| 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 |
| 32.1-a1 |
32.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{-106}) \) |
$2$ |
$[0, 1]$ |
32.1 |
\( 2^{5} \) |
\( 2^{24} \) |
$4.37632$ |
$(2,a)$ |
0 |
$\Z/4\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$2$ |
2Cs |
$4$ |
\( 2 \) |
$1$ |
$6.875185818$ |
0.333888539 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 4\) , \( 0\bigr] \) |
${y}^2={x}^3+4{x}$ |
| 32.1-a2 |
32.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{-106}) \) |
$2$ |
$[0, 1]$ |
32.1 |
\( 2^{5} \) |
\( 2^{12} \) |
$4.37632$ |
$(2,a)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$2$ |
2Cs |
$4$ |
\( 2 \) |
$1$ |
$6.875185818$ |
0.333888539 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -1\) , \( 0\bigr] \) |
${y}^2={x}^3-{x}$ |
| 32.1-a3 |
32.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{-106}) \) |
$2$ |
$[0, 1]$ |
32.1 |
\( 2^{5} \) |
\( 2^{18} \) |
$4.37632$ |
$(2,a)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-16$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2 \) |
$1$ |
$6.875185818$ |
0.333888539 |
\( 287496 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -11\) , \( -14\bigr] \) |
${y}^2={x}^3-11{x}-14$ |
| 32.1-a4 |
32.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{-106}) \) |
$2$ |
$[0, 1]$ |
32.1 |
\( 2^{5} \) |
\( 2^{18} \) |
$4.37632$ |
$(2,a)$ |
0 |
$\Z/4\Z$ |
$\textsf{potential}$ |
$-16$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$2$ |
2Cs |
$4$ |
\( 2 \) |
$1$ |
$6.875185818$ |
0.333888539 |
\( 287496 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -11\) , \( 14\bigr] \) |
${y}^2={x}^3-11{x}+14$ |
| 32.1-b1 |
32.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{-106}) \) |
$2$ |
$[0, 1]$ |
32.1 |
\( 2^{5} \) |
\( 2^{12} \) |
$4.37632$ |
$(2,a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2 \) |
$10.79263727$ |
$6.875185818$ |
7.207075791 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 1\) , \( 0\bigr] \) |
${y}^2={x}^3+{x}$ |
| 32.1-b2 |
32.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{-106}) \) |
$2$ |
$[0, 1]$ |
32.1 |
\( 2^{5} \) |
\( 2^{24} \) |
$4.37632$ |
$(2,a)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$21.58527455$ |
$6.875185818$ |
7.207075791 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -4\) , \( 0\bigr] \) |
${y}^2={x}^3-4{x}$ |
| 32.1-b3 |
32.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{-106}) \) |
$2$ |
$[0, 1]$ |
32.1 |
\( 2^{5} \) |
\( 2^{6} \) |
$4.37632$ |
$(2,a)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{potential}$ |
$-16$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2 \) |
$43.17054910$ |
$6.875185818$ |
7.207075791 |
\( 287496 \) |
\( \bigl[a\) , \( 1\) , \( 0\) , \( 214\) , \( -589\bigr] \) |
${y}^2+a{x}{y}={x}^3+{x}^2+214{x}-589$ |
| 32.1-b4 |
32.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{-106}) \) |
$2$ |
$[0, 1]$ |
32.1 |
\( 2^{5} \) |
\( 2^{6} \) |
$4.37632$ |
$(2,a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-16$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2 \) |
$10.79263727$ |
$6.875185818$ |
7.207075791 |
\( 287496 \) |
\( \bigl[a\) , \( 1\) , \( a\) , \( 267\) , \( -566\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^3+{x}^2+267{x}-566$ |
| 50.1-a1 |
50.1-a |
$2$ |
$5$ |
\(\Q(\sqrt{-106}) \) |
$2$ |
$[0, 1]$ |
50.1 |
\( 2 \cdot 5^{2} \) |
