| 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 |
| 10368.3-a1 |
10368.3-a |
$2$ |
$2$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
10368.3 |
\( 2^{7} \cdot 3^{4} \) |
\( 2^{16} \cdot 3^{11} \) |
$2.55039$ |
$(a), (-a-1), (a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$0.196252458$ |
$1.698770867$ |
3.771854182 |
\( \frac{167792}{9} a - \frac{21616}{9} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -18 a + 15\) , \( 2 a + 62\bigr] \) |
${y}^2={x}^{3}+\left(-18a+15\right){x}+2a+62$ |
| 10368.3-a2 |
10368.3-a |
$2$ |
$2$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
10368.3 |
\( 2^{7} \cdot 3^{4} \) |
\( 2^{8} \cdot 3^{10} \) |
$2.55039$ |
$(a), (-a-1), (a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.392504916$ |
$3.397541734$ |
3.771854182 |
\( -\frac{3584}{3} a + \frac{4096}{3} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -3 a\) , \( 2 a - 1\bigr] \) |
${y}^2={x}^{3}-3a{x}+2a-1$ |
| 10368.3-b1 |
10368.3-b |
$2$ |
$2$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
10368.3 |
\( 2^{7} \cdot 3^{4} \) |
\( 2^{16} \cdot 3^{12} \) |
$2.55039$ |
$(a), (-a-1), (a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$0.360566873$ |
$1.758903639$ |
3.587590466 |
\( 3456 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 12 a + 6\) , \( 4 a + 20\bigr] \) |
${y}^2={x}^{3}+\left(12a+6\right){x}+4a+20$ |
| 10368.3-b2 |
10368.3-b |
$2$ |
$2$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
10368.3 |
\( 2^{7} \cdot 3^{4} \) |
\( 2^{14} \cdot 3^{12} \) |
$2.55039$ |
$(a), (-a-1), (a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.721133747$ |
$1.758903639$ |
3.587590466 |
\( 23328 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 18 a + 9\) , \( 10 a + 50\bigr] \) |
${y}^2={x}^{3}+\left(18a+9\right){x}+10a+50$ |
| 10368.3-c1 |
10368.3-c |
$2$ |
$2$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
10368.3 |
\( 2^{7} \cdot 3^{4} \) |
\( 2^{16} \cdot 3^{12} \) |
$2.55039$ |
$(a), (-a-1), (a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$0.360566873$ |
$1.758903639$ |
3.587590466 |
\( 3456 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -12 a + 6\) , \( -4 a + 20\bigr] \) |
${y}^2={x}^{3}+\left(-12a+6\right){x}-4a+20$ |
| 10368.3-c2 |
10368.3-c |
$2$ |
$2$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
10368.3 |
\( 2^{7} \cdot 3^{4} \) |
\( 2^{14} \cdot 3^{12} \) |
$2.55039$ |
$(a), (-a-1), (a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.721133747$ |
$1.758903639$ |
3.587590466 |
\( 23328 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -18 a + 9\) , \( -10 a + 50\bigr] \) |
${y}^2={x}^{3}+\left(-18a+9\right){x}-10a+50$ |
| 10368.3-d1 |
10368.3-d |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
10368.3 |
\( 2^{7} \cdot 3^{4} \) |
\( 2^{16} \cdot 3^{14} \) |
$2.55039$ |
$(a), (-a-1), (a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$1.384050608$ |
1.957343141 |
\( -\frac{9472}{9} a - \frac{71552}{9} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 24 a - 6\) , \( 52 a + 44\bigr] \) |
${y}^2={x}^{3}+\left(24a-6\right){x}+52a+44$ |
| 10368.3-d2 |
10368.3-d |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
10368.3 |
\( 2^{7} \cdot 3^{4} \) |
\( 2^{7} \cdot 3^{20} \) |
$2.55039$ |
$(a), (-a-1), (a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$1.384050608$ |
1.957343141 |
\( \frac{15609244}{6561} a - \frac{20009248}{6561} \) |
\( \bigl[a\) , \( -1\) , \( 0\) , \( -21 a + 6\) , \( 31 a - 69\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-{x}^{2}+\left(-21a+6\right){x}+31a-69$ |
| 10368.3-d3 |
