| 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 |
| 180.1-a1 |
180.1-a |
$2$ |
$2$ |
\(\Q(\sqrt{85}) \) |
$2$ |
$[2, 0]$ |
180.1 |
\( 2^{2} \cdot 3^{2} \cdot 5 \) |
\( 2^{4} \cdot 3^{20} \cdot 5^{4} \) |
$3.01763$ |
$(3,a), (3,a+2), (5,a+2), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \cdot 7 \) |
$1$ |
$3.193283145$ |
4.849042622 |
\( -\frac{2344213}{43740} a - \frac{16041071}{72900} \) |
\( \bigl[a + 1\) , \( a - 1\) , \( a\) , \( -13 a - 57\) , \( -264 a - 1099\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-13a-57\right){x}-264a-1099$ |
| 180.1-a2 |
180.1-a |
$2$ |
$2$ |
\(\Q(\sqrt{85}) \) |
$2$ |
$[2, 0]$ |
180.1 |
\( 2^{2} \cdot 3^{2} \cdot 5 \) |
\( 2^{2} \cdot 3^{28} \cdot 5^{2} \) |
$3.01763$ |
$(3,a), (3,a+2), (5,a+2), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \cdot 7 \) |
$1$ |
$3.193283145$ |
4.849042622 |
\( \frac{1148198515307}{9565938} a + \frac{4282612495109}{7971615} \) |
\( \bigl[a + 1\) , \( a - 1\) , \( a\) , \( -363 a - 1557\) , \( -10134 a - 41779\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-363a-1557\right){x}-10134a-41779$ |
| 180.1-b1 |
180.1-b |
$8$ |
$12$ |
\(\Q(\sqrt{85}) \) |
$2$ |
$[2, 0]$ |
180.1 |
\( 2^{2} \cdot 3^{2} \cdot 5 \) |
\( 2^{24} \cdot 3^{2} \cdot 5^{6} \) |
$3.01763$ |
$(3,a), (3,a+2), (5,a+2), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2^{3} \cdot 3 \) |
$3.153476569$ |
$1.248395236$ |
5.124051602 |
\( -\frac{273359449}{1536000} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -14\) , \( -64\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-14{x}-64$ |
| 180.1-b2 |
180.1-b |
$8$ |
$12$ |
\(\Q(\sqrt{85}) \) |
$2$ |
$[2, 0]$ |
180.1 |
\( 2^{2} \cdot 3^{2} \cdot 5 \) |
\( 2^{8} \cdot 3^{6} \cdot 5^{2} \) |
$3.01763$ |
$(3,a), (3,a+2), (5,a+2), (2)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{3} \cdot 3^{2} \) |
$1.051158856$ |
$11.23555713$ |
5.124051602 |
\( \frac{357911}{2160} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( 1\) , \( 2\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}+2$ |
| 180.1-b3 |
180.1-b |
$8$ |
$12$ |
\(\Q(\sqrt{85}) \) |
$2$ |
$[2, 0]$ |
180.1 |
\( 2^{2} \cdot 3^{2} \cdot 5 \) |
\( 2^{6} \cdot 3^{2} \cdot 5^{24} \) |
$3.01763$ |
$(3,a), (3,a+2), (5,a+2), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2 \cdot 3 \) |
$12.61390627$ |
$1.248395236$ |
5.124051602 |
\( \frac{10316097499609}{5859375000} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -454\) , \( -544\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-454{x}-544$ |
| 180.1-b4 |
180.1-b |
$8$ |
$12$ |
\(\Q(\sqrt{85}) \) |
$2$ |
$[2, 0]$ |
180.1 |
\( 2^{2} \cdot 3^{2} \cdot 5 \) |
\( 2^{2} \cdot 3^{24} \cdot 5^{2} \) |
$3.01763$ |
$(3,a), (3,a+2), (5,a+2), (2)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{5} \cdot 3^{2} \) |
$1.051158856$ |
$2.808889283$ |
5.124051602 |
\( \frac{35578826569}{5314410} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -69\) , \( -194\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-69{x}-194$ |
| 180.1-b5 |
180.1-b |
$8$ |
$12$ |
\(\Q(\sqrt{85}) \) |
$2$ |
$[2, 0]$ |
180.1 |
\( 2^{2} \cdot 3^{2} \cdot 5 \) |
\( 2^{4} \cdot 3^{12} \cdot 5^{4} \) |
$3.01763$ |
$(3,a), (3,a+2), (5,a+2), (2)$ |
$1$ |
$\Z/2\Z\oplus\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2Cs, 3B.1.1 |
$1$ |
\( 2^{4} \cdot 3^{2} \) |
$2.102317712$ |
$11.23555713$ |
5.124051602 |
