| 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 |
| 16128.5-a1 |
16128.5-a |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
16128.5 |
\( 2^{8} \cdot 3^{2} \cdot 7 \) |
\( 2^{32} \cdot 3^{8} \cdot 7^{2} \) |
$2.66430$ |
$(a), (-a+1), (-2a+1), (3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{6} \) |
$1$ |
$0.660279918$ |
1.996498812 |
\( \frac{5744242075}{580608} a - \frac{638675959}{41472} \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( 13 a + 170\) , \( -644 a + 460\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(13a+170\right){x}-644a+460$ |
| 16128.5-a2 |
16128.5-a |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
16128.5 |
\( 2^{8} \cdot 3^{2} \cdot 7 \) |
\( 2^{28} \cdot 3^{16} \cdot 7^{4} \) |
$2.66430$ |
$(a), (-a+1), (-2a+1), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$1$ |
$0.330139959$ |
1.996498812 |
\( \frac{218546645}{1143072} a - \frac{2541633511}{5143824} \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( 213 a - 110\) , \( -2548 a - 868\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(213a-110\right){x}-2548a-868$ |
| 16128.5-a3 |
16128.5-a |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
16128.5 |
\( 2^{8} \cdot 3^{2} \cdot 7 \) |
\( 2^{43} \cdot 3^{4} \cdot 7 \) |
$2.66430$ |
$(a), (-a+1), (-2a+1), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$0.660279918$ |
1.996498812 |
\( -\frac{100686965405}{66060288} a + \frac{11094110413}{11010048} \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( -69 a - 25\) , \( 300 a + 92\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(-69a-25\right){x}+300a+92$ |
| 16128.5-a4 |
16128.5-a |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
16128.5 |
\( 2^{8} \cdot 3^{2} \cdot 7 \) |
\( 2^{25} \cdot 3^{4} \cdot 7 \) |
$2.66430$ |
$(a), (-a+1), (-2a+1), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$0.660279918$ |
1.996498812 |
\( -\frac{446668992275}{2016} a + \frac{21665210083}{336} \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( 543 a - 261\) , \( -3960 a - 3060\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(543a-261\right){x}-3960a-3060$ |
| 16128.5-b1 |
16128.5-b |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
16128.5 |
\( 2^{8} \cdot 3^{2} \cdot 7 \) |
\( 2^{25} \cdot 3^{4} \cdot 7 \) |
$2.66430$ |
$(a), (-a+1), (-2a+1), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$0.660279918$ |
1.996498812 |
\( \frac{446668992275}{2016} a - \frac{316677731777}{2016} \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( -543 a + 282\) , \( 3960 a - 7020\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(-543a+282\right){x}+3960a-7020$ |
| 16128.5-b2 |
16128.5-b |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
16128.5 |
\( 2^{8} \cdot 3^{2} \cdot 7 \) |
\( 2^{32} \cdot 3^{8} \cdot 7^{2} \) |
$2.66430$ |
$(a), (-a+1), (-2a+1), (3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{6} \) |
$1$ |
$0.660279918$ |
1.996498812 |
\( -\frac{5744242075}{580608} a - \frac{3197221351}{580608} \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( -13 a + 183\) , \( 644 a - 184\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(-13a+183\right){x}+644a-184$ |
| 16128.5-b3 |
16128.5-b |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
16128.5 |
\( 2^{8} \cdot 3^{2} \cdot 7 \) |
\( 2^{43} \cdot 3^{4} \cdot 7 \) |
$2.66430$ |
$(a), (-a+1), (-2a+1), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$0.660279918$ |
1.996498812 |
\( \frac{100686965405}{66060288} a - \frac{34122302927}{66060288} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 69 a - 94\) , \( -300 a + 392\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(69a-94\right){x}-300a+392$ |
| 16128.5-b4 |
16128.5-b |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
16128.5 |
\( 2^{8} \cdot 3^{2} \cdot 7 \) |
\( 2^{28} \cdot 3^{16} \cdot 7^{4} \) |
$2.66430$ |
$(a), (-a+1), (-2a+1), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$1$ |
$0.330139959$ |
1.996498812 |
