| 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 |
| 578.1-a1 |
578.1-a |
$2$ |
$2$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
578.1 |
\( 2 \cdot 17^{2} \) |
\( 2^{2} \cdot 17^{3} \) |
$1.23927$ |
$(a), (-3a-1), (3a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.135327928$ |
$13.88402977$ |
1.328580800 |
\( \frac{136747}{289} a + \frac{566707}{578} \) |
\( \bigl[a + 1\) , \( -1\) , \( 0\) , \( a + 2\) , \( 0\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}-{x}^{2}+\left(a+2\right){x}$ |
| 578.1-a2 |
578.1-a |
$2$ |
$2$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
578.1 |
\( 2 \cdot 17^{2} \) |
\( 2 \cdot 17^{6} \) |
$1.23927$ |
$(a), (-3a-1), (3a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.067663964$ |
$13.88402977$ |
1.328580800 |
\( -\frac{290433617}{167042} a + \frac{356500493}{83521} \) |
\( \bigl[a + 1\) , \( -1\) , \( 0\) , \( -4 a - 8\) , \( -3 a - 2\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}-{x}^{2}+\left(-4a-8\right){x}-3a-2$ |
| 578.1-b1 |
578.1-b |
$4$ |
$6$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
578.1 |
\( 2 \cdot 17^{2} \) |
\( 2^{3} \cdot 17^{8} \) |
$1.23927$ |
$(a), (-3a-1), (3a-1)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{2} \cdot 3^{2} \) |
$1$ |
$6.207967861$ |
2.194848086 |
\( -\frac{148930501097}{96550276} a + \frac{246751481021}{48275138} \) |
\( \bigl[a + 1\) , \( a - 1\) , \( a + 1\) , \( -19 a - 33\) , \( 26 a + 35\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-19a-33\right){x}+26a+35$ |
| 578.1-b2 |
578.1-b |
$4$ |
$6$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
578.1 |
\( 2 \cdot 17^{2} \) |
\( 2^{6} \cdot 17^{4} \) |
$1.23927$ |
$(a), (-3a-1), (3a-1)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2 \cdot 3^{2} \) |
$1$ |
$12.41593572$ |
2.194848086 |
\( \frac{157040667}{19652} a + \frac{789842483}{39304} \) |
\( \bigl[a + 1\) , \( a - 1\) , \( a + 1\) , \( -9 a - 13\) , \( -22 a - 29\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-9a-13\right){x}-22a-29$ |
| 578.1-b3 |
578.1-b |
$4$ |
$6$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
578.1 |
\( 2 \cdot 17^{2} \) |
\( 2 \cdot 17^{8} \) |
$1.23927$ |
$(a), (-3a-1), (3a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$9$ |
\( 2^{2} \) |
$1$ |
$0.689774206$ |
2.194848086 |
\( -\frac{4726411666683430367}{48275138} a + \frac{3342207255869872849}{24137569} \) |
\( \bigl[a + 1\) , \( a - 1\) , \( a + 1\) , \( -464 a - 1273\) , \( -10018 a - 19601\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-464a-1273\right){x}-10018a-19601$ |
| 578.1-b4 |
578.1-b |
$4$ |
$6$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
578.1 |
\( 2 \cdot 17^{2} \) |
\( 2^{2} \cdot 17^{4} \) |
$1.23927$ |
$(a), (-3a-1), (3a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$9$ |
\( 2 \) |
$1$ |
$1.379548413$ |
2.194848086 |
\( \frac{49996424570896377}{4913} a + \frac{141411248574761267}{9826} \) |
\( \bigl[1\) , \( -a - 1\) , \( 1\) , \( 445 a - 685\) , \( 6530 a - 9359\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(445a-685\right){x}+6530a-9359$ |
| 578.1-c1 |
578.1-c |
$2$ |
$2$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
578.1 |
\( 2 \cdot 17^{2} \) |
\( 2^{2} \cdot 17^{3} \) |
$1.23927$ |
$(a), (-3a-1), (3a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.135327928$ |
$13.88402977$ |
1.328580800 |
\( -\frac{136747}{289} a + \frac{566707}{578} \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( 0\) , \( -a + 2\) , \( 0\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-a+2\right){x}$ |
| 578.1-c2 |
578.1-c |
$2$ |
$2$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
578.1 |
\( 2 \cdot 17^{2} \) |
\( 2 \cdot 17^{6} \) |
$1.23927$ |
$(a), (-3a-1), (3a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.067663964$ |
$13.88402977$ |
1.328580800 |
\( \frac{290433617}{167042} a + \frac{356500493}{83521} \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( 0\) , \( 4 a - 8\) , \( 3 a - 2\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(4a-8\right){x}+3a-2$ |