10368.3-d |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
10368.3 |
\( 2^{7} \cdot 3^{4} \) |
\( 2^{14} \cdot 3^{16} \) |
$2.55039$ |
$(a), (-a-1), (a-1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$1$ |
$1.384050608$ |
1.957343141 |
\( -\frac{39872}{81} a - \frac{110368}{81} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 6 a + 21\) , \( -38 a + 26\bigr] \) |
${y}^2={x}^{3}+\left(6a+21\right){x}-38a+26$ |
| 10368.3-d4 |
10368.3-d |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
10368.3 |
\( 2^{7} \cdot 3^{4} \) |
\( 2^{7} \cdot 3^{14} \) |
$2.55039$ |
$(a), (-a-1), (a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$1.384050608$ |
1.957343141 |
\( \frac{18653188}{9} a + \frac{32152304}{9} \) |
\( \bigl[a\) , \( -1\) , \( 0\) , \( 24 a + 96\) , \( 229 a - 240\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-{x}^{2}+\left(24a+96\right){x}+229a-240$ |
| 10368.3-e1 |
10368.3-e |
$2$ |
$2$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
10368.3 |
\( 2^{7} \cdot 3^{4} \) |
\( 2^{16} \cdot 3^{21} \) |
$2.55039$ |
$(a), (-a-1), (a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$0.859112564$ |
$0.799426856$ |
3.885114242 |
\( \frac{335248}{729} a + \frac{350000}{729} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -30 a + 39\) , \( 146 a + 82\bigr] \) |
${y}^2={x}^{3}+\left(-30a+39\right){x}+146a+82$ |
| 10368.3-e2 |
10368.3-e |
$2$ |
$2$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
10368.3 |
\( 2^{7} \cdot 3^{4} \) |
\( 2^{8} \cdot 3^{18} \) |
$2.55039$ |
$(a), (-a-1), (a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$0.429556282$ |
$1.598853712$ |
3.885114242 |
\( -\frac{48640}{27} a + \frac{74752}{27} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 15 a - 6\) , \( 20 a + 19\bigr] \) |
${y}^2={x}^{3}+\left(15a-6\right){x}+20a+19$ |
| 10368.3-f1 |
10368.3-f |
$2$ |
$2$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
10368.3 |
\( 2^{7} \cdot 3^{4} \) |
\( 2^{16} \cdot 3^{21} \) |
$2.55039$ |
$(a), (-a-1), (a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$0.859112564$ |
$0.799426856$ |
3.885114242 |
\( -\frac{335248}{729} a + \frac{350000}{729} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 30 a + 39\) , \( -146 a + 82\bigr] \) |
${y}^2={x}^{3}+\left(30a+39\right){x}-146a+82$ |
| 10368.3-f2 |
10368.3-f |
$2$ |
$2$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
10368.3 |
\( 2^{7} \cdot 3^{4} \) |
\( 2^{8} \cdot 3^{18} \) |
$2.55039$ |
$(a), (-a-1), (a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$0.429556282$ |
$1.598853712$ |
3.885114242 |
\( \frac{48640}{27} a + \frac{74752}{27} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -15 a - 6\) , \( -20 a + 19\bigr] \) |
${y}^2={x}^{3}+\left(-15a-6\right){x}-20a+19$ |
| 10368.3-g1 |
10368.3-g |
$2$ |
$2$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
10368.3 |
\( 2^{7} \cdot 3^{4} \) |
\( 2^{16} \cdot 3^{11} \) |
$2.55039$ |
$(a), (-a-1), (a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$0.445708817$ |
$1.698770867$ |
4.283127666 |
\( -\frac{167792}{9} a - \frac{21616}{9} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 18 a + 15\) , \( 2 a - 62\bigr] \) |
${y}^2={x}^{3}+\left(18a+15\right){x}+2a-62$ |
| 10368.3-g2 |
10368.3-g |
$2$ |
$2$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
10368.3 |
\( 2^{7} \cdot 3^{4} \) |
\( 2^{8} \cdot 3^{10} \) |
$2.55039$ |
$(a), (-a-1), (a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$0.222854408$ |
$3.397541734$ |
4.283127666 |
\( \frac{3584}{3} a + \frac{4096}{3} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 3 a\) , \( 2 a + 1\bigr] \) |
