| 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-a3 |
171.1-a |
$4$ |
$6$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
171.1 |
\( 3^{2} \cdot 19 \) |
\( 3^{3} \cdot 19 \) |
$0.55969$ |
$(-2a+1), (-5a+3)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B.1.1[2] |
$1$ |
\( 2 \) |
$1$ |
$8.139412583$ |
0.522143560 |
\( -\frac{9153}{19} a + \frac{36801}{19} \) |
\( \bigl[1\) , \( -1\) , \( a + 1\) , \( 0\) , \( -a\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}-a$ |
| 3249.1-a3 |
3249.1-a |
$4$ |
$6$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
3249.1 |
\( 3^{2} \cdot 19^{2} \) |
\( 3^{9} \cdot 19^{7} \) |
$1.16852$ |
$(-2a+1), (-5a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B[2] |
$1$ |
\( 2^{2} \) |
$1$ |
$1.078091533$ |
1.244872874 |
\( -\frac{9153}{19} a + \frac{36801}{19} \) |
\( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( -45 a + 36\) , \( -48 a + 62\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-45a+36\right){x}-48a+62$ |
| 8379.1-a3 |
8379.1-a |
$4$ |
$6$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
8379.1 |
\( 3^{2} \cdot 7^{2} \cdot 19 \) |
\( 3^{9} \cdot 7^{6} \cdot 19 \) |
$1.48080$ |
$(-2a+1), (-3a+1), (-5a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B[2] |
$1$ |
\( 2^{2} \) |
$0.572854372$ |
$1.776165441$ |
2.349778965 |
\( -\frac{9153}{19} a + \frac{36801}{19} \) |
\( \bigl[a + 1\) , \( 0\) , \( 1\) , \( -17 a + 4\) , \( 9 a + 1\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(-17a+4\right){x}+9a+1$ |
| 8379.5-d3 |
8379.5-d |
$4$ |
$6$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
8379.5 |
\( 3^{2} \cdot 7^{2} \cdot 19 \) |
\( 3^{9} \cdot 7^{6} \cdot 19 \) |
$1.48080$ |
$(-2a+1), (3a-2), (-5a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B[2] |
$1$ |
\( 2^{2} \) |
$1$ |
$1.776165441$ |
2.050939191 |
\( -\frac{9153}{19} a + \frac{36801}{19} \) |
\( \bigl[a + 1\) , \( 0\) , \( 0\) , \( 15 a\) , \( 12 a - 16\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+15a{x}+12a-16$ |
| 28899.1-d3 |
28899.1-d |
$4$ |
$6$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
28899.1 |
\( 3^{2} \cdot 13^{2} \cdot 19 \) |
\( 3^{3} \cdot 13^{6} \cdot 19 \) |
$2.01799$ |
$(-2a+1), (-4a+1), (-5a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B[2] |
$1$ |
\( 2^{3} \) |
$0.290185131$ |
$2.257466878$ |
3.025700258 |
\( -\frac{9153}{19} a + \frac{36801}{19} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -a - 9\) , \( -3 a + 8\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}+\left(-a-9\right){x}-3a+8$ |
| 28899.5-c3 |
28899.5-c |
$4$ |
$6$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
28899.5 |
\( 3^{2} \cdot 13^{2} \cdot 19 \) |
\( 3^{3} \cdot 13^{6} \cdot 19 \) |
$2.01799$ |
$(-2a+1), (4a-3), (-5a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B[2] |
$1$ |
\( 2^{2} \) |
$1$ |
$2.257466878$ |
2.606698220 |
\( -\frac{9153}{19} a + \frac{36801}{19} \) |
\( \bigl[a + 1\) , \( 0\) , \( 0\) , \( 2 a + 8\) , \( -3 a\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(2a+8\right){x}-3a$ |
| 43776.1-b3 |
43776.1-b |
$4$ |
$6$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
43776.1 |
\( 2^{8} \cdot 3^{2} \cdot 19 \) |
\( 2^{24} \cdot 3^{9} \cdot 19 \) |
$2.23876$ |
$(-2a+1), (-5a+3), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B[2] |
$1$ |
\( 2^{3} \) |
$0.536765255$ |
$1.174823011$ |
2.912635915 |
\( -\frac{9153}{19} a + \frac{36801}{19} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 39 a - 24\) , \( -12 a - 30\bigr] \) |
${y}^2={x}^{3}+\left(39a-24\right){x}-12a-30$ |
| 43776.1-o3 |
43776.1-o |
$4$ |
$6$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
43776.1 |
\( 2^{8} \cdot 3^{2} \cdot 19 \) |
\( 2^{24} \cdot 3^{3} \cdot 19 \) |
$2.23876$ |
$(-2a+1), (-5a+3), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B[2] |
$1$ |
\( 2^{3} \) |
$0.398353658$ |
$2.034853145$ |
3.743960357 |
\( -\frac{9153}{19} a + \frac{36801}{19} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 5 a - 13\) , \( 8 a - 6\bigr] \) |
${y}^2={x}^{3}+\left(5a-13\right){x}+8a-6$ |
| 43776.1-q3 |
43776.1-q |
$4$ |
$6$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
43776.1 |
\( 2^{8} \cdot 3^{2} \cdot 19 \) |
\( 2^{24} \cdot 3^{9} \cdot 19 \) |
$2.23876$ |
$(-2a+1), (-5a+3), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B[2] |
$1$ |
\( 2^{3} \) |
$1$ |
$1.174823011$ |
2.713137527 |
\( -\frac{9153}{19} a + \frac{36801}{19} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -24 a - 15\) , \( 12 a + 30\bigr] \) |
${y}^2={x}^{3}+\left(-24a-15\right){x}+12a+30$ |
| 61731.3-c3 |
61731.3-c |
$4$ |
$6$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
61731.3 |
\( 3^{2} \cdot 19^{3} \) |
\( 3^{9} \cdot 19^{7} \) |
$2.43964$ |
$(-2a+1), (-5a+3), (-5a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B[2] |
$1$ |
\( 2^{2} \) |
$1$ |
$1.078091533$ |
1.244872874 |
\( -\frac{9153}{19} a + \frac{36801}{19} \) |
\( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( 18 a + 27\) , \( -45 a + 20\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(18a+27\right){x}-45a+20$ |
| 106875.1-a3 |
106875.1-a |
$4$ |
$6$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
106875.1 |
\( 3^{2} \cdot 5^{4} \cdot 19 \) |
\( 3^{3} \cdot 5^{12} \cdot 19 \) |
$2.79845$ |
$(-2a+1), (-5a+3), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B[2] |
$1$ |
\( 2^{2} \) |
$1$ |
$1.627882516$ |
1.879716818 |
\( -\frac{9153}{19} a + \frac{36801}{19} \) |
\( \bigl[1\) , \( -1\) , \( a\) , \( 12 a + 8\) , \( -19 a + 10\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(12a+8\right){x}-19a+10$ |
*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.
