| 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 |
| 612.1-a1 |
612.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
612.1 |
\( 2^{2} \cdot 3^{2} \cdot 17 \) |
\( 2^{2} \cdot 3^{8} \cdot 17^{4} \) |
$1.83253$ |
$(-a+2), (-a-1), (-2a+1), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.286507785$ |
$5.588174083$ |
1.553251872 |
\( \frac{46268279}{46818} \) |
\( \bigl[1\) , \( 1\) , \( 0\) , \( 8\) , \( 10\bigr] \) |
${y}^2+{x}{y}={x}^{3}+{x}^{2}+8{x}+10$ |
| 612.1-a2 |
612.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
612.1 |
\( 2^{2} \cdot 3^{2} \cdot 17 \) |
\( 2^{4} \cdot 3^{4} \cdot 17^{2} \) |
$1.83253$ |
$(-a+2), (-a-1), (-2a+1), (3)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$0.143253892$ |
$22.35269633$ |
1.553251872 |
\( \frac{1771561}{612} \) |
\( \bigl[1\) , \( 1\) , \( 0\) , \( -2\) , \( 0\bigr] \) |
${y}^2+{x}{y}={x}^{3}+{x}^{2}-2{x}$ |
| 612.1-a3 |
612.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
612.1 |
\( 2^{2} \cdot 3^{2} \cdot 17 \) |
\( 2^{5} \cdot 3^{2} \cdot 17 \) |
$1.83253$ |
$(-a+2), (-a-1), (-2a+1), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.286507785$ |
$22.35269633$ |
1.553251872 |
\( -\frac{825027005}{816} a + \frac{534896269}{204} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( 88 a - 226\) , \( -638 a + 1634\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(88a-226\right){x}-638a+1634$ |
| 612.1-a4 |
612.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
612.1 |
\( 2^{2} \cdot 3^{2} \cdot 17 \) |
\( 2^{5} \cdot 3^{2} \cdot 17 \) |
$1.83253$ |
$(-a+2), (-a-1), (-2a+1), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.286507785$ |
$22.35269633$ |
1.553251872 |
\( \frac{825027005}{816} a + \frac{1314558071}{816} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -88 a - 138\) , \( 638 a + 996\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(-88a-138\right){x}+638a+996$ |
| 612.1-b1 |
612.1-b |
$2$ |
$2$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
612.1 |
\( 2^{2} \cdot 3^{2} \cdot 17 \) |
\( - 2^{14} \cdot 3^{4} \cdot 17 \) |
$1.83253$ |
$(-a+2), (-a-1), (-2a+1), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \cdot 5 \) |
$0.042057657$ |
$15.27159940$ |
3.115552989 |
\( -\frac{921158491}{52224} a + \frac{7078524037}{156672} \) |
\( \bigl[1\) , \( a\) , \( 0\) , \( 6 a - 13\) , \( -12 a + 33\bigr] \) |
${y}^2+{x}{y}={x}^{3}+a{x}^{2}+\left(6a-13\right){x}-12a+33$ |
| 612.1-b2 |
612.1-b |
$2$ |
$2$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
612.1 |
\( 2^{2} \cdot 3^{2} \cdot 17 \) |
\( - 2^{13} \cdot 3^{2} \cdot 17^{2} \) |
$1.83253$ |
$(-a+2), (-a-1), (-2a+1), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \cdot 5 \) |
$0.084115315$ |
$15.27159940$ |
3.115552989 |
\( \frac{260665603}{13056} a + \frac{101758801}{3264} \) |
\( \bigl[1\) , \( -a + 1\) , \( 1\) , \( 7 a - 18\) , \( -857 a + 2195\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(7a-18\right){x}-857a+2195$ |
| 612.1-c1 |
612.1-c |
$2$ |
$2$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
612.1 |
\( 2^{2} \cdot 3^{2} \cdot 17 \) |
\( - 2^{13} \cdot 3^{2} \cdot 17^{2} \) |
$1.83253$ |
$(-a+2), (-a-1), (-2a+1), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \cdot 5 \) |
$0.084115315$ |
$15.27159940$ |
3.115552989 |
\( -\frac{260665603}{13056} a + \frac{667700807}{13056} \) |
