| 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 |
$6$ |
$18$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
196.1 |
\( 2^{2} \cdot 7^{2} \) |
\( - 2^{9} \cdot 7^{6} \) |
$2.52429$ |
$(a-4), (a+3), (2a+7), (-2a+9)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$9$ |
\( 2^{4} \cdot 3^{2} \) |
$1$ |
$0.202973786$ |
8.710589250 |
\( -\frac{69448190842641982779}{153664} a + \frac{148442628895451136037}{76832} \) |
\( \bigl[1\) , \( a - 1\) , \( a + 1\) , \( -719561 a - 2356498\) , \( -646387150 a - 2116864409\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-719561a-2356498\right){x}-646387150a-2116864409$ |
| 196.1-a2 |
196.1-a |
$6$ |
$18$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
196.1 |
\( 2^{2} \cdot 7^{2} \) |
\( - 2^{27} \cdot 7^{18} \) |
$2.52429$ |
$(a-4), (a+3), (2a+7), (-2a+9)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 3$ |
2B, 3Cs.1.1 |
$1$ |
\( 2^{4} \cdot 3^{6} \) |
$1$ |
$0.202973786$ |
8.710589250 |
\( -\frac{72721693282319026275}{3628410392018944} a + \frac{155398606541888511841}{1814205196009472} \) |
\( \bigl[1\) , \( a - 1\) , \( a + 1\) , \( -284721 a - 932433\) , \( -1414418097 a - 4632102181\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-284721a-932433\right){x}-1414418097a-4632102181$ |
| 196.1-a3 |
196.1-a |
$6$ |
$18$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
196.1 |
\( 2^{2} \cdot 7^{2} \) |
\( - 2^{81} \cdot 7^{6} \) |
$2.52429$ |
$(a-4), (a+3), (2a+7), (-2a+9)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{4} \cdot 3^{6} \) |
$1$ |
$0.202973786$ |
8.710589250 |
\( -\frac{122334963786919556603939}{43252570821266243584} a + \frac{261970144644601191214497}{21626285410633121792} \) |
\( \bigl[1\) , \( a - 1\) , \( a + 1\) , \( 2557279 a + 8374872\) , \( 37750816060 a + 123630797521\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(2557279a+8374872\right){x}+37750816060a+123630797521$ |
| 196.1-a4 |
196.1-a |
$6$ |
$18$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
196.1 |
\( 2^{2} \cdot 7^{2} \) |
\( - 2^{81} \cdot 7^{6} \) |
$2.52429$ |
$(a-4), (a+3), (2a+7), (-2a+9)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{4} \cdot 3^{6} \) |
$1$ |
$0.202973786$ |
8.710589250 |
\( \frac{122334963786919556603939}{43252570821266243584} a + \frac{57372189357468975117865}{6178938688752320512} \) |
\( \bigl[1\) , \( -a\) , \( a\) , \( -2557280 a + 10932152\) , \( -37750816061 a + 161381613582\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}-a{x}^{2}+\left(-2557280a+10932152\right){x}-37750816061a+161381613582$ |
| 196.1-a5 |
196.1-a |
$6$ |
$18$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
196.1 |
\( 2^{2} \cdot 7^{2} \) |
\( - 2^{27} \cdot 7^{18} \) |
$2.52429$ |
$(a-4), (a+3), (2a+7), (-2a+9)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 3$ |
2B, 3Cs.1.1 |
$1$ |
\( 2^{4} \cdot 3^{6} \) |
$1$ |
$0.202973786$ |
8.710589250 |
\( \frac{72721693282319026275}{3628410392018944} a + \frac{34010788543065428201}{518344341716992} \) |
\( \bigl[1\) , \( -a\) , \( a\) , \( 284720 a - 1217153\) , \( 1414418096 a - 6046520277\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}-a{x}^{2}+\left(284720a-1217153\right){x}+1414418096a-6046520277$ |
| 196.1-a6 |
196.1-a |
$6$ |
$18$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
196.1 |
\( 2^{2} \cdot 7^{2} \) |
\( - 2^{9} \cdot 7^{6} \) |