${y}^2={x}^{3}+3a{x}+2a+1$ |
| 10368.3-h1 |
10368.3-h |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
10368.3 |
\( 2^{7} \cdot 3^{4} \) |
\( 2^{16} \cdot 3^{14} \) |
$2.55039$ |
$(a), (-a-1), (a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$1.384050608$ |
1.957343141 |
\( \frac{9472}{9} a - \frac{71552}{9} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -24 a - 6\) , \( -52 a + 44\bigr] \) |
${y}^2={x}^{3}+\left(-24a-6\right){x}-52a+44$ |
| 10368.3-h2 |
10368.3-h |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
10368.3 |
\( 2^{7} \cdot 3^{4} \) |
\( 2^{7} \cdot 3^{20} \) |
$2.55039$ |
$(a), (-a-1), (a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$1.384050608$ |
1.957343141 |
\( -\frac{15609244}{6561} a - \frac{20009248}{6561} \) |
\( \bigl[a\) , \( -1\) , \( 0\) , \( 21 a + 6\) , \( -31 a - 69\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-{x}^{2}+\left(21a+6\right){x}-31a-69$ |
| 10368.3-h3 |
10368.3-h |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
10368.3 |
\( 2^{7} \cdot 3^{4} \) |
\( 2^{14} \cdot 3^{16} \) |
$2.55039$ |
$(a), (-a-1), (a-1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$1$ |
$1.384050608$ |
1.957343141 |
\( \frac{39872}{81} a - \frac{110368}{81} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -6 a + 21\) , \( 38 a + 26\bigr] \) |
${y}^2={x}^{3}+\left(-6a+21\right){x}+38a+26$ |
| 10368.3-h4 |
10368.3-h |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
10368.3 |
\( 2^{7} \cdot 3^{4} \) |
\( 2^{7} \cdot 3^{14} \) |
$2.55039$ |
$(a), (-a-1), (a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$1.384050608$ |
1.957343141 |
\( -\frac{18653188}{9} a + \frac{32152304}{9} \) |
\( \bigl[a\) , \( -1\) , \( 0\) , \( -24 a + 96\) , \( -229 a - 240\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-{x}^{2}+\left(-24a+96\right){x}-229a-240$ |
| 10368.3-i1 |
10368.3-i |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
10368.3 |
\( 2^{7} \cdot 3^{4} \) |
\( 2^{16} \cdot 3^{14} \) |
$2.55039$ |
$(a), (-a-1), (a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$1.384050608$ |
1.957343141 |
\( \frac{9472}{9} a - \frac{71552}{9} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -24 a - 6\) , \( 52 a - 44\bigr] \) |
${y}^2={x}^{3}+\left(-24a-6\right){x}+52a-44$ |
| 10368.3-i2 |
10368.3-i |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
10368.3 |
\( 2^{7} \cdot 3^{4} \) |
\( 2^{7} \cdot 3^{20} \) |
$2.55039$ |
$(a), (-a-1), (a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$1.384050608$ |
1.957343141 |
\( -\frac{15609244}{6561} a - \frac{20009248}{6561} \) |
\( \bigl[a\) , \( -1\) , \( a\) , \( 21 a + 7\) , \( 10 a + 64\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(21a+7\right){x}+10a+64$ |
| 10368.3-i3 |
10368.3-i |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
10368.3 |
\( 2^{7} \cdot 3^{4} \) |
\( 2^{14} \cdot 3^{16} \) |
$2.55039$ |
$(a), (-a-1), (a-1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$1$ |
$1.384050608$ |
1.957343141 |
\( \frac{39872}{81} a - \frac{110368}{81} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -6 a + 21\) , \( -38 a - 26\bigr] \) |
${y}^2={x}^{3}+\left(-6a+21\right){x}-38a-26$ |
| 10368.3-i4 |
10368.3-i |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
10368.3 |
\( 2^{7} \cdot 3^{4} \) |
\( 2^{7} \cdot 3^{14} \) |
$2.55039$ |
$(a), (-a-1), (a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$1.384050608$ |
1.957343141 |
\( -\frac{18653188}{9} a + \frac{32152304}{9} \) |
