| 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 |
| 27648.3-a1 |
27648.3-a |
$2$ |
$2$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
27648.3 |
\( 2^{10} \cdot 3^{3} \) |
\( 2^{14} \cdot 3^{5} \) |
$3.25911$ |
$(a), (-a-1), (a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.336099985$ |
$3.669414946$ |
3.488271764 |
\( -\frac{14624}{9} a - \frac{28192}{9} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 2 a - 2\) , \( 4 a + 2\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(2a-2\right){x}+4a+2$ |
| 27648.3-a2 |
27648.3-a |
$2$ |
$2$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
27648.3 |
\( 2^{10} \cdot 3^{3} \) |
\( 2^{16} \cdot 3^{4} \) |
$3.25911$ |
$(a), (-a-1), (a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.672199970$ |
$3.669414946$ |
3.488271764 |
\( \frac{1664}{3} a - \frac{5504}{3} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 3\) , \( -3 a + 3\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+3{x}-3a+3$ |
| 27648.3-b1 |
27648.3-b |
$8$ |
$16$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
27648.3 |
\( 2^{10} \cdot 3^{3} \) |
\( 2^{27} \cdot 3^{11} \) |
$3.25911$ |
$(a), (-a-1), (a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$3.521423100$ |
$0.342264428$ |
3.408984042 |
\( -\frac{15347957750}{81} a - \frac{35138997500}{81} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 126 a - 2817\) , \( 4863 a - 58305\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(126a-2817\right){x}+4863a-58305$ |
| 27648.3-b2 |
27648.3-b |
$8$ |
$16$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
27648.3 |
\( 2^{10} \cdot 3^{3} \) |
\( 2^{27} \cdot 3^{11} \) |
$3.25911$ |
$(a), (-a-1), (a-1)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$3.521423100$ |
$0.342264428$ |
3.408984042 |
\( \frac{15347957750}{81} a - \frac{35138997500}{81} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -1154 a + 2303\) , \( -25737 a - 46065\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(-1154a+2303\right){x}-25737a-46065$ |
| 27648.3-b3 |
27648.3-b |
$8$ |
$16$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
27648.3 |
\( 2^{10} \cdot 3^{3} \) |
\( 2^{18} \cdot 3^{14} \) |
$3.25911$ |
$(a), (-a-1), (a-1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$0.880355775$ |
$1.369057715$ |
3.408984042 |
\( -\frac{8000}{81} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 6 a + 3\) , \( -9 a - 45\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(6a+3\right){x}-9a-45$ |
| 27648.3-b4 |
27648.3-b |
$8$ |
$16$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
27648.3 |
\( 2^{10} \cdot 3^{3} \) |
\( 2^{27} \cdot 3^{23} \) |
$3.25911$ |
$(a), (-a-1), (a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$3.521423100$ |
$0.342264428$ |
3.408984042 |
\( -\frac{56997401750}{43046721} a + \frac{87757407500}{43046721} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -274 a + 223\) , \( -857 a + 2735\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(-274a+223\right){x}-857a+2735$ |
| 27648.3-b5 |
27648.3-b |
$8$ |
$16$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
27648.3 |
\( 2^{10} \cdot 3^{3} \) |
\( 2^{27} \cdot 3^{23} \) |
$3.25911$ |
$(a), (-a-1), (a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$3.521423100$ |
$0.342264428$ |
3.408984042 |
\( \frac{56997401750}{43046721} a + \frac{87757407500}{43046721} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -114 a - 417\) , \( 1743 a + 1695\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(-114a-417\right){x}+1743a+1695$ |
| 27648.3-b6 |
27648.3-b |
$8$ |
$16$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
27648.3 |
\( 2^{10} \cdot 3^{3} \) |
\( 2^{24} \cdot 3^{16} \) |
$3.25911$ |
$(a), (-a-1), (a-1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$1.760711550$ |
$0.684528857$ |
3.408984042 |
\( -\frac{100738000}{6561} a + \frac{45365000}{6561} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 6 a - 177\) , \( 135 a - 945\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(6a-177\right){x}+135a-945$ |
