| 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 |
| 11664.4-a1 |
11664.4-a |
$3$ |
$9$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
11664.4 |
\( 2^{4} \cdot 3^{6} \) |
\( 2^{15} \cdot 3^{12} \) |
$2.62661$ |
$(a), (-a-1), (a-1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3Cs |
$1$ |
\( 2^{2} \) |
$0.371595804$ |
$1.844395597$ |
3.877036303 |
\( \frac{4725}{4} a + 3753 \) |
\( \bigl[a\) , \( -1\) , \( a\) , \( 9 a + 13\) , \( -7 a + 16\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(9a+13\right){x}-7a+16$ |
| 11664.4-a2 |
11664.4-a |
$3$ |
$9$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
11664.4 |
\( 2^{4} \cdot 3^{6} \) |
\( 2^{21} \cdot 3^{8} \) |
$2.62661$ |
$(a), (-a-1), (a-1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B |
$1$ |
\( 2^{2} \cdot 3 \) |
$0.123865268$ |
$1.844395597$ |
3.877036303 |
\( -\frac{90933}{32} a + \frac{32829}{8} \) |
\( \bigl[a\) , \( -1\) , \( 0\) , \( 12 a - 6\) , \( -24 a - 6\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-{x}^{2}+\left(12a-6\right){x}-24a-6$ |
| 11664.4-a3 |
11664.4-a |
$3$ |
$9$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
11664.4 |
\( 2^{4} \cdot 3^{6} \) |
\( 2^{13} \cdot 3^{20} \) |
$2.62661$ |
$(a), (-a-1), (a-1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B |
$1$ |
\( 2^{2} \) |
$1.114787412$ |
$0.614798532$ |
3.877036303 |
\( -\frac{2245317}{2} a + 1184658 \) |
\( \bigl[a\) , \( -1\) , \( a\) , \( 189 a + 373\) , \( 1485 a - 3216\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(189a+373\right){x}+1485a-3216$ |
| 11664.4-b1 |
11664.4-b |
$2$ |
$3$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
11664.4 |
\( 2^{4} \cdot 3^{6} \) |
\( 2^{4} \cdot 3^{14} \) |
$2.62661$ |
$(a), (-a-1), (a-1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$3$ |
3B |
$1$ |
\( 1 \) |
$1.144634733$ |
$2.475504138$ |
4.007242038 |
\( -33792 a + 3072 \) |
\( \bigl[0\) , \( 0\) , \( a\) , \( -9 a + 9\) , \( 2 a + 24\bigr] \) |
${y}^2+a{y}={x}^{3}+\left(-9a+9\right){x}+2a+24$ |
| 11664.4-b2 |
11664.4-b |
$2$ |
$3$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
11664.4 |
\( 2^{4} \cdot 3^{6} \) |
\( 2^{4} \cdot 3^{14} \) |
$2.62661$ |
$(a), (-a-1), (a-1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$3$ |
3B |
$1$ |
\( 3 \) |
$0.381544911$ |
$2.475504138$ |
4.007242038 |
\( 33792 a + 3072 \) |
\( \bigl[0\) , \( 0\) , \( a\) , \( -3 a - 15\) , \( -7 a - 21\bigr] \) |
${y}^2+a{y}={x}^{3}+\left(-3a-15\right){x}-7a-21$ |
| 11664.4-c1 |
11664.4-c |
$1$ |
$1$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
11664.4 |
\( 2^{4} \cdot 3^{6} \) |
\( 2^{10} \cdot 3^{10} \) |
$2.62661$ |
$(a), (-a-1), (a-1)$ |
$2$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
✓ |
|
|
$1$ |
\( 2^{2} \cdot 3^{2} \) |
$0.016552564$ |
$3.152417319$ |
5.313204043 |
\( -6 \) |
\( \bigl[a\) , \( -1\) , \( 0\) , \( 0\) , \( -4\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-{x}^{2}-4$ |
| 11664.4-d1 |
11664.4-d |
$1$ |
$1$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
11664.4 |
\( 2^{4} \cdot 3^{6} \) |
\( 2^{4} \cdot 3^{22} \) |
$2.62661$ |
$(a), (-a-1), (a-1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
✓ |
|
|
$1$ |
\( 1 \) |
$1$ |
$1.390586984$ |
0.983293486 |
\( -3072 \) |
\( \bigl[0\) , \( 0\) , \( a\) , \( -27\) , \( -67\bigr] \) |
${y}^2+a{y}={x}^{3}-27{x}-67$ |