\( -\frac{218546645}{1143072} a - \frac{3116347217}{10287648} \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( -213 a + 103\) , \( 2548 a - 3416\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(-213a+103\right){x}+2548a-3416$ |
| 16128.5-c1 |
16128.5-c |
$2$ |
$2$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
16128.5 |
\( 2^{8} \cdot 3^{2} \cdot 7 \) |
\( 2^{16} \cdot 3^{4} \cdot 7 \) |
$2.66430$ |
$(a), (-a+1), (-2a+1), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$2.612839424$ |
1.975120952 |
\( \frac{57248}{7} a - \frac{3420496}{63} \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( 11 a - 5\) , \( -12 a - 4\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(11a-5\right){x}-12a-4$ |
| 16128.5-c2 |
16128.5-c |
$2$ |
$2$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
16128.5 |
\( 2^{8} \cdot 3^{2} \cdot 7 \) |
\( 2^{8} \cdot 3^{2} \cdot 7^{2} \) |
$2.66430$ |
$(a), (-a+1), (-2a+1), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$5.225678848$ |
1.975120952 |
\( -\frac{10240}{21} a + \frac{2048}{3} \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( a\) , \( -a + 1\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+a{x}-a+1$ |
| 16128.5-d1 |
16128.5-d |
$2$ |
$2$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
16128.5 |
\( 2^{8} \cdot 3^{2} \cdot 7 \) |
\( 2^{16} \cdot 3^{4} \cdot 7 \) |
$2.66430$ |
$(a), (-a+1), (-2a+1), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$2.612839424$ |
1.975120952 |
\( -\frac{57248}{7} a - \frac{2905264}{63} \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( -11 a + 6\) , \( 12 a - 16\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(-11a+6\right){x}+12a-16$ |
| 16128.5-d2 |
16128.5-d |
$2$ |
$2$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
16128.5 |
\( 2^{8} \cdot 3^{2} \cdot 7 \) |
\( 2^{8} \cdot 3^{2} \cdot 7^{2} \) |
$2.66430$ |
$(a), (-a+1), (-2a+1), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$5.225678848$ |
1.975120952 |
\( \frac{10240}{21} a + \frac{4096}{21} \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( -a + 1\) , \( a\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(-a+1\right){x}+a$ |
| 16128.5-e1 |
16128.5-e |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
16128.5 |
\( 2^{8} \cdot 3^{2} \cdot 7 \) |
\( 2^{8} \cdot 3^{6} \cdot 7^{8} \) |
$2.66430$ |
$(a), (-a+1), (-2a+1), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$1.390851865$ |
1.577077777 |
\( -\frac{2725888}{64827} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -7\) , \( -52\bigr] \) |
${y}^2={x}^{3}+{x}^{2}-7{x}-52$ |
| 16128.5-e2 |
16128.5-e |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
16128.5 |
\( 2^{8} \cdot 3^{2} \cdot 7 \) |
\( 2^{20} \cdot 3^{24} \cdot 7^{2} \) |
$2.66430$ |
$(a), (-a+1), (-2a+1), (3)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \cdot 3 \) |
$1$ |
$0.347712966$ |
1.577077777 |
\( \frac{6522128932}{3720087} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -392\) , \( 228\bigr] \) |
${y}^2={x}^{3}+{x}^{2}-392{x}+228$ |
| 16128.5-e3 |
16128.5-e |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
16128.5 |
\( 2^{8} \cdot 3^{2} \cdot 7 \) |
\( 2^{16} \cdot 3^{12} \cdot 7^{4} \) |
$2.66430$ |
$(a), (-a+1), (-2a+1), (3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \cdot 3 \) |
$1$ |
$0.695425932$ |
1.577077777 |
\( \frac{6940769488}{35721} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -252\) , \( -1620\bigr] \) |
${y}^2={x}^{3}+{x}^{2}-252{x}-1620$ |
| 16128.5-e4 |
16128.5-e |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
16128.5 |
\( 2^{8} \cdot 3^{2} \cdot 7 \) |
\( 2^{20} \cdot 3^{6} \cdot 7^{2} \) |
$2.66430$ |
$(a), (-a+1), (-2a+1), (3)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \cdot 3 \) |
$1$ |
$0.347712966$ |
1.577077777 |
\( \frac{7080974546692}{189} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -4032\) , \( -99900\bigr] \) |
${y}^2={x}^{3}+{x}^{2}-4032{x}-99900$ |
| 16128.5-f1 |
16128.5-f |
$4$ |
$6$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
16128.5 |
\( 2^{8} \cdot 3^{2} \cdot 7 \) |
\( 2^{8} \cdot 3^{2} \cdot 7^{12} \) |
