| 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 |
| 242.4-a3 |
242.4-a |
$4$ |
$33$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
242.4 |
\( 2 \cdot 11^{2} \) |
\( 2^{11} \cdot 11^{4} \) |
$0.93248$ |
$(-a+1), (-2a+3)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3, 11$ |
3B.1.1, 11B.3.2 |
$1$ |
\( 3 \) |
$1$ |
$2.651529103$ |
0.668122533 |
\( \frac{14067329}{2048} a + \frac{51999917}{1024} \) |
\( \bigl[a\) , \( -a + 1\) , \( 1\) , \( -11 a + 7\) , \( 7 a - 25\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-11a+7\right){x}+7a-25$ |
| 1936.13-b3 |
1936.13-b |
$4$ |
$33$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
1936.13 |
\( 2^{4} \cdot 11^{2} \) |
\( 2^{23} \cdot 11^{10} \) |
$1.56825$ |
$(-a+1), (-2a+3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3, 11$ |
3B, 11B |
$1$ |
\( 2^{2} \) |
$0.830482658$ |
$0.399733052$ |
2.007574132 |
\( \frac{14067329}{2048} a + \frac{51999917}{1024} \) |
\( \bigl[0\) , \( a - 1\) , \( a + 1\) , \( -450 a + 71\) , \( 4024 a - 4020\bigr] \) |
${y}^2+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-450a+71\right){x}+4024a-4020$ |
| 3872.4-d3 |
3872.4-d |
$4$ |
$33$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
3872.4 |
\( 2^{5} \cdot 11^{2} \) |
\( 2^{23} \cdot 11^{10} \) |
$1.86497$ |
$(a), (-a+1), (-2a+3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3, 11$ |
3B, 11B |
$1$ |
\( 11 \) |
$1$ |
$0.399733052$ |
3.323867636 |
\( \frac{14067329}{2048} a + \frac{51999917}{1024} \) |
\( \bigl[a\) , \( 1\) , \( a\) , \( 464 a - 230\) , \( 3180 a + 2423\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}+\left(464a-230\right){x}+3180a+2423$ |
| 7744.19-a3 |
7744.19-a |
$4$ |
$33$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
7744.19 |
\( 2^{6} \cdot 11^{2} \) |
\( 2^{29} \cdot 11^{4} \) |
$2.21783$ |
$(-a+1), (-2a+3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3, 11$ |
3B, 11B |
$1$ |
\( 2 \) |
$1$ |
$0.937457104$ |
1.417301922 |
\( \frac{14067329}{2048} a + \frac{51999917}{1024} \) |
\( \bigl[0\) , \( a\) , \( a + 1\) , \( -57 a - 54\) , \( 267 a + 80\bigr] \) |
${y}^2+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(-57a-54\right){x}+267a+80$ |
| 7744.19-b3 |
7744.19-b |
$4$ |
$33$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
7744.19 |
\( 2^{6} \cdot 11^{2} \) |
\( 2^{29} \cdot 11^{10} \) |
$2.21783$ |
$(-a+1), (-2a+3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3, 11$ |
3B, 11B |
$1$ |
\( 2^{2} \) |
$1.674243465$ |
$0.282653952$ |
2.861835308 |
\( \frac{14067329}{2048} a + \frac{51999917}{1024} \) |
\( \bigl[0\) , \( -a - 1\) , \( a + 1\) , \( 829 a - 971\) , \( 12069 a - 4011\bigr] \) |
${y}^2+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(829a-971\right){x}+12069a-4011$ |
| 11858.4-b3 |
11858.4-b |
$4$ |
$33$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
11858.4 |
\( 2 \cdot 7^{2} \cdot 11^{2} \) |
\( 2^{11} \cdot 7^{6} \cdot 11^{10} \) |
$2.46712$ |
$(-a+1), (-2a+1), (-2a+3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3, 11$ |
3B, 11B |
$1$ |
\( 2 \) |
$2.770854713$ |
$0.302169785$ |
2.531662201 |
\( \frac{14067329}{2048} a + \frac{51999917}{1024} \) |
\( \bigl[a\) , \( a\) , \( a + 1\) , \( -104 a + 1118\) , \( -9479 a + 2361\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(-104a+1118\right){x}-9479a+2361$ |
| 15488.4-a3 |
15488.4-a |
$4$ |
$33$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
15488.4 |
\( 2^{7} \cdot 11^{2} \) |
\( 2^{17} \cdot 11^{10} \) |
$2.63746$ |
$(a), (-a+1), (-2a+3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3, 11$ |
3B, 11B |
$1$ |
\( 1 \) |
$2.795036346$ |
$0.565307904$ |
2.388820344 |
\( \frac{14067329}{2048} a + \frac{51999917}{1024} \) |
\( \bigl[a\) , \( 0\) , \( a\) , \( -175 a + 291\) , \( 492 a + 1704\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-175a+291\right){x}+492a+1704$ |
| 15488.4-g3 |
15488.4-g |
$4$ |
$33$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
15488.4 |
\( 2^{7} \cdot 11^{2} \) |
\( 2^{17} \cdot 11^{4} \) |
$2.63746$ |
$(a), (-a+1), (-2a+3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3, 11$ |
3B, 11B |
$1$ |
\( 3 \cdot 11 \) |
$0.063386714$ |
$1.874914209$ |
5.929315373 |
\( \frac{14067329}{2048} a + \frac{51999917}{1024} \) |
\( \bigl[a\) , \( -1\) , \( a\) , \( 17 a + 8\) , \( -4 a - 63\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(17a+8\right){x}-4a-63$ |
| 19602.4-b3 |
19602.4-b |
$4$ |
$33$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
19602.4 |
\( 2 \cdot 3^{4} \cdot 11^{2} \) |
\( 2^{11} \cdot 3^{12} \cdot 11^{4} \) |
$2.79745$ |
$(-a+1), (-2a+3), (3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3, 11$ |
3B.1.2, 11B |
$1$ |
\( 2 \cdot 11 \) |
$0.188459624$ |
$0.883843034$ |
5.540221346 |
\( \frac{14067329}{2048} a + \frac{51999917}{1024} \) |
\( \bigl[a\) , \( -a - 1\) , \( a + 1\) , \( -94 a + 67\) , \( -161 a + 480\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-94a+67\right){x}-161a+480$ |
| 29282.8-b3 |
29282.8-b |
$4$ |
$33$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
29282.8 |
\( 2 \cdot 11^{4} \) |
\( 2^{11} \cdot 11^{16} \) |
$3.09270$ |
$(-a+1), (-2a+3), (2a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3, 11$ |
3B, 11B.3.1 |
$1$ |
\( 11 \) |
$1$ |
$0.241048100$ |
2.004367600 |
\( \frac{14067329}{2048} a + \frac{51999917}{1024} \) |
\( \bigl[a\) , \( -a + 1\) , \( a + 1\) , \( -1264 a + 883\) , \( -10667 a + 27094\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-1264a+883\right){x}-10667a+27094$ |
| 30976.13-b3 |
30976.13-b |
$4$ |
$33$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
30976.13 |
\( 2^{8} \cdot 11^{2} \) |
\( 2^{35} \cdot 11^{4} \) |
$3.13649$ |
$(a), (-a+1), (-2a+3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3, 11$ |
3B, 11B |
$1$ |
\( 2 \) |
$1$ |
$0.662882275$ |
1.002183800 |
\( \frac{14067329}{2048} a + \frac{51999917}{1024} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -167 a + 117\) , \( -563 a + 1365\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+\left(-167a+117\right){x}-563a+1365$ |
*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.
