| 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 |
| 171.2-a4 |
171.2-a |
$4$ |
$6$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
171.2 |
\( 3^{2} \cdot 19 \) |
\( 3^{3} \cdot 19^{2} \) |
$0.55969$ |
$(-2a+1), (-5a+2)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B.1.1[2] |
$1$ |
\( 2^{2} \) |
$1$ |
$4.069706291$ |
0.522143560 |
\( \frac{363527109}{361} a - \frac{76135923}{361} \) |
\( \bigl[1\) , \( -1\) , \( a\) , \( -6 a + 11\) , \( 10 a + 1\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(-6a+11\right){x}+10a+1$ |
| 3249.3-a4 |
3249.3-a |
$4$ |
$6$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
3249.3 |
\( 3^{2} \cdot 19^{2} \) |
\( 3^{9} \cdot 19^{8} \) |
$1.16852$ |
$(-2a+1), (-5a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B[2] |
$1$ |
\( 2^{3} \) |
$1$ |
$0.539045766$ |
1.244872874 |
\( \frac{363527109}{361} a - \frac{76135923}{361} \) |
\( \bigl[a + 1\) , \( 0\) , \( a\) , \( -427 a + 599\) , \( 2309 a + 3294\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(-427a+599\right){x}+2309a+3294$ |
| 8379.2-d4 |
8379.2-d |
$4$ |
$6$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
8379.2 |
\( 3^{2} \cdot 7^{2} \cdot 19 \) |
\( 3^{9} \cdot 7^{6} \cdot 19^{2} \) |
$1.48080$ |
$(-2a+1), (-3a+1), (-5a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B[2] |
$1$ |
\( 2^{3} \) |
$1$ |
$0.888082720$ |
2.050939191 |
\( \frac{363527109}{361} a - \frac{76135923}{361} \) |
\( \bigl[a + 1\) , \( 0\) , \( 0\) , \( -30 a - 180\) , \( -297 a - 910\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-30a-180\right){x}-297a-910$ |
| 8379.6-a4 |
8379.6-a |
$4$ |
$6$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
8379.6 |
\( 3^{2} \cdot 7^{2} \cdot 19 \) |
\( 3^{9} \cdot 7^{6} \cdot 19^{2} \) |
$1.48080$ |
$(-2a+1), (3a-2), (-5a+2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B[2] |
$1$ |
\( 2^{4} \) |
$0.286427186$ |
$0.888082720$ |
2.349778965 |
\( \frac{363527109}{361} a - \frac{76135923}{361} \) |
\( \bigl[a + 1\) , \( 0\) , \( 1\) , \( -35 a + 211\) , \( -1149 a + 364\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(-35a+211\right){x}-1149a+364$ |
| 28899.2-c1 |
28899.2-c |
$4$ |
$6$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
28899.2 |
\( 3^{2} \cdot 13^{2} \cdot 19 \) |
\( 3^{3} \cdot 13^{6} \cdot 19^{2} \) |
$2.01799$ |
$(-2a+1), (-4a+1), (-5a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B[2] |
$1$ |
\( 2^{3} \) |
$1$ |
$1.128733439$ |
2.606698220 |
\( \frac{363527109}{361} a - \frac{76135923}{361} \) |
\( \bigl[a + 1\) , \( 0\) , \( 0\) , \( -118 a - 7\) , \( 564 a - 231\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-118a-7\right){x}+564a-231$ |
| 28899.6-d1 |
28899.6-d |
$4$ |
$6$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
28899.6 |
\( 3^{2} \cdot 13^{2} \cdot 19 \) |
\( 3^{3} \cdot 13^{6} \cdot 19^{2} \) |
$2.01799$ |
$(-2a+1), (4a-3), (-5a+2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B[2] |
$1$ |
\( 2^{3} \) |
$0.580370262$ |
$1.128733439$ |
3.025700258 |
\( \frac{363527109}{361} a - \frac{76135923}{361} \) |
\( \bigl[a\) , \( -a + 1\) , \( 1\) , \( 123 a - 4\) , \( 27 a + 533\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(123a-4\right){x}+27a+533$ |
| 43776.2-d1 |
43776.2-d |
$4$ |
$6$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
43776.2 |
\( 2^{8} \cdot 3^{2} \cdot 19 \) |
\( 2^{24} \cdot 3^{9} \cdot 19^{2} \) |
$2.23876$ |
$(-2a+1), (-5a+2), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B[2] |
$1$ |
\( 2^{3} \) |
$1.073530510$ |
$0.587411505$ |
2.912635915 |
\( \frac{363527109}{361} a - \frac{76135923}{361} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 264 a - 519\) , \( 3036 a - 4074\bigr] \) |
${y}^2={x}^{3}+\left(264a-519\right){x}+3036a-4074$ |
| 43776.2-i1 |
43776.2-i |
$4$ |
$6$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
43776.2 |
\( 2^{8} \cdot 3^{2} \cdot 19 \) |
\( 2^{24} \cdot 3^{3} \cdot 19^{2} \) |
$2.23876$ |
$(-2a+1), (-5a+2), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B[2] |
$1$ |
\( 2^{3} \) |
$0.796707316$ |
$1.017426572$ |
3.743960357 |
\( \frac{363527109}{361} a - \frac{76135923}{361} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -88 a + 173\) , \( -568 a - 222\bigr] \) |
${y}^2={x}^{3}+\left(-88a+173\right){x}-568a-222$ |
| 43776.2-q1 |
43776.2-q |
$4$ |
$6$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
43776.2 |
\( 2^{8} \cdot 3^{2} \cdot 19 \) |
\( 2^{24} \cdot 3^{9} \cdot 19^{2} \) |
$2.23876$ |
$(-2a+1), (-5a+2), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B[2] |
$1$ |
\( 2^{4} \) |
$1$ |
$0.587411505$ |
2.713137527 |
\( \frac{363527109}{361} a - \frac{76135923}{361} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 264 a - 519\) , \( -3036 a + 4074\bigr] \) |
${y}^2={x}^{3}+\left(264a-519\right){x}-3036a+4074$ |
| 61731.2-c1 |
61731.2-c |
$4$ |
$6$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
61731.2 |
\( 3^{2} \cdot 19^{3} \) |
\( 3^{9} \cdot 19^{8} \) |
$2.43964$ |
$(-2a+1), (-5a+3), (-5a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B[2] |
$1$ |
\( 2^{3} \) |
$1$ |
$0.539045766$ |
1.244872874 |
\( \frac{363527109}{361} a - \frac{76135923}{361} \) |
\( \bigl[1\) , \( -1\) , \( a\) , \( 601 a - 417\) , \( 4772 a - 273\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(601a-417\right){x}+4772a-273$ |
| 106875.2-a1 |
106875.2-a |
$4$ |
$6$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
106875.2 |
\( 3^{2} \cdot 5^{4} \cdot 19 \) |
\( 3^{3} \cdot 5^{12} \cdot 19^{2} \) |
$2.79845$ |
$(-2a+1), (-5a+2), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B[2] |
$1$ |
\( 2^{3} \) |
$1$ |
$0.813941258$ |
1.879716818 |
\( \frac{363527109}{361} a - \frac{76135923}{361} \) |
\( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( 269 a - 133\) , \( 1143 a + 366\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(269a-133\right){x}+1143a+366$ |
*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.
