| 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 |
| 27648.2-a1 |
27648.2-a |
$2$ |
$2$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
27648.2 |
\( 2^{10} \cdot 3^{3} \) |
\( 2^{22} \cdot 3^{5} \) |
$3.25911$ |
$(a), (-a-1), (a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$0.250014161$ |
$2.080560907$ |
2.942524130 |
\( \frac{167792}{9} a - \frac{21616}{9} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -10 a - 13\) , \( -31 a - 5\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(-10a-13\right){x}-31a-5$ |
| 27648.2-a2 |
27648.2-a |
$2$ |
$2$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
27648.2 |
\( 2^{10} \cdot 3^{3} \) |
\( 2^{14} \cdot 3^{4} \) |
$3.25911$ |
$(a), (-a-1), (a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.500028323$ |
$4.161121815$ |
2.942524130 |
\( -\frac{3584}{3} a + \frac{4096}{3} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -3\) , \( -a + 1\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}-3{x}-a+1$ |
| 27648.2-b1 |
27648.2-b |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
27648.2 |
\( 2^{10} \cdot 3^{3} \) |
\( 2^{14} \cdot 3^{7} \) |
$3.25911$ |
$(a), (-a-1), (a-1)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1.590064514$ |
$2.654047663$ |
5.968132565 |
\( -\frac{79904}{3} a - \frac{65312}{3} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 8 a + 8\) , \( 2 a + 16\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(8a+8\right){x}+2a+16$ |
| 27648.2-b2 |
27648.2-b |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
27648.2 |
\( 2^{10} \cdot 3^{3} \) |
\( 2^{16} \cdot 3^{8} \) |
$3.25911$ |
$(a), (-a-1), (a-1)$ |
$2$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$0.397516128$ |
$2.654047663$ |
5.968132565 |
\( -\frac{1408}{9} a + \frac{128}{9} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 3\) , \( -a - 5\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+3{x}-a-5$ |
| 27648.2-b3 |
27648.2-b |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
27648.2 |
\( 2^{10} \cdot 3^{3} \) |
\( 2^{23} \cdot 3^{10} \) |
$3.25911$ |
$(a), (-a-1), (a-1)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$0.397516128$ |
$1.327023831$ |
5.968132565 |
\( \frac{414344}{81} a + \frac{534752}{81} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -10 a - 37\) , \( -55 a - 77\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(-10a-37\right){x}-55a-77$ |
| 27648.2-b4 |
27648.2-b |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
27648.2 |
\( 2^{10} \cdot 3^{3} \) |
\( 2^{23} \cdot 3^{7} \) |
$3.25911$ |
$(a), (-a-1), (a-1)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1.590064514$ |
$1.327023831$ |
5.968132565 |
\( \frac{749576}{3} a + \frac{321776}{3} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -30 a + 63\) , \( -103 a - 161\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(-30a+63\right){x}-103a-161$ |
| 27648.2-c1 |
27648.2-c |
$8$ |
$16$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
27648.2 |
\( 2^{10} \cdot 3^{3} \) |
\( 2^{27} \cdot 3^{11} \) |
$3.25911$ |
$(a), (-a-1), (a-1)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$3.521423100$ |
$0.342264428$ |
3.408984042 |
\( -\frac{15347957750}{81} a - \frac{35138997500}{81} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 1154 a + 2303\) , \( 25737 a - 46065\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(1154a+2303\right){x}+25737a-46065$ |
| 27648.2-c2 |
27648.2-c |
$8$ |
$16$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
27648.2 |
\( 2^{10} \cdot 3^{3} \) |
\( 2^{27} \cdot 3^{11} \) |
$3.25911$ |
$(a), (-a-1), (a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$3.521423100$ |
$0.342264428$ |
3.408984042 |
\( \frac{15347957750}{81} a - \frac{35138997500}{81} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -126 a - 2817\) , \( -4863 a - 58305\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(-126a-2817\right){x}-4863a-58305$ |
| 27648.2-c3 |
27648.2-c |
$8$ |
$16$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
