| 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 |
| 147.1-a1 |
147.1-a |
$6$ |
$8$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
147.1 |
\( 3 \cdot 7^{2} \) |
\( 3^{16} \cdot 7^{9} \) |
$2.34912$ |
$(4a+13), (2a+7), (-2a+9)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$1$ |
$2.410774548$ |
2.554519116 |
\( -\frac{179111175231458}{37822859361} a - \frac{523032267366475}{37822859361} \) |
\( \bigl[1\) , \( -a - 1\) , \( a\) , \( -2480 a + 10607\) , \( 19995 a - 85484\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-2480a+10607\right){x}+19995a-85484$ |
| 147.1-a2 |
147.1-a |
$6$ |
$8$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
147.1 |
\( 3 \cdot 7^{2} \) |
\( 3^{2} \cdot 7^{9} \) |
$2.34912$ |
$(4a+13), (2a+7), (-2a+9)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$4.821549097$ |
2.554519116 |
\( \frac{471855278}{17294403} a - \frac{94507563}{823543} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( 5989 a + 19613\) , \( 14860056 a + 48665453\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(5989a+19613\right){x}+14860056a+48665453$ |
| 147.1-a3 |
147.1-a |
$6$ |
$8$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
147.1 |
\( 3 \cdot 7^{2} \) |
\( 3^{2} \cdot 7^{3} \) |
$2.34912$ |
$(4a+13), (2a+7), (-2a+9)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 2^{2} \) |
$1$ |
$4.821549097$ |
2.554519116 |
\( -\frac{4990857981374}{147} a + \frac{1015976434299}{7} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -a - 24\) , \( -37\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(-a-24\right){x}-37$ |
| 147.1-a4 |
147.1-a |
$6$ |
$8$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
147.1 |
\( 3 \cdot 7^{2} \) |
\( 3^{4} \cdot 7^{6} \) |
$2.34912$ |
$(4a+13), (2a+7), (-2a+9)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$1$ |
$9.643098194$ |
2.554519116 |
\( -\frac{1349438432}{21609} a + \frac{933880607}{3087} \) |
\( \bigl[1\) , \( -a - 1\) , \( a\) , \( 470 a - 2003\) , \( 11141 a - 47636\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(470a-2003\right){x}+11141a-47636$ |
| 147.1-a5 |
147.1-a |
$6$ |
$8$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
147.1 |
\( 3 \cdot 7^{2} \) |
\( 3^{8} \cdot 7^{6} \) |
$2.34912$ |
$(4a+13), (2a+7), (-2a+9)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$1$ |
$9.643098194$ |
2.554519116 |
\( \frac{31215323293328}{194481} a + \frac{34075981778011}{64827} \) |
\( \bigl[1\) , \( -a - 1\) , \( a\) , \( 630 a - 2688\) , \( 3310 a - 14157\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(630a-2688\right){x}+3310a-14157$ |
| 147.1-a6 |
147.1-a |
$6$ |
$8$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
147.1 |
\( 3 \cdot 7^{2} \) |
\( 3^{4} \cdot 7^{3} \) |
$2.34912$ |
$(4a+13), (2a+7), (-2a+9)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$9.643098194$ |
2.554519116 |
\( \frac{85774476164160945554}{441} a + \frac{280904308823739479395}{441} \) |
\( \bigl[1\) , \( -a - 1\) , \( a\) , \( 6300 a - 26943\) , \( -521039 a + 2227446\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(6300a-26943\right){x}-521039a+2227446$ |
| 147.1-b1 |
147.1-b |
$6$ |
$8$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
147.1 |
\( 3 \cdot 7^{2} \) |
\( 3^{2} \cdot 7^{9} \) |
$2.34912$ |
$(4a+13), (2a+7), (-2a+9)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$0.690325832$ |
$6.055870532$ |
1.107447826 |
\( -\frac{471855278}{17294403} a - \frac{1512803545}{17294403} \) |
\( \bigl[1\) , \( -a\) , \( a\) , \( -a + 3\) , \( 2 a + 2\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}-a{x}^{2}+\left(-a+3\right){x}+2a+2$ |
| 147.1-b2 |