\( 2^{20} \cdot 5^{6} \cdot 11^{12} \) |
$4.89287$ |
$(2,a), (5,a+2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$5$ |
5B |
$1$ |
\( 2^{2} \) |
$1.737335582$ |
$0.976226823$ |
1.317866763 |
\( -\frac{9814089221}{1024} \) |
\( \bigl[1\) , \( a - 1\) , \( a\) , \( 2140 a - 15602\) , \( 158462 a - 304634\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^3+\left(a-1\right){x}^2+\left(2140a-15602\right){x}+158462a-304634$ |
| 50.1-a2 |
50.1-a |
$2$ |
$5$ |
\(\Q(\sqrt{-106}) \) |
$2$ |
$[0, 1]$ |
50.1 |
\( 2 \cdot 5^{2} \) |
\( 2^{4} \cdot 5^{6} \cdot 11^{12} \) |
$4.89287$ |
$(2,a), (5,a+2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$5$ |
5B |
$1$ |
\( 2^{2} \) |
$0.347467116$ |
$4.881134117$ |
1.317866763 |
\( \frac{6859}{4} \) |
\( \bigl[1\) , \( a - 1\) , \( a\) , \( -20 a + 103\) , \( 59 a + 655\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^3+\left(a-1\right){x}^2+\left(-20a+103\right){x}+59a+655$ |
| 50.1-b1 |
50.1-b |
$1$ |
$1$ |
\(\Q(\sqrt{-106}) \) |
$2$ |
$[0, 1]$ |
50.1 |
\( 2 \cdot 5^{2} \) |
\( 2^{34} \cdot 5^{18} \) |
$4.89287$ |
$(2,a), (5,a+2)$ |
$0 \le r \le 1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cn |
|
\( 2 \) |
$1$ |
$0.871867282$ |
5.134897869 |
\( -\frac{25153757}{131072} \) |
\( \bigl[a + 1\) , \( a + 1\) , \( 0\) , \( 48 a + 249\) , \( -1782 a - 26573\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^3+\left(a+1\right){x}^2+\left(48a+249\right){x}-1782a-26573$ |
| 50.1-c1 |
50.1-c |
$1$ |
$1$ |
\(\Q(\sqrt{-106}) \) |
$2$ |
$[0, 1]$ |
50.1 |
\( 2 \cdot 5^{2} \) |
\( 2^{34} \cdot 5^{6} \cdot 11^{12} \) |
$4.89287$ |
$(2,a), (5,a+2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cn |
$1$ |
\( 2 \cdot 17 \) |
$1$ |
$0.871867282$ |
2.879230042 |
\( -\frac{25153757}{131072} \) |
\( \bigl[1\) , \( -a - 1\) , \( a + 1\) , \( 293 a - 2166\) , \( -25649 a + 48213\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^3+\left(-a-1\right){x}^2+\left(293a-2166\right){x}-25649a+48213$ |
| 50.1-d1 |
50.1-d |
$2$ |
$5$ |
\(\Q(\sqrt{-106}) \) |
$2$ |
$[0, 1]$ |
50.1 |
\( 2 \cdot 5^{2} \) |
\( 2^{20} \cdot 5^{18} \) |
$4.89287$ |
$(2,a), (5,a+2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$5$ |
5B |
$1$ |
\( 2^{3} \cdot 5 \) |
$1$ |
$0.976226823$ |
3.792781248 |
\( -\frac{9814089221}{1024} \) |
\( \bigl[a + 1\) , \( a - 1\) , \( a + 1\) , \( 507 a + 1068\) , \( 3894 a + 100007\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^3+\left(a-1\right){x}^2+\left(507a+1068\right){x}+3894a+100007$ |
| 50.1-d2 |
50.1-d |
$2$ |
$5$ |
\(\Q(\sqrt{-106}) \) |
$2$ |
$[0, 1]$ |
50.1 |
\( 2 \cdot 5^{2} \) |
\( 2^{4} \cdot 5^{18} \) |
$4.89287$ |
$(2,a), (5,a+2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$5$ |
5B |
$1$ |
\( 2^{3} \) |
$1$ |
$4.881134117$ |
3.792781248 |
\( \frac{6859}{4} \) |
\( \bigl[a + 1\) , \( a - 1\) , \( a + 1\) , \( -33 a + 213\) , \( 150 a + 329\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^3+\left(a-1\right){x}^2+\left(-33a+213\right){x}+150a+329$ |
| 50.3-a1 |
50.3-a |
$2$ |
$5$ |
\(\Q(\sqrt{-106}) \) |
$2$ |
$[0, 1]$ |
50.3 |
\( 2 \cdot 5^{2} \) |
\( 2^{20} \cdot 5^{6} \cdot 11^{12} \) |
$4.89287$ |
$(2,a), (5,a+3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$5$ |
5B |
$1$ |
\( 2^{2} \) |
$1.737335582$ |
$0.976226823$ |
1.317866763 |
\( -\frac{9814089221}{1024} \) |