| 11664.4-e1 |
11664.4-e |
$3$ |
$9$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
11664.4 |
\( 2^{4} \cdot 3^{6} \) |
\( 2^{14} \cdot 3^{18} \) |
$2.62661$ |
$(a), (-a-1), (a-1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$3$ |
3B |
$1$ |
\( 2^{2} \cdot 3^{2} \) |
$0.077107140$ |
$0.939189204$ |
3.686932492 |
\( -\frac{132651}{2} \) |
\( \bigl[a\) , \( -1\) , \( 0\) , \( -114\) , \( -422\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-{x}^{2}-114{x}-422$ |
| 11664.4-e2 |
11664.4-e |
$3$ |
$9$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
11664.4 |
\( 2^{4} \cdot 3^{6} \) |
\( 2^{30} \cdot 3^{10} \) |
$2.62661$ |
$(a), (-a-1), (a-1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$3$ |
3B |
$1$ |
\( 2^{2} \) |
$0.693964260$ |
$0.939189204$ |
3.686932492 |
\( -\frac{1167051}{512} \) |
\( \bigl[a\) , \( -1\) , \( 0\) , \( -54\) , \( 234\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-{x}^{2}-54{x}+234$ |
| 11664.4-e3 |
11664.4-e |
$3$ |
$9$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
11664.4 |
\( 2^{4} \cdot 3^{6} \) |
\( 2^{18} \cdot 3^{6} \) |
$2.62661$ |
$(a), (-a-1), (a-1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$3$ |
3Cs |
$1$ |
\( 2^{2} \) |
$0.231321420$ |
$2.817567613$ |
3.686932492 |
\( \frac{9261}{8} \) |
\( \bigl[a\) , \( -1\) , \( 0\) , \( 6\) , \( -6\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-{x}^{2}+6{x}-6$ |
| 11664.4-f1 |
11664.4-f |
$3$ |
$9$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
11664.4 |
\( 2^{4} \cdot 3^{6} \) |
\( 2^{12} \cdot 3^{12} \) |
$2.62661$ |
$(a), (-a-1), (a-1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$3$ |
3Cs |
$1$ |
\( 1 \) |
$1$ |
$2.231466654$ |
1.577885203 |
\( -1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 6 a - 3\) , \( 10 a + 4\bigr] \) |
${y}^2={x}^{3}+\left(6a-3\right){x}+10a+4$ |
| 11664.4-f2 |
11664.4-f |
$3$ |
$9$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
11664.4 |
\( 2^{4} \cdot 3^{6} \) |
\( 2^{12} \cdot 3^{20} \) |
$2.62661$ |
$(a), (-a-1), (a-1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$3$ |
3B |
$1$ |
\( 3 \) |
$1$ |
$0.743822218$ |
1.577885203 |
\( -287232 a + 262464 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -54 a - 243\) , \( 486 a + 1404\bigr] \) |
${y}^2={x}^{3}+\left(-54a-243\right){x}+486a+1404$ |
| 11664.4-f3 |
11664.4-f |
$3$ |
$9$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
11664.4 |
\( 2^{4} \cdot 3^{6} \) |
\( 2^{12} \cdot 3^{8} \) |
$2.62661$ |
$(a), (-a-1), (a-1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$3$ |
3B |
$1$ |
\( 1 \) |
$1$ |
$2.231466654$ |
1.577885203 |
\( 287232 a + 262464 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 6 a - 27\) , \( 18 a - 52\bigr] \) |
${y}^2={x}^{3}+\left(6a-27\right){x}+18a-52$ |
| 11664.4-g1 |
11664.4-g |
$2$ |
$3$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
11664.4 |
\( 2^{4} \cdot 3^{6} \) |
\( 2^{4} \cdot 3^{14} \) |
$2.62661$ |
$(a), (-a-1), (a-1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$3$ |
3B |
$1$ |
\( 1 \) |
$1$ |
$2.755650344$ |
1.948539045 |
\( -2496 a + 9456 \) |
\( \bigl[a\) , \( -1\) , \( 0\) , \( 3 a + 9\) , \( -7 a + 2\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-{x}^{2}+\left(3a+9\right){x}-7a+2$ |
| 11664.4-g2 |
11664.4-g |
$2$ |
