| 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 |
| 20736.3-CMb1 |
20736.3-CMb |
$1$ |
$1$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
20736.3 |
\( 2^{8} \cdot 3^{4} \) |
\( 2^{12} \cdot 3^{12} \) |
$3.03295$ |
$(a), (-a-1), (a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{yes}$ |
$-8$ |
$\mathrm{U}(1)$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2^{2} \) |
$1$ |
$2.114997822$ |
1.495529302 |
\( 8000 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 15\) , \( 14 a\bigr] \) |
${y}^2={x}^{3}+15{x}+14a$ |
| 20736.3-CMa1 |
20736.3-CMa |
$1$ |
$1$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
20736.3 |
\( 2^{8} \cdot 3^{4} \) |
\( 2^{12} \cdot 3^{12} \) |
$3.03295$ |
$(a), (-a-1), (a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{yes}$ |
$-8$ |
$\mathrm{U}(1)$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2^{2} \) |
$1$ |
$2.114997822$ |
1.495529302 |
\( 8000 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 15\) , \( -14 a\bigr] \) |
${y}^2={x}^{3}+15{x}-14a$ |
| 20736.3-a1 |
20736.3-a |
$2$ |
$2$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
20736.3 |
\( 2^{8} \cdot 3^{4} \) |
\( 2^{16} \cdot 3^{17} \) |
$3.03295$ |
$(a), (-a-1), (a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1.489911970$ |
$0.980785817$ |
4.133136802 |
\( \frac{167792}{9} a - \frac{21616}{9} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 48 a + 57\) , \( 52 a - 314\bigr] \) |
${y}^2={x}^{3}+\left(48a+57\right){x}+52a-314$ |
| 20736.3-a2 |
20736.3-a |
$2$ |
$2$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
20736.3 |
\( 2^{8} \cdot 3^{4} \) |
\( 2^{8} \cdot 3^{16} \) |
$3.03295$ |
$(a), (-a-1), (a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.744955985$ |
$1.961571635$ |
4.133136802 |
\( -\frac{3584}{3} a + \frac{4096}{3} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 3 a + 12\) , \( -11 a + 1\bigr] \) |
${y}^2={x}^{3}+\left(3a+12\right){x}-11a+1$ |
| 20736.3-b1 |
20736.3-b |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
20736.3 |
\( 2^{8} \cdot 3^{4} \) |
\( 2^{19} \cdot 3^{17} \) |
$3.03295$ |
$(a), (-a-1), (a-1)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$0.395445231$ |
$0.715431344$ |
6.401611099 |
\( -\frac{4137500}{81} a - \frac{12439000}{81} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 90 a + 195\) , \( 630 a - 1046\bigr] \) |
${y}^2={x}^{3}+\left(90a+195\right){x}+630a-1046$ |
| 20736.3-b2 |
20736.3-b |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
20736.3 |
\( 2^{8} \cdot 3^{4} \) |
\( 2^{19} \cdot 3^{17} \) |
$3.03295$ |
$(a), (-a-1), (a-1)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$0.395445231$ |
$0.715431344$ |
6.401611099 |
\( \frac{4137500}{81} a - \frac{12439000}{81} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -90 a + 195\) , \( -630 a - 1046\bigr] \) |
${y}^2={x}^{3}+\left(-90a+195\right){x}-630a-1046$ |
| 20736.3-b3 |
20736.3-b |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
20736.3 |
\( 2^{8} \cdot 3^{4} \) |
\( 2^{14} \cdot 3^{16} \) |
$3.03295$ |
$(a), (-a-1), (a-1)$ |
$2$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{6} \) |
$0.395445231$ |
$1.430862689$ |
6.401611099 |
\( \frac{4000}{9} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 15\) , \( -38\bigr] \) |
${y}^2={x}^{3}+15{x}-38$ |
| 20736.3-b4 |
20736.3-b |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
20736.3 |
\( 2^{8} \cdot 3^{4} \) |
\( 2^{16} \cdot 3^{14} \) |
$3.03295$ |
$(a), (-a-1), (a-1)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{6} \) |
$0.098861307$ |
$1.430862689$ |
6.401611099 |
\( \frac{16000}{3} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -30\) , \( 52\bigr] \) |
${y}^2={x}^{3}-30{x}+52$ |
| 20736.3-c1 |
20736.3-c |
$2$ |
$2$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
20736.3 |