$2.52429$ |
$(a-4), (a+3), (2a+7), (-2a+9)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$9$ |
\( 2^{4} \cdot 3^{2} \) |
$1$ |
$0.202973786$ |
8.710589250 |
\( \frac{69448190842641982779}{153664} a + \frac{32491009564037184185}{21952} \) |
\( \bigl[1\) , \( -a\) , \( a\) , \( 719560 a - 3076058\) , \( 646387149 a - 2763251558\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}-a{x}^{2}+\left(719560a-3076058\right){x}+646387149a-2763251558$ |
| 196.1-b1 |
196.1-b |
$2$ |
$2$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
196.1 |
\( 2^{2} \cdot 7^{2} \) |
\( - 2^{19} \cdot 7^{6} \) |
$2.52429$ |
$(a-4), (a+3), (2a+7), (-2a+9)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$0.737540134$ |
$3.868396811$ |
3.023216394 |
\( -\frac{9459305507}{39337984} a + \frac{20218851489}{19668992} \) |
\( \bigl[1\) , \( 1\) , \( 0\) , \( -362 a - 1185\) , \( -8952728 a - 29319443\bigr] \) |
${y}^2+{x}{y}={x}^{3}+{x}^{2}+\left(-362a-1185\right){x}-8952728a-29319443$ |
| 196.1-b2 |
196.1-b |
$2$ |
$2$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
196.1 |
\( 2^{2} \cdot 7^{2} \) |
\( - 2^{17} \cdot 7^{6} \) |
$2.52429$ |
$(a-4), (a+3), (2a+7), (-2a+9)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1.475080269$ |
$3.868396811$ |
3.023216394 |
\( \frac{17700018491}{2458624} a + \frac{8858353849}{351232} \) |
\( \bigl[1\) , \( a - 1\) , \( a\) , \( -1226 a + 5243\) , \( -8599 a + 36757\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-1226a+5243\right){x}-8599a+36757$ |
| 196.1-c1 |
196.1-c |
$8$ |
$12$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
196.1 |
\( 2^{2} \cdot 7^{2} \) |
\( 2^{16} \cdot 7^{4} \) |
$2.52429$ |
$(a-4), (a+3), (2a+7), (-2a+9)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{4} \cdot 3 \) |
$1$ |
$9.878018431$ |
3.925126510 |
\( -\frac{5197213125}{1404928} a - \frac{7402883625}{702464} \) |
\( \bigl[1\) , \( -a + 1\) , \( a + 1\) , \( -491 a - 1600\) , \( 12334 a + 40395\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-491a-1600\right){x}+12334a+40395$ |
| 196.1-c2 |
196.1-c |
$8$ |
$12$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
196.1 |
\( 2^{2} \cdot 7^{2} \) |
\( 2^{16} \cdot 7^{4} \) |
$2.52429$ |
$(a-4), (a+3), (2a+7), (-2a+9)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{4} \cdot 3 \) |
$1$ |
$9.878018431$ |
3.925126510 |
\( \frac{5197213125}{1404928} a - \frac{2857568625}{200704} \) |
\( \bigl[1\) , \( a\) , \( a\) , \( 490 a - 2090\) , \( -12335 a + 52730\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+a{x}^{2}+\left(490a-2090\right){x}-12335a+52730$ |
| 196.1-c3 |
196.1-c |
$8$ |
$12$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
196.1 |
\( 2^{2} \cdot 7^{2} \) |
\( 2^{8} \cdot 7^{8} \) |
$2.52429$ |
$(a-4), (a+3), (2a+7), (-2a+9)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 3$ |
2Cs, 3B |
$1$ |
\( 2^{4} \cdot 3 \) |
$1$ |
$9.878018431$ |
3.925126510 |
\( -\frac{731856197548125}{7529536} a + \frac{446948414969625}{1075648} \) |
\( \bigl[1\) , \( a\) , \( a\) , \( 7910 a - 33810\) , \( -751991 a + 3214698\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+a{x}^{2}+\left(7910a-33810\right){x}-751991a+3214698$ |
| 196.1-c4 |
196.1-c |
$8$ |
$12$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
196.1 |
\( 2^{2} \cdot 7^{2} \) |
\( 2^{4} \cdot 7^{16} \) |
$2.52429$ |