\( \bigl[1\) , \( -a - 1\) , \( a\) , \( -2141 a - 15602\) , \( -158462 a - 304634\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^3+\left(-a-1\right){x}^2+\left(-2141a-15602\right){x}-158462a-304634$ |
| 50.3-a2 |
50.3-a |
$2$ |
$5$ |
\(\Q(\sqrt{-106}) \) |
$2$ |
$[0, 1]$ |
50.3 |
\( 2 \cdot 5^{2} \) |
\( 2^{4} \cdot 5^{6} \cdot 11^{12} \) |
$4.89287$ |
$(2,a), (5,a+3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$5$ |
5B |
$1$ |
\( 2^{2} \) |
$0.347467116$ |
$4.881134117$ |
1.317866763 |
\( \frac{6859}{4} \) |
\( \bigl[1\) , \( -a - 1\) , \( a\) , \( 19 a + 103\) , \( -59 a + 655\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^3+\left(-a-1\right){x}^2+\left(19a+103\right){x}-59a+655$ |
| 50.3-b1 |
50.3-b |
$1$ |
$1$ |
\(\Q(\sqrt{-106}) \) |
$2$ |
$[0, 1]$ |
50.3 |
\( 2 \cdot 5^{2} \) |
\( 2^{34} \cdot 5^{18} \) |
$4.89287$ |
$(2,a), (5,a+3)$ |
$0 \le r \le 1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cn |
|
\( 2 \) |
$1$ |
$0.871867282$ |
5.134897869 |
\( -\frac{25153757}{131072} \) |
\( \bigl[a + 1\) , \( a + 1\) , \( a\) , \( -99 a + 302\) , \( 2084 a - 18782\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^3+\left(a+1\right){x}^2+\left(-99a+302\right){x}+2084a-18782$ |
| 50.3-c1 |
50.3-c |
$1$ |
$1$ |
\(\Q(\sqrt{-106}) \) |
$2$ |
$[0, 1]$ |
50.3 |
\( 2 \cdot 5^{2} \) |
\( 2^{34} \cdot 5^{6} \cdot 11^{12} \) |
$4.89287$ |
$(2,a), (5,a+3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cn |
$1$ |
\( 2 \cdot 17 \) |
$1$ |
$0.871867282$ |
2.879230042 |
\( -\frac{25153757}{131072} \) |
\( \bigl[1\) , \( a - 1\) , \( a + 1\) , \( -294 a - 2166\) , \( 25648 a + 48213\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^3+\left(a-1\right){x}^2+\left(-294a-2166\right){x}+25648a+48213$ |
| 50.3-d1 |
50.3-d |
$2$ |
$5$ |
\(\Q(\sqrt{-106}) \) |
$2$ |
$[0, 1]$ |
50.3 |
\( 2 \cdot 5^{2} \) |
\( 2^{20} \cdot 5^{18} \) |
$4.89287$ |
$(2,a), (5,a+3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$5$ |
5B |
$1$ |
\( 2^{3} \cdot 5 \) |
$1$ |
$0.976226823$ |
3.792781248 |
\( -\frac{9814089221}{1024} \) |
\( \bigl[a + 1\) , \( a - 1\) , \( 1\) , \( -563 a + 1015\) , \( -2826 a + 156717\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^3+\left(a-1\right){x}^2+\left(-563a+1015\right){x}-2826a+156717$ |
| 50.3-d2 |
50.3-d |
$2$ |
$5$ |
\(\Q(\sqrt{-106}) \) |
$2$ |
$[0, 1]$ |
50.3 |
\( 2 \cdot 5^{2} \) |
\( 2^{4} \cdot 5^{18} \) |
$4.89287$ |
$(2,a), (5,a+3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$5$ |
5B |
$1$ |
\( 2^{3} \) |
$1$ |
$4.881134117$ |
3.792781248 |
\( \frac{6859}{4} \) |
\( \bigl[a + 1\) , \( a - 1\) , \( 1\) , \( -23 a + 160\) , \( 63 a - 201\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^3+\left(a-1\right){x}^2+\left(-23a+160\right){x}+63a-201$ |
| 53.1-a1 |
53.1-a |
$1$ |
$1$ |
\(\Q(\sqrt{-106}) \) |
$2$ |
$[0, 1]$ |
53.1 |
\( 53 \) |
\( 53^{2} \) |
$4.96467$ |
$(53,a)$ |
$1 \le r \le 3$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
|
|
$16$ |
\( 2 \) |
$0.092981484$ |
$7.221736064$ |
4.174121917 |
\( \frac{3375}{53} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( 0\) , \( 0\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3-{x}^2$ |
| 53.1-b1 |
53.1-b |
$1$ |
$1$ |
\(\Q(\sqrt{-106}) \) |
$2$ |
$[0, 1]$ |
53.1 |
\( 53 \) |
\( 2^{12} \cdot 53^{2} \) |
$4.96467$ |
$(53,a)$ |
$2$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
|
|
$1$ |
\( 2 \) |
$2.446179104$ |
$7.221736064$ |