\( \bigl[a\) , \( -1\) , \( a\) , \( -24 a + 97\) , \( 253 a + 145\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(-24a+97\right){x}+253a+145$ |
| 10368.3-j1 |
10368.3-j |
$2$ |
$2$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
10368.3 |
\( 2^{7} \cdot 3^{4} \) |
\( 2^{16} \cdot 3^{11} \) |
$2.55039$ |
$(a), (-a-1), (a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$0.196252458$ |
$1.698770867$ |
3.771854182 |
\( -\frac{167792}{9} a - \frac{21616}{9} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 18 a + 15\) , \( -2 a + 62\bigr] \) |
${y}^2={x}^{3}+\left(18a+15\right){x}-2a+62$ |
| 10368.3-j2 |
10368.3-j |
$2$ |
$2$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
10368.3 |
\( 2^{7} \cdot 3^{4} \) |
\( 2^{8} \cdot 3^{10} \) |
$2.55039$ |
$(a), (-a-1), (a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.392504916$ |
$3.397541734$ |
3.771854182 |
\( \frac{3584}{3} a + \frac{4096}{3} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 3 a\) , \( -2 a - 1\bigr] \) |
${y}^2={x}^{3}+3a{x}-2a-1$ |
| 10368.3-k1 |
10368.3-k |
$2$ |
$2$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
10368.3 |
\( 2^{7} \cdot 3^{4} \) |
\( 2^{16} \cdot 3^{21} \) |
$2.55039$ |
$(a), (-a-1), (a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$0.799426856$ |
2.261120604 |
\( \frac{335248}{729} a + \frac{350000}{729} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -30 a + 39\) , \( -146 a - 82\bigr] \) |
${y}^2={x}^{3}+\left(-30a+39\right){x}-146a-82$ |
| 10368.3-k2 |
10368.3-k |
$2$ |
$2$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
10368.3 |
\( 2^{7} \cdot 3^{4} \) |
\( 2^{8} \cdot 3^{18} \) |
$2.55039$ |
$(a), (-a-1), (a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$1.598853712$ |
2.261120604 |
\( -\frac{48640}{27} a + \frac{74752}{27} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 15 a - 6\) , \( -20 a - 19\bigr] \) |
${y}^2={x}^{3}+\left(15a-6\right){x}-20a-19$ |
| 10368.3-l1 |
10368.3-l |
$2$ |
$2$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
10368.3 |
\( 2^{7} \cdot 3^{4} \) |
\( 2^{16} \cdot 3^{21} \) |
$2.55039$ |
$(a), (-a-1), (a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$0.799426856$ |
2.261120604 |
\( -\frac{335248}{729} a + \frac{350000}{729} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 30 a + 39\) , \( 146 a - 82\bigr] \) |
${y}^2={x}^{3}+\left(30a+39\right){x}+146a-82$ |
| 10368.3-l2 |
10368.3-l |
$2$ |
$2$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
10368.3 |
\( 2^{7} \cdot 3^{4} \) |
\( 2^{8} \cdot 3^{18} \) |
$2.55039$ |
$(a), (-a-1), (a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$1.598853712$ |
2.261120604 |
\( \frac{48640}{27} a + \frac{74752}{27} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -15 a - 6\) , \( 20 a - 19\bigr] \) |
${y}^2={x}^{3}+\left(-15a-6\right){x}+20a-19$ |
| 10368.3-m1 |
10368.3-m |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
10368.3 |
\( 2^{7} \cdot 3^{4} \) |
\( 2^{16} \cdot 3^{14} \) |
$2.55039$ |
$(a), (-a-1), (a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$1.384050608$ |
1.957343141 |
\( -\frac{9472}{9} a - \frac{71552}{9} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 24 a - 6\) , \( -52 a - 44\bigr] \) |
${y}^2={x}^{3}+\left(24a-6\right){x}-52a-44$ |
| 10368.3-m2 |
10368.3-m |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
10368.3 |
\( 2^{7} \cdot 3^{4} \) |
\( 2^{7} \cdot 3^{20} \) |
$2.55039$ |
$(a), (-a-1), (a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$1.384050608$ |
1.957343141 |
\( \frac{15609244}{6561} a - \frac{20009248}{6561} \) |
