| 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 |
| 196.1-a1 |
196.1-a |
$4$ |
$6$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
196.1 |
\( 2^{2} \cdot 7^{2} \) |
\( 2^{23} \cdot 7^{4} \) |
$1.37856$ |
$(-a+2), (-a-1), (7)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{2} \cdot 3^{2} \) |
$1$ |
$7.185533263$ |
1.742747801 |
\( -\frac{17119345409}{1835008} a - \frac{44411405067}{3211264} \) |
\( \bigl[1\) , \( a\) , \( 1\) , \( -94 a + 242\) , \( -787 a + 2016\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+a{x}^{2}+\left(-94a+242\right){x}-787a+2016$ |
| 196.1-a2 |
196.1-a |
$4$ |
$6$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
196.1 |
\( 2^{2} \cdot 7^{2} \) |
\( 2^{21} \cdot 7^{12} \) |
$1.37856$ |
$(-a+2), (-a-1), (7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2^{2} \cdot 3^{2} \) |
$1$ |
$0.798392584$ |
1.742747801 |
\( \frac{334127886601}{550731776} a - \frac{467423890123}{3855122432} \) |
\( \bigl[1\) , \( a\) , \( 1\) , \( 921 a - 2353\) , \( 34853 a - 89272\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+a{x}^{2}+\left(921a-2353\right){x}+34853a-89272$ |
| 196.1-a3 |
196.1-a |
$4$ |
$6$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
196.1 |
\( 2^{2} \cdot 7^{2} \) |
\( 2^{33} \cdot 7^{6} \) |
$1.37856$ |
$(-a+2), (-a-1), (7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2 \cdot 3^{2} \) |
$1$ |
$1.596785169$ |
1.742747801 |
\( -\frac{259350300719862479}{368293445632} a + \frac{665103127813666203}{368293445632} \) |
\( \bigl[1\) , \( -a + 1\) , \( 0\) , \( 62 a - 339\) , \( 1068 a - 2275\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(62a-339\right){x}+1068a-2275$ |
| 196.1-a4 |
196.1-a |
$4$ |
$6$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
196.1 |
\( 2^{2} \cdot 7^{2} \) |
\( 2^{19} \cdot 7^{2} \) |
$1.37856$ |
$(-a+2), (-a-1), (7)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2 \cdot 3^{2} \) |
$1$ |
$14.37106652$ |
1.742747801 |
\( \frac{2572367873807}{7168} a + \frac{4016914630531}{7168} \) |
\( \bigl[1\) , \( -a + 1\) , \( 0\) , \( -33 a - 64\) , \( 185 a + 292\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-33a-64\right){x}+185a+292$ |
| 196.1-b1 |
196.1-b |
$6$ |
$18$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
196.1 |
\( 2^{2} \cdot 7^{2} \) |
\( 2^{36} \cdot 7^{2} \) |
$1.37856$ |
$(-a+2), (-a-1), (7)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2^{2} \) |
$5.552971857$ |
$0.436190660$ |
1.174917493 |
\( -\frac{548347731625}{1835008} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -171\) , \( -874\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-171{x}-874$ |
| 196.1-b2 |
196.1-b |
$6$ |
$18$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
196.1 |
\( 2^{2} \cdot 7^{2} \) |
\( 2^{4} \cdot 7^{2} \) |
$1.37856$ |
$(-a+2), (-a-1), (7)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{2} \) |
$0.616996873$ |
$35.33144352$ |
1.174917493 |
\( -\frac{15625}{28} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -1\) , \( 0\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}$ |
| 196.1-b3 |
196.1-b |
$6$ |
$18$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
196.1 |
\( 2^{2} \cdot 7^{2} \) |
\( 2^{12} \cdot 7^{6} \) |
$1.37856$ |
$(-a+2), (-a-1), (7)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3Cs.1.1 |
$1$ |
\( 2^{2} \cdot 3 \) |
$1.850990619$ |
$3.925715946$ |
1.174917493 |
\( \frac{9938375}{21952} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( 4\) , \( -6\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+4{x}-6$ |
| 196.1-b4 |
196.1-b |
$6$ |
$18$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
196.1 |
\( 2^{2} \cdot 7^{2} \) |
\( 2^{6} \cdot 7^{12} \) |
$1.37856$ |
$(-a+2), (-a-1), (7)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3Cs.1.1 |
$1$ |
\( 2 \cdot 3 \) |
$3.701981238$ |
$3.925715946$ |
1.174917493 |
\( \frac{4956477625}{941192} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -36\) , \( -70\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-36{x}-70$ |
| 196.1-b5 |
196.1-b |
$6$ |
$18$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
196.1 |
\( 2^{2} \cdot 7^{2} \) |
\( 2^{2} \cdot 7^{4} \) |
$1.37856$ |
$(-a+2), (-a-1), (7)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2 \) |
$1.233993746$ |
$35.33144352$ |
1.174917493 |