$(a-4), (a+3), (2a+7), (-2a+9)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 3$ |
2B, 3B |
$4$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$2.469504607$ |
3.925126510 |
\( -\frac{1208244364806375}{110730297608} a + \frac{4123971273387375}{55365148804} \) |
\( \bigl[1\) , \( -a + 1\) , \( a + 1\) , \( -7981 a - 26130\) , \( 738202 a + 2417551\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-7981a-26130\right){x}+738202a+2417551$ |
| 196.1-c5 |
196.1-c |
$8$ |
$12$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
196.1 |
\( 2^{2} \cdot 7^{2} \) |
\( 2^{4} \cdot 7^{16} \) |
$2.52429$ |
$(a-4), (a+3), (2a+7), (-2a+9)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 3$ |
2B, 3B |
$4$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$2.469504607$ |
3.925126510 |
\( \frac{1208244364806375}{110730297608} a + \frac{1005671168852625}{15818613944} \) |
\( \bigl[1\) , \( a\) , \( a\) , \( 7980 a - 34110\) , \( -738203 a + 3155754\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+a{x}^{2}+\left(7980a-34110\right){x}-738203a+3155754$ |
| 196.1-c6 |
196.1-c |
$8$ |
$12$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
196.1 |
\( 2^{2} \cdot 7^{2} \) |
\( 2^{4} \cdot 7^{4} \) |
$2.52429$ |
$(a-4), (a+3), (2a+7), (-2a+9)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 3$ |
2B, 3B |
$4$ |
\( 3 \) |
$1$ |
$9.878018431$ |
3.925126510 |
\( -\frac{195721247496543926625}{2744} a + \frac{119527447254612089625}{392} \) |
\( \bigl[1\) , \( a\) , \( a\) , \( 126560 a - 541030\) , \( -47744643 a + 204104394\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+a{x}^{2}+\left(126560a-541030\right){x}-47744643a+204104394$ |
| 196.1-c7 |
196.1-c |
$8$ |
$12$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
196.1 |
\( 2^{2} \cdot 7^{2} \) |
\( 2^{8} \cdot 7^{8} \) |
$2.52429$ |
$(a-4), (a+3), (2a+7), (-2a+9)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 3$ |
2Cs, 3B |
$1$ |
\( 2^{4} \cdot 3 \) |
$1$ |
$9.878018431$ |
3.925126510 |
\( \frac{731856197548125}{7529536} a + \frac{1198391353619625}{3764768} \) |
\( \bigl[1\) , \( -a + 1\) , \( a + 1\) , \( -7911 a - 25900\) , \( 751990 a + 2462707\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-7911a-25900\right){x}+751990a+2462707$ |
| 196.1-c8 |
196.1-c |
$8$ |
$12$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
196.1 |
\( 2^{2} \cdot 7^{2} \) |
\( 2^{4} \cdot 7^{4} \) |
$2.52429$ |
$(a-4), (a+3), (2a+7), (-2a+9)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 3$ |
2B, 3B |
$4$ |
\( 3 \) |
$1$ |
$9.878018431$ |
3.925126510 |
\( \frac{195721247496543926625}{2744} a + \frac{320485441642870350375}{1372} \) |
\( \bigl[1\) , \( -a + 1\) , \( a + 1\) , \( -126561 a - 414470\) , \( 47744642 a + 156359751\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-126561a-414470\right){x}+47744642a+156359751$ |
| 196.1-d1 |
196.1-d |
$2$ |
$2$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
196.1 |
\( 2^{2} \cdot 7^{2} \) |
\( - 2^{17} \cdot 7^{6} \) |
$2.52429$ |
$(a-4), (a+3), (2a+7), (-2a+9)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1.475080269$ |
$3.868396811$ |
3.023216394 |
\( -\frac{17700018491}{2458624} a + \frac{39854247717}{1229312} \) |
\( \bigl[1\) , \( -a\) , \( a + 1\) , \( 1225 a + 4017\) , \( 8598 a + 28158\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(1225a+4017\right){x}+8598a+28158$ |
| 196.1-d2 |
196.1-d |