| 27648.3-b7 |
27648.3-b |
$8$ |
$16$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
27648.3 |
\( 2^{10} \cdot 3^{3} \) |
\( 2^{24} \cdot 3^{16} \) |
$3.25911$ |
$(a), (-a-1), (a-1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$1.760711550$ |
$0.684528857$ |
3.408984042 |
\( \frac{100738000}{6561} a + \frac{45365000}{6561} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -74 a + 143\) , \( -465 a - 705\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(-74a+143\right){x}-465a-705$ |
| 27648.3-b8 |
27648.3-b |
$8$ |
$16$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
27648.3 |
\( 2^{10} \cdot 3^{3} \) |
\( 2^{18} \cdot 3^{10} \) |
$3.25911$ |
$(a), (-a-1), (a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$0.440177887$ |
$1.369057715$ |
3.408984042 |
\( \frac{2744000}{9} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 46 a + 23\) , \( 51 a + 255\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(46a+23\right){x}+51a+255$ |
| 27648.3-c1 |
27648.3-c |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
27648.3 |
\( 2^{10} \cdot 3^{3} \) |
\( 2^{14} \cdot 3^{7} \) |
$3.25911$ |
$(a), (-a-1), (a-1)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1.590064514$ |
$2.654047663$ |
5.968132565 |
\( \frac{79904}{3} a - \frac{65312}{3} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -8 a + 8\) , \( -2 a + 16\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(-8a+8\right){x}-2a+16$ |
| 27648.3-c2 |
27648.3-c |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
27648.3 |
\( 2^{10} \cdot 3^{3} \) |
\( 2^{16} \cdot 3^{8} \) |
$3.25911$ |
$(a), (-a-1), (a-1)$ |
$2$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$0.397516128$ |
$2.654047663$ |
5.968132565 |
\( \frac{1408}{9} a + \frac{128}{9} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 3\) , \( a - 5\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+3{x}+a-5$ |
| 27648.3-c3 |
27648.3-c |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
27648.3 |
\( 2^{10} \cdot 3^{3} \) |
\( 2^{23} \cdot 3^{10} \) |
$3.25911$ |
$(a), (-a-1), (a-1)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$0.397516128$ |
$1.327023831$ |
5.968132565 |
\( -\frac{414344}{81} a + \frac{534752}{81} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 10 a - 37\) , \( 55 a - 77\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(10a-37\right){x}+55a-77$ |
| 27648.3-c4 |
27648.3-c |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
27648.3 |
\( 2^{10} \cdot 3^{3} \) |
\( 2^{23} \cdot 3^{7} \) |
$3.25911$ |
$(a), (-a-1), (a-1)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1.590064514$ |
$1.327023831$ |
5.968132565 |
\( -\frac{749576}{3} a + \frac{321776}{3} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 30 a + 63\) , \( 103 a - 161\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(30a+63\right){x}+103a-161$ |
| 27648.3-d1 |
27648.3-d |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
27648.3 |
\( 2^{10} \cdot 3^{3} \) |
\( 2^{23} \cdot 3^{20} \) |
$3.25911$ |
$(a), (-a-1), (a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1.864418437$ |
$0.589460860$ |
3.108446208 |
\( \frac{105306568}{531441} a + \frac{136151936}{531441} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 50 a + 43\) , \( -353 a - 253\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(50a+43\right){x}-353a-253$ |
| 27648.3-d2 |
27648.3-d |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
27648.3 |
\( 2^{10} \cdot 3^{3} \) |
\( 2^{16} \cdot 3^{16} \) |
$3.25911$ |
$(a), (-a-1), (a-1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$0.932209218$ |
$1.178921721$ |
3.108446208 |
\( -\frac{1668992}{729} a + \frac{3939968}{729} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -20 a - 37\) , \( -51 a - 93\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(-20a-37\right){x}-51a-93$ |
| 27648.3-d3 |
27648.3-d |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
27648.3 |
\( 2^{10} \cdot 3^{3} \) |
\( 2^{14} \cdot 3^{17} \) |
$3.25911$ |
