{363527109}{361} a + \frac{287391186}{361} \) |
\( \bigl[a + 1\) , \( 0\) , \( 0\) , \( 180 a + 30\) , \( 297 a - 1207\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(180a+30\right){x}+297a-1207$ |
| 28899.1-d4 |
28899.1-d |
$4$ |
$6$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
28899.1 |
\( 3^{2} \cdot 13^{2} \cdot 19 \) |
\( 3^{3} \cdot 13^{6} \cdot 19^{2} \) |
$2.01799$ |
$(-2a+1), (-4a+1), (-5a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B[2] |
$1$ |
\( 2^{3} \) |
$0.580370262$ |
$1.128733439$ |
3.025700258 |
\( -\frac{363527109}{361} a + \frac{287391186}{361} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( 4 a - 124\) , \( -27 a + 560\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}+\left(4a-124\right){x}-27a+560$ |
| 28899.5-c4 |
28899.5-c |
$4$ |
$6$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
28899.5 |
\( 3^{2} \cdot 13^{2} \cdot 19 \) |
\( 3^{3} \cdot 13^{6} \cdot 19^{2} \) |
$2.01799$ |
$(-2a+1), (4a-3), (-5a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B[2] |
$1$ |
\( 2^{3} \) |
$1$ |
$1.128733439$ |
2.606698220 |
\( -\frac{363527109}{361} a + \frac{287391186}{361} \) |
\( \bigl[a + 1\) , \( 0\) , \( 0\) , \( 7 a + 118\) , \( -564 a + 333\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(7a+118\right){x}-564a+333$ |
| 43776.1-b4 |
43776.1-b |
$4$ |
$6$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
43776.1 |
\( 2^{8} \cdot 3^{2} \cdot 19 \) |
\( 2^{24} \cdot 3^{9} \cdot 19^{2} \) |
$2.23876$ |
$(-2a+1), (-5a+3), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B[2] |
$1$ |
\( 2^{3} \) |
$1.073530510$ |
$0.587411505$ |
2.912635915 |
\( -\frac{363527109}{361} a + \frac{287391186}{361} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 519 a - 264\) , \( -3036 a - 1038\bigr] \) |
${y}^2={x}^{3}+\left(519a-264\right){x}-3036a-1038$ |
| 43776.1-o4 |
43776.1-o |
$4$ |
$6$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
43776.1 |
\( 2^{8} \cdot 3^{2} \cdot 19 \) |
\( 2^{24} \cdot 3^{3} \cdot 19^{2} \) |
$2.23876$ |
$(-2a+1), (-5a+3), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B[2] |
$1$ |
\( 2^{3} \) |
$0.796707316$ |
$1.017426572$ |
3.743960357 |
\( -\frac{363527109}{361} a + \frac{287391186}{361} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 85 a - 173\) , \( 568 a - 790\bigr] \) |
${y}^2={x}^{3}+\left(85a-173\right){x}+568a-790$ |
| 43776.1-q4 |
43776.1-q |
$4$ |
$6$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
43776.1 |
\( 2^{8} \cdot 3^{2} \cdot 19 \) |
\( 2^{24} \cdot 3^{9} \cdot 19^{2} \) |
$2.23876$ |
$(-2a+1), (-5a+3), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B[2] |
$1$ |
\( 2^{4} \) |
$1$ |
$0.587411505$ |
2.713137527 |
\( -\frac{363527109}{361} a + \frac{287391186}{361} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -264 a - 255\) , \( 3036 a + 1038\bigr] \) |
${y}^2={x}^{3}+\left(-264a-255\right){x}+3036a+1038$ |
| 61731.3-c4 |
61731.3-c |
$4$ |
$6$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
61731.3 |
\( 3^{2} \cdot 19^{3} \) |
\( 3^{9} \cdot 19^{8} \) |
$2.43964$ |
$(-2a+1), (-5a+3), (-5a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B[2] |
$1$ |
\( 2^{3} \) |
$1$ |
$0.539045766$ |
1.244872874 |
\( -\frac{363527109}{361} a + \frac{287391186}{361} \) |
\( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( 183 a + 417\) , \( -4773 a + 4499\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(183a+417\right){x}-4773a+4499$ |
| 106875.1-a4 |
106875.1-a |
$4$ |
$6$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
106875.1 |
\( 3^{2} \cdot 5^{4} \cdot 19 \) |
\( 3^{3} \cdot 5^{12} \cdot 19^{2} \) |
$2.79845$ |
$(-2a+1), (-5a+3), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B[2] |
$1$ |
\( 2^{3} \) |
$1$ |
$0.813941258$ |
1.879716818 |
\( -\frac{363527109}{361} a + \frac{287391186}{361} \) |
\( \bigl[1\) , \( -1\) , \( a\) , \( 137 a + 133\) , \( -1144 a + 1510\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(137a+133\right){x}-1144a+1510$ |
*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.