$3$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
11664.4 |
\( 2^{4} \cdot 3^{6} \) |
\( 2^{4} \cdot 3^{14} \) |
$2.62661$ |
$(a), (-a-1), (a-1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$3$ |
3B |
$1$ |
\( 1 \) |
$1$ |
$2.755650344$ |
1.948539045 |
\( 2496 a + 9456 \) |
\( \bigl[a\) , \( -1\) , \( a\) , \( 6 a - 2\) , \( -10 a + 1\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(6a-2\right){x}-10a+1$ |
| 11664.4-h1 |
11664.4-h |
$3$ |
$9$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
11664.4 |
\( 2^{4} \cdot 3^{6} \) |
\( 2^{15} \cdot 3^{12} \) |
$2.62661$ |
$(a), (-a-1), (a-1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3Cs |
$1$ |
\( 2^{2} \) |
$0.371595804$ |
$1.844395597$ |
3.877036303 |
\( -\frac{4725}{4} a + 3753 \) |
\( \bigl[a\) , \( -1\) , \( a\) , \( -9 a + 13\) , \( 7 a + 16\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(-9a+13\right){x}+7a+16$ |
| 11664.4-h2 |
11664.4-h |
$3$ |
$9$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
11664.4 |
\( 2^{4} \cdot 3^{6} \) |
\( 2^{21} \cdot 3^{8} \) |
$2.62661$ |
$(a), (-a-1), (a-1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B |
$1$ |
\( 2^{2} \cdot 3 \) |
$0.123865268$ |
$1.844395597$ |
3.877036303 |
\( \frac{90933}{32} a + \frac{32829}{8} \) |
\( \bigl[a\) , \( -1\) , \( 0\) , \( -12 a - 6\) , \( 24 a - 6\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-{x}^{2}+\left(-12a-6\right){x}+24a-6$ |
| 11664.4-h3 |
11664.4-h |
$3$ |
$9$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
11664.4 |
\( 2^{4} \cdot 3^{6} \) |
\( 2^{13} \cdot 3^{20} \) |
$2.62661$ |
$(a), (-a-1), (a-1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B |
$1$ |
\( 2^{2} \) |
$1.114787412$ |
$0.614798532$ |
3.877036303 |
\( \frac{2245317}{2} a + 1184658 \) |
\( \bigl[a\) , \( -1\) , \( a\) , \( -189 a + 373\) , \( -1485 a - 3216\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(-189a+373\right){x}-1485a-3216$ |
| 11664.4-i1 |
11664.4-i |
$2$ |
$3$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
11664.4 |
\( 2^{4} \cdot 3^{6} \) |
\( 2^{4} \cdot 3^{6} \) |
$2.62661$ |
$(a), (-a-1), (a-1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{potential}$ |
$-3$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
|
|
$1$ |
\( 1 \) |
$0.450320685$ |
$6.435822518$ |
4.098651131 |
\( 0 \) |
\( \bigl[0\) , \( 0\) , \( a\) , \( 0\) , \( 1\bigr] \) |
${y}^2+a{y}={x}^{3}+1$ |
| 11664.4-i2 |
11664.4-i |
$2$ |
$3$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
11664.4 |
\( 2^{4} \cdot 3^{6} \) |
\( 2^{4} \cdot 3^{18} \) |
$2.62661$ |
$(a), (-a-1), (a-1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{potential}$ |
$-3$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
|
|
$1$ |
\( 3^{2} \) |
$0.150106895$ |
$2.145274172$ |
4.098651131 |
\( 0 \) |
\( \bigl[0\) , \( 0\) , \( a\) , \( 0\) , \( -13\bigr] \) |
${y}^2+a{y}={x}^{3}-13$ |
| 11664.4-j1 |
11664.4-j |
$4$ |
$27$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
11664.4 |
\( 2^{4} \cdot 3^{6} \) |
\( 2^{12} \cdot 3^{10} \) |
$2.62661$ |
$(a), (-a-1), (a-1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{potential}$ |
$-27$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
|
|
$1$ |
\( 3^{2} \) |
$0.251525634$ |
$1.351438044$ |
4.326491958 |
\( -12288000 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -120\) , \( 506\bigr] \) |