27648.2 |
\( 2^{10} \cdot 3^{3} \) |
\( 2^{18} \cdot 3^{14} \) |
$3.25911$ |
$(a), (-a-1), (a-1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$0.880355775$ |
$1.369057715$ |
3.408984042 |
\( -\frac{8000}{81} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -6 a + 3\) , \( 9 a - 45\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(-6a+3\right){x}+9a-45$ |
| 27648.2-c4 |
27648.2-c |
$8$ |
$16$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
27648.2 |
\( 2^{10} \cdot 3^{3} \) |
\( 2^{27} \cdot 3^{23} \) |
$3.25911$ |
$(a), (-a-1), (a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$3.521423100$ |
$0.342264428$ |
3.408984042 |
\( -\frac{56997401750}{43046721} a + \frac{87757407500}{43046721} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 114 a - 417\) , \( -1743 a + 1695\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(114a-417\right){x}-1743a+1695$ |
| 27648.2-c5 |
27648.2-c |
$8$ |
$16$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
27648.2 |
\( 2^{10} \cdot 3^{3} \) |
\( 2^{27} \cdot 3^{23} \) |
$3.25911$ |
$(a), (-a-1), (a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$3.521423100$ |
$0.342264428$ |
3.408984042 |
\( \frac{56997401750}{43046721} a + \frac{87757407500}{43046721} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 274 a + 223\) , \( 857 a + 2735\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(274a+223\right){x}+857a+2735$ |
| 27648.2-c6 |
27648.2-c |
$8$ |
$16$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
27648.2 |
\( 2^{10} \cdot 3^{3} \) |
\( 2^{24} \cdot 3^{16} \) |
$3.25911$ |
$(a), (-a-1), (a-1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$1.760711550$ |
$0.684528857$ |
3.408984042 |
\( -\frac{100738000}{6561} a + \frac{45365000}{6561} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 74 a + 143\) , \( 465 a - 705\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(74a+143\right){x}+465a-705$ |
| 27648.2-c7 |
27648.2-c |
$8$ |
$16$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
27648.2 |
\( 2^{10} \cdot 3^{3} \) |
\( 2^{24} \cdot 3^{16} \) |
$3.25911$ |
$(a), (-a-1), (a-1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$1.760711550$ |
$0.684528857$ |
3.408984042 |
\( \frac{100738000}{6561} a + \frac{45365000}{6561} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -6 a - 177\) , \( -135 a - 945\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(-6a-177\right){x}-135a-945$ |
| 27648.2-c8 |
27648.2-c |
$8$ |
$16$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
27648.2 |
\( 2^{10} \cdot 3^{3} \) |
\( 2^{18} \cdot 3^{10} \) |
$3.25911$ |
$(a), (-a-1), (a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$0.440177887$ |
$1.369057715$ |
3.408984042 |
\( \frac{2744000}{9} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -46 a + 23\) , \( -51 a + 255\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(-46a+23\right){x}-51a+255$ |
| 27648.2-d1 |
27648.2-d |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
27648.2 |
\( 2^{10} \cdot 3^{3} \) |
\( 2^{14} \cdot 3^{9} \) |
$3.25911$ |
$(a), (-a-1), (a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1.395981564$ |
$1.821628123$ |
3.596287499 |
\( -\frac{2820064}{9} a - \frac{1154272}{9} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -24 a - 24\) , \( 58 a + 20\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(-24a-24\right){x}+58a+20$ |
| 27648.2-d2 |
27648.2-d |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
27648.2 |
\( 2^{10} \cdot 3^{3} \) |
\( 2^{23} \cdot 3^{12} \) |
$3.25911$ |
$(a), (-a-1), (a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$0.348995391$ |
$0.910814061$ |
3.596287499 |
\( \frac{8113672}{81} a - \frac{1280704}{81} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -98 a - 5\) , \( 297 a - 365\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(-98a-5\right){x}+297a-365$ |
| 27648.2-d3 |
27648.2-d |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
27648.2 |
\( 2^{10} \cdot 3^{3} \) |
\( 2^{16} \cdot 3^{12} \) |