\( \frac{702595369}{72900} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -19\) , \( 26\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-19{x}+26$ |
| 180.1-b6 |
180.1-b |
$8$ |
$12$ |
\(\Q(\sqrt{85}) \) |
$2$ |
$[2, 0]$ |
180.1 |
\( 2^{2} \cdot 3^{2} \cdot 5 \) |
\( 2^{12} \cdot 3^{4} \cdot 5^{12} \) |
$3.01763$ |
$(3,a), (3,a+2), (5,a+2), (2)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2Cs, 3B.1.2 |
$1$ |
\( 2^{4} \cdot 3 \) |
$6.306953138$ |
$1.248395236$ |
5.124051602 |
\( \frac{4102915888729}{9000000} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -334\) , \( -2368\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-334{x}-2368$ |
| 180.1-b7 |
180.1-b |
$8$ |
$12$ |
\(\Q(\sqrt{85}) \) |
$2$ |
$[2, 0]$ |
180.1 |
\( 2^{2} \cdot 3^{2} \cdot 5 \) |
\( 2^{2} \cdot 3^{6} \cdot 5^{8} \) |
$3.01763$ |
$(3,a), (3,a+2), (5,a+2), (2)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2 \cdot 3^{2} \) |
$4.204635425$ |
$11.23555713$ |
5.124051602 |
\( \frac{2656166199049}{33750} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -289\) , \( 1862\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-289{x}+1862$ |
| 180.1-b8 |
180.1-b |
$8$ |
$12$ |
\(\Q(\sqrt{85}) \) |
$2$ |
$[2, 0]$ |
180.1 |
\( 2^{2} \cdot 3^{2} \cdot 5 \) |
\( 2^{6} \cdot 3^{8} \cdot 5^{6} \) |
$3.01763$ |
$(3,a), (3,a+2), (5,a+2), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2^{5} \cdot 3 \) |
$3.153476569$ |
$0.312098809$ |
5.124051602 |
\( \frac{16778985534208729}{81000} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -5334\) , \( -150368\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-5334{x}-150368$ |
| 180.1-c1 |
180.1-c |
$2$ |
$2$ |
\(\Q(\sqrt{85}) \) |
$2$ |
$[2, 0]$ |
180.1 |
\( 2^{2} \cdot 3^{2} \cdot 5 \) |
\( - 2^{4} \cdot 3^{17} \cdot 5 \) |
$3.01763$ |
$(3,a), (3,a+2), (5,a+2), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.337491133$ |
$28.53736028$ |
2.089280249 |
\( -\frac{15127127}{1620} a - \frac{59363779}{1620} \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( a\) , \( -352 a - 1443\) , \( 7363 a + 30262\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-352a-1443\right){x}+7363a+30262$ |
| 180.1-c2 |
180.1-c |
$2$ |
$2$ |
\(\Q(\sqrt{85}) \) |
$2$ |
$[2, 0]$ |
180.1 |
\( 2^{2} \cdot 3^{2} \cdot 5 \) |
\( 2^{2} \cdot 3^{16} \cdot 5^{2} \) |
$3.01763$ |
$(3,a), (3,a+2), (5,a+2), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.168745566$ |
$28.53736028$ |
2.089280249 |
\( \frac{7854737171}{10} a + \frac{145276438487}{45} \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( a\) , \( -5622 a - 23103\) , \( 486409 a + 1999030\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-5622a-23103\right){x}+486409a+1999030$ |
| 180.1-d1 |
180.1-d |
$2$ |
$2$ |
\(\Q(\sqrt{85}) \) |
$2$ |
$[2, 0]$ |
180.1 |
\( 2^{2} \cdot 3^{2} \cdot 5 \) |
\( 2^{4} \cdot 3^{20} \cdot 5^{4} \) |
$3.01763$ |
$(3,a), (3,a+2), (5,a+2), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \cdot 7 \) |
$1$ |
$3.193283145$ |
4.849042622 |
\( \frac{2344213}{43740} a - \frac{29922139}{109350} \) |
\( \bigl[1\) , \( a - 1\) , \( a\) , \( 2 a + 15\) , \( -365 a - 1508\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(2a+15\right){x}-365a-1508$ |
| 180.1-d2 |
180.1-d |
$2$ |
$2$ |
\(\Q(\sqrt{85}) \) |
$2$ |
$[2, 0]$ |
180.1 |
\( 2^{2} \cdot 3^{2} \cdot 5 \) |
\( 2^{2} \cdot 3^{28} \cdot 5^{2} \) |
$3.01763$ |
$(3,a), (3,a+2), (5,a+2), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \cdot 7 \) |
$1$ |
$3.193283145$ |
4.849042622 |