\( 2^{8} \cdot 3^{4} \) |
\( 2^{16} \cdot 3^{6} \) |
$3.03295$ |
$(a), (-a-1), (a-1)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$0.185476610$ |
$3.046510469$ |
6.392883816 |
\( 3456 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -6\) , \( -4\bigr] \) |
${y}^2={x}^{3}-6{x}-4$ |
| 20736.3-c2 |
20736.3-c |
$2$ |
$2$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
20736.3 |
\( 2^{8} \cdot 3^{4} \) |
\( 2^{14} \cdot 3^{6} \) |
$3.03295$ |
$(a), (-a-1), (a-1)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$0.185476610$ |
$3.046510469$ |
6.392883816 |
\( 23328 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -9\) , \( -10\bigr] \) |
${y}^2={x}^{3}-9{x}-10$ |
| 20736.3-d1 |
20736.3-d |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
20736.3 |
\( 2^{8} \cdot 3^{4} \) |
\( 2^{19} \cdot 3^{27} \) |
$3.03295$ |
$(a), (-a-1), (a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$1$ |
$0.342474833$ |
1.937330218 |
\( -\frac{5577343220}{531441} a - \frac{1362907864}{531441} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -450 a + 123\) , \( 2394 a - 5470\bigr] \) |
${y}^2={x}^{3}+\left(-450a+123\right){x}+2394a-5470$ |
| 20736.3-d2 |
20736.3-d |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
20736.3 |
\( 2^{8} \cdot 3^{4} \) |
\( 2^{19} \cdot 3^{27} \) |
$3.03295$ |
$(a), (-a-1), (a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$1$ |
$0.342474833$ |
1.937330218 |
\( \frac{5577343220}{531441} a - \frac{1362907864}{531441} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 450 a + 123\) , \( -2394 a - 5470\bigr] \) |
${y}^2={x}^{3}+\left(450a+123\right){x}-2394a-5470$ |
| 20736.3-d3 |
20736.3-d |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
20736.3 |
\( 2^{8} \cdot 3^{4} \) |
\( 2^{14} \cdot 3^{24} \) |
$3.03295$ |
$(a), (-a-1), (a-1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{6} \) |
$1$ |
$0.684949667$ |
1.937330218 |
\( -\frac{219488}{729} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -57\) , \( -430\bigr] \) |
${y}^2={x}^{3}-57{x}-430$ |
| 20736.3-d4 |
20736.3-d |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
20736.3 |
\( 2^{8} \cdot 3^{4} \) |
\( 2^{16} \cdot 3^{18} \) |
$3.03295$ |
$(a), (-a-1), (a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$0.684949667$ |
1.937330218 |
\( \frac{19056256}{27} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -318\) , \( 2180\bigr] \) |
${y}^2={x}^{3}-318{x}+2180$ |
| 20736.3-e1 |
20736.3-e |
$2$ |
$2$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
20736.3 |
\( 2^{8} \cdot 3^{4} \) |
\( 2^{16} \cdot 3^{18} \) |
$3.03295$ |
$(a), (-a-1), (a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1.513210019$ |
$1.015503489$ |
4.346359268 |
\( 3456 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -54\) , \( -108\bigr] \) |
${y}^2={x}^{3}-54{x}-108$ |
| 20736.3-e2 |
20736.3-e |
$2$ |
$2$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
20736.3 |
\( 2^{8} \cdot 3^{4} \) |
\( 2^{14} \cdot 3^{18} \) |
$3.03295$ |
$(a), (-a-1), (a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$0.756605009$ |
$1.015503489$ |
4.346359268 |
\( 23328 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -81\) , \( -270\bigr] \) |
${y}^2={x}^{3}-81{x}-270$ |
| 20736.3-f1 |
20736.3-f |
$2$ |
$2$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
20736.3 |
\( 2^{8} \cdot 3^{4} \) |
\( 2^{16} \cdot 3^{15} \) |
$3.03295$ |
$(a), (-a-1), (a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$1.384647931$ |
1.958187884 |
\( -\frac{335248}{729} a + \frac{350000}{729} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -12 a + 9\) , \( 24 a - 26\bigr] \) |
${y}^2={x}^{3}+\left(-12a+9\right){x}+24a-26$ |
| 20736.3-f2 |
20736.3-f |
$2$ |
$2$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
20736.3 |
\( 2^{8} \cdot 3^{4} \) |
\( 2^{8} \cdot 3^{12} \) |