147.1-b |
$6$ |
$8$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
147.1 |
\( 3 \cdot 7^{2} \) |
\( 3^{16} \cdot 7^{9} \) |
$2.34912$ |
$(4a+13), (2a+7), (-2a+9)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$5.522606659$ |
$0.756983816$ |
1.107447826 |
\( \frac{179111175231458}{37822859361} a - \frac{11145134009491}{600362847} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( 12972 a - 55454\) , \( 1607058 a - 6870040\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}+\left(12972a-55454\right){x}+1607058a-6870040$ |
| 147.1-b3 |
147.1-b |
$6$ |
$8$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
147.1 |
\( 3 \cdot 7^{2} \) |
\( 3^{8} \cdot 7^{6} \) |
$2.34912$ |
$(4a+13), (2a+7), (-2a+9)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$2.761303329$ |
$3.027935266$ |
1.107447826 |
\( -\frac{31215323293328}{194481} a + \frac{19063324089623}{27783} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( 13062 a - 55839\) , \( 1584258 a - 6772572\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}+\left(13062a-55839\right){x}+1584258a-6772572$ |
| 147.1-b4 |
147.1-b |
$6$ |
$8$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
147.1 |
\( 3 \cdot 7^{2} \) |
\( 3^{4} \cdot 7^{3} \) |
$2.34912$ |
$(4a+13), (2a+7), (-2a+9)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$5.522606659$ |
$0.756983816$ |
1.107447826 |
\( -\frac{85774476164160945554}{441} a + \frac{17460894523233353569}{21} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( 208992 a - 893424\) , \( 101131314 a - 432327996\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}+\left(208992a-893424\right){x}+101131314a-432327996$ |
| 147.1-b5 |
147.1-b |
$6$ |
$8$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
147.1 |
\( 3 \cdot 7^{2} \) |
\( 3^{4} \cdot 7^{6} \) |
$2.34912$ |
$(4a+13), (2a+7), (-2a+9)$ |
$1$ |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$1.380651664$ |
$12.11174106$ |
1.107447826 |
\( \frac{1349438432}{21609} a + \frac{1729241939}{7203} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( 822 a - 3514\) , \( 24654 a - 105394\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}+\left(822a-3514\right){x}+24654a-105394$ |
| 147.1-b6 |
147.1-b |
$6$ |
$8$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
147.1 |
\( 3 \cdot 7^{2} \) |
\( 3^{2} \cdot 7^{3} \) |
$2.34912$ |
$(4a+13), (2a+7), (-2a+9)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.690325832$ |
$24.22348212$ |
1.107447826 |
\( \frac{4990857981374}{147} a + \frac{16344647138905}{147} \) |
\( \bigl[1\) , \( -a\) , \( a\) , \( -244571 a - 800944\) , \( 128243685 a + 419987451\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}-a{x}^{2}+\left(-244571a-800944\right){x}+128243685a+419987451$ |
| 147.1-c1 |
147.1-c |
$6$ |
$8$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
147.1 |
\( 3 \cdot 7^{2} \) |
\( 3^{2} \cdot 7^{16} \) |
$2.34912$ |
$(4a+13), (2a+7), (-2a+9)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$3.651881942$ |
0.967407159 |
\( -\frac{4354703137}{17294403} \) |
\( \bigl[1\) , \( a - 1\) , \( a\) , \( 410971 a - 1756865\) , \( -781852853 a + 3342356220\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(410971a-1756865\right){x}-781852853a+3342356220$ |
| 147.1-c2 |
147.1-c |
$6$ |
$8$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
147.1 |
\( 3 \cdot 7^{2} \) |
\( 3^{4} \cdot 7^{2} \) |
$2.34912$ |
$(4a+13), (2a+7), (-2a+9)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$14.60752776$ |
0.967407159 |
\( \frac{103823}{63} \) |
\( \bigl[1\) , \( -a\) , \( a + 1\) , \( 11828 a + 38741\) , \( 283917 a + 929805\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(11828a+38741\right){x}+283917a+929805$ |