$2$ |
$2$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
196.1 |
\( 2^{2} \cdot 7^{2} \) |
\( - 2^{19} \cdot 7^{6} \) |
$2.52429$ |
$(a-4), (a+3), (2a+7), (-2a+9)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$0.737540134$ |
$3.868396811$ |
3.023216394 |
\( \frac{9459305507}{39337984} a + \frac{4425485353}{5619712} \) |
\( \bigl[1\) , \( 1\) , \( 0\) , \( 362 a - 1547\) , \( 8952728 a - 38272171\bigr] \) |
${y}^2+{x}{y}={x}^{3}+{x}^{2}+\left(362a-1547\right){x}+8952728a-38272171$ |
| 196.1-e1 |
196.1-e |
$6$ |
$18$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
196.1 |
\( 2^{2} \cdot 7^{2} \) |
\( 2^{36} \cdot 7^{2} \) |
$2.52429$ |
$(a-4), (a+3), (2a+7), (-2a+9)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{2} \cdot 3^{4} \) |
$1$ |
$7.027708105$ |
8.377584104 |
\( -\frac{548347731625}{1835008} \) |
\( \bigl[1\) , \( -a\) , \( a\) , \( -2059892 a - 6745970\) , \( 3138470553 a + 10278231250\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}-a{x}^{2}+\left(-2059892a-6745970\right){x}+3138470553a+10278231250$ |
| 196.1-e2 |
196.1-e |
$6$ |
$18$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
196.1 |
\( 2^{2} \cdot 7^{2} \) |
\( 2^{4} \cdot 7^{2} \) |
$2.52429$ |
$(a-4), (a+3), (2a+7), (-2a+9)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$9$ |
\( 2^{2} \) |
$1$ |
$7.027708105$ |
8.377584104 |
\( -\frac{15625}{28} \) |
\( \bigl[1\) , \( -a\) , \( a\) , \( -6292 a - 20600\) , \( -1059817 a - 3470814\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}-a{x}^{2}+\left(-6292a-20600\right){x}-1059817a-3470814$ |
| 196.1-e3 |
196.1-e |
$6$ |
$18$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
196.1 |
\( 2^{2} \cdot 7^{2} \) |
\( 2^{12} \cdot 7^{6} \) |
$2.52429$ |
$(a-4), (a+3), (2a+7), (-2a+9)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3Cs.1.1 |
$1$ |
\( 2^{2} \cdot 3^{4} \) |
$1$ |
$7.027708105$ |
8.377584104 |
\( \frac{9938375}{21952} \) |
\( \bigl[1\) , \( -a\) , \( a\) , \( 54108 a + 177205\) , \( 22267918 a + 72925587\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}-a{x}^{2}+\left(54108a+177205\right){x}+22267918a+72925587$ |
| 196.1-e4 |
196.1-e |
$6$ |
$18$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
196.1 |
\( 2^{2} \cdot 7^{2} \) |
\( 2^{6} \cdot 7^{12} \) |
$2.52429$ |
$(a-4), (a+3), (2a+7), (-2a+9)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3Cs.1.1 |
$1$ |
\( 2^{2} \cdot 3^{4} \) |
$1$ |
$7.027708105$ |
8.377584104 |
\( \frac{4956477625}{941192} \) |
\( \bigl[1\) , \( -a\) , \( a\) , \( -429092 a - 1405235\) , \( 244235478 a + 799850971\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}-a{x}^{2}+\left(-429092a-1405235\right){x}+244235478a+799850971$ |
| 196.1-e5 |
196.1-e |
$6$ |
$18$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
196.1 |
\( 2^{2} \cdot 7^{2} \) |
\( 2^{2} \cdot 7^{4} \) |
$2.52429$ |
$(a-4), (a+3), (2a+7), (-2a+9)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$9$ |
\( 2^{2} \) |
$1$ |
$7.027708105$ |
8.377584104 |
\( \frac{128787625}{98} \) |
\( \bigl[1\) , \( -a\) , \( a\) , \( -127092 a - 416210\) , \( -47715287 a - 156263616\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}-a{x}^{2}+\left(-127092a-416210\right){x}-47715287a-156263616$ |
| 196.1-e6 |
196.1-e |
$6$ |
$18$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
196.1 |
\( 2^{2} \cdot 7^{2} \) |