\( \bigl[1\) , \( a\) , \( 1\) , \( -7 a - 11\) , \( 857 a + 1338\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+a{x}^{2}+\left(-7a-11\right){x}+857a+1338$ |
| 612.1-c2 |
612.1-c |
$2$ |
$2$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
612.1 |
\( 2^{2} \cdot 3^{2} \cdot 17 \) |
\( - 2^{14} \cdot 3^{4} \cdot 17 \) |
$1.83253$ |
$(-a+2), (-a-1), (-2a+1), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \cdot 5 \) |
$0.042057657$ |
$15.27159940$ |
3.115552989 |
\( \frac{921158491}{52224} a + \frac{1078762141}{39168} \) |
\( \bigl[1\) , \( -a + 1\) , \( 0\) , \( -6 a - 7\) , \( 12 a + 21\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-6a-7\right){x}+12a+21$ |
| 612.1-d1 |
612.1-d |
$6$ |
$8$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
612.1 |
\( 2^{2} \cdot 3^{2} \cdot 17 \) |
\( - 2^{10} \cdot 3^{4} \cdot 17 \) |
$1.83253$ |
$(-a+2), (-a-1), (-2a+1), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.191755805$ |
$8.426251030$ |
1.567539326 |
\( -\frac{25352251372987}{13056} a + \frac{194823392446501}{39168} \) |
\( \bigl[1\) , \( -a\) , \( a + 1\) , \( 2 a - 6\) , \( -112 a - 168\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(2a-6\right){x}-112a-168$ |
| 612.1-d2 |
612.1-d |
$6$ |
$8$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
612.1 |
\( 2^{2} \cdot 3^{2} \cdot 17 \) |
\( - 2^{5} \cdot 3^{2} \cdot 17^{8} \) |
$1.83253$ |
$(-a+2), (-a-1), (-2a+1), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$0.383511611$ |
$2.106562757$ |
1.567539326 |
\( -\frac{335289536353}{1336336} a + \frac{37967182255}{58956} \) |
\( \bigl[1\) , \( -a - 1\) , \( a\) , \( 256 a + 395\) , \( 1559 a + 2427\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(256a+395\right){x}+1559a+2427$ |
| 612.1-d3 |
612.1-d |
$6$ |
$8$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
612.1 |
\( 2^{2} \cdot 3^{2} \cdot 17 \) |
\( 2^{10} \cdot 3^{4} \cdot 17^{4} \) |
$1.83253$ |
$(-a+2), (-a-1), (-2a+1), (3)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$0.191755805$ |
$8.426251030$ |
1.567539326 |
\( \frac{16457771}{221952} a + \frac{348290797}{166464} \) |
\( \bigl[1\) , \( -a - 1\) , \( a\) , \( -74 a - 115\) , \( 329 a + 513\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-74a-115\right){x}+329a+513$ |
| 612.1-d4 |
612.1-d |
$6$ |
$8$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
612.1 |
\( 2^{2} \cdot 3^{2} \cdot 17 \) |
\( 2^{8} \cdot 3^{8} \cdot 17^{2} \) |
$1.83253$ |
$(-a+2), (-a-1), (-2a+1), (3)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$0.383511611$ |
$8.426251030$ |
1.567539326 |
\( -\frac{3831982}{459} a + \frac{1700591297}{22032} \) |
\( \bigl[1\) , \( a + 1\) , \( a\) , \( 25 a - 66\) , \( -106 a + 260\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(25a-66\right){x}-106a+260$ |
| 612.1-d5 |
612.1-d |
$6$ |
$8$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
612.1 |
\( 2^{2} \cdot 3^{2} \cdot 17 \) |
\( - 2^{17} \cdot 3^{2} \cdot 17^{2} \) |
$1.83253$ |
$(-a+2), (-a-1), (-2a+1), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.383511611$ |
$8.426251030$ |
1.567539326 |
\( \frac{517728441833}{1114112} a + \frac{607604140655}{835584} \) |
\( \bigl[1\) , \( a - 1\) , \( a\) , \( -11 a + 2\) , \( 14 a - 2\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-11a+2\right){x}+14a-2$ |
| 612.1-d6 |
612.1-d |
$6$ |