| 147.1-c3 |
147.1-c |
$6$ |
$8$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
147.1 |
\( 3 \cdot 7^{2} \) |
\( 3^{8} \cdot 7^{4} \) |
$2.34912$ |
$(4a+13), (2a+7), (-2a+9)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1$ |
$14.60752776$ |
0.967407159 |
\( \frac{7189057}{3969} \) |
\( \bigl[1\) , \( -a\) , \( a + 1\) , \( -48572 a - 159064\) , \( 2493022 a + 8164441\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(-48572a-159064\right){x}+2493022a+8164441$ |
| 147.1-c4 |
147.1-c |
$6$ |
$8$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
147.1 |
\( 3 \cdot 7^{2} \) |
\( 3^{16} \cdot 7^{2} \) |
$2.34912$ |
$(4a+13), (2a+7), (-2a+9)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$4$ |
\( 2 \) |
$1$ |
$3.651881942$ |
0.967407159 |
\( \frac{6570725617}{45927} \) |
\( \bigl[1\) , \( -a\) , \( a + 1\) , \( -471372 a - 1543699\) , \( -339559003 a - 1112027625\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(-471372a-1543699\right){x}-339559003a-1112027625$ |
| 147.1-c5 |
147.1-c |
$6$ |
$8$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
147.1 |
\( 3 \cdot 7^{2} \) |
\( 3^{4} \cdot 7^{8} \) |
$2.34912$ |
$(4a+13), (2a+7), (-2a+9)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1$ |
$14.60752776$ |
0.967407159 |
\( \frac{13027640977}{21609} \) |
\( \bigl[1\) , \( -a\) , \( a + 1\) , \( -592172 a - 1939309\) , \( 482038087 a + 1578634831\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(-592172a-1939309\right){x}+482038087a+1578634831$ |
| 147.1-c6 |
147.1-c |
$6$ |
$8$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
147.1 |
\( 3 \cdot 7^{2} \) |
\( 3^{2} \cdot 7^{4} \) |
$2.34912$ |
$(4a+13), (2a+7), (-2a+9)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$14.60752776$ |
0.967407159 |
\( \frac{53297461115137}{147} \) |
\( \bigl[1\) , \( a - 1\) , \( a\) , \( 9470971 a - 40487615\) , \( -30838100363 a + 131830326198\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(9470971a-40487615\right){x}-30838100363a+131830326198$ |
| 147.1-d1 |
147.1-d |
$6$ |
$8$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
147.1 |
\( 3 \cdot 7^{2} \) |
\( 3^{2} \cdot 7^{16} \) |
$2.34912$ |
$(4a+13), (2a+7), (-2a+9)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$3.694208115$ |
$0.814020435$ |
1.593232766 |
\( -\frac{4354703137}{17294403} \) |
\( \bigl[1\) , \( 0\) , \( 0\) , \( -34\) , \( -217\bigr] \) |
${y}^2+{x}{y}={x}^{3}-34{x}-217$ |
| 147.1-d2 |
147.1-d |
$6$ |
$8$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
147.1 |
\( 3 \cdot 7^{2} \) |
\( 3^{4} \cdot 7^{2} \) |
$2.34912$ |
$(4a+13), (2a+7), (-2a+9)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1.847104057$ |
$13.02432697$ |
1.593232766 |
\( \frac{103823}{63} \) |
\( \bigl[1\) , \( 0\) , \( 0\) , \( 1\) , \( 0\bigr] \) |
${y}^2+{x}{y}={x}^{3}+{x}$ |
| 147.1-d3 |
147.1-d |
$6$ |
$8$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
147.1 |
\( 3 \cdot 7^{2} \) |
\( 3^{8} \cdot 7^{4} \) |
$2.34912$ |
$(4a+13), (2a+7), (-2a+9)$ |
$1$ |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$0.923552028$ |
$13.02432697$ |
1.593232766 |
\( \frac{7189057}{3969} \) |
\( \bigl[1\) , \( 0\) , \( 0\) , \( -4\) , \( -1\bigr] \) |
${y}^2+{x}{y}={x}^{3}-4{x}-1$ |
| 147.1-d4 |
147.1-d |
$6$ |
$8$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
147.1 |
\( 3 \cdot 7^{2} \) |
\( 3^{16} \cdot 7^{2} \) |
$2.34912$ |
$(4a+13), (2a+7), (-2a+9)$ |
$1$ |
$\Z/8\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1.847104057$ |
$13.02432697$ |
1.593232766 |
\( \frac{6570725617}{45927} \) |