${y}^2={x}^{3}-120{x}+506$ |
| 11664.4-j2 |
11664.4-j |
$4$ |
$27$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
11664.4 |
\( 2^{4} \cdot 3^{6} \) |
\( 2^{12} \cdot 3^{22} \) |
$2.62661$ |
$(a), (-a-1), (a-1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{potential}$ |
$-27$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
|
|
$1$ |
\( 1 \) |
$6.791192128$ |
$0.450479348$ |
4.326491958 |
\( -12288000 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -1080\) , \( -13662\bigr] \) |
${y}^2={x}^{3}-1080{x}-13662$ |
| 11664.4-j3 |
11664.4-j |
$4$ |
$27$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
11664.4 |
\( 2^{4} \cdot 3^{6} \) |
\( 2^{12} \cdot 3^{6} \) |
$2.62661$ |
$(a), (-a-1), (a-1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{potential}$ |
$-3$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$3$ |
3Cs |
$1$ |
\( 1 \) |
$0.754576903$ |
$4.054314132$ |
4.326491958 |
\( 0 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 0\) , \( 2\bigr] \) |
${y}^2={x}^{3}+2$ |
| 11664.4-j4 |
11664.4-j |
$4$ |
$27$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
11664.4 |
\( 2^{4} \cdot 3^{6} \) |
\( 2^{12} \cdot 3^{18} \) |
$2.62661$ |
$(a), (-a-1), (a-1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{potential}$ |
$-3$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$3$ |
3Cs |
$1$ |
\( 1 \) |
$2.263730709$ |
$1.351438044$ |
4.326491958 |
\( 0 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 0\) , \( -54\bigr] \) |
${y}^2={x}^{3}-54$ |
| 11664.4-k1 |
11664.4-k |
$3$ |
$9$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
11664.4 |
\( 2^{4} \cdot 3^{6} \) |
\( 2^{15} \cdot 3^{12} \) |
$2.62661$ |
$(a), (-a-1), (a-1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3Cs |
$1$ |
\( 2 \) |
$1$ |
$1.844395597$ |
2.608369268 |
\( -\frac{4725}{4} a + 3753 \) |
\( \bigl[a\) , \( -1\) , \( 0\) , \( 12 a\) , \( -16 a - 16\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-{x}^{2}+12a{x}-16a-16$ |
| 11664.4-k2 |
11664.4-k |
$3$ |
$9$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
11664.4 |
\( 2^{4} \cdot 3^{6} \) |
\( 2^{21} \cdot 3^{20} \) |
$2.62661$ |
$(a), (-a-1), (a-1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B |
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$0.614798532$ |
2.608369268 |
\( \frac{90933}{32} a + \frac{32829}{8} \) |
\( \bigl[a\) , \( -1\) , \( 0\) , \( -108 a - 60\) , \( -432 a + 280\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-{x}^{2}+\left(-108a-60\right){x}-432a+280$ |
| 11664.4-k3 |
11664.4-k |
$3$ |
$9$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
11664.4 |
\( 2^{4} \cdot 3^{6} \) |
\( 2^{13} \cdot 3^{8} \) |
$2.62661$ |
$(a), (-a-1), (a-1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B |
$1$ |
\( 2 \) |
$1$ |
$1.844395597$ |
2.608369268 |
\( \frac{2245317}{2} a + 1184658 \) |
\( \bigl[a\) , \( -1\) , \( a\) , \( -21 a + 43\) , \( 69 a + 92\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(-21a+43\right){x}+69a+92$ |
| 11664.4-l1 |
11664.4-l |
$2$ |
$3$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
11664.4 |
\( 2^{4} \cdot 3^{6} \) |
\( 2^{4} \cdot 3^{14} \) |
$2.62661$ |
$(a), (-a-1), (a-1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$3$ |
3B |
$1$ |
\( 1 \) |
$1$ |
$2.755650344$ |
1.948539045 |
\( -2496 a + 9456 \) |