\( 2^{18} \cdot 7^{4} \) |
$2.52429$ |
$(a-4), (a+3), (2a+7), (-2a+9)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{2} \cdot 3^{4} \) |
$1$ |
$7.027708105$ |
8.377584104 |
\( \frac{2251439055699625}{25088} \) |
\( \bigl[1\) , \( -a\) , \( a\) , \( -32984692 a - 108022130\) , \( 200392463513 a + 656268729042\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}-a{x}^{2}+\left(-32984692a-108022130\right){x}+200392463513a+656268729042$ |
| 196.1-f1 |
196.1-f |
$8$ |
$12$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
196.1 |
\( 2^{2} \cdot 7^{2} \) |
\( 2^{16} \cdot 7^{4} \) |
$2.52429$ |
$(a-4), (a+3), (2a+7), (-2a+9)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \) |
$1$ |
$2.807395548$ |
0.371848624 |
\( -\frac{5197213125}{1404928} a - \frac{7402883625}{702464} \) |
\( \bigl[1\) , \( a\) , \( a + 1\) , \( -265 a + 1137\) , \( 1682 a - 7194\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(-265a+1137\right){x}+1682a-7194$ |
| 196.1-f2 |
196.1-f |
$8$ |
$12$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
196.1 |
\( 2^{2} \cdot 7^{2} \) |
\( 2^{16} \cdot 7^{4} \) |
$2.52429$ |
$(a-4), (a+3), (2a+7), (-2a+9)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \) |
$1$ |
$2.807395548$ |
0.371848624 |
\( \frac{5197213125}{1404928} a - \frac{2857568625}{200704} \) |
\( \bigl[1\) , \( -a + 1\) , \( a\) , \( 264 a + 873\) , \( -1683 a - 5511\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(264a+873\right){x}-1683a-5511$ |
| 196.1-f3 |
196.1-f |
$8$ |
$12$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
196.1 |
\( 2^{2} \cdot 7^{2} \) |
\( 2^{8} \cdot 7^{8} \) |
$2.52429$ |
$(a-4), (a+3), (2a+7), (-2a+9)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 3$ |
2Cs, 3B |
$1$ |
\( 2^{4} \) |
$1$ |
$2.807395548$ |
0.371848624 |
\( -\frac{731856197548125}{7529536} a + \frac{446948414969625}{1075648} \) |
\( \bigl[1\) , \( -a + 1\) , \( a\) , \( -1116 a - 3647\) , \( -10467 a - 34279\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-1116a-3647\right){x}-10467a-34279$ |
| 196.1-f4 |
196.1-f |
$8$ |
$12$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
196.1 |
\( 2^{2} \cdot 7^{2} \) |
\( 2^{4} \cdot 7^{16} \) |
$2.52429$ |
$(a-4), (a+3), (2a+7), (-2a+9)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \) |
$1$ |
$2.807395548$ |
0.371848624 |
\( -\frac{1208244364806375}{110730297608} a + \frac{4123971273387375}{55365148804} \) |
\( \bigl[1\) , \( a\) , \( a + 1\) , \( 10245 a - 43793\) , \( -1098406 a + 4695590\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(10245a-43793\right){x}-1098406a+4695590$ |
| 196.1-f5 |
196.1-f |
$8$ |
$12$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
196.1 |
\( 2^{2} \cdot 7^{2} \) |
\( 2^{4} \cdot 7^{16} \) |
$2.52429$ |
$(a-4), (a+3), (2a+7), (-2a+9)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \) |
$1$ |
$2.807395548$ |
0.371848624 |
\( \frac{1208244364806375}{110730297608} a + \frac{1005671168852625}{15818613944} \) |
\( \bigl[1\) , \( -a + 1\) , \( a\) , \( -10246 a - 33547\) , \( 1098405 a + 3597185\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-10246a-33547\right){x}+1098405a+3597185$ |
| 196.1-f6 |
196.1-f |
$8$ |
$12$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
196.1 |
\( 2^{2} \cdot 7^{2} \) |
\( 2^{4} \cdot 7^{4} \) |
$2.52429$ |
$(a-4), (a+3), (2a+7), (-2a+9)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 3$ |