\( -\frac{1148198515307}{9565938} a + \frac{31436667547189}{47829690} \) |
\( \bigl[1\) , \( a - 1\) , \( a\) , \( -348 a - 1485\) , \( -8145 a - 33578\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-348a-1485\right){x}-8145a-33578$ |
| 180.1-e1 |
180.1-e |
$6$ |
$8$ |
\(\Q(\sqrt{85}) \) |
$2$ |
$[2, 0]$ |
180.1 |
\( 2^{2} \cdot 3^{2} \cdot 5 \) |
\( - 2^{2} \cdot 3^{28} \cdot 5^{8} \) |
$3.01763$ |
$(3,a), (3,a+2), (5,a+2), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 2^{5} \) |
$1$ |
$0.521581734$ |
1.810351430 |
\( -\frac{195415073843819921}{353036920601250} a - \frac{9642543054157138}{35303692060125} \) |
\( \bigl[a\) , \( -a - 1\) , \( 1\) , \( -166 a - 820\) , \( -3496 a - 15021\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-166a-820\right){x}-3496a-15021$ |
| 180.1-e2 |
180.1-e |
$6$ |
$8$ |
\(\Q(\sqrt{85}) \) |
$2$ |
$[2, 0]$ |
180.1 |
\( 2^{2} \cdot 3^{2} \cdot 5 \) |
\( - 2^{4} \cdot 3^{5} \cdot 5 \) |
$3.01763$ |
$(3,a), (3,a+2), (5,a+2), (2)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$16$ |
\( 2^{2} \) |
$1$ |
$4.172653875$ |
1.810351430 |
\( -\frac{3053379042813353661631}{540} a + \frac{15602071436498735333053}{540} \) |
\( \bigl[a\) , \( -a - 1\) , \( 1\) , \( 174 a - 630\) , \( -2000 a + 7871\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(174a-630\right){x}-2000a+7871$ |
| 180.1-e3 |
180.1-e |
$6$ |
$8$ |
\(\Q(\sqrt{85}) \) |
$2$ |
$[2, 0]$ |
180.1 |
\( 2^{2} \cdot 3^{2} \cdot 5 \) |
\( 2^{8} \cdot 3^{10} \cdot 5^{2} \) |
$3.01763$ |
$(3,a), (3,a+2), (5,a+2), (2)$ |
0 |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$4$ |
\( 2^{5} \) |
$1$ |
$8.345307750$ |
1.810351430 |
\( -\frac{45672631270721}{58320} a + \frac{116688505355683}{29160} \) |
\( \bigl[a\) , \( -a - 1\) , \( 1\) , \( -6 a - 90\) , \( -56 a - 121\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-6a-90\right){x}-56a-121$ |
| 180.1-e4 |
180.1-e |
$6$ |
$8$ |
\(\Q(\sqrt{85}) \) |
$2$ |
$[2, 0]$ |
180.1 |
\( 2^{2} \cdot 3^{2} \cdot 5 \) |
\( - 2^{16} \cdot 3^{5} \cdot 5 \) |
$3.01763$ |
$(3,a), (3,a+2), (5,a+2), (2)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$16.69061550$ |
1.810351430 |
\( \frac{372855259}{34560} a - \frac{1378637737}{34560} \) |
\( \bigl[a\) , \( -a - 1\) , \( 1\) , \( -6 a - 10\) , \( 8 a + 39\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-6a-10\right){x}+8a+39$ |
| 180.1-e5 |
180.1-e |
$6$ |
$8$ |
\(\Q(\sqrt{85}) \) |
$2$ |
$[2, 0]$ |
180.1 |
\( 2^{2} \cdot 3^{2} \cdot 5 \) |
\( 2^{4} \cdot 3^{20} \cdot 5^{4} \) |
$3.01763$ |
$(3,a), (3,a+2), (5,a+2), (2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$4$ |
\( 2^{5} \) |
$1$ |
$2.086326937$ |
1.810351430 |
\( \frac{82532880318161}{53144100} a + \frac{343746744417613}{53144100} \) |
\( \bigl[a\) , \( -a - 1\) , \( 1\) , \( -186 a - 830\) , \( -3168 a - 12913\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-186a-830\right){x}-3168a-12913$ |
| 180.1-e6 |
180.1-e |
$6$ |
$8$ |
\(\Q(\sqrt{85}) \) |
$2$ |
$[2, 0]$ |
180.1 |
\( 2^{2} \cdot 3^{2} \cdot 5 \) |
\( - 2^{2} \cdot 3^{22} \cdot 5^{2} \) |
$3.01763$ |
$(3,a), (3,a+2), (5,a+2), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$16$ |
\( 2^{3} \) |
$1$ |
$0.521581734$ |
1.810351430 |
\( \frac{9685745985830031694213}{430467210} a + \frac{6634368311047847405222}{71744535} \) |
\( \bigl[a\) , \( -a - 1\) , \( 1\) , \( -3086 a - 12680\) , \( -200808 a - 824533\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-3086a-12680\right){x}-200808a-824533$ |