$8$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
612.1 |
\( 2^{2} \cdot 3^{2} \cdot 17 \) |
\( - 2^{4} \cdot 3^{16} \cdot 17 \) |
$1.83253$ |
$(-a+2), (-a-1), (-2a+1), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.767023222$ |
$2.106562757$ |
1.567539326 |
\( \frac{54662458323803}{74358} a + \frac{512149891963367}{446148} \) |
\( \bigl[1\) , \( a + 1\) , \( a\) , \( -15 a - 46\) , \( -358 a + 488\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-15a-46\right){x}-358a+488$ |
| 612.1-e1 |
612.1-e |
$8$ |
$16$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
612.1 |
\( 2^{2} \cdot 3^{2} \cdot 17 \) |
\( 2^{2} \cdot 3^{4} \cdot 17^{16} \) |
$1.83253$ |
$(-a+2), (-a-1), (-2a+1), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$16$ |
\( 2^{5} \) |
$1$ |
$0.136840423$ |
4.248150726 |
\( -\frac{491411892194497}{125563633938} \) |
\( \bigl[1\) , \( 0\) , \( 0\) , \( -1644\) , \( -30942\bigr] \) |
${y}^2+{x}{y}={x}^{3}-1644{x}-30942$ |
| 612.1-e2 |
612.1-e |
$8$ |
$16$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
612.1 |
\( 2^{2} \cdot 3^{2} \cdot 17 \) |
\( - 2^{20} \cdot 3^{4} \cdot 17 \) |
$1.83253$ |
$(-a+2), (-a-1), (-2a+1), (3)$ |
0 |
$\Z/8\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{7} \) |
$1$ |
$8.757787080$ |
4.248150726 |
\( -\frac{326799140223409}{10027008} a + \frac{837114254307557}{10027008} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( 86 a + 131\) , \( 2522 a + 3939\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}+\left(86a+131\right){x}+2522a+3939$ |
| 612.1-e3 |
612.1-e |
$8$ |
$16$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
612.1 |
\( 2^{2} \cdot 3^{2} \cdot 17 \) |
\( 2^{4} \cdot 3^{32} \cdot 17^{2} \) |
$1.83253$ |
$(-a+2), (-a-1), (-2a+1), (3)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$4$ |
\( 2^{7} \) |
$1$ |
$0.547361692$ |
4.248150726 |
\( \frac{1276229915423}{2927177028} \) |
\( \bigl[1\) , \( 0\) , \( 0\) , \( 226\) , \( -2232\bigr] \) |
${y}^2+{x}{y}={x}^{3}+226{x}-2232$ |
| 612.1-e4 |
612.1-e |
$8$ |
$16$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
612.1 |
\( 2^{2} \cdot 3^{2} \cdot 17 \) |
\( 2^{8} \cdot 3^{16} \cdot 17^{4} \) |
$1.83253$ |
$(-a+2), (-a-1), (-2a+1), (3)$ |
0 |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{9} \) |
$1$ |
$2.189446770$ |
4.248150726 |
\( \frac{163936758817}{30338064} \) |
\( \bigl[1\) , \( 0\) , \( 0\) , \( -114\) , \( -396\bigr] \) |
${y}^2+{x}{y}={x}^{3}-114{x}-396$ |
| 612.1-e5 |
612.1-e |
$8$ |
$16$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
612.1 |
\( 2^{2} \cdot 3^{2} \cdot 17 \) |
\( 2^{16} \cdot 3^{8} \cdot 17^{2} \) |
$1.83253$ |
$(-a+2), (-a-1), (-2a+1), (3)$ |
0 |
$\Z/2\Z\oplus\Z/8\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{9} \) |
$1$ |
$8.757787080$ |
4.248150726 |
\( \frac{4354703137}{352512} \) |
\( \bigl[1\) , \( 0\) , \( 0\) , \( -34\) , \( 68\bigr] \) |
${y}^2+{x}{y}={x}^{3}-34{x}+68$ |
| 612.1-e6 |
612.1-e |
$8$ |
$16$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
612.1 |
\( 2^{2} \cdot 3^{2} \cdot 17 \) |
\( 2^{4} \cdot 3^{8} \cdot 17^{8} \) |
$1.83253$ |
$(-a+2), (-a-1), (-2a+1), (3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$4$ |
\( 2^{7} \) |
$1$ |
$0.547361692$ |
4.248150726 |
\( \frac{576615941610337}{27060804} \) |
\( \bigl[1\) , \( 0\) , \( 0\) , \( -1734\) , \( -27936\bigr] \) |