$3.03295$ |
$(a), (-a-1), (a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$2.769295863$ |
1.958187884 |
\( \frac{48640}{27} a + \frac{74752}{27} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 3 a - 6\) , \( 3 a - 5\bigr] \) |
${y}^2={x}^{3}+\left(3a-6\right){x}+3a-5$ |
| 20736.3-g1 |
20736.3-g |
$2$ |
$2$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
20736.3 |
\( 2^{8} \cdot 3^{4} \) |
\( 2^{16} \cdot 3^{15} \) |
$3.03295$ |
$(a), (-a-1), (a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$1.384647931$ |
1.958187884 |
\( \frac{335248}{729} a + \frac{350000}{729} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 12 a + 9\) , \( -24 a - 26\bigr] \) |
${y}^2={x}^{3}+\left(12a+9\right){x}-24a-26$ |
| 20736.3-g2 |
20736.3-g |
$2$ |
$2$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
20736.3 |
\( 2^{8} \cdot 3^{4} \) |
\( 2^{8} \cdot 3^{12} \) |
$3.03295$ |
$(a), (-a-1), (a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$2.769295863$ |
1.958187884 |
\( -\frac{48640}{27} a + \frac{74752}{27} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -3 a - 6\) , \( -3 a - 5\bigr] \) |
${y}^2={x}^{3}+\left(-3a-6\right){x}-3a-5$ |
| 20736.3-h1 |
20736.3-h |
$2$ |
$2$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
20736.3 |
\( 2^{8} \cdot 3^{4} \) |
\( 2^{16} \cdot 3^{12} \) |
$3.03295$ |
$(a), (-a-1), (a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$0.408235845$ |
$1.848264670$ |
4.268254303 |
\( 128 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 6\) , \( -20\bigr] \) |
${y}^2={x}^{3}+6{x}-20$ |
| 20736.3-h2 |
20736.3-h |
$2$ |
$2$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
20736.3 |
\( 2^{8} \cdot 3^{4} \) |
\( 2^{14} \cdot 3^{12} \) |
$3.03295$ |
$(a), (-a-1), (a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.816471691$ |
$1.848264670$ |
4.268254303 |
\( 10976 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -21\) , \( 34\bigr] \) |
${y}^2={x}^{3}-21{x}+34$ |
| 20736.3-i1 |
20736.3-i |
$2$ |
$2$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
20736.3 |
\( 2^{8} \cdot 3^{4} \) |
\( 2^{16} \cdot 3^{17} \) |
$3.03295$ |
$(a), (-a-1), (a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$0.980785817$ |
1.387040605 |
\( -\frac{167792}{9} a - \frac{21616}{9} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -48 a + 57\) , \( 52 a + 314\bigr] \) |
${y}^2={x}^{3}+\left(-48a+57\right){x}+52a+314$ |
| 20736.3-i2 |
20736.3-i |
$2$ |
$2$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
20736.3 |
\( 2^{8} \cdot 3^{4} \) |
\( 2^{8} \cdot 3^{16} \) |
$3.03295$ |
$(a), (-a-1), (a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$1.961571635$ |
1.387040605 |
\( \frac{3584}{3} a + \frac{4096}{3} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -3 a + 12\) , \( -11 a - 1\bigr] \) |
${y}^2={x}^{3}+\left(-3a+12\right){x}-11a-1$ |
| 20736.3-j1 |
20736.3-j |
$2$ |
$2$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
20736.3 |
\( 2^{8} \cdot 3^{4} \) |
\( 2^{12} \cdot 3^{12} \) |
$3.03295$ |
$(a), (-a-1), (a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2^{3} \) |
$0.711675809$ |
$2.291728606$ |
4.613073595 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -6 a - 3\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(-6a-3\right){x}$ |
| 20736.3-j2 |
20736.3-j |
$2$ |
$2$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
20736.3 |
\( 2^{8} \cdot 3^{4} \) |
\( 2^{12} \cdot 3^{12} \) |
$3.03295$ |
$(a), (-a-1), (a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2^{2} \) |
$1.423351618$ |
$2.291728606$ |
4.613073595 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 6 a + 3\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(6a+3\right){x}$ |
| 20736.3-k1 |
20736.3-k |
$8$ |
$20$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
20736.3 |
\( 2^{8} \cdot 3^{4} \) |