$2.66430$ |
$(a), (-a+1), (-2a+1), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B |
$9$ |
\( 2 \) |
$1$ |
$0.872431843$ |
2.967734177 |
\( -\frac{10061824000}{352947} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -113\) , \( 516\bigr] \) |
${y}^2={x}^{3}-{x}^{2}-113{x}+516$ |
| 16128.5-f2 |
16128.5-f |
$4$ |
$6$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
16128.5 |
\( 2^{8} \cdot 3^{2} \cdot 7 \) |
\( 2^{8} \cdot 3^{6} \cdot 7^{4} \) |
$2.66430$ |
$(a), (-a+1), (-2a+1), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$2.617295530$ |
2.967734177 |
\( \frac{2048000}{1323} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( 7\) , \( 0\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+7{x}$ |
| 16128.5-f3 |
16128.5-f |
$4$ |
$6$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
16128.5 |
\( 2^{8} \cdot 3^{2} \cdot 7 \) |
\( 2^{16} \cdot 3^{12} \cdot 7^{2} \) |
$2.66430$ |
$(a), (-a+1), (-2a+1), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$1.308647765$ |
2.967734177 |
\( \frac{9826000}{5103} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -28\) , \( 28\bigr] \) |
${y}^2={x}^{3}-{x}^{2}-28{x}+28$ |
| 16128.5-f4 |
16128.5-f |
$4$ |
$6$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
16128.5 |
\( 2^{8} \cdot 3^{2} \cdot 7 \) |
\( 2^{16} \cdot 3^{4} \cdot 7^{6} \) |
$2.66430$ |
$(a), (-a+1), (-2a+1), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B |
$9$ |
\( 2^{2} \) |
$1$ |
$0.436215921$ |
2.967734177 |
\( \frac{2640279346000}{3087} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -1828\) , \( 30700\bigr] \) |
${y}^2={x}^{3}-{x}^{2}-1828{x}+30700$ |
| 16128.5-g1 |
16128.5-g |
$2$ |
$2$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
16128.5 |
\( 2^{8} \cdot 3^{2} \cdot 7 \) |
\( 2^{12} \cdot 3^{4} \cdot 7 \) |
$2.66430$ |
$(a), (-a+1), (-2a+1), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1.444046319$ |
$4.058115200$ |
4.429823994 |
\( -\frac{7312}{21} a + \frac{79904}{63} \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( -3\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}-3{x}$ |
| 16128.5-g2 |
16128.5-g |
$2$ |
$2$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
16128.5 |
\( 2^{8} \cdot 3^{2} \cdot 7 \) |
\( 2^{12} \cdot 3^{2} \cdot 7^{2} \) |
$2.66430$ |
$(a), (-a+1), (-2a+1), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.722023159$ |
$4.058115200$ |
4.429823994 |
\( \frac{13936}{21} a + \frac{42544}{21} \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( -2 a + 1\) , \( 0\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(-2a+1\right){x}$ |
| 16128.5-h1 |
16128.5-h |
$2$ |
$2$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
16128.5 |
\( 2^{8} \cdot 3^{2} \cdot 7 \) |
\( 2^{12} \cdot 3^{4} \cdot 7 \) |
$2.66430$ |
$(a), (-a+1), (-2a+1), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1.444046319$ |
$4.058115200$ |
4.429823994 |
\( \frac{7312}{21} a + \frac{57968}{63} \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( -3\) , \( 0\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}-3{x}$ |
| 16128.5-h2 |
16128.5-h |
$2$ |
$2$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
16128.5 |
\( 2^{8} \cdot 3^{2} \cdot 7 \) |
\( 2^{12} \cdot 3^{2} \cdot 7^{2} \) |
$2.66430$ |
$(a), (-a+1), (-2a+1), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.722023159$ |
$4.058115200$ |
4.429823994 |
\( -\frac{13936}{21} a + \frac{56480}{21} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 2 a - 1\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(2a-1\right){x}$ |
| 16128.5-i1 |
16128.5-i |
$8$ |
$16$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
16128.5 |
\( 2^{8} \cdot 3^{2} \cdot 7 \) |
\( 2^{24} \cdot 3^{2} \cdot 7^{16} \) |
$2.66430$ |
$(a), (-a+1), (-2a+1), (3)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{8} \) |
$0.746299208$ |
$0.215519232$ |
3.890719903 |
\( -\frac{4354703137}{17294403} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -544\) , \( 13888\bigr] \) |
${y}^2={x}^{3}-{x}^{2}-544{x}+13888$ |