| 578.1-d1 |
578.1-d |
$8$ |
$12$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
578.1 |
\( 2 \cdot 17^{2} \) |
\( - 2^{3} \cdot 17^{5} \) |
$1.23927$ |
$(a), (-3a-1), (3a-1)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2 \cdot 3 \) |
$1.874461377$ |
$10.10549437$ |
2.232378405 |
\( -\frac{1712717194041788375}{334084} a + \frac{605536970972065000}{83521} \) |
\( \bigl[1\) , \( 0\) , \( 0\) , \( 230 a - 363\) , \( -2390 a + 3513\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(230a-363\right){x}-2390a+3513$ |
| 578.1-d2 |
578.1-d |
$8$ |
$12$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
578.1 |
\( 2 \cdot 17^{2} \) |
\( - 2 \cdot 17^{15} \) |
$1.23927$ |
$(a), (-3a-1), (3a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2 \) |
$5.623384133$ |
$1.122832707$ |
2.232378405 |
\( -\frac{10008966027980714375}{1165244474459522} a + \frac{7568104598365729000}{582622237229761} \) |
\( \bigl[1\) , \( 0\) , \( 0\) , \( 355 a - 193\) , \( -3135 a + 2315\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(355a-193\right){x}-3135a+2315$ |
| 578.1-d3 |
578.1-d |
$8$ |
$12$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
578.1 |
\( 2 \cdot 17^{2} \) |
\( 2^{12} \cdot 17^{2} \) |
$1.23927$ |
$(a), (-3a-1), (3a-1)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{2} \cdot 3 \) |
$0.468615344$ |
$20.21098874$ |
2.232378405 |
\( \frac{3048625}{1088} \) |
\( \bigl[1\) , \( 0\) , \( 0\) , \( -3\) , \( 1\bigr] \) |
${y}^2+{x}{y}={x}^{3}-3{x}+1$ |
| 578.1-d4 |
578.1-d |
$8$ |
$12$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
578.1 |
\( 2 \cdot 17^{2} \) |
\( 2^{2} \cdot 17^{12} \) |
$1.23927$ |
$(a), (-3a-1), (3a-1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2Cs, 3B.1.2 |
$1$ |
\( 2^{3} \) |
$2.811692066$ |
$2.245665415$ |
2.232378405 |
\( \frac{159661140625}{48275138} \) |
\( \bigl[1\) , \( 0\) , \( 0\) , \( -113\) , \( -329\bigr] \) |
${y}^2+{x}{y}={x}^{3}-113{x}-329$ |
| 578.1-d5 |
578.1-d |
$8$ |
$12$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
578.1 |
\( 2 \cdot 17^{2} \) |
\( - 2 \cdot 17^{15} \) |
$1.23927$ |
$(a), (-3a-1), (3a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2 \) |
$5.623384133$ |
$1.122832707$ |
2.232378405 |
\( \frac{10008966027980714375}{1165244474459522} a + \frac{7568104598365729000}{582622237229761} \) |
\( \bigl[1\) , \( 0\) , \( 0\) , \( -355 a - 193\) , \( 3135 a + 2315\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(-355a-193\right){x}+3135a+2315$ |
| 578.1-d6 |
578.1-d |
$8$ |
$12$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
578.1 |
\( 2 \cdot 17^{2} \) |
\( 2^{6} \cdot 17^{4} \) |
$1.23927$ |
$(a), (-3a-1), (3a-1)$ |
$1$ |
$\Z/2\Z\oplus\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2Cs, 3B.1.1 |
$1$ |
\( 2^{3} \cdot 3 \) |
$0.937230688$ |
$20.21098874$ |
2.232378405 |
\( \frac{8805624625}{2312} \) |
\( \bigl[1\) , \( 0\) , \( 0\) , \( -43\) , \( 105\bigr] \) |
${y}^2+{x}{y}={x}^{3}-43{x}+105$ |
| 578.1-d7 |
578.1-d |
$8$ |
$12$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
578.1 |
\( 2 \cdot 17^{2} \) |
\( 2^{4} \cdot 17^{6} \) |
$1.23927$ |
$(a), (-3a-1), (3a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2^{2} \) |
$1.405846033$ |
$2.245665415$ |
2.232378405 |
\( \frac{120920208625}{19652} \) |
\( \bigl[1\) , \( 0\) , \( 0\) , \( -103\) , \( -411\bigr] \) |
${y}^2+{x}{y}={x}^{3}-103{x}-411$ |
| 578.1-d8 |
578.1-d |
$8$ |
$12$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
578.1 |
\( 2 \cdot 17^{2} \) |
\( - 2^{3} \cdot 17^{5} \) |
$1.23927$ |
$(a), (-3a-1), (3a-1)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2 \cdot 3 \) |
$1.874461377$ |
$10.10549437$ |
2.232378405 |
\( \frac{1712717194041788375}{334084} a + \frac{605536970972065000}{83521} \) |
\( \bigl[1\) , \( 0\) , \( 0\) , \( -230 a - 363\) , \( 2390 a + 3513\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(-230a-363\right){x}+2390a+3513$ |