${y}^2+{x}{y}={x}^{3}-1734{x}-27936$ |
| 612.1-e7 |
612.1-e |
$8$ |
$16$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
612.1 |
\( 2^{2} \cdot 3^{2} \cdot 17 \) |
\( - 2^{20} \cdot 3^{4} \cdot 17 \) |
$1.83253$ |
$(-a+2), (-a-1), (-2a+1), (3)$ |
0 |
$\Z/8\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{7} \) |
$1$ |
$8.757787080$ |
4.248150726 |
\( \frac{326799140223409}{10027008} a + \frac{127578778521037}{2506752} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -86 a + 217\) , \( -2522 a + 6461\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}+\left(-86a+217\right){x}-2522a+6461$ |
| 612.1-e8 |
612.1-e |
$8$ |
$16$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
612.1 |
\( 2^{2} \cdot 3^{2} \cdot 17 \) |
\( 2^{2} \cdot 3^{4} \cdot 17^{4} \) |
$1.83253$ |
$(-a+2), (-a-1), (-2a+1), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$64$ |
\( 2^{3} \) |
$1$ |
$0.136840423$ |
4.248150726 |
\( \frac{2361739090258884097}{5202} \) |
\( \bigl[1\) , \( 0\) , \( 0\) , \( -27744\) , \( -1781010\bigr] \) |
${y}^2+{x}{y}={x}^{3}-27744{x}-1781010$ |
| 612.1-f1 |
612.1-f |
$4$ |
$6$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
612.1 |
\( 2^{2} \cdot 3^{2} \cdot 17 \) |
\( - 2^{60} \cdot 3^{4} \cdot 17^{3} \) |
$1.83253$ |
$(-a+2), (-a-1), (-2a+1), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$9$ |
\( 2^{3} \cdot 3 \) |
$1$ |
$0.144022077$ |
1.886246168 |
\( -\frac{1397539108647287243438603}{15618483507720880128} a - \frac{6304574046564551083866091}{46855450523162640384} \) |
\( \bigl[1\) , \( a\) , \( 1\) , \( -92659 a - 144800\) , \( -22192717 a - 34655406\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+a{x}^{2}+\left(-92659a-144800\right){x}-22192717a-34655406$ |
| 612.1-f2 |
612.1-f |
$4$ |
$6$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
612.1 |
\( 2^{2} \cdot 3^{2} \cdot 17 \) |
\( - 2^{36} \cdot 3^{12} \cdot 17 \) |
$1.83253$ |
$(-a+2), (-a-1), (-2a+1), (3)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{3} \cdot 3^{3} \) |
$1$ |
$1.296198698$ |
1.886246168 |
\( -\frac{59582139343925}{180486144} a + \frac{2748456780638401}{3248750592} \) |
\( \bigl[1\) , \( a\) , \( 1\) , \( 2246 a + 3475\) , \( -152779 a - 238488\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+a{x}^{2}+\left(2246a+3475\right){x}-152779a-238488$ |
| 612.1-f3 |
612.1-f |
$4$ |
$6$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
612.1 |
\( 2^{2} \cdot 3^{2} \cdot 17 \) |
\( - 2^{45} \cdot 3^{6} \cdot 17^{2} \) |
$1.83253$ |
$(-a+2), (-a-1), (-2a+1), (3)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{3} \cdot 3^{3} \) |
$1$ |
$1.296198698$ |
1.886246168 |
\( \frac{49436370625448675}{31542239821824} a + \frac{14757024390205943}{7885559955456} \) |
\( \bigl[1\) , \( -a + 1\) , \( 0\) , \( -57 a - 345\) , \( -1521 a + 585\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-57a-345\right){x}-1521a+585$ |
| 612.1-f4 |
612.1-f |
$4$ |
$6$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
612.1 |
\( 2^{2} \cdot 3^{2} \cdot 17 \) |
\( - 2^{39} \cdot 3^{2} \cdot 17^{6} \) |
$1.83253$ |
$(-a+2), (-a-1), (-2a+1), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$9$ |
\( 2^{3} \cdot 3 \) |
$1$ |
$0.144022077$ |
1.886246168 |
\( \frac{63746903716782243398507}{1978235092992} a + \frac{99544157725677098909465}{1978235092992} \) |