\( \frac{128787625}{98} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -11\) , \( 12\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-11{x}+12$ |
| 196.1-b6 |
196.1-b |
$6$ |
$18$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
196.1 |
\( 2^{2} \cdot 7^{2} \) |
\( 2^{18} \cdot 7^{4} \) |
$1.37856$ |
$(-a+2), (-a-1), (7)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2 \) |
$11.10594371$ |
$0.436190660$ |
1.174917493 |
\( \frac{2251439055699625}{25088} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -2731\) , \( -55146\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-2731{x}-55146$ |
| 196.1-c1 |
196.1-c |
$2$ |
$2$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
196.1 |
\( 2^{2} \cdot 7^{2} \) |
\( 2^{3} \cdot 7^{4} \) |
$1.37856$ |
$(-a+2), (-a-1), (7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$6.402652160$ |
1.552871243 |
\( \frac{943}{28} a - \frac{17259}{196} \) |
\( \bigl[1\) , \( -a\) , \( 0\) , \( 1\) , \( -2 a - 3\bigr] \) |
${y}^2+{x}{y}={x}^{3}-a{x}^{2}+{x}-2a-3$ |
| 196.1-c2 |
196.1-c |
$2$ |
$2$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
196.1 |
\( 2^{2} \cdot 7^{2} \) |
\( 2^{3} \cdot 7^{2} \) |
$1.37856$ |
$(-a+2), (-a-1), (7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$12.80530432$ |
1.552871243 |
\( -\frac{2045551}{28} a + \frac{3781961}{14} \) |
\( \bigl[1\) , \( a + 1\) , \( 1\) , \( 7 a - 14\) , \( 11 a - 27\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(7a-14\right){x}+11a-27$ |
| 196.1-d1 |
196.1-d |
$8$ |
$16$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
196.1 |
\( 2^{2} \cdot 7^{2} \) |
\( 2^{34} \cdot 7^{2} \) |
$1.37856$ |
$(-a+2), (-a-1), (7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$4.040671280$ |
0.980006734 |
\( -\frac{110451307316625}{30064771072} a - \frac{38766248686125}{7516192768} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -115 a + 293\) , \( 1379 a - 3531\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}+\left(-115a+293\right){x}+1379a-3531$ |
| 196.1-d2 |
196.1-d |
$8$ |
$16$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
196.1 |
\( 2^{2} \cdot 7^{2} \) |
\( 2^{8} \cdot 7^{16} \) |
$1.37856$ |
$(-a+2), (-a-1), (7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$2.020335640$ |
0.980006734 |
\( \frac{4869777375}{92236816} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -565 a + 1448\) , \( -59003 a + 151140\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}+\left(-565a+1448\right){x}-59003a+151140$ |
| 196.1-d3 |
196.1-d |
$8$ |
$16$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
196.1 |
\( 2^{2} \cdot 7^{2} \) |
\( 2^{34} \cdot 7^{2} \) |
$1.37856$ |
$(-a+2), (-a-1), (7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$4.040671280$ |
0.980006734 |
\( \frac{110451307316625}{30064771072} a - \frac{265516302061125}{30064771072} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( 115 a + 178\) , \( -1379 a - 2152\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}+\left(115a+178\right){x}-1379a-2152$ |
| 196.1-d4 |
196.1-d |
$8$ |
$16$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
196.1 |
\( 2^{2} \cdot 7^{2} \) |
\( 2^{20} \cdot 7^{4} \) |
$1.37856$ |
$(-a+2), (-a-1), (7)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1$ |
$8.081342561$ |
0.980006734 |
\( -\frac{182305211999625}{3211264} a + \frac{466998623380125}{3211264} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( 65 a - 187\) , \( -481 a + 1209\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}+\left(65a-187\right){x}-481a+1209$ |
| 196.1-d5 |
196.1-d |
$8$ |
$16$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
196.1 |
\( 2^{2} \cdot 7^{2} \) |
\( 2^{16} \cdot 7^{8} \) |
$1.37856$ |
$(-a+2), (-a-1), (7)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1$ |
$8.081342561$ |
0.980006734 |
\( \frac{9869198625}{614656} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -715 a - 1117\) , \( 14299 a + 22329\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}+\left(-715a-1117\right){x}+14299a+22329$ |
| 196.1-d6 |
196.1-d |
$8$ |
$16$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
196.1 |
\( 2^{2} \cdot 7^{2} \) |
\( 2^{10} \cdot 7^{2} \) |
$1.37856$ |
$(-a+2), (-a-1), (7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$4.040671280$ |
0.980006734 |