| 578.1-e1 |
578.1-e |
$2$ |
$2$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
578.1 |
\( 2 \cdot 17^{2} \) |
\( 2^{2} \cdot 17^{2} \) |
$1.23927$ |
$(a), (-3a-1), (3a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$11.80034313$ |
2.086025662 |
\( -\frac{5957997}{17} a + \frac{17828243}{34} \) |
\( \bigl[a + 1\) , \( 1\) , \( 1\) , \( 4 a - 6\) , \( 7 a - 11\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+{x}^{2}+\left(4a-6\right){x}+7a-11$ |
| 578.1-e2 |
578.1-e |
$2$ |
$2$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
578.1 |
\( 2 \cdot 17^{2} \) |
\( 2 \cdot 17^{4} \) |
$1.23927$ |
$(a), (-3a-1), (3a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$5.900171567$ |
2.086025662 |
\( \frac{159858748711}{578} a + \frac{113037774733}{289} \) |
\( \bigl[a + 1\) , \( 1\) , \( 1\) , \( -a - 16\) , \( -11 a - 29\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+{x}^{2}+\left(-a-16\right){x}-11a-29$ |
| 578.1-f1 |
578.1-f |
$4$ |
$6$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
578.1 |
\( 2 \cdot 17^{2} \) |
\( 2^{3} \cdot 17^{8} \) |
$1.23927$ |
$(a), (-3a-1), (3a-1)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{2} \cdot 3^{2} \) |
$1$ |
$6.207967861$ |
2.194848086 |
\( \frac{148930501097}{96550276} a + \frac{246751481021}{48275138} \) |
\( \bigl[a + 1\) , \( a - 1\) , \( 1\) , \( 17 a - 32\) , \( -59 a + 71\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(17a-32\right){x}-59a+71$ |
| 578.1-f2 |
578.1-f |
$4$ |
$6$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
578.1 |
\( 2 \cdot 17^{2} \) |
\( 2^{6} \cdot 17^{4} \) |
$1.23927$ |
$(a), (-3a-1), (3a-1)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2 \cdot 3^{2} \) |
$1$ |
$12.41593572$ |
2.194848086 |
\( -\frac{157040667}{19652} a + \frac{789842483}{39304} \) |
\( \bigl[a + 1\) , \( a - 1\) , \( 1\) , \( 7 a - 12\) , \( 9 a - 13\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(7a-12\right){x}+9a-13$ |
| 578.1-f3 |
578.1-f |
$4$ |
$6$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
578.1 |
\( 2 \cdot 17^{2} \) |
\( 2^{2} \cdot 17^{4} \) |
$1.23927$ |
$(a), (-3a-1), (3a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$9$ |
\( 2 \) |
$1$ |
$1.379548413$ |
2.194848086 |
\( -\frac{49996424570896377}{4913} a + \frac{141411248574761267}{9826} \) |
\( \bigl[1\) , \( a - 1\) , \( 1\) , \( -445 a - 685\) , \( -6530 a - 9359\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-445a-685\right){x}-6530a-9359$ |
| 578.1-f4 |
578.1-f |
$4$ |
$6$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
578.1 |
\( 2 \cdot 17^{2} \) |
\( 2 \cdot 17^{8} \) |
$1.23927$ |
$(a), (-3a-1), (3a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$9$ |
\( 2^{2} \) |
$1$ |
$0.689774206$ |
2.194848086 |
\( \frac{4726411666683430367}{48275138} a + \frac{3342207255869872849}{24137569} \) |
\( \bigl[a + 1\) , \( a - 1\) , \( 1\) , \( 462 a - 1272\) , \( 8745 a - 18675\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(462a-1272\right){x}+8745a-18675$ |
| 578.1-g1 |
578.1-g |
$2$ |
$2$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
578.1 |
\( 2 \cdot 17^{2} \) |
\( 2 \cdot 17^{4} \) |
$1.23927$ |
$(a), (-3a-1), (3a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$5.900171567$ |
2.086025662 |
\( -\frac{159858748711}{578} a + \frac{113037774733}{289} \) |
\( \bigl[a + 1\) , \( -a + 1\) , \( 1\) , \( -16\) , \( 11 a - 29\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(-a+1\right){x}^{2}-16{x}+11a-29$ |
| 578.1-g2 |
578.1-g |
$2$ |
$2$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
578.1 |
\( 2 \cdot 17^{2} \) |
\( 2^{2} \cdot 17^{2} \) |
$1.23927$ |
$(a), (-3a-1), (3a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$11.80034313$ |
2.086025662 |
\( \frac{5957997}{17} a + \frac{17828243}{34} \) |
\( \bigl[a + 1\) , \( -a + 1\) , \( 1\) , \( -5 a - 6\) , \( -7 a - 11\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-5a-6\right){x}-7a-11$ |
*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.