\( 2^{12} \cdot 3^{32} \) |
$3.03295$ |
$(a), (-a-1), (a-1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 5$ |
2Cs, 5B |
$1$ |
\( 2^{5} \) |
$5.001477534$ |
$0.324313097$ |
4.587835145 |
\( -\frac{873722816}{59049} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 717\) , \( 5522 a\bigr] \) |
${y}^2={x}^{3}+717{x}+5522a$ |
| 20736.3-k2 |
20736.3-k |
$8$ |
$20$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
20736.3 |
\( 2^{8} \cdot 3^{4} \) |
\( 2^{18} \cdot 3^{37} \) |
$3.03295$ |
$(a), (-a-1), (a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 5$ |
2B, 5B |
$1$ |
\( 2^{5} \) |
$2.500738767$ |
$0.162156548$ |
4.587835145 |
\( -\frac{2514081593672}{3486784401} a - \frac{1943385699640}{3486784401} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -990 a + 627\) , \( 11066 a - 30114\bigr] \) |
${y}^2={x}^{3}+\left(-990a+627\right){x}+11066a-30114$ |
| 20736.3-k3 |
20736.3-k |
$8$ |
$20$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
20736.3 |
\( 2^{8} \cdot 3^{4} \) |
\( 2^{18} \cdot 3^{37} \) |
$3.03295$ |
$(a), (-a-1), (a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 5$ |
2B, 5B |
$1$ |
\( 2^{5} \) |
$2.500738767$ |
$0.162156548$ |
4.587835145 |
\( \frac{2514081593672}{3486784401} a - \frac{1943385699640}{3486784401} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 990 a + 627\) , \( 11066 a + 30114\bigr] \) |
${y}^2={x}^{3}+\left(990a+627\right){x}+11066a+30114$ |
| 20736.3-k4 |
20736.3-k |
$8$ |
$20$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
20736.3 |
\( 2^{8} \cdot 3^{4} \) |
\( 2^{12} \cdot 3^{16} \) |
$3.03295$ |
$(a), (-a-1), (a-1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 5$ |
2Cs, 5B |
$1$ |
\( 2^{5} \) |
$1.000295506$ |
$1.621565487$ |
4.587835145 |
\( \frac{64}{9} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -3\) , \( -22 a\bigr] \) |
${y}^2={x}^{3}-3{x}-22a$ |
| 20736.3-k5 |
20736.3-k |
$8$ |
$20$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
20736.3 |
\( 2^{8} \cdot 3^{4} \) |
\( 2^{12} \cdot 3^{14} \) |
$3.03295$ |
$(a), (-a-1), (a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 5$ |
2B, 5B |
$1$ |
\( 2^{4} \) |
$0.500147753$ |
$1.621565487$ |
4.587835145 |
\( \frac{85184}{3} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 33\) , \( 50 a\bigr] \) |
${y}^2={x}^{3}+33{x}+50a$ |
| 20736.3-k6 |
20736.3-k |
$8$ |
$20$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
20736.3 |
\( 2^{8} \cdot 3^{4} \) |
\( 2^{18} \cdot 3^{17} \) |
$3.03295$ |
$(a), (-a-1), (a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 5$ |
2B, 5B |
$1$ |
\( 2^{5} \) |
$0.500147753$ |
$0.810782743$ |
4.587835145 |
\( -\frac{2400472}{81} a + \frac{4984520}{81} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -90 a - 93\) , \( -526 a - 126\bigr] \) |
${y}^2={x}^{3}+\left(-90a-93\right){x}-526a-126$ |
| 20736.3-k7 |
20736.3-k |
$8$ |
$20$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
20736.3 |
\( 2^{8} \cdot 3^{4} \) |
\( 2^{18} \cdot 3^{17} \) |
$3.03295$ |
$(a), (-a-1), (a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 5$ |
2B, 5B |
$1$ |
\( 2^{5} \) |
$0.500147753$ |
$0.810782743$ |
4.587835145 |
\( \frac{2400472}{81} a + \frac{4984520}{81} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 90 a - 93\) , \( -526 a + 126\bigr] \) |
${y}^2={x}^{3}+\left(90a-93\right){x}-526a+126$ |
| 20736.3-k8 |
20736.3-k |
$8$ |
$20$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
20736.3 |
\( 2^{8} \cdot 3^{4} \) |
\( 2^{12} \cdot 3^{22} \) |
$3.03295$ |
$(a), (-a-1), (a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 5$ |
2B, 5B |
$1$ |
\( 2^{4} \) |
$2.500738767$ |
$0.324313097$ |
4.587835145 |
\( \frac{58591911104}{243} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 2913\) , \( -42790 a\bigr] \) |
${y}^2={x}^{3}+2913{x}-42790a$ |
| 20736.3-l1 |
20736.3-l |