| 180.1-f1 |
180.1-f |
$4$ |
$6$ |
\(\Q(\sqrt{85}) \) |
$2$ |
$[2, 0]$ |
180.1 |
\( 2^{2} \cdot 3^{2} \cdot 5 \) |
\( 2^{18} \cdot 3^{4} \cdot 5^{2} \) |
$3.01763$ |
$(3,a), (3,a+2), (5,a+2), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$9$ |
\( 2^{3} \cdot 3^{2} \) |
$1$ |
$0.253823467$ |
4.460025323 |
\( -\frac{390887209858829319081127}{160} a + \frac{57523524752728523871702317}{4608} \) |
\( \bigl[a + 1\) , \( 0\) , \( 1\) , \( -5453 a - 24838\) , \( 212238 a + 824159\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(-5453a-24838\right){x}+212238a+824159$ |
| 180.1-f2 |
180.1-f |
$4$ |
$6$ |
\(\Q(\sqrt{85}) \) |
$2$ |
$[2, 0]$ |
180.1 |
\( 2^{2} \cdot 3^{2} \cdot 5 \) |
\( - 2^{12} \cdot 3^{15} \cdot 5^{3} \) |
$3.01763$ |
$(3,a), (3,a+2), (5,a+2), (2)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{3} \cdot 3^{4} \) |
$1$ |
$2.284411208$ |
4.460025323 |
\( \frac{4503089116819}{850305600} a + \frac{2431620027893}{141717600} \) |
\( \bigl[a + 1\) , \( 0\) , \( 1\) , \( -298 a - 1223\) , \( 5040 a + 20711\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(-298a-1223\right){x}+5040a+20711$ |
| 180.1-f3 |
180.1-f |
$4$ |
$6$ |
\(\Q(\sqrt{85}) \) |
$2$ |
$[2, 0]$ |
180.1 |
\( 2^{2} \cdot 3^{2} \cdot 5 \) |
\( - 2^{36} \cdot 3^{5} \cdot 5 \) |
$3.01763$ |
$(3,a), (3,a+2), (5,a+2), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$9$ |
\( 2^{3} \cdot 3^{2} \) |
$1$ |
$0.253823467$ |
4.460025323 |
\( \frac{54007759831079221}{3317760} a - \frac{2943649403363940817}{35389440} \) |
\( \bigl[a + 1\) , \( 0\) , \( 1\) , \( -2893 a - 12038\) , \( -190194 a - 782497\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(-2893a-12038\right){x}-190194a-782497$ |
| 180.1-f4 |
180.1-f |
$4$ |
$6$ |
\(\Q(\sqrt{85}) \) |
$2$ |
$[2, 0]$ |
180.1 |
\( 2^{2} \cdot 3^{2} \cdot 5 \) |
\( 2^{6} \cdot 3^{12} \cdot 5^{6} \) |
$3.01763$ |
$(3,a), (3,a+2), (5,a+2), (2)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{3} \cdot 3^{4} \) |
$1$ |
$2.284411208$ |
4.460025323 |
\( \frac{5451285492263}{27000} a + \frac{625483869500593}{729000} \) |
\( \bigl[a + 1\) , \( 0\) , \( 1\) , \( -4778 a - 19663\) , \( 371808 a + 1527959\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(-4778a-19663\right){x}+371808a+1527959$ |
| 180.1-g1 |
180.1-g |
$4$ |
$6$ |
\(\Q(\sqrt{85}) \) |
$2$ |
$[2, 0]$ |
180.1 |
\( 2^{2} \cdot 3^{2} \cdot 5 \) |
\( - 2^{36} \cdot 3^{5} \cdot 5 \) |
$3.01763$ |
$(3,a), (3,a+2), (5,a+2), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$9$ |
\( 2^{3} \cdot 3^{2} \) |
$1$ |
$0.253823467$ |
4.460025323 |
\( -\frac{54007759831079221}{3317760} a - \frac{7102699895497287379}{106168320} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -781628756 a - 3212316155\) , \( -25539050572356 a - 104959680788266\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(-781628756a-3212316155\right){x}-25539050572356a-104959680788266$ |
| 180.1-g2 |
180.1-g |
$4$ |
$6$ |
\(\Q(\sqrt{85}) \) |
$2$ |
$[2, 0]$ |
180.1 |
\( 2^{2} \cdot 3^{2} \cdot 5 \) |
\( - 2^{12} \cdot 3^{15} \cdot 5^{3} \) |
$3.01763$ |
$(3,a), (3,a+2), (5,a+2), (2)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{3} \cdot 3^{4} \) |
$1$ |
$2.284411208$ |
4.460025323 |
\( -\frac{4503089116819}{850305600} a + \frac{19092809284177}{850305600} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -9214676 a - 37870220\) , \( -38335577820 a - 157550493094\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(-9214676a-37870220\right){x}-38335577820a-157550493094$ |