| 16128.5-i2 |
16128.5-i |
$8$ |
$16$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
16128.5 |
\( 2^{8} \cdot 3^{2} \cdot 7 \) |
\( 2^{24} \cdot 3^{4} \cdot 7^{2} \) |
$2.66430$ |
$(a), (-a+1), (-2a+1), (3)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{6} \) |
$0.373149604$ |
$1.724153859$ |
3.890719903 |
\( \frac{103823}{63} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( 16\) , \( 0\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+16{x}$ |
| 16128.5-i3 |
16128.5-i |
$8$ |
$16$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
16128.5 |
\( 2^{8} \cdot 3^{2} \cdot 7 \) |
\( 2^{24} \cdot 3^{8} \cdot 7^{4} \) |
$2.66430$ |
$(a), (-a+1), (-2a+1), (3)$ |
$1$ |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{8} \) |
$0.746299208$ |
$0.862076929$ |
3.890719903 |
\( \frac{7189057}{3969} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -64\) , \( 64\bigr] \) |
${y}^2={x}^{3}-{x}^{2}-64{x}+64$ |
| 16128.5-i4 |
16128.5-i |
$8$ |
$16$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
16128.5 |
\( 2^{8} \cdot 3^{2} \cdot 7 \) |
\( 2^{24} \cdot 3^{2} \cdot 7 \) |
$2.66430$ |
$(a), (-a+1), (-2a+1), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.746299208$ |
$1.724153859$ |
3.890719903 |
\( \frac{2940226}{21} a + \frac{2980207}{21} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -31 a + 26\) , \( -22 a + 88\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(-31a+26\right){x}-22a+88$ |
| 16128.5-i5 |
16128.5-i |
$8$ |
$16$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
16128.5 |
\( 2^{8} \cdot 3^{2} \cdot 7 \) |
\( 2^{24} \cdot 3^{16} \cdot 7^{2} \) |
$2.66430$ |
$(a), (-a+1), (-2a+1), (3)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{6} \) |
$1.492598417$ |
$0.431038464$ |
3.890719903 |
\( \frac{6570725617}{45927} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -624\) , \( -5760\bigr] \) |
${y}^2={x}^{3}-{x}^{2}-624{x}-5760$ |
| 16128.5-i6 |
16128.5-i |
$8$ |
$16$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
16128.5 |
\( 2^{8} \cdot 3^{2} \cdot 7 \) |
\( 2^{24} \cdot 3^{2} \cdot 7 \) |
$2.66430$ |
$(a), (-a+1), (-2a+1), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.746299208$ |
$1.724153859$ |
3.890719903 |
\( -\frac{2940226}{21} a + \frac{5920433}{21} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 33 a - 6\) , \( 54 a + 60\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(33a-6\right){x}+54a+60$ |
| 16128.5-i7 |
16128.5-i |
$8$ |
$16$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
16128.5 |
\( 2^{8} \cdot 3^{2} \cdot 7 \) |
\( 2^{24} \cdot 3^{4} \cdot 7^{8} \) |
$2.66430$ |
$(a), (-a+1), (-2a+1), (3)$ |
$1$ |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{8} \) |
$1.492598417$ |
$0.431038464$ |
3.890719903 |
\( \frac{13027640977}{21609} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -784\) , \( 8704\bigr] \) |
${y}^2={x}^{3}-{x}^{2}-784{x}+8704$ |
| 16128.5-i8 |
16128.5-i |
$8$ |
$16$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
16128.5 |
\( 2^{8} \cdot 3^{2} \cdot 7 \) |
\( 2^{24} \cdot 3^{2} \cdot 7^{4} \) |
$2.66430$ |
$(a), (-a+1), (-2a+1), (3)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$4$ |
\( 2^{4} \) |
$2.985196834$ |
$0.215519232$ |
3.890719903 |
\( \frac{53297461115137}{147} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -12544\) , \( 544960\bigr] \) |
${y}^2={x}^{3}-{x}^{2}-12544{x}+544960$ |
| 16128.5-j1 |
16128.5-j |
$2$ |
$2$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
16128.5 |
\( 2^{8} \cdot 3^{2} \cdot 7 \) |
\( 2^{8} \cdot 3^{2} \cdot 7^{4} \) |
$2.66430$ |
$(a), (-a+1), (-2a+1), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.730558919$ |
$3.823324891$ |
4.222867190 |
\( -\frac{16384}{147} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -1\) , \( 2\bigr] \) |
${y}^2={x}^{3}+{x}^{2}-{x}+2$ |
| 16128.5-j2 |
16128.5-j |
$2$ |
$2$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
16128.5 |
\( 2^{8} \cdot 3^{2} \cdot 7 \) |
\( 2^{16} \cdot 3^{4} \cdot 7^{2} \) |
$2.66430$ |