$3.25911$ |
$(a), (-a-1), (a-1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$0.697990782$ |
$1.821628123$ |
3.596287499 |
\( -\frac{15232}{81} a + \frac{106112}{81} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -8 a - 5\) , \( -9 a - 5\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(-8a-5\right){x}-9a-5$ |
| 27648.2-d4 |
27648.2-d |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
27648.2 |
\( 2^{10} \cdot 3^{3} \) |
\( 2^{23} \cdot 3^{15} \) |
$3.25911$ |
$(a), (-a-1), (a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$0.348995391$ |
$0.910814061$ |
3.596287499 |
\( \frac{1905752}{6561} a + \frac{14345072}{6561} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 42 a + 15\) , \( -23 a - 97\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(42a+15\right){x}-23a-97$ |
| 27648.2-e1 |
27648.2-e |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
27648.2 |
\( 2^{10} \cdot 3^{3} \) |
\( 2^{23} \cdot 3^{8} \) |
$3.25911$ |
$(a), (-a-1), (a-1)$ |
$2$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1.995328312$ |
$1.088072633$ |
6.140691021 |
\( -\frac{110584}{3} a - 1178880 \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 34 a + 127\) , \( 425 a - 289\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(34a+127\right){x}+425a-289$ |
| 27648.2-e2 |
27648.2-e |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
27648.2 |
\( 2^{10} \cdot 3^{3} \) |
\( 2^{23} \cdot 3^{11} \) |
$3.25911$ |
$(a), (-a-1), (a-1)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$0.498832078$ |
$1.088072633$ |
6.140691021 |
\( \frac{1862600}{81} a - \frac{2730832}{81} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 54 a + 27\) , \( 81 a + 243\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(54a+27\right){x}+81a+243$ |
| 27648.2-e3 |
27648.2-e |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
27648.2 |
\( 2^{10} \cdot 3^{3} \) |
\( 2^{16} \cdot 3^{10} \) |
$3.25911$ |
$(a), (-a-1), (a-1)$ |
$2$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$0.498832078$ |
$2.176145266$ |
6.140691021 |
\( -640 a + \frac{6784}{9} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 4 a + 7\) , \( 11 a - 1\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(4a+7\right){x}+11a-1$ |
| 27648.2-e4 |
27648.2-e |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
27648.2 |
\( 2^{10} \cdot 3^{3} \) |
\( 2^{14} \cdot 3^{11} \) |
$3.25911$ |
$(a), (-a-1), (a-1)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.498832078$ |
$2.176145266$ |
6.140691021 |
\( \frac{109408}{81} a + \frac{158240}{81} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -6 a - 6\) , \( -12 a + 6\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(-6a-6\right){x}-12a+6$ |
| 27648.2-f1 |
27648.2-f |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
27648.2 |
\( 2^{10} \cdot 3^{3} \) |
\( 2^{23} \cdot 3^{20} \) |
$3.25911$ |
$(a), (-a-1), (a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$0.589460860$ |
1.667247087 |
\( \frac{105306568}{531441} a + \frac{136151936}{531441} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -58 a + 11\) , \( -207 a - 477\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(-58a+11\right){x}-207a-477$ |
| 27648.2-f2 |
27648.2-f |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
27648.2 |
\( 2^{10} \cdot 3^{3} \) |
\( 2^{16} \cdot 3^{16} \) |
$3.25911$ |
$(a), (-a-1), (a-1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$1$ |
$1.178921721$ |
1.667247087 |
\( -\frac{1668992}{729} a + \frac{3939968}{729} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 32 a + 11\) , \( -9 a - 117\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(32a+11\right){x}-9a-117$ |
| 27648.2-f3 |
27648.2-f |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
27648.2 |
\( 2^{10} \cdot 3^{3} \) |
\( 2^{14} \cdot 3^{17} \) |
$3.25911$ |
$(a), (-a-1), (a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$1.178921721$ |
1.667247087 |