\( \bigl[1\) , \( 0\) , \( 0\) , \( -39\) , \( 90\bigr] \) |
${y}^2+{x}{y}={x}^{3}-39{x}+90$ |
| 147.1-d5 |
147.1-d |
$6$ |
$8$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
147.1 |
\( 3 \cdot 7^{2} \) |
\( 3^{4} \cdot 7^{8} \) |
$2.34912$ |
$(4a+13), (2a+7), (-2a+9)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$1.847104057$ |
$3.256081743$ |
1.593232766 |
\( \frac{13027640977}{21609} \) |
\( \bigl[1\) , \( 0\) , \( 0\) , \( -49\) , \( -136\bigr] \) |
${y}^2+{x}{y}={x}^{3}-49{x}-136$ |
| 147.1-d6 |
147.1-d |
$6$ |
$8$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
147.1 |
\( 3 \cdot 7^{2} \) |
\( 3^{2} \cdot 7^{4} \) |
$2.34912$ |
$(4a+13), (2a+7), (-2a+9)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$3.694208115$ |
$0.814020435$ |
1.593232766 |
\( \frac{53297461115137}{147} \) |
\( \bigl[1\) , \( 0\) , \( 0\) , \( -784\) , \( -8515\bigr] \) |
${y}^2+{x}{y}={x}^{3}-784{x}-8515$ |
| 147.1-e1 |
147.1-e |
$6$ |
$8$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
147.1 |
\( 3 \cdot 7^{2} \) |
\( 3^{2} \cdot 7^{9} \) |
$2.34912$ |
$(4a+13), (2a+7), (-2a+9)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$4.821549097$ |
2.554519116 |
\( -\frac{471855278}{17294403} a - \frac{1512803545}{17294403} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -5989 a + 25602\) , \( -14860056 a + 63525509\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(-5989a+25602\right){x}-14860056a+63525509$ |
| 147.1-e2 |
147.1-e |
$6$ |
$8$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
147.1 |
\( 3 \cdot 7^{2} \) |
\( 3^{16} \cdot 7^{9} \) |
$2.34912$ |
$(4a+13), (2a+7), (-2a+9)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$1$ |
$2.410774548$ |
2.554519116 |
\( \frac{179111175231458}{37822859361} a - \frac{11145134009491}{600362847} \) |
\( \bigl[1\) , \( a + 1\) , \( a\) , \( 2481 a + 8127\) , \( -17515 a - 57362\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(2481a+8127\right){x}-17515a-57362$ |
| 147.1-e3 |
147.1-e |
$6$ |
$8$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
147.1 |
\( 3 \cdot 7^{2} \) |
\( 3^{8} \cdot 7^{6} \) |
$2.34912$ |
$(4a+13), (2a+7), (-2a+9)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$1$ |
$9.643098194$ |
2.554519116 |
\( -\frac{31215323293328}{194481} a + \frac{19063324089623}{27783} \) |
\( \bigl[1\) , \( a + 1\) , \( a\) , \( -629 a - 2058\) , \( -3940 a - 12905\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-629a-2058\right){x}-3940a-12905$ |
| 147.1-e4 |
147.1-e |
$6$ |
$8$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
147.1 |
\( 3 \cdot 7^{2} \) |
\( 3^{4} \cdot 7^{3} \) |
$2.34912$ |
$(4a+13), (2a+7), (-2a+9)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$9.643098194$ |
2.554519116 |
\( -\frac{85774476164160945554}{441} a + \frac{17460894523233353569}{21} \) |
\( \bigl[1\) , \( a + 1\) , \( a\) , \( -6299 a - 20643\) , \( 514739 a + 1685764\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-6299a-20643\right){x}+514739a+1685764$ |
| 147.1-e5 |
147.1-e |
$6$ |
$8$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
147.1 |
\( 3 \cdot 7^{2} \) |
\( 3^{4} \cdot 7^{6} \) |
$2.34912$ |
$(4a+13), (2a+7), (-2a+9)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$1$ |
$9.643098194$ |
2.554519116 |
\( \frac{1349438432}{21609} a + \frac{1729241939}{7203} \) |
\( \bigl[1\) , \( a + 1\) , \( a\) , \( -469 a - 1533\) , \( -11611 a - 38028\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-469a-1533\right){x}-11611a-38028$ |
| 147.1-e6 |
147.1-e |
$6$ |
$8$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
147.1 |
\( 3 \cdot 7^{2} \) |
\( 3^{2} \cdot 7^{3} \) |