\( \bigl[1\) , \( -a + 1\) , \( 0\) , \( -9762 a - 13020\) , \( -672588 a - 1114656\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-9762a-13020\right){x}-672588a-1114656$ |
| 612.1-g1 |
612.1-g |
$6$ |
$8$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
612.1 |
\( 2^{2} \cdot 3^{2} \cdot 17 \) |
\( - 2^{4} \cdot 3^{16} \cdot 17 \) |
$1.83253$ |
$(-a+2), (-a-1), (-2a+1), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.767023222$ |
$2.106562757$ |
1.567539326 |
\( -\frac{54662458323803}{74358} a + \frac{840124641906185}{446148} \) |
\( \bigl[1\) , \( -a - 1\) , \( a\) , \( 16 a - 62\) , \( 342 a + 192\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(16a-62\right){x}+342a+192$ |
| 612.1-g2 |
612.1-g |
$6$ |
$8$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
612.1 |
\( 2^{2} \cdot 3^{2} \cdot 17 \) |
\( - 2^{17} \cdot 3^{2} \cdot 17^{2} \) |
$1.83253$ |
$(-a+2), (-a-1), (-2a+1), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.383511611$ |
$8.426251030$ |
1.567539326 |
\( -\frac{517728441833}{1114112} a + \frac{3983601888119}{3342336} \) |
\( \bigl[1\) , \( -a\) , \( a + 1\) , \( 10 a - 9\) , \( -15 a + 12\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(10a-9\right){x}-15a+12$ |
| 612.1-g3 |
612.1-g |
$6$ |
$8$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
612.1 |
\( 2^{2} \cdot 3^{2} \cdot 17 \) |
\( 2^{10} \cdot 3^{4} \cdot 17^{4} \) |
$1.83253$ |
$(-a+2), (-a-1), (-2a+1), (3)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$0.191755805$ |
$8.426251030$ |
1.567539326 |
\( -\frac{16457771}{221952} a + \frac{1442536501}{665856} \) |
\( \bigl[1\) , \( a + 1\) , \( a\) , \( 75 a - 189\) , \( -255 a + 653\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(75a-189\right){x}-255a+653$ |
| 612.1-g4 |
612.1-g |
$6$ |
$8$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
612.1 |
\( 2^{2} \cdot 3^{2} \cdot 17 \) |
\( 2^{8} \cdot 3^{8} \cdot 17^{2} \) |
$1.83253$ |
$(-a+2), (-a-1), (-2a+1), (3)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$0.383511611$ |
$8.426251030$ |
1.567539326 |
\( \frac{3831982}{459} a + \frac{1516656161}{22032} \) |
\( \bigl[1\) , \( -a - 1\) , \( a\) , \( -24 a - 42\) , \( 130 a + 196\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-24a-42\right){x}+130a+196$ |
| 612.1-g5 |
612.1-g |
$6$ |
$8$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
612.1 |
\( 2^{2} \cdot 3^{2} \cdot 17 \) |
\( - 2^{5} \cdot 3^{2} \cdot 17^{8} \) |
$1.83253$ |
$(-a+2), (-a-1), (-2a+1), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$0.383511611$ |
$2.106562757$ |
1.567539326 |
\( \frac{335289536353}{1336336} a + \frac{1575899784281}{4009008} \) |
\( \bigl[1\) , \( a + 1\) , \( a\) , \( -255 a + 651\) , \( -1815 a + 4637\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-255a+651\right){x}-1815a+4637$ |
| 612.1-g6 |
612.1-g |
$6$ |
$8$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
612.1 |
\( 2^{2} \cdot 3^{2} \cdot 17 \) |
\( - 2^{10} \cdot 3^{4} \cdot 17 \) |
$1.83253$ |
$(-a+2), (-a-1), (-2a+1), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.191755805$ |
$8.426251030$ |
1.567539326 |
\( \frac{25352251372987}{13056} a + \frac{29691659581885}{9792} \) |
\( \bigl[1\) , \( a - 1\) , \( a\) , \( -3 a - 3\) , \( 111 a - 279\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-3a-3\right){x}+111a-279$ |
| 612.1-h1 |
612.1-h |
$2$ |