$(a), (-a+1), (-2a+1), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1.461117838$ |
$1.911662445$ |
4.222867190 |
\( \frac{20720464}{63} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -36\) , \( 72\bigr] \) |
${y}^2={x}^{3}+{x}^{2}-36{x}+72$ |
| 16128.5-k1 |
16128.5-k |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
16128.5 |
\( 2^{8} \cdot 3^{2} \cdot 7 \) |
\( 2^{20} \cdot 3^{2} \cdot 7^{8} \) |
$2.66430$ |
$(a), (-a+1), (-2a+1), (3)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{7} \) |
$0.381417612$ |
$0.986178417$ |
4.549432176 |
\( \frac{11696828}{7203} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( 48\) , \( -48\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+48{x}-48$ |
| 16128.5-k2 |
16128.5-k |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
16128.5 |
\( 2^{8} \cdot 3^{2} \cdot 7 \) |
\( 2^{16} \cdot 3^{4} \cdot 7^{4} \) |
$2.66430$ |
$(a), (-a+1), (-2a+1), (3)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$0.762835224$ |
$1.972356834$ |
4.549432176 |
\( \frac{810448}{441} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -12\) , \( 0\bigr] \) |
${y}^2={x}^{3}-{x}^{2}-12{x}$ |
| 16128.5-k3 |
16128.5-k |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
16128.5 |
\( 2^{8} \cdot 3^{2} \cdot 7 \) |
\( 2^{8} \cdot 3^{2} \cdot 7^{2} \) |
$2.66430$ |
$(a), (-a+1), (-2a+1), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1.525670448$ |
$3.944713669$ |
4.549432176 |
\( \frac{2725888}{21} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -7\) , \( 10\bigr] \) |
${y}^2={x}^{3}-{x}^{2}-7{x}+10$ |
| 16128.5-k4 |
16128.5-k |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
16128.5 |
\( 2^{8} \cdot 3^{2} \cdot 7 \) |
\( 2^{20} \cdot 3^{8} \cdot 7^{2} \) |
$2.66430$ |
$(a), (-a+1), (-2a+1), (3)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$1.525670448$ |
$0.986178417$ |
4.549432176 |
\( \frac{381775972}{567} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -152\) , \( -672\bigr] \) |
${y}^2={x}^{3}-{x}^{2}-152{x}-672$ |
| 16128.5-l1 |
16128.5-l |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
16128.5 |
\( 2^{8} \cdot 3^{2} \cdot 7 \) |
\( 2^{24} \cdot 3^{2} \cdot 7^{4} \) |
$2.66430$ |
$(a), (-a+1), (-2a+1), (3)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{6} \) |
$1$ |
$0.846553346$ |
2.559736715 |
\( -\frac{125632169}{196} a - \frac{31841287}{12} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -191 a + 130\) , \( 574 a - 1476\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(-191a+130\right){x}+574a-1476$ |
| 16128.5-l2 |
16128.5-l |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
16128.5 |
\( 2^{8} \cdot 3^{2} \cdot 7 \) |
\( 2^{18} \cdot 3^{8} \cdot 7 \) |
$2.66430$ |
$(a), (-a+1), (-2a+1), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$1.693106692$ |
2.559736715 |
\( \frac{14150117}{756} a - \frac{42134837}{2268} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -19 a - 6\) , \( 54 a - 20\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+\left(-19a-6\right){x}+54a-20$ |
| 16128.5-l3 |
16128.5-l |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
16128.5 |
\( 2^{8} \cdot 3^{2} \cdot 7 \) |
\( 2^{30} \cdot 3^{2} \cdot 7 \) |
$2.66430$ |
$(a), (-a+1), (-2a+1), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$1.693106692$ |
2.559736715 |
\( \frac{2117957}{1792} a + \frac{1884523}{5376} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -8 a - 8\) , \( 16 a - 12\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+\left(-8a-8\right){x}+16a-12$ |
| 16128.5-l4 |
16128.5-l |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
16128.5 |
\( 2^{8} \cdot 3^{2} \cdot 7 \) |
\( 2^{24} \cdot 3^{4} \cdot 7^{2} \) |
$2.66430$ |
$(a), (-a+1), (-2a+1), (3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$1$ |
$1.693106692$ |
2.559736715 |
\( -\frac{413801}{336} a + \frac{1624825}{1008} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -11 a + 10\) , \( 10 a - 12\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(-11a+10\right){x}+10a-12$ |
| 16128.5-m1 |