\( -\frac{23813446589082500625}{1792} a + \frac{60999401116425061125}{1792} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( 1045 a - 2987\) , \( -30077 a + 75017\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}+\left(1045a-2987\right){x}-30077a+75017$ |
| 196.1-d7 |
196.1-d |
$8$ |
$16$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
196.1 |
\( 2^{2} \cdot 7^{2} \) |
\( 2^{20} \cdot 7^{4} \) |
$1.37856$ |
$(-a+2), (-a-1), (7)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1$ |
$8.081342561$ |
0.980006734 |
\( \frac{182305211999625}{3211264} a + \frac{71173352845125}{802816} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -65 a - 122\) , \( 481 a + 728\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}+\left(-65a-122\right){x}+481a+728$ |
| 196.1-d8 |
196.1-d |
$8$ |
$16$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
196.1 |
\( 2^{2} \cdot 7^{2} \) |
\( 2^{10} \cdot 7^{2} \) |
$1.37856$ |
$(-a+2), (-a-1), (7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$4.040671280$ |
0.980006734 |
\( \frac{23813446589082500625}{1792} a + \frac{9296488631835640125}{448} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -1045 a - 1942\) , \( 30077 a + 44940\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}+\left(-1045a-1942\right){x}+30077a+44940$ |
| 196.1-e1 |
196.1-e |
$2$ |
$2$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
196.1 |
\( 2^{2} \cdot 7^{2} \) |
\( 2^{3} \cdot 7^{4} \) |
$1.37856$ |
$(-a+2), (-a-1), (7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$6.402652160$ |
1.552871243 |
\( -\frac{943}{28} a - \frac{5329}{98} \) |
\( \bigl[1\) , \( a - 1\) , \( 0\) , \( 1\) , \( 2 a - 5\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(a-1\right){x}^{2}+{x}+2a-5$ |
| 196.1-e2 |
196.1-e |
$2$ |
$2$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
196.1 |
\( 2^{2} \cdot 7^{2} \) |
\( 2^{3} \cdot 7^{2} \) |
$1.37856$ |
$(-a+2), (-a-1), (7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$12.80530432$ |
1.552871243 |
\( \frac{2045551}{28} a + \frac{5518371}{28} \) |
\( \bigl[1\) , \( -a - 1\) , \( 0\) , \( -5 a - 8\) , \( -5 a - 8\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-5a-8\right){x}-5a-8$ |
| 196.1-f1 |
196.1-f |
$4$ |
$6$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
196.1 |
\( 2^{2} \cdot 7^{2} \) |
\( 2^{21} \cdot 7^{12} \) |
$1.37856$ |
$(-a+2), (-a-1), (7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2^{2} \cdot 3^{2} \) |
$1$ |
$0.798392584$ |
1.742747801 |
\( -\frac{334127886601}{550731776} a + \frac{467867829021}{963780608} \) |
\( \bigl[1\) , \( -a + 1\) , \( 1\) , \( -921 a - 1432\) , \( -34853 a - 54419\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-921a-1432\right){x}-34853a-54419$ |
| 196.1-f2 |
196.1-f |
$4$ |
$6$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
196.1 |
\( 2^{2} \cdot 7^{2} \) |
\( 2^{23} \cdot 7^{4} \) |
$1.37856$ |
$(-a+2), (-a-1), (7)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{2} \cdot 3^{2} \) |
$1$ |
$7.185533263$ |
1.742747801 |
\( \frac{17119345409}{1835008} a - \frac{297481038131}{12845056} \) |
\( \bigl[1\) , \( -a + 1\) , \( 1\) , \( 94 a + 148\) , \( 787 a + 1229\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(94a+148\right){x}+787a+1229$ |
| 196.1-f3 |
196.1-f |
$4$ |
$6$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
196.1 |
\( 2^{2} \cdot 7^{2} \) |
\( 2^{19} \cdot 7^{2} \) |
$1.37856$ |
$(-a+2), (-a-1), (7)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2 \cdot 3^{2} \) |
$1$ |
$14.37106652$ |
1.742747801 |
\( -\frac{2572367873807}{7168} a + \frac{3294641252169}{3584} \) |
\( \bigl[1\) , \( a\) , \( 0\) , \( 33 a - 97\) , \( -185 a + 477\bigr] \) |
${y}^2+{x}{y}={x}^{3}+a{x}^{2}+\left(33a-97\right){x}-185a+477$ |
| 196.1-f4 |
196.1-f |
$4$ |
$6$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
196.1 |
\( 2^{2} \cdot 7^{2} \) |
\( 2^{33} \cdot 7^{6} \) |
$1.37856$ |
$(-a+2), (-a-1), (7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2 \cdot 3^{2} \) |
$1$ |
$1.596785169$ |
1.742747801 |
\( \frac{259350300719862479}{368293445632} a + \frac{101438206773450931}{92073361408} \) |
\( \bigl[1\) , \( a\) , \( 0\) , \( -62 a - 277\) , \( -1068 a - 1207\bigr] \) |
${y}^2+{x}{y}={x}^{3}+a{x}^{2}+\left(-62a-277\right){x}-1068a-1207$ |
*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.