2B, 3B |
$16$ |
\( 1 \) |
$1$ |
$0.701848887$ |
0.371848624 |
\( -\frac{195721247496543926625}{2744} a + \frac{119527447254612089625}{392} \) |
\( \bigl[1\) , \( -a + 1\) , \( a\) , \( -14066 a - 46067\) , \( -1748315 a - 5725615\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-14066a-46067\right){x}-1748315a-5725615$ |
| 196.1-f7 |
196.1-f |
$8$ |
$12$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
196.1 |
\( 2^{2} \cdot 7^{2} \) |
\( 2^{8} \cdot 7^{8} \) |
$2.52429$ |
$(a-4), (a+3), (2a+7), (-2a+9)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 3$ |
2Cs, 3B |
$1$ |
\( 2^{4} \) |
$1$ |
$2.807395548$ |
0.371848624 |
\( \frac{731856197548125}{7529536} a + \frac{1198391353619625}{3764768} \) |
\( \bigl[1\) , \( a\) , \( a + 1\) , \( 1115 a - 4763\) , \( 10466 a - 44746\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(1115a-4763\right){x}+10466a-44746$ |
| 196.1-f8 |
196.1-f |
$8$ |
$12$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
196.1 |
\( 2^{2} \cdot 7^{2} \) |
\( 2^{4} \cdot 7^{4} \) |
$2.52429$ |
$(a-4), (a+3), (2a+7), (-2a+9)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 3$ |
2B, 3B |
$16$ |
\( 1 \) |
$1$ |
$0.701848887$ |
0.371848624 |
\( \frac{195721247496543926625}{2744} a + \frac{320485441642870350375}{1372} \) |
\( \bigl[1\) , \( a\) , \( a + 1\) , \( 14065 a - 60133\) , \( 1748314 a - 7473930\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(14065a-60133\right){x}+1748314a-7473930$ |
| 196.1-g1 |
196.1-g |
$2$ |
$2$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
196.1 |
\( 2^{2} \cdot 7^{2} \) |
\( - 2^{17} \cdot 7^{6} \) |
$2.52429$ |
$(a-4), (a+3), (2a+7), (-2a+9)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \cdot 5 \cdot 7 \) |
$0.052906623$ |
$6.339381956$ |
6.219386851 |
\( -\frac{17700018491}{2458624} a + \frac{39854247717}{1229312} \) |
\( \bigl[1\) , \( 0\) , \( 0\) , \( 637 a - 2723\) , \( -16685 a + 71327\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(637a-2723\right){x}-16685a+71327$ |
| 196.1-g2 |
196.1-g |
$2$ |
$2$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
196.1 |
\( 2^{2} \cdot 7^{2} \) |
\( - 2^{19} \cdot 7^{6} \) |
$2.52429$ |
$(a-4), (a+3), (2a+7), (-2a+9)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{4} \cdot 5 \cdot 7 \) |
$0.026453311$ |
$6.339381956$ |
6.219386851 |
\( \frac{9459305507}{39337984} a + \frac{4425485353}{5619712} \) |
\( \bigl[1\) , \( a + 1\) , \( a + 1\) , \( -9 a - 27\) , \( -25 a - 81\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-9a-27\right){x}-25a-81$ |
| 196.1-h1 |
196.1-h |
$6$ |
$18$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
196.1 |
\( 2^{2} \cdot 7^{2} \) |
\( 2^{36} \cdot 7^{2} \) |
$2.52429$ |
$(a-4), (a+3), (2a+7), (-2a+9)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$9$ |
\( 2^{2} \) |
$1$ |
$0.436190660$ |
0.519973779 |
\( -\frac{548347731625}{1835008} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -171\) , \( -874\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-171{x}-874$ |
| 196.1-h2 |
196.1-h |
$6$ |
$18$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
196.1 |
\( 2^{2} \cdot 7^{2} \) |
\( 2^{4} \cdot 7^{2} \) |
$2.52429$ |
$(a-4), (a+3), (2a+7), (-2a+9)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{2} \) |
$1$ |
$35.33144352$ |
0.519973779 |