16128.5-m |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
16128.5 |
\( 2^{8} \cdot 3^{2} \cdot 7 \) |
\( 2^{24} \cdot 3^{2} \cdot 7^{4} \) |
$2.66430$ |
$(a), (-a+1), (-2a+1), (3)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{6} \) |
$1$ |
$0.846553346$ |
2.559736715 |
\( \frac{125632169}{196} a - \frac{968559785}{294} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 193 a - 62\) , \( -766 a - 840\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(193a-62\right){x}-766a-840$ |
| 16128.5-m2 |
16128.5-m |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
16128.5 |
\( 2^{8} \cdot 3^{2} \cdot 7 \) |
\( 2^{18} \cdot 3^{8} \cdot 7 \) |
$2.66430$ |
$(a), (-a+1), (-2a+1), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$1.693106692$ |
2.559736715 |
\( -\frac{14150117}{756} a + \frac{157757}{1134} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( 19 a - 25\) , \( -54 a + 34\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+\left(19a-25\right){x}-54a+34$ |
| 16128.5-m3 |
16128.5-m |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
16128.5 |
\( 2^{8} \cdot 3^{2} \cdot 7 \) |
\( 2^{24} \cdot 3^{4} \cdot 7^{2} \) |
$2.66430$ |
$(a), (-a+1), (-2a+1), (3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$1$ |
$1.693106692$ |
2.559736715 |
\( \frac{413801}{336} a + \frac{191711}{504} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 13 a - 2\) , \( -22 a\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(13a-2\right){x}-22a$ |
| 16128.5-m4 |
16128.5-m |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
16128.5 |
\( 2^{8} \cdot 3^{2} \cdot 7 \) |
\( 2^{30} \cdot 3^{2} \cdot 7 \) |
$2.66430$ |
$(a), (-a+1), (-2a+1), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$1.693106692$ |
2.559736715 |
\( -\frac{2117957}{1792} a + \frac{4119197}{2688} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( 8 a - 16\) , \( -16 a + 4\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+\left(8a-16\right){x}-16a+4$ |
| 16128.5-n1 |
16128.5-n |
$8$ |
$16$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
16128.5 |
\( 2^{8} \cdot 3^{2} \cdot 7 \) |
\( 2^{44} \cdot 3^{2} \cdot 7 \) |
$2.66430$ |
$(a), (-a+1), (-2a+1), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$2.310811814$ |
$0.685091833$ |
4.786899797 |
\( \frac{12134104351}{1376256} a - \frac{12253997573}{1376256} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 33 a - 166\) , \( 234 a - 744\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(33a-166\right){x}+234a-744$ |
| 16128.5-n2 |
16128.5-n |
$8$ |
$16$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
16128.5 |
\( 2^{8} \cdot 3^{2} \cdot 7 \) |
\( 2^{40} \cdot 3^{4} \cdot 7^{2} \) |
$2.66430$ |
$(a), (-a+1), (-2a+1), (3)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{6} \) |
$1.155405907$ |
$0.685091833$ |
4.786899797 |
\( -\frac{7189057}{16128} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -64\) , \( -460\bigr] \) |
${y}^2={x}^{3}+{x}^{2}-64{x}-460$ |
| 16128.5-n3 |
16128.5-n |
$8$ |
$16$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
16128.5 |
\( 2^{8} \cdot 3^{2} \cdot 7 \) |
\( 2^{44} \cdot 3^{2} \cdot 7 \) |
$2.66430$ |
$(a), (-a+1), (-2a+1), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$2.310811814$ |
$0.685091833$ |
4.786899797 |
\( -\frac{12134104351}{1376256} a - \frac{59946611}{688128} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -31 a - 134\) , \( -266 a - 644\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(-31a-134\right){x}-266a-644$ |
| 16128.5-n4 |
16128.5-n |
$8$ |
$16$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
16128.5 |
\( 2^{8} \cdot 3^{2} \cdot 7 \) |
\( 2^{26} \cdot 3^{32} \cdot 7^{4} \) |
$2.66430$ |
$(a), (-a+1), (-2a+1), (3)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{8} \) |
$2.310811814$ |
$0.085636479$ |
4.786899797 |
\( \frac{6359387729183}{4218578658} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( 6176\) , \( -69388\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+6176{x}-69388$ |
*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.