$(a), (-a-1), (a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1.864418437$ |
$1.178921721$ |
3.108446208 |
\( \frac{24685856}{6561} a + \frac{51528992}{6561} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -28 a - 32\) , \( -86 a - 52\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(-28a-32\right){x}-86a-52$ |
| 27648.3-d4 |
27648.3-d |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
27648.3 |
\( 2^{10} \cdot 3^{3} \) |
\( 2^{23} \cdot 3^{11} \) |
$3.25911$ |
$(a), (-a-1), (a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1.864418437$ |
$0.589460860$ |
3.108446208 |
\( -\frac{576294904}{27} a + \frac{292647184}{27} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -290 a - 577\) , \( -3993 a - 4737\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(-290a-577\right){x}-3993a-4737$ |
| 27648.3-e1 |
27648.3-e |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
27648.3 |
\( 2^{10} \cdot 3^{3} \) |
\( 2^{23} \cdot 3^{8} \) |
$3.25911$ |
$(a), (-a-1), (a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1.359626274$ |
$1.088072633$ |
4.184296289 |
\( -\frac{110584}{3} a - 1178880 \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 30 a - 129\) , \( 255 a - 561\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(30a-129\right){x}+255a-561$ |
| 27648.3-e2 |
27648.3-e |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
27648.3 |
\( 2^{10} \cdot 3^{3} \) |
\( 2^{23} \cdot 3^{11} \) |
$3.25911$ |
$(a), (-a-1), (a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1.359626274$ |
$1.088072633$ |
4.184296289 |
\( \frac{1862600}{81} a - \frac{2730832}{81} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -30 a - 69\) , \( 159 a + 147\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(-30a-69\right){x}+159a+147$ |
| 27648.3-e3 |
27648.3-e |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
27648.3 |
\( 2^{10} \cdot 3^{3} \) |
\( 2^{16} \cdot 3^{10} \) |
$3.25911$ |
$(a), (-a-1), (a-1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$0.679813137$ |
$2.176145266$ |
4.184296289 |
\( -640 a + \frac{6784}{9} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -9\) , \( 9 a - 9\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}-9{x}+9a-9$ |
| 27648.3-e4 |
27648.3-e |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
27648.3 |
\( 2^{10} \cdot 3^{3} \) |
\( 2^{14} \cdot 3^{11} \) |
$3.25911$ |
$(a), (-a-1), (a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$0.339906568$ |
$2.176145266$ |
4.184296289 |
\( \frac{109408}{81} a + \frac{158240}{81} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 2 a + 10\) , \( -8 a + 14\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(2a+10\right){x}-8a+14$ |
| 27648.3-f1 |
27648.3-f |
$8$ |
$16$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
27648.3 |
\( 2^{10} \cdot 3^{3} \) |
\( 2^{28} \cdot 3^{22} \) |
$3.25911$ |
$(a), (-a-1), (a-1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$4.030505696$ |
$0.371031051$ |
4.229750882 |
\( \frac{207646}{6561} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 62 a + 31\) , \( -1737 a + 751\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(62a+31\right){x}-1737a+751$ |
| 27648.3-f2 |
27648.3-f |
$8$ |
$16$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
27648.3 |
\( 2^{10} \cdot 3^{3} \) |
\( 2^{14} \cdot 3^{8} \) |
$3.25911$ |
$(a), (-a-1), (a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.503813212$ |
$2.968248410$ |
4.229750882 |
\( \frac{2048}{3} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 2 a + 1\) , \( 3 a + 1\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(2a+1\right){x}+3a+1$ |
| 27648.3-f3 |
27648.3-f |
$8$ |
$16$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
27648.3 |
\( 2^{10} \cdot 3^{3} \) |
\( 2^{22} \cdot 3^{10} \) |
$3.25911$ |
$(a), (-a-1), (a-1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$1.007626424$ |
$1.484124205$ |
4.229750882 |
\( \frac{35152}{9} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -18 a - 9\) , \( 23 a - 25\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(-18a-9\right){x}+23a-25$ |