\( -\frac{15625}{28} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -1\) , \( 0\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}$ |
| 196.1-h3 |
196.1-h |
$6$ |
$18$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
196.1 |
\( 2^{2} \cdot 7^{2} \) |
\( 2^{12} \cdot 7^{6} \) |
$2.52429$ |
$(a-4), (a+3), (2a+7), (-2a+9)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3Cs.1.1 |
$1$ |
\( 2^{2} \cdot 3^{2} \) |
$1$ |
$3.925715946$ |
0.519973779 |
\( \frac{9938375}{21952} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( 4\) , \( -6\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+4{x}-6$ |
| 196.1-h4 |
196.1-h |
$6$ |
$18$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
196.1 |
\( 2^{2} \cdot 7^{2} \) |
\( 2^{6} \cdot 7^{12} \) |
$2.52429$ |
$(a-4), (a+3), (2a+7), (-2a+9)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3Cs.1.1 |
$1$ |
\( 2^{2} \cdot 3^{2} \) |
$1$ |
$3.925715946$ |
0.519973779 |
\( \frac{4956477625}{941192} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -36\) , \( -70\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-36{x}-70$ |
| 196.1-h5 |
196.1-h |
$6$ |
$18$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
196.1 |
\( 2^{2} \cdot 7^{2} \) |
\( 2^{2} \cdot 7^{4} \) |
$2.52429$ |
$(a-4), (a+3), (2a+7), (-2a+9)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{2} \) |
$1$ |
$35.33144352$ |
0.519973779 |
\( \frac{128787625}{98} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -11\) , \( 12\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-11{x}+12$ |
| 196.1-h6 |
196.1-h |
$6$ |
$18$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
196.1 |
\( 2^{2} \cdot 7^{2} \) |
\( 2^{18} \cdot 7^{4} \) |
$2.52429$ |
$(a-4), (a+3), (2a+7), (-2a+9)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$9$ |
\( 2^{2} \) |
$1$ |
$0.436190660$ |
0.519973779 |
\( \frac{2251439055699625}{25088} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -2731\) , \( -55146\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-2731{x}-55146$ |
| 196.1-i1 |
196.1-i |
$2$ |
$2$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
196.1 |
\( 2^{2} \cdot 7^{2} \) |
\( - 2^{19} \cdot 7^{6} \) |
$2.52429$ |
$(a-4), (a+3), (2a+7), (-2a+9)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{4} \cdot 5 \cdot 7 \) |
$0.026453311$ |
$6.339381956$ |
6.219386851 |
\( -\frac{9459305507}{39337984} a + \frac{20218851489}{19668992} \) |
\( \bigl[1\) , \( -a - 1\) , \( a + 1\) , \( 10 a - 37\) , \( 14 a - 69\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(10a-37\right){x}+14a-69$ |
| 196.1-i2 |
196.1-i |
$2$ |
$2$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
196.1 |
\( 2^{2} \cdot 7^{2} \) |
\( - 2^{17} \cdot 7^{6} \) |
$2.52429$ |
$(a-4), (a+3), (2a+7), (-2a+9)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \cdot 5 \cdot 7 \) |
$0.052906623$ |
$6.339381956$ |
6.219386851 |
\( \frac{17700018491}{2458624} a + \frac{8858353849}{351232} \) |
\( \bigl[1\) , \( 0\) , \( 0\) , \( -637 a - 2086\) , \( 16685 a + 54642\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(-637a-2086\right){x}+16685a+54642$ |
| 196.1-j1 |
196.1-j |
$6$ |
$18$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
196.1 |
\( 2^{2} \cdot 7^{2} \) |
\( - 2^{9} \cdot 7^{6} \) |
$2.52429$ |
$(a-4), (a+3), (2a+7), (-2a+9)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{4} \) |
$1$ |
$6.576937944$ |
0.387171871 |