| 180.1-g3 |
180.1-g |
$4$ |
$6$ |
\(\Q(\sqrt{85}) \) |
$2$ |
$[2, 0]$ |
180.1 |
\( 2^{2} \cdot 3^{2} \cdot 5 \) |
\( 2^{6} \cdot 3^{12} \cdot 5^{6} \) |
$3.01763$ |
$(3,a), (3,a+2), (5,a+2), (2)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{3} \cdot 3^{4} \) |
$1$ |
$2.284411208$ |
4.460025323 |
\( -\frac{5451285492263}{27000} a + \frac{386334288895847}{364500} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -154397116 a - 634536980\) , \( -2242078562716 a - 9214432211494\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(-154397116a-634536980\right){x}-2242078562716a-9214432211494$ |
| 180.1-g4 |
180.1-g |
$4$ |
$6$ |
\(\Q(\sqrt{85}) \) |
$2$ |
$[2, 0]$ |
180.1 |
\( 2^{2} \cdot 3^{2} \cdot 5 \) |
\( 2^{18} \cdot 3^{4} \cdot 5^{2} \) |
$3.01763$ |
$(3,a), (3,a+2), (5,a+2), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$9$ |
\( 2^{3} \cdot 3^{2} \) |
$1$ |
$0.253823467$ |
4.460025323 |
\( \frac{390887209858829319081127}{160} a + \frac{231329865543971197410829297}{23040} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -12506060116 a - 51397058555\) , \( -1634496104626756 a - 6717406698625834\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(-12506060116a-51397058555\right){x}-1634496104626756a-6717406698625834$ |
| 180.1-h1 |
180.1-h |
$2$ |
$2$ |
\(\Q(\sqrt{85}) \) |
$2$ |
$[2, 0]$ |
180.1 |
\( 2^{2} \cdot 3^{2} \cdot 5 \) |
\( 2^{4} \cdot 3^{8} \cdot 5^{4} \) |
$3.01763$ |
$(3,a), (3,a+2), (5,a+2), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$5.028219013$ |
$3.193283145$ |
3.483149758 |
\( -\frac{2344213}{43740} a - \frac{16041071}{72900} \) |
\( \bigl[1\) , \( 1\) , \( 0\) , \( -23 a - 94\) , \( -283 a - 1163\bigr] \) |
${y}^2+{x}{y}={x}^{3}+{x}^{2}+\left(-23a-94\right){x}-283a-1163$ |
| 180.1-h2 |
180.1-h |
$2$ |
$2$ |
\(\Q(\sqrt{85}) \) |
$2$ |
$[2, 0]$ |
180.1 |
\( 2^{2} \cdot 3^{2} \cdot 5 \) |
\( 2^{2} \cdot 3^{16} \cdot 5^{2} \) |
$3.01763$ |
$(3,a), (3,a+2), (5,a+2), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$2.514109506$ |
$3.193283145$ |
3.483149758 |
\( \frac{1148198515307}{9565938} a + \frac{4282612495109}{7971615} \) |
\( \bigl[1\) , \( 1\) , \( 0\) , \( -473 a - 1944\) , \( -12213 a - 50193\bigr] \) |
${y}^2+{x}{y}={x}^{3}+{x}^{2}+\left(-473a-1944\right){x}-12213a-50193$ |
| 180.1-i1 |
180.1-i |
$6$ |
$8$ |
\(\Q(\sqrt{85}) \) |
$2$ |
$[2, 0]$ |
180.1 |
\( 2^{2} \cdot 3^{2} \cdot 5 \) |
\( - 2^{2} \cdot 3^{40} \cdot 5^{8} \) |
$3.01763$ |
$(3,a), (3,a+2), (5,a+2), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{6} \cdot 3 \) |
$1.290125389$ |
$0.521581734$ |
7.006741036 |
\( -\frac{195415073843819921}{353036920601250} a - \frac{9642543054157138}{35303692060125} \) |
\( \bigl[1\) , \( a - 1\) , \( a + 1\) , \( 1605 a - 9518\) , \( 26068 a - 158163\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(1605a-9518\right){x}+26068a-158163$ |
| 180.1-i2 |
180.1-i |
$6$ |
$8$ |
\(\Q(\sqrt{85}) \) |
$2$ |
$[2, 0]$ |
180.1 |
\( 2^{2} \cdot 3^{2} \cdot 5 \) |
\( - 2^{4} \cdot 3^{17} \cdot 5 \) |
$3.01763$ |
$(3,a), (3,a+2), (5,a+2), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 2^{2} \cdot 3 \) |
$0.645062694$ |
$4.172653875$ |
7.006741036 |
\( -\frac{3053379042813353661631}{540} a + \frac{15602071436498735333053}{540} \) |
\( \bigl[1\) , \( a - 1\) , \( a + 1\) , \( 15155 a - 77228\) , \( -2200360 a + 11241951\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(15155a-77228\right){x}-2200360a+11241951$ |