\( \bigl[a\) , \( -1\) , \( a\) , \( -21 a + 7\) , \( -10 a + 64\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(-21a+7\right){x}-10a+64$ |
| 10368.3-m3 |
10368.3-m |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
10368.3 |
\( 2^{7} \cdot 3^{4} \) |
\( 2^{14} \cdot 3^{16} \) |
$2.55039$ |
$(a), (-a-1), (a-1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$1$ |
$1.384050608$ |
1.957343141 |
\( -\frac{39872}{81} a - \frac{110368}{81} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 6 a + 21\) , \( 38 a - 26\bigr] \) |
${y}^2={x}^{3}+\left(6a+21\right){x}+38a-26$ |
| 10368.3-m4 |
10368.3-m |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
10368.3 |
\( 2^{7} \cdot 3^{4} \) |
\( 2^{7} \cdot 3^{14} \) |
$2.55039$ |
$(a), (-a-1), (a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$1.384050608$ |
1.957343141 |
\( \frac{18653188}{9} a + \frac{32152304}{9} \) |
\( \bigl[a\) , \( -1\) , \( a\) , \( 24 a + 97\) , \( -253 a + 145\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(24a+97\right){x}-253a+145$ |
| 10368.3-n1 |
10368.3-n |
$2$ |
$2$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
10368.3 |
\( 2^{7} \cdot 3^{4} \) |
\( 2^{16} \cdot 3^{12} \) |
$2.55039$ |
$(a), (-a-1), (a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$1.758903639$ |
2.487465382 |
\( 3456 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 12 a + 6\) , \( -4 a - 20\bigr] \) |
${y}^2={x}^{3}+\left(12a+6\right){x}-4a-20$ |
| 10368.3-n2 |
10368.3-n |
$2$ |
$2$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
10368.3 |
\( 2^{7} \cdot 3^{4} \) |
\( 2^{14} \cdot 3^{12} \) |
$2.55039$ |
$(a), (-a-1), (a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$1.758903639$ |
2.487465382 |
\( 23328 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 18 a + 9\) , \( -10 a - 50\bigr] \) |
${y}^2={x}^{3}+\left(18a+9\right){x}-10a-50$ |
| 10368.3-o1 |
10368.3-o |
$2$ |
$2$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
10368.3 |
\( 2^{7} \cdot 3^{4} \) |
\( 2^{16} \cdot 3^{12} \) |
$2.55039$ |
$(a), (-a-1), (a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$1.758903639$ |
2.487465382 |
\( 3456 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -12 a + 6\) , \( 4 a - 20\bigr] \) |
${y}^2={x}^{3}+\left(-12a+6\right){x}+4a-20$ |
| 10368.3-o2 |
10368.3-o |
$2$ |
$2$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
10368.3 |
\( 2^{7} \cdot 3^{4} \) |
\( 2^{14} \cdot 3^{12} \) |
$2.55039$ |
$(a), (-a-1), (a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$1.758903639$ |
2.487465382 |
\( 23328 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -18 a + 9\) , \( 10 a - 50\bigr] \) |
${y}^2={x}^{3}+\left(-18a+9\right){x}+10a-50$ |
| 10368.3-p1 |
10368.3-p |
$2$ |
$2$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
10368.3 |
\( 2^{7} \cdot 3^{4} \) |
\( 2^{16} \cdot 3^{11} \) |
$2.55039$ |
$(a), (-a-1), (a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$0.445708817$ |
$1.698770867$ |
4.283127666 |
\( \frac{167792}{9} a - \frac{21616}{9} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -18 a + 15\) , \( -2 a - 62\bigr] \) |
${y}^2={x}^{3}+\left(-18a+15\right){x}-2a-62$ |
| 10368.3-p2 |
10368.3-p |
$2$ |
$2$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
10368.3 |
\( 2^{7} \cdot 3^{4} \) |
\( 2^{8} \cdot 3^{10} \) |
$2.55039$ |
$(a), (-a-1), (a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$0.222854408$ |
$3.397541734$ |
4.283127666 |
\( -\frac{3584}{3} a + \frac{4096}{3} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -3 a\) , \( -2 a + 1\bigr] \) |
${y}^2={x}^{3}-3a{x}-2a+1$ |
*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.