$2$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
612.1 |
\( 2^{2} \cdot 3^{2} \cdot 17 \) |
\( - 2^{11} \cdot 3^{2} \cdot 17^{2} \) |
$1.83253$ |
$(-a+2), (-a-1), (-2a+1), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \cdot 7 \) |
$0.067296704$ |
$13.67892833$ |
3.125715497 |
\( -\frac{2348860547}{6528} a + \frac{1506032047}{1632} \) |
\( \bigl[1\) , \( -a\) , \( 1\) , \( 8 a + 10\) , \( 5 a + 8\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-a{x}^{2}+\left(8a+10\right){x}+5a+8$ |
| 612.1-h2 |
612.1-h |
$2$ |
$2$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
612.1 |
\( 2^{2} \cdot 3^{2} \cdot 17 \) |
\( - 2^{16} \cdot 3^{4} \cdot 17 \) |
$1.83253$ |
$(-a+2), (-a-1), (-2a+1), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \cdot 7 \) |
$0.033648352$ |
$13.67892833$ |
3.125715497 |
\( \frac{646879387}{835584} a + \frac{367941997}{626688} \) |
\( \bigl[1\) , \( a + 1\) , \( 0\) , \( 7 a - 14\) , \( -23 a + 60\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(7a-14\right){x}-23a+60$ |
| 612.1-i1 |
612.1-i |
$2$ |
$2$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
612.1 |
\( 2^{2} \cdot 3^{2} \cdot 17 \) |
\( - 2^{16} \cdot 3^{4} \cdot 17 \) |
$1.83253$ |
$(-a+2), (-a-1), (-2a+1), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \cdot 7 \) |
$0.033648352$ |
$13.67892833$ |
3.125715497 |
\( -\frac{646879387}{835584} a + \frac{3412406149}{2506752} \) |
\( \bigl[1\) , \( -a - 1\) , \( 1\) , \( -5 a - 9\) , \( 29 a + 45\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-5a-9\right){x}+29a+45$ |
| 612.1-i2 |
612.1-i |
$2$ |
$2$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
612.1 |
\( 2^{2} \cdot 3^{2} \cdot 17 \) |
\( - 2^{11} \cdot 3^{2} \cdot 17^{2} \) |
$1.83253$ |
$(-a+2), (-a-1), (-2a+1), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \cdot 7 \) |
$0.067296704$ |
$13.67892833$ |
3.125715497 |
\( \frac{2348860547}{6528} a + \frac{3675267641}{6528} \) |
\( \bigl[1\) , \( a - 1\) , \( 1\) , \( -8 a + 18\) , \( -5 a + 13\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-8a+18\right){x}-5a+13$ |
| 612.1-j1 |
612.1-j |
$6$ |
$8$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
612.1 |
\( 2^{2} \cdot 3^{2} \cdot 17 \) |
\( - 2^{5} \cdot 3^{2} \cdot 17^{8} \) |
$1.83253$ |
$(-a+2), (-a-1), (-2a+1), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$16$ |
\( 2^{5} \) |
$1$ |
$0.145250350$ |
4.509233219 |
\( -\frac{272053023767751340411}{4009008} a + \frac{696878183520625294751}{4009008} \) |
\( \bigl[1\) , \( -a + 1\) , \( a + 1\) , \( -6007 a - 10823\) , \( -388147 a - 628623\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-6007a-10823\right){x}-388147a-628623$ |
| 612.1-j2 |
612.1-j |
$6$ |
$8$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
612.1 |
\( 2^{2} \cdot 3^{2} \cdot 17 \) |
\( - 2^{34} \cdot 3^{4} \cdot 17 \) |
$1.83253$ |
$(-a+2), (-a-1), (-2a+1), (3)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{7} \) |
$1$ |
$2.324005606$ |
4.509233219 |
\( -\frac{772974353612923}{219043332096} a + \frac{5606437348248485}{657129996288} \) |
\( \bigl[1\) , \( 0\) , \( 0\) , \( 196 a - 505\) , \( -2004 a + 5129\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(196a-505\right){x}-2004a+5129$ |
| 612.1-j3 |
612.1-j |
$6$ |
$8$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
612.1 |
\( 2^{2} \cdot 3^{2} \cdot 17 \) |