\( \bigl[a\) , \( -1\) , \( a\) , \( -6 a - 2\) , \( 10 a + 1\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(-6a-2\right){x}+10a+1$ |
| 11664.4-l2 |
11664.4-l |
$2$ |
$3$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
11664.4 |
\( 2^{4} \cdot 3^{6} \) |
\( 2^{4} \cdot 3^{14} \) |
$2.62661$ |
$(a), (-a-1), (a-1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$3$ |
3B |
$1$ |
\( 1 \) |
$1$ |
$2.755650344$ |
1.948539045 |
\( 2496 a + 9456 \) |
\( \bigl[a\) , \( -1\) , \( 0\) , \( -3 a + 9\) , \( 7 a + 2\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-{x}^{2}+\left(-3a+9\right){x}+7a+2$ |
| 11664.4-m1 |
11664.4-m |
$3$ |
$9$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
11664.4 |
\( 2^{4} \cdot 3^{6} \) |
\( 2^{12} \cdot 3^{12} \) |
$2.62661$ |
$(a), (-a-1), (a-1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$3$ |
3Cs |
$1$ |
\( 1 \) |
$1$ |
$2.231466654$ |
1.577885203 |
\( -1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -6 a - 3\) , \( -10 a + 4\bigr] \) |
${y}^2={x}^{3}+\left(-6a-3\right){x}-10a+4$ |
| 11664.4-m2 |
11664.4-m |
$3$ |
$9$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
11664.4 |
\( 2^{4} \cdot 3^{6} \) |
\( 2^{12} \cdot 3^{8} \) |
$2.62661$ |
$(a), (-a-1), (a-1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$3$ |
3B |
$1$ |
\( 1 \) |
$1$ |
$2.231466654$ |
1.577885203 |
\( -287232 a + 262464 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -6 a - 27\) , \( -18 a - 52\bigr] \) |
${y}^2={x}^{3}+\left(-6a-27\right){x}-18a-52$ |
| 11664.4-m3 |
11664.4-m |
$3$ |
$9$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
11664.4 |
\( 2^{4} \cdot 3^{6} \) |
\( 2^{12} \cdot 3^{20} \) |
$2.62661$ |
$(a), (-a-1), (a-1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$3$ |
3B |
$1$ |
\( 3 \) |
$1$ |
$0.743822218$ |
1.577885203 |
\( 287232 a + 262464 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 54 a - 243\) , \( -486 a + 1404\bigr] \) |
${y}^2={x}^{3}+\left(54a-243\right){x}-486a+1404$ |
| 11664.4-n1 |
11664.4-n |
$3$ |
$9$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
11664.4 |
\( 2^{4} \cdot 3^{6} \) |
\( 2^{14} \cdot 3^{6} \) |
$2.62661$ |
$(a), (-a-1), (a-1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$3$ |
3B |
$1$ |
\( 2^{2} \) |
$0.282606480$ |
$2.817567613$ |
4.504342982 |
\( -\frac{132651}{2} \) |
\( \bigl[a\) , \( -1\) , \( 0\) , \( -12\) , \( 24\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-{x}^{2}-12{x}+24$ |
| 11664.4-n2 |
11664.4-n |
$3$ |
$9$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
11664.4 |
\( 2^{4} \cdot 3^{6} \) |
\( 2^{30} \cdot 3^{22} \) |
$2.62661$ |
$(a), (-a-1), (a-1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$3$ |
3B |
$1$ |
\( 2^{2} \) |
$2.543458324$ |
$0.313063068$ |
4.504342982 |
\( -\frac{1167051}{512} \) |
\( \bigl[a\) , \( -1\) , \( 0\) , \( -492\) , \( -5336\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-{x}^{2}-492{x}-5336$ |
| 11664.4-n3 |
11664.4-n |
$3$ |
$9$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
11664.4 |
\( 2^{4} \cdot 3^{6} \) |
\( 2^{18} \cdot 3^{18} \) |
$2.62661$ |
$(a), (-a-1), (a-1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$3$ |
3Cs |
$1$ |
\( 2^{2} \) |
$0.847819441$ |
$0.939189204$ |
4.504342982 |
\( \frac{9261}{8} \) |
\( \bigl[a\) , \( -1\) , \( 0\) , \( 48\) , \( 64\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-{x}^{2}+48{x}+64$ |