$8$ |
$20$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
20736.3 |
\( 2^{8} \cdot 3^{4} \) |
\( 2^{12} \cdot 3^{32} \) |
$3.03295$ |
$(a), (-a-1), (a-1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 5$ |
2Cs, 5B |
$1$ |
\( 2^{5} \) |
$5.001477534$ |
$0.324313097$ |
4.587835145 |
\( -\frac{873722816}{59049} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 717\) , \( -5522 a\bigr] \) |
${y}^2={x}^{3}+717{x}-5522a$ |
| 20736.3-l2 |
20736.3-l |
$8$ |
$20$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
20736.3 |
\( 2^{8} \cdot 3^{4} \) |
\( 2^{18} \cdot 3^{37} \) |
$3.03295$ |
$(a), (-a-1), (a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 5$ |
2B, 5B |
$1$ |
\( 2^{5} \) |
$2.500738767$ |
$0.162156548$ |
4.587835145 |
\( -\frac{2514081593672}{3486784401} a - \frac{1943385699640}{3486784401} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -990 a + 627\) , \( -11066 a + 30114\bigr] \) |
${y}^2={x}^{3}+\left(-990a+627\right){x}-11066a+30114$ |
| 20736.3-l3 |
20736.3-l |
$8$ |
$20$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
20736.3 |
\( 2^{8} \cdot 3^{4} \) |
\( 2^{18} \cdot 3^{37} \) |
$3.03295$ |
$(a), (-a-1), (a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 5$ |
2B, 5B |
$1$ |
\( 2^{5} \) |
$2.500738767$ |
$0.162156548$ |
4.587835145 |
\( \frac{2514081593672}{3486784401} a - \frac{1943385699640}{3486784401} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 990 a + 627\) , \( -11066 a - 30114\bigr] \) |
${y}^2={x}^{3}+\left(990a+627\right){x}-11066a-30114$ |
| 20736.3-l4 |
20736.3-l |
$8$ |
$20$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
20736.3 |
\( 2^{8} \cdot 3^{4} \) |
\( 2^{12} \cdot 3^{16} \) |
$3.03295$ |
$(a), (-a-1), (a-1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 5$ |
2Cs, 5B |
$1$ |
\( 2^{5} \) |
$1.000295506$ |
$1.621565487$ |
4.587835145 |
\( \frac{64}{9} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -3\) , \( 22 a\bigr] \) |
${y}^2={x}^{3}-3{x}+22a$ |
| 20736.3-l5 |
20736.3-l |
$8$ |
$20$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
20736.3 |
\( 2^{8} \cdot 3^{4} \) |
\( 2^{12} \cdot 3^{14} \) |
$3.03295$ |
$(a), (-a-1), (a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 5$ |
2B, 5B |
$1$ |
\( 2^{4} \) |
$0.500147753$ |
$1.621565487$ |
4.587835145 |
\( \frac{85184}{3} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 33\) , \( -50 a\bigr] \) |
${y}^2={x}^{3}+33{x}-50a$ |
| 20736.3-l6 |
20736.3-l |
$8$ |
$20$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
20736.3 |
\( 2^{8} \cdot 3^{4} \) |
\( 2^{18} \cdot 3^{17} \) |
$3.03295$ |
$(a), (-a-1), (a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 5$ |
2B, 5B |
$1$ |
\( 2^{5} \) |
$0.500147753$ |
$0.810782743$ |
4.587835145 |
\( -\frac{2400472}{81} a + \frac{4984520}{81} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -90 a - 93\) , \( 526 a + 126\bigr] \) |
${y}^2={x}^{3}+\left(-90a-93\right){x}+526a+126$ |
| 20736.3-l7 |
20736.3-l |
$8$ |
$20$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
20736.3 |
\( 2^{8} \cdot 3^{4} \) |
\( 2^{18} \cdot 3^{17} \) |
$3.03295$ |
$(a), (-a-1), (a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 5$ |
2B, 5B |
$1$ |
\( 2^{5} \) |
$0.500147753$ |
$0.810782743$ |
4.587835145 |
\( \frac{2400472}{81} a + \frac{4984520}{81} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 90 a - 93\) , \( 526 a - 126\bigr] \) |
${y}^2={x}^{3}+\left(90a-93\right){x}+526a-126$ |
| 20736.3-l8 |
20736.3-l |
$8$ |
$20$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
20736.3 |
\( 2^{8} \cdot 3^{4} \) |
\( 2^{12} \cdot 3^{22} \) |
$3.03295$ |
$(a), (-a-1), (a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 5$ |
2B, 5B |
$1$ |
\( 2^{4} \) |
$2.500738767$ |
$0.324313097$ |
4.587835145 |
\( \frac{58591911104}{243} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 2913\) , \( 42790 a\bigr] \) |