\( - 2^{16} \cdot 3^{16} \cdot 17 \) |
$1.83253$ |
$(-a+2), (-a-1), (-2a+1), (3)$ |
0 |
$\Z/8\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{9} \) |
$1$ |
$2.324005606$ |
4.509233219 |
\( \frac{1763114683}{4758912} a + \frac{30922769255}{28553472} \) |
\( \bigl[1\) , \( a\) , \( a\) , \( -34 a + 76\) , \( 219 a - 580\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+a{x}^{2}+\left(-34a+76\right){x}+219a-580$ |
| 612.1-j4 |
612.1-j |
$6$ |
$8$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
612.1 |
\( 2^{2} \cdot 3^{2} \cdot 17 \) |
\( 2^{20} \cdot 3^{8} \cdot 17^{2} \) |
$1.83253$ |
$(-a+2), (-a-1), (-2a+1), (3)$ |
0 |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{9} \) |
$1$ |
$2.324005606$ |
4.509233219 |
\( \frac{8609976710797}{30081024} a + \frac{40775485333421}{90243072} \) |
\( \bigl[1\) , \( -a + 1\) , \( a + 1\) , \( -397 a - 623\) , \( -6013 a - 9399\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-397a-623\right){x}-6013a-9399$ |
| 612.1-j5 |
612.1-j |
$6$ |
$8$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
612.1 |
\( 2^{2} \cdot 3^{2} \cdot 17 \) |
\( 2^{10} \cdot 3^{4} \cdot 17^{4} \) |
$1.83253$ |
$(-a+2), (-a-1), (-2a+1), (3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$4$ |
\( 2^{7} \) |
$1$ |
$0.581001401$ |
4.509233219 |
\( \frac{75498472794434789}{221952} a + \frac{353695695997329221}{665856} \) |
\( \bigl[1\) , \( -a + 1\) , \( a + 1\) , \( -6337 a - 9983\) , \( -393337 a - 614631\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-6337a-9983\right){x}-393337a-614631$ |
| 612.1-j6 |
612.1-j |
$6$ |
$8$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
612.1 |
\( 2^{2} \cdot 3^{2} \cdot 17 \) |
\( - 2^{5} \cdot 3^{2} \cdot 17^{2} \) |
$1.83253$ |
$(-a+2), (-a-1), (-2a+1), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$64$ |
\( 2^{3} \) |
$1$ |
$0.145250350$ |
4.509233219 |
\( \frac{389298908879232008322837611}{816} a + \frac{607910806183773254485392689}{816} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( 89804 a - 230134\) , \( 25887554 a - 66312741\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}+\left(89804a-230134\right){x}+25887554a-66312741$ |
| 612.1-k1 |
612.1-k |
$4$ |
$6$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
612.1 |
\( 2^{2} \cdot 3^{2} \cdot 17 \) |
\( - 2^{45} \cdot 3^{6} \cdot 17^{2} \) |
$1.83253$ |
$(-a+2), (-a-1), (-2a+1), (3)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{3} \cdot 3^{3} \) |
$1$ |
$1.296198698$ |
1.886246168 |
\( -\frac{49436370625448675}{31542239821824} a + \frac{108464468186272447}{31542239821824} \) |
\( \bigl[1\) , \( a\) , \( 0\) , \( 57 a - 402\) , \( 1521 a - 936\bigr] \) |
${y}^2+{x}{y}={x}^{3}+a{x}^{2}+\left(57a-402\right){x}+1521a-936$ |
| 612.1-k2 |
612.1-k |
$4$ |
$6$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
612.1 |
\( 2^{2} \cdot 3^{2} \cdot 17 \) |
\( - 2^{39} \cdot 3^{2} \cdot 17^{6} \) |
$1.83253$ |
$(-a+2), (-a-1), (-2a+1), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$9$ |
\( 2^{3} \cdot 3 \) |
$1$ |
$0.144022077$ |
1.886246168 |
\( -\frac{63746903716782243398507}{1978235092992} a + \frac{40822765360614835576993}{494558773248} \) |
\( \bigl[1\) , \( a\) , \( 0\) , \( 9762 a - 22782\) , \( 672588 a - 1787244\bigr] \) |
${y}^2+{x}{y}={x}^{3}+a{x}^{2}+\left(9762a-22782\right){x}+672588a-1787244$ |
| 612.1-k3 |
612.1-k |