| 27648.3-f4 |
27648.3-f |
$8$ |
$16$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
27648.3 |
\( 2^{10} \cdot 3^{3} \) |
\( 2^{26} \cdot 3^{14} \) |
$3.25911$ |
$(a), (-a-1), (a-1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$2.015252848$ |
$0.742062102$ |
4.229750882 |
\( \frac{1556068}{81} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -98 a - 49\) , \( -457 a + 95\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(-98a-49\right){x}-457a+95$ |
| 27648.3-f5 |
27648.3-f |
$8$ |
$16$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
27648.3 |
\( 2^{10} \cdot 3^{3} \) |
\( 2^{29} \cdot 3^{26} \) |
$3.25911$ |
$(a), (-a-1), (a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$8.061011393$ |
$0.185515525$ |
4.229750882 |
\( -\frac{2327042746553}{43046721} a + \frac{2081263802600}{43046721} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 1902 a - 1569\) , \( -45913 a + 623\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(1902a-1569\right){x}-45913a+623$ |
| 27648.3-f6 |
27648.3-f |
$8$ |
$16$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
27648.3 |
\( 2^{10} \cdot 3^{3} \) |
\( 2^{29} \cdot 3^{26} \) |
$3.25911$ |
$(a), (-a-1), (a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$2.015252848$ |
$0.185515525$ |
4.229750882 |
\( \frac{2327042746553}{43046721} a + \frac{2081263802600}{43046721} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 782 a + 2911\) , \( -40761 a + 36463\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(782a+2911\right){x}-40761a+36463$ |
| 27648.3-f7 |
27648.3-f |
$8$ |
$16$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
27648.3 |
\( 2^{10} \cdot 3^{3} \) |
\( 2^{26} \cdot 3^{8} \) |
$3.25911$ |
$(a), (-a-1), (a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$2.015252848$ |
$0.742062102$ |
4.229750882 |
\( \frac{28756228}{3} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -258 a - 129\) , \( 1943 a - 1009\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(-258a-129\right){x}+1943a-1009$ |
| 27648.3-f8 |
27648.3-f |
$8$ |
$16$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
27648.3 |
\( 2^{10} \cdot 3^{3} \) |
\( 2^{28} \cdot 3^{10} \) |
$3.25911$ |
$(a), (-a-1), (a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$4.030505696$ |
$0.371031051$ |
4.229750882 |
\( \frac{3065617154}{9} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -1538 a - 769\) , \( -29257 a + 10319\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(-1538a-769\right){x}-29257a+10319$ |
| 27648.3-g1 |
27648.3-g |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
27648.3 |
\( 2^{10} \cdot 3^{3} \) |
\( 2^{25} \cdot 3^{21} \) |
$3.25911$ |
$(a), (-a-1), (a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$0.775452707$ |
$0.419444296$ |
3.679887945 |
\( -\frac{5577343220}{531441} a - \frac{1362907864}{531441} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -46 a + 427\) , \( 2223 a + 1075\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(-46a+427\right){x}+2223a+1075$ |
| 27648.3-g2 |
27648.3-g |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
27648.3 |
\( 2^{10} \cdot 3^{3} \) |
\( 2^{25} \cdot 3^{21} \) |
$3.25911$ |
$(a), (-a-1), (a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$3.101810829$ |
$0.419444296$ |
3.679887945 |
\( \frac{5577343220}{531441} a - \frac{1362907864}{531441} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 154 a - 373\) , \( 1847 a - 2605\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(154a-373\right){x}+1847a-2605$ |
| 27648.3-g3 |
27648.3-g |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
27648.3 |
\( 2^{10} \cdot 3^{3} \) |
\( 2^{20} \cdot 3^{18} \) |
$3.25911$ |
$(a), (-a-1), (a-1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$1.550905414$ |
$0.838888592$ |
3.679887945 |
\( -\frac{219488}{729} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -26 a - 13\) , \( 155 a - 85\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(-26a-13\right){x}+155a-85$ |
| 27648.3-g4 |