\( \frac{24685856}{6561} a + \frac{51528992}{6561} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 36 a\) , \( -54 a - 108\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+36a{x}-54a-108$ |
| 27648.2-f4 |
27648.2-f |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
27648.2 |
\( 2^{10} \cdot 3^{3} \) |
\( 2^{23} \cdot 3^{11} \) |
$3.25911$ |
$(a), (-a-1), (a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$0.589460860$ |
1.667247087 |
\( -\frac{576294904}{27} a + \frac{292647184}{27} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 482 a + 191\) , \( -1647 a - 6993\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(482a+191\right){x}-1647a-6993$ |
| 27648.2-g1 |
27648.2-g |
$6$ |
$8$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
27648.2 |
\( 2^{10} \cdot 3^{3} \) |
\( 2^{27} \cdot 3^{16} \) |
$3.25911$ |
$(a), (-a-1), (a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$0.686045887$ |
$0.478745482$ |
3.715889911 |
\( -\frac{1056226562}{6561} a - \frac{605268760}{6561} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -390 a + 15\) , \( 2281 a - 3409\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(-390a+15\right){x}+2281a-3409$ |
| 27648.2-g2 |
27648.2-g |
$6$ |
$8$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
27648.2 |
\( 2^{10} \cdot 3^{3} \) |
\( 2^{27} \cdot 3^{16} \) |
$3.25911$ |
$(a), (-a-1), (a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$2.744183548$ |
$0.478745482$ |
3.715889911 |
\( \frac{1056226562}{6561} a - \frac{605268760}{6561} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -310 a + 335\) , \( 697 a + 5231\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(-310a+335\right){x}+697a+5231$ |
| 27648.2-g3 |
27648.2-g |
$6$ |
$8$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
27648.2 |
\( 2^{10} \cdot 3^{3} \) |
\( 2^{24} \cdot 3^{14} \) |
$3.25911$ |
$(a), (-a-1), (a-1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$1.372091774$ |
$0.957490965$ |
3.715889911 |
\( \frac{97336}{81} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -30 a + 15\) , \( 49 a + 47\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(-30a+15\right){x}+49a+47$ |
| 27648.2-g4 |
27648.2-g |
$6$ |
$8$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
27648.2 |
\( 2^{10} \cdot 3^{3} \) |
\( 2^{18} \cdot 3^{10} \) |
$3.25911$ |
$(a), (-a-1), (a-1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$0.686045887$ |
$1.914981930$ |
3.715889911 |
\( \frac{21952}{9} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 10 a - 5\) , \( 9 a - 5\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(10a-5\right){x}+9a-5$ |
| 27648.2-g5 |
27648.2-g |
$6$ |
$8$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
27648.2 |
\( 2^{10} \cdot 3^{3} \) |
\( 2^{18} \cdot 3^{8} \) |
$3.25911$ |
$(a), (-a-1), (a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1.372091774$ |
$1.914981930$ |
3.715889911 |
\( \frac{140608}{3} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 18 a - 9\) , \( 37 a - 1\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(18a-9\right){x}+37a-1$ |
| 27648.2-g6 |
27648.2-g |
$6$ |
$8$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
27648.2 |
\( 2^{10} \cdot 3^{3} \) |
\( 2^{24} \cdot 3^{8} \) |
$3.25911$ |
$(a), (-a-1), (a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1.372091774$ |
$0.957490965$ |
3.715889911 |
\( \frac{7301384}{3} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 130 a - 65\) , \( 729 a + 175\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(130a-65\right){x}+729a+175$ |
| 27648.2-h1 |
27648.2-h |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
27648.2 |
\( 2^{10} \cdot 3^{3} \) |
\( 2^{25} \cdot 3^{11} \) |
$3.25911$ |
$(a), (-a-1), (a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1.560307655$ |
$0.876220870$ |
3.866952399 |
\( -\frac{4137500}{81} a - \frac{12439000}{81} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -66 a + 123\) , \( 313 a + 707\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(-66a+123\right){x}+313a+707$ |
| 27648.2-h2 |