\( -\frac{69448190842641982779}{153664} a + \frac{148442628895451136037}{76832} \) |
\( \bigl[1\) , \( a + 1\) , \( a\) , \( 22092 a - 94493\) , \( -3489327 a + 14916653\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(22092a-94493\right){x}-3489327a+14916653$ |
| 196.1-j2 |
196.1-j |
$6$ |
$18$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
196.1 |
\( 2^{2} \cdot 7^{2} \) |
\( - 2^{27} \cdot 7^{18} \) |
$2.52429$ |
$(a-4), (a+3), (2a+7), (-2a+9)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 3$ |
2B, 3Cs.1.1 |
$1$ |
\( 2^{4} \cdot 3^{2} \) |
$1$ |
$0.730770882$ |
0.387171871 |
\( -\frac{72721693282319026275}{3628410392018944} a + \frac{155398606541888511841}{1814205196009472} \) |
\( \bigl[1\) , \( a + 1\) , \( a\) , \( 22132 a - 94628\) , \( -3477680 a + 14867140\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(22132a-94628\right){x}-3477680a+14867140$ |
| 196.1-j3 |
196.1-j |
$6$ |
$18$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
196.1 |
\( 2^{2} \cdot 7^{2} \) |
\( - 2^{81} \cdot 7^{6} \) |
$2.52429$ |
$(a-4), (a+3), (2a+7), (-2a+9)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$9$ |
\( 2^{4} \) |
$1$ |
$0.081196764$ |
0.387171871 |
\( -\frac{122334963786919556603939}{43252570821266243584} a + \frac{261970144644601191214497}{21626285410633121792} \) |
\( \bigl[1\) , \( a + 1\) , \( a\) , \( 139732 a - 597123\) , \( 52849143 a - 225935667\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(139732a-597123\right){x}+52849143a-225935667$ |
| 196.1-j4 |
196.1-j |
$6$ |
$18$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
196.1 |
\( 2^{2} \cdot 7^{2} \) |
\( - 2^{81} \cdot 7^{6} \) |
$2.52429$ |
$(a-4), (a+3), (2a+7), (-2a+9)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$9$ |
\( 2^{4} \) |
$1$ |
$0.081196764$ |
0.387171871 |
\( \frac{122334963786919556603939}{43252570821266243584} a + \frac{57372189357468975117865}{6178938688752320512} \) |
\( \bigl[1\) , \( -a - 1\) , \( a\) , \( -139731 a - 457392\) , \( -52709412 a - 172629132\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-139731a-457392\right){x}-52709412a-172629132$ |
| 196.1-j5 |
196.1-j |
$6$ |
$18$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
196.1 |
\( 2^{2} \cdot 7^{2} \) |
\( - 2^{27} \cdot 7^{18} \) |
$2.52429$ |
$(a-4), (a+3), (2a+7), (-2a+9)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 3$ |
2B, 3Cs.1.1 |
$1$ |
\( 2^{4} \cdot 3^{2} \) |
$1$ |
$0.730770882$ |
0.387171871 |
\( \frac{72721693282319026275}{3628410392018944} a + \frac{34010788543065428201}{518344341716992} \) |
\( \bigl[1\) , \( -a - 1\) , \( a\) , \( -22131 a - 72497\) , \( 3499811 a + 11461957\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-22131a-72497\right){x}+3499811a+11461957$ |
| 196.1-j6 |
196.1-j |
$6$ |
$18$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
196.1 |
\( 2^{2} \cdot 7^{2} \) |
\( - 2^{9} \cdot 7^{6} \) |
$2.52429$ |
$(a-4), (a+3), (2a+7), (-2a+9)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{4} \) |
$1$ |
$6.576937944$ |
0.387171871 |
\( \frac{69448190842641982779}{153664} a + \frac{32491009564037184185}{21952} \) |
\( \bigl[1\) , \( -a - 1\) , \( a\) , \( -22091 a - 72402\) , \( 3511418 a + 11499728\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-22091a-72402\right){x}+3511418a+11499728$ |
*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.