| 180.1-i3 |
180.1-i |
$6$ |
$8$ |
\(\Q(\sqrt{85}) \) |
$2$ |
$[2, 0]$ |
180.1 |
\( 2^{2} \cdot 3^{2} \cdot 5 \) |
\( 2^{8} \cdot 3^{22} \cdot 5^{2} \) |
$3.01763$ |
$(3,a), (3,a+2), (5,a+2), (2)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{6} \cdot 3 \) |
$0.322531347$ |
$8.345307750$ |
7.006741036 |
\( -\frac{45672631270721}{58320} a + \frac{116688505355683}{29160} \) |
\( \bigl[1\) , \( a - 1\) , \( a + 1\) , \( 935 a - 4868\) , \( -35572 a + 181347\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(935a-4868\right){x}-35572a+181347$ |
| 180.1-i4 |
180.1-i |
$6$ |
$8$ |
\(\Q(\sqrt{85}) \) |
$2$ |
$[2, 0]$ |
180.1 |
\( 2^{2} \cdot 3^{2} \cdot 5 \) |
\( - 2^{16} \cdot 3^{17} \cdot 5 \) |
$3.01763$ |
$(3,a), (3,a+2), (5,a+2), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{4} \cdot 3 \) |
$0.161265673$ |
$16.69061550$ |
7.006741036 |
\( \frac{372855259}{34560} a - \frac{1378637737}{34560} \) |
\( \bigl[1\) , \( a - 1\) , \( a + 1\) , \( 55 a - 308\) , \( -628 a + 3219\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(55a-308\right){x}-628a+3219$ |
| 180.1-i5 |
180.1-i |
$6$ |
$8$ |
\(\Q(\sqrt{85}) \) |
$2$ |
$[2, 0]$ |
180.1 |
\( 2^{2} \cdot 3^{2} \cdot 5 \) |
\( 2^{4} \cdot 3^{32} \cdot 5^{4} \) |
$3.01763$ |
$(3,a), (3,a+2), (5,a+2), (2)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{7} \cdot 3 \) |
$0.645062694$ |
$2.086326937$ |
7.006741036 |
\( \frac{82532880318161}{53144100} a + \frac{343746744417613}{53144100} \) |
\( \bigl[1\) , \( a - 1\) , \( a + 1\) , \( 795 a - 5468\) , \( -37760 a + 170535\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(795a-5468\right){x}-37760a+170535$ |
| 180.1-i6 |
180.1-i |
$6$ |
$8$ |
\(\Q(\sqrt{85}) \) |
$2$ |
$[2, 0]$ |
180.1 |
\( 2^{2} \cdot 3^{2} \cdot 5 \) |
\( - 2^{2} \cdot 3^{34} \cdot 5^{2} \) |
$3.01763$ |
$(3,a), (3,a+2), (5,a+2), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{6} \cdot 3 \) |
$1.290125389$ |
$0.521581734$ |
7.006741036 |
\( \frac{9685745985830031694213}{430467210} a + \frac{6634368311047847405222}{71744535} \) |
\( \bigl[1\) , \( a - 1\) , \( a + 1\) , \( -2255 a - 11018\) , \( -231460 a - 152895\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-2255a-11018\right){x}-231460a-152895$ |
| 180.1-j1 |
180.1-j |
$2$ |
$2$ |
\(\Q(\sqrt{85}) \) |
$2$ |
$[2, 0]$ |
180.1 |
\( 2^{2} \cdot 3^{2} \cdot 5 \) |
\( - 2^{4} \cdot 3^{17} \cdot 5 \) |
$3.01763$ |
$(3,a), (3,a+2), (5,a+2), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.337491133$ |
$28.53736028$ |
2.089280249 |
\( \frac{15127127}{1620} a - \frac{12415151}{270} \) |
\( \bigl[1\) , \( -a - 1\) , \( a\) , \( 6 a - 30\) , \( -12 a + 63\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(6a-30\right){x}-12a+63$ |
| 180.1-j2 |
180.1-j |
$2$ |
$2$ |
\(\Q(\sqrt{85}) \) |
$2$ |
$[2, 0]$ |
180.1 |
\( 2^{2} \cdot 3^{2} \cdot 5 \) |
\( 2^{2} \cdot 3^{16} \cdot 5^{2} \) |
$3.01763$ |
$(3,a), (3,a+2), (5,a+2), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.168745566$ |
$28.53736028$ |
2.089280249 |
\( -\frac{7854737171}{10} a + \frac{361245511513}{90} \) |
\( \bigl[1\) , \( -a - 1\) , \( a\) , \( 96 a - 570\) , \( -1092 a + 6057\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(96a-570\right){x}-1092a+6057$ |
| 180.1-k1 |
180.1-k |
$4$ |
$6$ |
\(\Q(\sqrt{85}) \) |
$2$ |
$[2, 0]$ |
180.1 |
\( 2^{2} \cdot 3^{2} \cdot 5 \) |
\( - 2^{36} \cdot 3^{17} \cdot 5 \) |