| 11664.4-o1 |
11664.4-o |
$1$ |
$1$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
11664.4 |
\( 2^{4} \cdot 3^{6} \) |
\( 2^{4} \cdot 3^{10} \) |
$2.62661$ |
$(a), (-a-1), (a-1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
✓ |
|
|
$1$ |
\( 1 \) |
$1$ |
$4.171760953$ |
2.949880459 |
\( -3072 \) |
\( \bigl[0\) , \( 0\) , \( a\) , \( -3\) , \( 3\bigr] \) |
${y}^2+a{y}={x}^{3}-3{x}+3$ |
| 11664.4-p1 |
11664.4-p |
$1$ |
$1$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
11664.4 |
\( 2^{4} \cdot 3^{6} \) |
\( 2^{10} \cdot 3^{22} \) |
$2.62661$ |
$(a), (-a-1), (a-1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
✓ |
|
|
$1$ |
\( 2^{2} \) |
$1$ |
$1.050805773$ |
2.972127551 |
\( -6 \) |
\( \bigl[a\) , \( -1\) , \( 0\) , \( -6\) , \( 118\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-{x}^{2}-6{x}+118$ |
| 11664.4-q1 |
11664.4-q |
$2$ |
$3$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
11664.4 |
\( 2^{4} \cdot 3^{6} \) |
\( 2^{4} \cdot 3^{14} \) |
$2.62661$ |
$(a), (-a-1), (a-1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$3$ |
3B |
$1$ |
\( 3 \) |
$0.381544911$ |
$2.475504138$ |
4.007242038 |
\( -33792 a + 3072 \) |
\( \bigl[0\) , \( 0\) , \( a\) , \( 3 a - 15\) , \( 7 a - 21\bigr] \) |
${y}^2+a{y}={x}^{3}+\left(3a-15\right){x}+7a-21$ |
| 11664.4-q2 |
11664.4-q |
$2$ |
$3$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
11664.4 |
\( 2^{4} \cdot 3^{6} \) |
\( 2^{4} \cdot 3^{14} \) |
$2.62661$ |
$(a), (-a-1), (a-1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$3$ |
3B |
$1$ |
\( 1 \) |
$1.144634733$ |
$2.475504138$ |
4.007242038 |
\( 33792 a + 3072 \) |
\( \bigl[0\) , \( 0\) , \( a\) , \( 9 a + 9\) , \( -2 a + 24\bigr] \) |
${y}^2+a{y}={x}^{3}+\left(9a+9\right){x}-2a+24$ |
| 11664.4-r1 |
11664.4-r |
$3$ |
$9$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
11664.4 |
\( 2^{4} \cdot 3^{6} \) |
\( 2^{15} \cdot 3^{12} \) |
$2.62661$ |
$(a), (-a-1), (a-1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3Cs |
$1$ |
\( 2 \) |
$1$ |
$1.844395597$ |
2.608369268 |
\( \frac{4725}{4} a + 3753 \) |
\( \bigl[a\) , \( -1\) , \( 0\) , \( -12 a\) , \( 16 a - 16\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-{x}^{2}-12a{x}+16a-16$ |
| 11664.4-r2 |
11664.4-r |
$3$ |
$9$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
11664.4 |
\( 2^{4} \cdot 3^{6} \) |
\( 2^{21} \cdot 3^{20} \) |
$2.62661$ |
$(a), (-a-1), (a-1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B |
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$0.614798532$ |
2.608369268 |
\( -\frac{90933}{32} a + \frac{32829}{8} \) |
\( \bigl[a\) , \( -1\) , \( 0\) , \( 108 a - 60\) , \( 432 a + 280\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-{x}^{2}+\left(108a-60\right){x}+432a+280$ |
| 11664.4-r3 |
11664.4-r |
$3$ |
$9$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
11664.4 |
\( 2^{4} \cdot 3^{6} \) |
\( 2^{13} \cdot 3^{8} \) |
$2.62661$ |
$(a), (-a-1), (a-1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B |
$1$ |
\( 2 \) |
$1$ |
$1.844395597$ |
2.608369268 |
\( -\frac{2245317}{2} a + 1184658 \) |
\( \bigl[a\) , \( -1\) , \( a\) , \( 21 a + 43\) , \( -69 a + 92\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(21a+43\right){x}-69a+92$ |
*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.