27648.2-h |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
27648.2 |
\( 2^{10} \cdot 3^{3} \) |
\( 2^{25} \cdot 3^{11} \) |
$3.25911$ |
$(a), (-a-1), (a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$0.390076913$ |
$0.876220870$ |
3.866952399 |
\( \frac{4137500}{81} a - \frac{12439000}{81} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -106 a - 37\) , \( 433 a - 253\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(-106a-37\right){x}+433a-253$ |
| 27648.2-h3 |
27648.2-h |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
27648.2 |
\( 2^{10} \cdot 3^{3} \) |
\( 2^{20} \cdot 3^{10} \) |
$3.25911$ |
$(a), (-a-1), (a-1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$0.780153827$ |
$1.752441741$ |
3.866952399 |
\( \frac{4000}{9} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -6 a + 3\) , \( 13 a + 11\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(-6a+3\right){x}+13a+11$ |
| 27648.2-h4 |
27648.2-h |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
27648.2 |
\( 2^{10} \cdot 3^{3} \) |
\( 2^{10} \cdot 3^{8} \) |
$3.25911$ |
$(a), (-a-1), (a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1.560307655$ |
$3.504883482$ |
3.866952399 |
\( \frac{16000}{3} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 4 a - 2\) , \( 3 a - 2\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(4a-2\right){x}+3a-2$ |
| 27648.2-i1 |
27648.2-i |
$2$ |
$2$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
27648.2 |
\( 2^{10} \cdot 3^{3} \) |
\( 2^{16} \cdot 3^{14} \) |
$3.25911$ |
$(a), (-a-1), (a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$1.084415963$ |
0.766797881 |
\( \frac{1369984}{243} a - \frac{60155264}{243} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -72 a - 33\) , \( -325 a + 175\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(-72a-33\right){x}-325a+175$ |
| 27648.2-i2 |
27648.2-i |
$2$ |
$2$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
27648.2 |
\( 2^{10} \cdot 3^{3} \) |
\( 2^{14} \cdot 3^{19} \) |
$3.25911$ |
$(a), (-a-1), (a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$1.084415963$ |
0.766797881 |
\( -\frac{4722784}{59049} a + \frac{38018528}{59049} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -20 a + 4\) , \( 46 a + 48\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(-20a+4\right){x}+46a+48$ |
| 27648.2-j1 |
27648.2-j |
$2$ |
$2$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
27648.2 |
\( 2^{10} \cdot 3^{3} \) |
\( 2^{22} \cdot 3^{9} \) |
$3.25911$ |
$(a), (-a-1), (a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$1.695840453$ |
2.398280568 |
\( -\frac{335248}{729} a + \frac{350000}{729} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -6 a - 9\) , \( a + 23\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(-6a-9\right){x}+a+23$ |
| 27648.2-j2 |
27648.2-j |
$2$ |
$2$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
27648.2 |
\( 2^{10} \cdot 3^{3} \) |
\( 2^{14} \cdot 3^{6} \) |
$3.25911$ |
$(a), (-a-1), (a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$3.391680906$ |
2.398280568 |
\( \frac{48640}{27} a + \frac{74752}{27} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 4 a + 1\) , \( 3 a + 1\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(4a+1\right){x}+3a+1$ |
| 27648.2-k1 |
27648.2-k |
$2$ |
$2$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
27648.2 |
\( 2^{10} \cdot 3^{3} \) |
\( 2^{14} \cdot 3^{11} \) |
$3.25911$ |
$(a), (-a-1), (a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$2.118537706$ |
1.498032378 |
\( \frac{14624}{9} a - \frac{28192}{9} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 12\) , \( -10 a + 4\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+12{x}-10a+4$ |
| 27648.2-k2 |
27648.2-k |
$2$ |
$2$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
27648.2 |
\( 2^{10} \cdot 3^{3} \) |
\( 2^{16} \cdot 3^{10} \) |
$3.25911$ |
$(a), (-a-1), (a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$2.118537706$ |
1.498032378 |