$3.01763$ |
$(3,a), (3,a+2), (5,a+2), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \cdot 3^{2} \) |
$7.224250334$ |
$0.253823467$ |
3.580037714 |
\( -\frac{54007759831079221}{3317760} a - \frac{7102699895497287379}{106168320} \) |
\( \bigl[a\) , \( a\) , \( a + 1\) , \( -89897 a - 369861\) , \( -31874062 a - 130998173\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(-89897a-369861\right){x}-31874062a-130998173$ |
| 180.1-k2 |
180.1-k |
$4$ |
$6$ |
\(\Q(\sqrt{85}) \) |
$2$ |
$[2, 0]$ |
180.1 |
\( 2^{2} \cdot 3^{2} \cdot 5 \) |
\( - 2^{12} \cdot 3^{27} \cdot 5^{3} \) |
$3.01763$ |
$(3,a), (3,a+2), (5,a+2), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \cdot 3 \) |
$2.408083444$ |
$2.284411208$ |
3.580037714 |
\( -\frac{4503089116819}{850305600} a + \frac{19092809284177}{850305600} \) |
\( \bigl[a\) , \( a\) , \( a + 1\) , \( -1052 a - 4371\) , \( -51439 a - 211307\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(-1052a-4371\right){x}-51439a-211307$ |
| 180.1-k3 |
180.1-k |
$4$ |
$6$ |
\(\Q(\sqrt{85}) \) |
$2$ |
$[2, 0]$ |
180.1 |
\( 2^{2} \cdot 3^{2} \cdot 5 \) |
\( 2^{6} \cdot 3^{24} \cdot 5^{6} \) |
$3.01763$ |
$(3,a), (3,a+2), (5,a+2), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \cdot 3 \) |
$1.204041722$ |
$2.284411208$ |
3.580037714 |
\( -\frac{5451285492263}{27000} a + \frac{386334288895847}{364500} \) |
\( \bigl[a\) , \( a\) , \( a + 1\) , \( -17692 a - 73371\) , \( -2837231 a - 11653955\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(-17692a-73371\right){x}-2837231a-11653955$ |
| 180.1-k4 |
180.1-k |
$4$ |
$6$ |
\(\Q(\sqrt{85}) \) |
$2$ |
$[2, 0]$ |
180.1 |
\( 2^{2} \cdot 3^{2} \cdot 5 \) |
\( 2^{18} \cdot 3^{16} \cdot 5^{2} \) |
$3.01763$ |
$(3,a), (3,a+2), (5,a+2), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \cdot 3^{2} \) |
$3.612125167$ |
$0.253823467$ |
3.580037714 |
\( \frac{390887209858829319081127}{160} a + \frac{231329865543971197410829297}{23040} \) |
\( \bigl[a\) , \( a\) , \( a + 1\) , \( -1439017 a - 5914821\) , \( -2023214606 a - 8314947485\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(-1439017a-5914821\right){x}-2023214606a-8314947485$ |
| 180.1-l1 |
180.1-l |
$4$ |
$6$ |
\(\Q(\sqrt{85}) \) |
$2$ |
$[2, 0]$ |
180.1 |
\( 2^{2} \cdot 3^{2} \cdot 5 \) |
\( 2^{18} \cdot 3^{16} \cdot 5^{2} \) |
$3.01763$ |
$(3,a), (3,a+2), (5,a+2), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \cdot 3^{2} \) |
$3.612125167$ |
$0.253823467$ |
3.580037714 |
\( -\frac{390887209858829319081127}{160} a + \frac{57523524752728523871702317}{4608} \) |
\( \bigl[1\) , \( -a - 1\) , \( a\) , \( 185597952 a - 948363258\) , \( 2955242763762 a - 15100617403179\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(185597952a-948363258\right){x}+2955242763762a-15100617403179$ |
| 180.1-l2 |
180.1-l |
$4$ |
$6$ |
\(\Q(\sqrt{85}) \) |
$2$ |
$[2, 0]$ |
180.1 |
\( 2^{2} \cdot 3^{2} \cdot 5 \) |
\( - 2^{12} \cdot 3^{27} \cdot 5^{3} \) |
$3.01763$ |
$(3,a), (3,a+2), (5,a+2), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \cdot 3 \) |
$2.408083444$ |
$2.284411208$ |
3.580037714 |
\( \frac{4503089116819}{850305600} a + \frac{2431620027893}{141717600} \) |
\( \bigl[1\) , \( -a - 1\) , \( a\) , \( 136752 a - 698763\) , \( 69459387 a - 354921660\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(136752a-698763\right){x}+69459387a-354921660$ |
| 180.1-l3 |
180.1-l |
$4$ |
$6$ |
\(\Q(\sqrt{85}) \) |
$2$ |
$[2, 0]$ |
180.1 |
