| 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-a3 |
171.2-a |
$4$ |
$6$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
171.2 |
\( 3^{2} \cdot 19 \) |
\( 3^{3} \cdot 19 \) |
$0.55969$ |
$(-2a+1), (-5a+2)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B.1.1[2] |
$1$ |
\( 2 \) |
$1$ |
$8.139412583$ |
0.522143560 |
\( \frac{9153}{19} a + \frac{27648}{19} \) |
\( \bigl[1\) , \( -1\) , \( a\) , \( -a + 1\) , \( 0\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(-a+1\right){x}$ |
| 3249.3-a3 |
3249.3-a |
$4$ |
$6$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
3249.3 |
\( 3^{2} \cdot 19^{2} \) |
\( 3^{9} \cdot 19^{7} \) |
$1.16852$ |
$(-2a+1), (-5a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B[2] |
$1$ |
\( 2^{2} \) |
$1$ |
$1.078091533$ |
1.244872874 |
\( \frac{9153}{19} a + \frac{27648}{19} \) |
\( \bigl[a + 1\) , \( 0\) , \( a\) , \( -37 a + 44\) , \( 47 a + 15\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(-37a+44\right){x}+47a+15$ |
| 8379.2-d3 |
8379.2-d |
$4$ |
$6$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
8379.2 |
\( 3^{2} \cdot 7^{2} \cdot 19 \) |
\( 3^{9} \cdot 7^{6} \cdot 19 \) |
$1.48080$ |
$(-2a+1), (-3a+1), (-5a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B[2] |
$1$ |
\( 2^{2} \) |
$1$ |
$1.776165441$ |
2.050939191 |
\( \frac{9153}{19} a + \frac{27648}{19} \) |
\( \bigl[a + 1\) , \( 0\) , \( 0\) , \( -15\) , \( -12 a - 4\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}-15{x}-12a-4$ |
| 8379.6-a3 |
8379.6-a |
$4$ |
$6$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
8379.6 |
\( 3^{2} \cdot 7^{2} \cdot 19 \) |
\( 3^{9} \cdot 7^{6} \cdot 19 \) |
$1.48080$ |
$(-2a+1), (3a-2), (-5a+2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B[2] |
$1$ |
\( 2^{2} \) |
$0.572854372$ |
$1.776165441$ |
2.349778965 |
\( \frac{9153}{19} a + \frac{27648}{19} \) |
\( \bigl[a + 1\) , \( 0\) , \( 1\) , \( -5 a + 16\) , \( -9 a + 10\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(-5a+16\right){x}-9a+10$ |
| 28899.2-c4 |
28899.2-c |
$4$ |
$6$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
28899.2 |
\( 3^{2} \cdot 13^{2} \cdot 19 \) |
\( 3^{3} \cdot 13^{6} \cdot 19 \) |
$2.01799$ |
$(-2a+1), (-4a+1), (-5a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B[2] |
$1$ |
\( 2^{2} \) |
$1$ |
$2.257466878$ |
2.606698220 |
\( \frac{9153}{19} a + \frac{27648}{19} \) |
\( \bigl[a + 1\) , \( 0\) , \( 0\) , \( -8 a - 2\) , \( 3 a - 3\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-8a-2\right){x}+3a-3$ |
| 28899.6-d4 |
28899.6-d |
$4$ |
$6$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
28899.6 |
\( 3^{2} \cdot 13^{2} \cdot 19 \) |
\( 3^{3} \cdot 13^{6} \cdot 19 \) |
$2.01799$ |
$(-2a+1), (4a-3), (-5a+2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B[2] |
$1$ |
\( 2^{3} \) |
$0.290185131$ |
$2.257466878$ |
3.025700258 |
\( \frac{9153}{19} a + \frac{27648}{19} \) |
\( \bigl[a\) , \( -a + 1\) , \( 1\) , \( 8 a + 1\) , \( 3 a + 5\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(8a+1\right){x}+3a+5$ |
| 43776.2-d4 |
43776.2-d |
$4$ |
$6$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
43776.2 |
\( 2^{8} \cdot 3^{2} \cdot 19 \) |
\( 2^{24} \cdot 3^{9} \cdot 19 \) |
$2.23876$ |
$(-2a+1), (-5a+2), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B[2] |
$1$ |
\( 2^{3} \) |
$0.536765255$ |
$1.174823011$ |
2.912635915 |
\( \frac{9153}{19} a + \frac{27648}{19} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 24 a - 39\) , \( 12 a - 42\bigr] \) |
${y}^2={x}^{3}+\left(24a-39\right){x}+12a-42$ |
| 43776.2-i4 |
43776.2-i |
$4$ |
$6$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
43776.2 |
\( 2^{8} \cdot 3^{2} \cdot 19 \) |
\( 2^{24} \cdot 3^{3} \cdot 19 \) |
$2.23876$ |
$(-2a+1), (-5a+2), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B[2] |
$1$ |
\( 2^{3} \) |
$0.398353658$ |
$2.034853145$ |
3.743960357 |
\( \frac{9153}{19} a + \frac{27648}{19} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -8 a + 13\) , \( -8 a + 2\bigr] \) |
${y}^2={x}^{3}+\left(-8a+13\right){x}-8a+2$ |
| 43776.2-q4 |
43776.2-q |
$4$ |
$6$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
43776.2 |
\( 2^{8} \cdot 3^{2} \cdot 19 \) |
\( 2^{24} \cdot 3^{9} \cdot 19 \) |
$2.23876$ |
$(-2a+1), (-5a+2), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B[2] |
$1$ |
\( 2^{3} \) |
$1$ |
$1.174823011$ |
2.713137527 |
\( \frac{9153}{19} a + \frac{27648}{19} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 24 a - 39\) , \( -12 a + 42\bigr] \) |
${y}^2={x}^{3}+\left(24a-39\right){x}-12a+42$ |
| 61731.2-c4 |
61731.2-c |
$4$ |
$6$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
61731.2 |
\( 3^{2} \cdot 19^{3} \) |
\( 3^{9} \cdot 19^{7} \) |
$2.43964$ |
$(-2a+1), (-5a+3), (-5a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B[2] |
$1$ |
\( 2^{2} \) |
$1$ |
$1.078091533$ |
1.244872874 |
\( \frac{9153}{19} a + \frac{27648}{19} \) |
\( \bigl[1\) , \( -1\) , \( a\) , \( 46 a - 27\) , \( 44 a - 24\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(46a-27\right){x}+44a-24$ |
| 106875.2-a4 |
106875.2-a |
$4$ |
$6$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
106875.2 |
\( 3^{2} \cdot 5^{4} \cdot 19 \) |
\( 3^{3} \cdot 5^{12} \cdot 19 \) |
$2.79845$ |
$(-2a+1), (-5a+2), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B[2] |
$1$ |
\( 2^{2} \) |
$1$ |
$1.627882516$ |
1.879716818 |
\( \frac{9153}{19} a + \frac{27648}{19} \) |
\( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( 19 a - 8\) , \( 18 a - 9\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(19a-8\right){x}+18a-9$ |
*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.