27648.3-g |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
27648.3 |
\( 2^{10} \cdot 3^{3} \) |
\( 2^{10} \cdot 3^{12} \) |
$3.25911$ |
$(a), (-a-1), (a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$3.101810829$ |
$1.677777184$ |
3.679887945 |
\( \frac{19056256}{27} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -36 a - 18\) , \( 95 a - 70\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(-36a-18\right){x}+95a-70$ |
| 27648.3-h1 |
27648.3-h |
$2$ |
$2$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
27648.3 |
\( 2^{10} \cdot 3^{3} \) |
\( 2^{22} \cdot 3^{5} \) |
$3.25911$ |
$(a), (-a-1), (a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$0.250014161$ |
$2.080560907$ |
2.942524130 |
\( -\frac{167792}{9} a - \frac{21616}{9} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 10 a - 13\) , \( 31 a - 5\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(10a-13\right){x}+31a-5$ |
| 27648.3-h2 |
27648.3-h |
$2$ |
$2$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
27648.3 |
\( 2^{10} \cdot 3^{3} \) |
\( 2^{14} \cdot 3^{4} \) |
$3.25911$ |
$(a), (-a-1), (a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.500028323$ |
$4.161121815$ |
2.942524130 |
\( \frac{3584}{3} a + \frac{4096}{3} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -3\) , \( a + 1\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}-3{x}+a+1$ |
| 27648.3-i1 |
27648.3-i |
$2$ |
$2$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
27648.3 |
\( 2^{10} \cdot 3^{3} \) |
\( 2^{16} \cdot 3^{14} \) |
$3.25911$ |
$(a), (-a-1), (a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$1.084415963$ |
0.766797881 |
\( -\frac{1369984}{243} a - \frac{60155264}{243} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 72 a - 33\) , \( 325 a + 175\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(72a-33\right){x}+325a+175$ |
| 27648.3-i2 |
27648.3-i |
$2$ |
$2$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
27648.3 |
\( 2^{10} \cdot 3^{3} \) |
\( 2^{14} \cdot 3^{19} \) |
$3.25911$ |
$(a), (-a-1), (a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$1.084415963$ |
0.766797881 |
\( \frac{4722784}{59049} a + \frac{38018528}{59049} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 20 a + 4\) , \( -46 a + 48\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(20a+4\right){x}-46a+48$ |
| 27648.3-j1 |
27648.3-j |
$2$ |
$2$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
27648.3 |
\( 2^{10} \cdot 3^{3} \) |
\( 2^{22} \cdot 3^{15} \) |
$3.25911$ |
$(a), (-a-1), (a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$0.979093942$ |
1.384647931 |
\( \frac{335248}{729} a + \frac{350000}{729} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 10 a + 35\) , \( -17 a + 139\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(10a+35\right){x}-17a+139$ |
| 27648.3-j2 |
27648.3-j |
$2$ |
$2$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
27648.3 |
\( 2^{10} \cdot 3^{3} \) |
\( 2^{14} \cdot 3^{12} \) |
$3.25911$ |
$(a), (-a-1), (a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$1.958187884$ |
1.384647931 |
\( -\frac{48640}{27} a + \frac{74752}{27} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -15\) , \( a + 13\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}-15{x}+a+13$ |
| 27648.3-k1 |
27648.3-k |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
27648.3 |
\( 2^{10} \cdot 3^{3} \) |
\( 2^{23} \cdot 3^{8} \) |
$3.25911$ |
$(a), (-a-1), (a-1)$ |
$2$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1.995328312$ |
$1.088072633$ |
6.140691021 |
\( \frac{110584}{3} a - 1178880 \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -34 a + 127\) , \( -425 a - 289\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(-34a+127\right){x}-425a-289$ |
| 27648.3-k2 |
27648.3-k |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
27648.3 |
\( 2^{10} \cdot 3^{3} \) |
\( 2^{23} \cdot 3^{11} \) |
$3.25911$ |
$(a), (-a-1), (a-1)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$0.498832078$ |
$1.088072633$ |
6.140691021 |