\( 2^{2} \cdot 3^{2} \cdot 5 \) |
\( - 2^{36} \cdot 3^{17} \cdot 5 \) |
$3.01763$ |
$(3,a), (3,a+2), (5,a+2), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \cdot 3^{2} \) |
$7.224250334$ |
$0.253823467$ |
3.580037714 |
\( \frac{54007759831079221}{3317760} a - \frac{2943649403363940817}{35389440} \) |
\( \bigl[1\) , \( -a - 1\) , \( a\) , \( 11599872 a - 59272698\) , \( 46185411570 a - 235996933419\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(11599872a-59272698\right){x}+46185411570a-235996933419$ |
| 180.1-l4 |
180.1-l |
$4$ |
$6$ |
\(\Q(\sqrt{85}) \) |
$2$ |
$[2, 0]$ |
180.1 |
\( 2^{2} \cdot 3^{2} \cdot 5 \) |
\( 2^{6} \cdot 3^{24} \cdot 5^{6} \) |
$3.01763$ |
$(3,a), (3,a+2), (5,a+2), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \cdot 3 \) |
$1.204041722$ |
$2.284411208$ |
3.580037714 |
\( \frac{5451285492263}{27000} a + \frac{625483869500593}{729000} \) |
\( \bigl[1\) , \( -a - 1\) , \( a\) , \( 2291352 a - 11708283\) , \( 4056039627 a - 20725438644\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(2291352a-11708283\right){x}+4056039627a-20725438644$ |
| 180.1-m1 |
180.1-m |
$6$ |
$8$ |
\(\Q(\sqrt{85}) \) |
$2$ |
$[2, 0]$ |
180.1 |
\( 2^{2} \cdot 3^{2} \cdot 5 \) |
\( - 2^{16} \cdot 3^{5} \cdot 5 \) |
$3.01763$ |
$(3,a), (3,a+2), (5,a+2), (2)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$16.69061550$ |
1.810351430 |
\( -\frac{372855259}{34560} a - \frac{167630413}{5760} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -3972 a - 16324\) , \( 293892 a + 1207829\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}+\left(-3972a-16324\right){x}+293892a+1207829$ |
| 180.1-m2 |
180.1-m |
$6$ |
$8$ |
\(\Q(\sqrt{85}) \) |
$2$ |
$[2, 0]$ |
180.1 |
\( 2^{2} \cdot 3^{2} \cdot 5 \) |
\( - 2^{2} \cdot 3^{22} \cdot 5^{2} \) |
$3.01763$ |
$(3,a), (3,a+2), (5,a+2), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$16$ |
\( 2^{3} \) |
$1$ |
$0.521581734$ |
1.810351430 |
\( -\frac{9685745985830031694213}{430467210} a + \frac{9898391170423423225109}{86093442} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -12862 a - 52864\) , \( 47720796 a + 196121597\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}+\left(-12862a-52864\right){x}+47720796a+196121597$ |
| 180.1-m3 |
180.1-m |
$6$ |
$8$ |
\(\Q(\sqrt{85}) \) |
$2$ |
$[2, 0]$ |
180.1 |
\( 2^{2} \cdot 3^{2} \cdot 5 \) |
\( - 2^{2} \cdot 3^{28} \cdot 5^{8} \) |
$3.01763$ |
$(3,a), (3,a+2), (5,a+2), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 2^{5} \) |
$1$ |
$0.521581734$ |
1.810351430 |
\( \frac{195415073843819921}{353036920601250} a - \frac{97280168128463767}{117678973533750} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -117842 a - 484304\) , \( -17532036 a - 72052675\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}+\left(-117842a-484304\right){x}-17532036a-72052675$ |
| 180.1-m4 |
180.1-m |
$6$ |
$8$ |
\(\Q(\sqrt{85}) \) |
$2$ |
$[2, 0]$ |
180.1 |
\( 2^{2} \cdot 3^{2} \cdot 5 \) |
\( 2^{4} \cdot 3^{20} \cdot 5^{4} \) |
$3.01763$ |
$(3,a), (3,a+2), (5,a+2), (2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$4$ |
\( 2^{5} \) |
$1$ |
$2.086326937$ |
1.810351430 |
\( -\frac{82532880318161}{53144100} a + \frac{71046604122629}{8857350} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -63912 a - 262664\) , \( 18665316 a + 76710197\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}+\left(-63912a-262664\right){x}+18665316a+76710197$ |
*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.