${y}^2={x}^{3}+2913{x}+42790a$ |
| 20736.3-m1 |
20736.3-m |
$4$ |
$6$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
20736.3 |
\( 2^{8} \cdot 3^{4} \) |
\( 2^{8} \cdot 3^{12} \) |
$3.03295$ |
$(a), (-a-1), (a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-3$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$2.949171984$ |
2.085379509 |
\( 0 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 0\) , \( a + 5\bigr] \) |
${y}^2={x}^{3}+a+5$ |
| 20736.3-m2 |
20736.3-m |
$4$ |
$6$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
20736.3 |
\( 2^{8} \cdot 3^{4} \) |
\( 2^{8} \cdot 3^{12} \) |
$3.03295$ |
$(a), (-a-1), (a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-3$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$2.949171984$ |
2.085379509 |
\( 0 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 0\) , \( a - 5\bigr] \) |
${y}^2={x}^{3}+a-5$ |
| 20736.3-m3 |
20736.3-m |
$4$ |
$6$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
20736.3 |
\( 2^{8} \cdot 3^{4} \) |
\( 2^{16} \cdot 3^{12} \) |
$3.03295$ |
$(a), (-a-1), (a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-12$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2^{3} \) |
$1$ |
$1.474585992$ |
2.085379509 |
\( 54000 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -30 a + 15\) , \( 22 a - 110\bigr] \) |
${y}^2={x}^{3}+\left(-30a+15\right){x}+22a-110$ |
| 20736.3-m4 |
20736.3-m |
$4$ |
$6$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
20736.3 |
\( 2^{8} \cdot 3^{4} \) |
\( 2^{16} \cdot 3^{12} \) |
$3.03295$ |
$(a), (-a-1), (a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-12$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2^{3} \) |
$1$ |
$1.474585992$ |
2.085379509 |
\( 54000 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 30 a + 15\) , \( 22 a + 110\bigr] \) |
${y}^2={x}^{3}+\left(30a+15\right){x}+22a+110$ |
| 20736.3-n1 |
20736.3-n |
$4$ |
$6$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
20736.3 |
\( 2^{8} \cdot 3^{4} \) |
\( 2^{8} \cdot 3^{12} \) |
$3.03295$ |
$(a), (-a-1), (a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-3$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$2.949171984$ |
2.085379509 |
\( 0 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 0\) , \( -a + 5\bigr] \) |
${y}^2={x}^{3}-a+5$ |
| 20736.3-n2 |
20736.3-n |
$4$ |
$6$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
20736.3 |
\( 2^{8} \cdot 3^{4} \) |
\( 2^{8} \cdot 3^{12} \) |
$3.03295$ |
$(a), (-a-1), (a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-3$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$2.949171984$ |
2.085379509 |
\( 0 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 0\) , \( -a - 5\bigr] \) |
${y}^2={x}^{3}-a-5$ |
| 20736.3-n3 |
20736.3-n |
$4$ |
$6$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
20736.3 |
\( 2^{8} \cdot 3^{4} \) |
\( 2^{16} \cdot 3^{12} \) |
$3.03295$ |
$(a), (-a-1), (a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-12$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2^{3} \) |
$1$ |
$1.474585992$ |
2.085379509 |
\( 54000 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -30 a + 15\) , \( -22 a + 110\bigr] \) |
${y}^2={x}^{3}+\left(-30a+15\right){x}-22a+110$ |
| 20736.3-n4 |
20736.3-n |
$4$ |
$6$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
20736.3 |
\( 2^{8} \cdot 3^{4} \) |
\( 2^{16} \cdot 3^{12} \) |
$3.03295$ |
$(a), (-a-1), (a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-12$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2^{3} \) |
$1$ |
$1.474585992$ |
2.085379509 |
\( 54000 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 30 a + 15\) , \( -22 a - 110\bigr] \) |
${y}^2={x}^{3}+\left(30a+15\right){x}-22a-110$ |
*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.