\( -\frac{1862600}{81} a - \frac{2730832}{81} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -54 a + 27\) , \( -81 a + 243\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(-54a+27\right){x}-81a+243$ |
| 27648.3-k3 |
27648.3-k |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
27648.3 |
\( 2^{10} \cdot 3^{3} \) |
\( 2^{16} \cdot 3^{10} \) |
$3.25911$ |
$(a), (-a-1), (a-1)$ |
$2$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$0.498832078$ |
$2.176145266$ |
6.140691021 |
\( 640 a + \frac{6784}{9} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -4 a + 7\) , \( -11 a - 1\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(-4a+7\right){x}-11a-1$ |
| 27648.3-k4 |
27648.3-k |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
27648.3 |
\( 2^{10} \cdot 3^{3} \) |
\( 2^{14} \cdot 3^{11} \) |
$3.25911$ |
$(a), (-a-1), (a-1)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.498832078$ |
$2.176145266$ |
6.140691021 |
\( -\frac{109408}{81} a + \frac{158240}{81} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 6 a - 6\) , \( 12 a + 6\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(6a-6\right){x}+12a+6$ |
| 27648.3-l1 |
27648.3-l |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
27648.3 |
\( 2^{10} \cdot 3^{3} \) |
\( 2^{14} \cdot 3^{9} \) |
$3.25911$ |
$(a), (-a-1), (a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1.395981564$ |
$1.821628123$ |
3.596287499 |
\( \frac{2820064}{9} a - \frac{1154272}{9} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 24 a - 24\) , \( -58 a + 20\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(24a-24\right){x}-58a+20$ |
| 27648.3-l2 |
27648.3-l |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
27648.3 |
\( 2^{10} \cdot 3^{3} \) |
\( 2^{23} \cdot 3^{12} \) |
$3.25911$ |
$(a), (-a-1), (a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$0.348995391$ |
$0.910814061$ |
3.596287499 |
\( -\frac{8113672}{81} a - \frac{1280704}{81} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 98 a - 5\) , \( -297 a - 365\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(98a-5\right){x}-297a-365$ |
| 27648.3-l3 |
27648.3-l |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
27648.3 |
\( 2^{10} \cdot 3^{3} \) |
\( 2^{16} \cdot 3^{12} \) |
$3.25911$ |
$(a), (-a-1), (a-1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$0.697990782$ |
$1.821628123$ |
3.596287499 |
\( \frac{15232}{81} a + \frac{106112}{81} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 8 a - 5\) , \( 9 a - 5\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(8a-5\right){x}+9a-5$ |
| 27648.3-l4 |
27648.3-l |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
27648.3 |
\( 2^{10} \cdot 3^{3} \) |
\( 2^{23} \cdot 3^{15} \) |
$3.25911$ |
$(a), (-a-1), (a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$0.348995391$ |
$0.910814061$ |
3.596287499 |
\( -\frac{1905752}{6561} a + \frac{14345072}{6561} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -42 a + 15\) , \( 23 a - 97\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(-42a+15\right){x}+23a-97$ |
| 27648.3-m1 |
27648.3-m |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
27648.3 |
\( 2^{10} \cdot 3^{3} \) |
\( 2^{23} \cdot 3^{20} \) |
$3.25911$ |
$(a), (-a-1), (a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$0.589460860$ |
1.667247087 |
\( -\frac{105306568}{531441} a + \frac{136151936}{531441} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 58 a + 11\) , \( 207 a - 477\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(58a+11\right){x}+207a-477$ |
| 27648.3-m2 |
27648.3-m |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
27648.3 |
\( 2^{10} \cdot 3^{3} \) |
\( 2^{16} \cdot 3^{16} \) |
$3.25911$ |
$(a), (-a-1), (a-1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$1$ |
$1.178921721$ |
1.667247087 |
\( \frac{1668992}{729} a + \frac{3939968}{729} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -32 a + 11\) , \( 9 a - 117\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(-32a+11\right){x}+9a-117$ |
*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.