$4$ |
$6$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
612.1 |
\( 2^{2} \cdot 3^{2} \cdot 17 \) |
\( - 2^{60} \cdot 3^{4} \cdot 17^{3} \) |
$1.83253$ |
$(-a+2), (-a-1), (-2a+1), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$9$ |
\( 2^{3} \cdot 3 \) |
$1$ |
$0.144022077$ |
1.886246168 |
\( \frac{1397539108647287243438603}{15618483507720880128} a - \frac{2624297843126603203545475}{11713862630790660096} \) |
\( \bigl[1\) , \( -a + 1\) , \( 1\) , \( 92659 a - 237459\) , \( 22192717 a - 56848123\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(92659a-237459\right){x}+22192717a-56848123$ |
| 612.1-k4 |
612.1-k |
$4$ |
$6$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
612.1 |
\( 2^{2} \cdot 3^{2} \cdot 17 \) |
\( - 2^{36} \cdot 3^{12} \cdot 17 \) |
$1.83253$ |
$(-a+2), (-a-1), (-2a+1), (3)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{3} \cdot 3^{3} \) |
$1$ |
$1.296198698$ |
1.886246168 |
\( \frac{59582139343925}{180486144} a + \frac{1675978272447751}{3248750592} \) |
\( \bigl[1\) , \( -a + 1\) , \( 1\) , \( -2246 a + 5721\) , \( 152779 a - 391267\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-2246a+5721\right){x}+152779a-391267$ |
| 612.1-l1 |
612.1-l |
$8$ |
$12$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
612.1 |
\( 2^{2} \cdot 3^{2} \cdot 17 \) |
\( 2^{6} \cdot 3^{24} \cdot 17^{4} \) |
$1.83253$ |
$(-a+2), (-a-1), (-2a+1), (3)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{3} \cdot 3 \) |
$2.670603982$ |
$1.940539524$ |
1.675892899 |
\( -\frac{1107111813625}{1228691592} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -216\) , \( 2062\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-216{x}+2062$ |
| 612.1-l2 |
612.1-l |
$8$ |
$12$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
612.1 |
\( 2^{2} \cdot 3^{2} \cdot 17 \) |
\( 2^{18} \cdot 3^{8} \cdot 17^{12} \) |
$1.83253$ |
$(-a+2), (-a-1), (-2a+1), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2^{3} \) |
$8.011811947$ |
$0.215615502$ |
1.675892899 |
\( \frac{655215969476375}{1001033261568} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( 1809\) , \( -37790\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+1809{x}-37790$ |
| 612.1-l3 |
612.1-l |
$8$ |
$12$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
612.1 |
\( 2^{2} \cdot 3^{2} \cdot 17 \) |
\( 2^{15} \cdot 3^{6} \cdot 17 \) |
$1.83253$ |
$(-a+2), (-a-1), (-2a+1), (3)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2 \cdot 3 \) |
$2.670603982$ |
$7.762158097$ |
1.675892899 |
\( -\frac{2465827881495290125}{1880064} a + \frac{1579087087568258375}{470016} \) |
\( \bigl[1\) , \( -a + 1\) , \( a\) , \( -1941 a - 3037\) , \( 36391 a + 56829\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-1941a-3037\right){x}+36391a+56829$ |
| 612.1-l4 |
612.1-l |
$8$ |
$12$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
612.1 |
\( 2^{2} \cdot 3^{2} \cdot 17 \) |
\( 2^{36} \cdot 3^{4} \cdot 17^{6} \) |
$1.83253$ |
$(-a+2), (-a-1), (-2a+1), (3)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2Cs, 3B.1.2 |
$1$ |
\( 2^{4} \) |
$4.005905973$ |
$0.862462010$ |
1.675892899 |
\( \frac{46753267515625}{11591221248} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -751\) , \( -6046\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-751{x}-6046$ |
*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.