$2.34912$ |
$(4a+13), (2a+7), (-2a+9)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 2^{2} \) |
$1$ |
$4.821549097$ |
2.554519116 |
\( \frac{4990857981374}{147} a + \frac{16344647138905}{147} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( a - 25\) , \( -37\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(a-25\right){x}-37$ |
| 147.1-f1 |
147.1-f |
$6$ |
$8$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
147.1 |
\( 3 \cdot 7^{2} \) |
\( 3^{16} \cdot 7^{9} \) |
$2.34912$ |
$(4a+13), (2a+7), (-2a+9)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$5.522606659$ |
$0.756983816$ |
1.107447826 |
\( -\frac{179111175231458}{37822859361} a - \frac{523032267366475}{37822859361} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -12972 a - 42482\) , \( -1607058 a - 5262982\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}+\left(-12972a-42482\right){x}-1607058a-5262982$ |
| 147.1-f2 |
147.1-f |
$6$ |
$8$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
147.1 |
\( 3 \cdot 7^{2} \) |
\( 3^{2} \cdot 7^{9} \) |
$2.34912$ |
$(4a+13), (2a+7), (-2a+9)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$0.690325832$ |
$6.055870532$ |
1.107447826 |
\( \frac{471855278}{17294403} a - \frac{94507563}{823543} \) |
\( \bigl[1\) , \( a - 1\) , \( a + 1\) , \( 2\) , \( -3 a + 4\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+2{x}-3a+4$ |
| 147.1-f3 |
147.1-f |
$6$ |
$8$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
147.1 |
\( 3 \cdot 7^{2} \) |
\( 3^{2} \cdot 7^{3} \) |
$2.34912$ |
$(4a+13), (2a+7), (-2a+9)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.690325832$ |
$24.22348212$ |
1.107447826 |
\( -\frac{4990857981374}{147} a + \frac{1015976434299}{7} \) |
\( \bigl[1\) , \( a - 1\) , \( a + 1\) , \( 244570 a - 1045515\) , \( -128243686 a + 548231136\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(244570a-1045515\right){x}-128243686a+548231136$ |
| 147.1-f4 |
147.1-f |
$6$ |
$8$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
147.1 |
\( 3 \cdot 7^{2} \) |
\( 3^{4} \cdot 7^{6} \) |
$2.34912$ |
$(4a+13), (2a+7), (-2a+9)$ |
$1$ |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$1.380651664$ |
$12.11174106$ |
1.107447826 |
\( -\frac{1349438432}{21609} a + \frac{933880607}{3087} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -822 a - 2692\) , \( -24654 a - 80740\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}+\left(-822a-2692\right){x}-24654a-80740$ |
| 147.1-f5 |
147.1-f |
$6$ |
$8$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
147.1 |
\( 3 \cdot 7^{2} \) |
\( 3^{8} \cdot 7^{6} \) |
$2.34912$ |
$(4a+13), (2a+7), (-2a+9)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$2.761303329$ |
$3.027935266$ |
1.107447826 |
\( \frac{31215323293328}{194481} a + \frac{34075981778011}{64827} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -13062 a - 42777\) , \( -1584258 a - 5188314\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}+\left(-13062a-42777\right){x}-1584258a-5188314$ |
| 147.1-f6 |
147.1-f |
$6$ |
$8$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
147.1 |
\( 3 \cdot 7^{2} \) |
\( 3^{4} \cdot 7^{3} \) |
$2.34912$ |
$(4a+13), (2a+7), (-2a+9)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$5.522606659$ |
$0.756983816$ |
1.107447826 |
\( \frac{85774476164160945554}{441} a + \frac{280904308823739479395}{441} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -208992 a - 684432\) , \( -101131314 a - 331196682\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}+\left(-208992a-684432\right){x}-101131314a-331196682$ |
*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.