\( -\frac{1664}{3} a - \frac{5504}{3} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 8 a - 1\) , \( 11 a + 7\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(8a-1\right){x}+11a+7$ |
| 27648.2-l1 |
27648.2-l |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
27648.2 |
\( 2^{10} \cdot 3^{3} \) |
\( 2^{23} \cdot 3^{20} \) |
$3.25911$ |
$(a), (-a-1), (a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1.864418437$ |
$0.589460860$ |
3.108446208 |
\( -\frac{105306568}{531441} a + \frac{136151936}{531441} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -50 a + 43\) , \( 353 a - 253\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(-50a+43\right){x}+353a-253$ |
| 27648.2-l2 |
27648.2-l |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
27648.2 |
\( 2^{10} \cdot 3^{3} \) |
\( 2^{16} \cdot 3^{16} \) |
$3.25911$ |
$(a), (-a-1), (a-1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$0.932209218$ |
$1.178921721$ |
3.108446208 |
\( \frac{1668992}{729} a + \frac{3939968}{729} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 20 a - 37\) , \( 51 a - 93\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(20a-37\right){x}+51a-93$ |
| 27648.2-l3 |
27648.2-l |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
27648.2 |
\( 2^{10} \cdot 3^{3} \) |
\( 2^{14} \cdot 3^{17} \) |
$3.25911$ |
$(a), (-a-1), (a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1.864418437$ |
$1.178921721$ |
3.108446208 |
\( -\frac{24685856}{6561} a + \frac{51528992}{6561} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 28 a - 32\) , \( 86 a - 52\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(28a-32\right){x}+86a-52$ |
| 27648.2-l4 |
27648.2-l |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
27648.2 |
\( 2^{10} \cdot 3^{3} \) |
\( 2^{23} \cdot 3^{11} \) |
$3.25911$ |
$(a), (-a-1), (a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1.864418437$ |
$0.589460860$ |
3.108446208 |
\( \frac{576294904}{27} a + \frac{292647184}{27} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 290 a - 577\) , \( 3993 a - 4737\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(290a-577\right){x}+3993a-4737$ |
| 27648.2-m1 |
27648.2-m |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
27648.2 |
\( 2^{10} \cdot 3^{3} \) |
\( 2^{23} \cdot 3^{8} \) |
$3.25911$ |
$(a), (-a-1), (a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1.359626274$ |
$1.088072633$ |
4.184296289 |
\( \frac{110584}{3} a - 1178880 \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -30 a - 129\) , \( -255 a - 561\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(-30a-129\right){x}-255a-561$ |
| 27648.2-m2 |
27648.2-m |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
27648.2 |
\( 2^{10} \cdot 3^{3} \) |
\( 2^{23} \cdot 3^{11} \) |
$3.25911$ |
$(a), (-a-1), (a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1.359626274$ |
$1.088072633$ |
4.184296289 |
\( -\frac{1862600}{81} a - \frac{2730832}{81} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 30 a - 69\) , \( -159 a + 147\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(30a-69\right){x}-159a+147$ |
| 27648.2-m3 |
27648.2-m |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
27648.2 |
\( 2^{10} \cdot 3^{3} \) |
\( 2^{16} \cdot 3^{10} \) |
$3.25911$ |
$(a), (-a-1), (a-1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$0.679813137$ |
$2.176145266$ |
4.184296289 |
\( 640 a + \frac{6784}{9} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -9\) , \( -9 a - 9\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}-9{x}-9a-9$ |
| 27648.2-m4 |
27648.2-m |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
27648.2 |
\( 2^{10} \cdot 3^{3} \) |
\( 2^{14} \cdot 3^{11} \) |
$3.25911$ |
$(a), (-a-1), (a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$0.339906568$ |
$2.176145266$ |
4.184296289 |
\( -\frac{109408}{81} a + \frac{158240}{81} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -2 a + 10\) , \( 8 a + 14\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(-2a+10\right){x}+8a+14$ |
*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.