13.72672453 |
\( \frac{3375}{53} \) |
\( \bigl[a\) , \( 1\) , \( a\) , \( 271\) , \( -601\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^3+{x}^2+271{x}-601$ |
| 55.1-a1 |
55.1-a |
$2$ |
$3$ |
\(\Q(\sqrt{-106}) \) |
$2$ |
$[0, 1]$ |
55.1 |
\( 5 \cdot 11 \) |
\( 5^{2} \cdot 11^{14} \) |
$5.01086$ |
$(5,a+2), (11,a+2)$ |
$0 \le r \le 1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1 |
|
\( 2^{2} \) |
$1$ |
$5.531032214$ |
4.785098045 |
\( \frac{24059392}{3025} a - \frac{7360704}{3025} \) |
\( \bigl[a\) , \( -a + 1\) , \( a + 1\) , \( -19 a + 35\) , \( -18 a + 306\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^3+\left(-a+1\right){x}^2+\left(-19a+35\right){x}-18a+306$ |
| 55.1-a2 |
55.1-a |
$2$ |
$3$ |
\(\Q(\sqrt{-106}) \) |
$2$ |
$[0, 1]$ |
55.1 |
\( 5 \cdot 11 \) |
\( 5^{6} \cdot 11^{18} \) |
$5.01086$ |
$(5,a+2), (11,a+2)$ |
$0 \le r \le 1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1 |
|
\( 2^{2} \) |
$1$ |
$1.843677404$ |
4.785098045 |
\( \frac{2541855346688}{27680640625} a + \frac{27390419367744}{27680640625} \) |
\( \bigl[a\) , \( -a + 1\) , \( a + 1\) , \( 166 a + 215\) , \( -3446 a + 4489\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^3+\left(-a+1\right){x}^2+\left(166a+215\right){x}-3446a+4489$ |
| 55.1-b1 |
55.1-b |
$2$ |
$3$ |
\(\Q(\sqrt{-106}) \) |
$2$ |
$[0, 1]$ |
55.1 |
\( 5 \cdot 11 \) |
\( 5^{14} \cdot 11^{2} \) |
$5.01086$ |
$(5,a+2), (11,a+2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 2^{2} \) |
$1$ |
$5.531032214$ |
2.148885357 |
\( \frac{24059392}{3025} a - \frac{7360704}{3025} \) |
\( \bigl[a\) , \( -1\) , \( a + 1\) , \( -3 a + 223\) , \( 9 a - 266\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^3-{x}^2+\left(-3a+223\right){x}+9a-266$ |
| 55.1-b2 |
55.1-b |
$2$ |
$3$ |
\(\Q(\sqrt{-106}) \) |
$2$ |
$[0, 1]$ |
55.1 |
\( 5 \cdot 11 \) |
\( 5^{18} \cdot 11^{6} \) |
$5.01086$ |
$(5,a+2), (11,a+2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$1.843677404$ |
2.148885357 |
\( \frac{2541855346688}{27680640625} a + \frac{27390419367744}{27680640625} \) |
\( \bigl[a\) , \( -1\) , \( a + 1\) , \( 22 a + 523\) , \( -282 a - 4633\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^3-{x}^2+\left(22a+523\right){x}-282a-4633$ |
| 55.2-a1 |
55.2-a |
$1$ |
$1$ |
\(\Q(\sqrt{-106}) \) |
$2$ |
$[0, 1]$ |
55.2 |
\( 5 \cdot 11 \) |
\( 5^{10} \cdot 11^{14} \) |
$5.01086$ |
$(5,a+2), (11,a+9)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2^{2} \) |
$1$ |
$1.084708409$ |
0.421424777 |
\( -\frac{2734676695743488}{1181640625} a + \frac{17162649294593856}{1181640625} \) |
\( \bigl[a\) , \( -1\) , \( a + 1\) , \( -161 a - 24501\) , \( 16064 a + 1727907\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^3-{x}^2+\left(-161a-24501\right){x}+16064a+1727907$ |
| 55.2-b1 |
55.2-b |
$1$ |
$1$ |
\(\Q(\sqrt{-106}) \) |
$2$ |
$[0, 1]$ |
55.2 |
\( 5 \cdot 11 \) |
\( 5^{22} \cdot 11^{2} \) |
$5.01086$ |
$(5,a+2), (11,a+9)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2^{2} \cdot 5 \) |
$1.346990674$ |
$1.084708409$ |
5.676552447 |
\( -\frac{2734676695743488}{1181640625} a + \frac{17162649294593856}{1181640625} \) |
\( \bigl[a\) , \( -a + 1\) , \( a + 1\) , \( -353 a - 3217\) , \( 17287 a + 60545\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^3+\left(-a+1\right){x}^2+\left(-353a-3217\right){x}+17287a+60545$ |
| 55.3-a1 |
55.3-a |
$1$ |
$1$ |
\(\Q(\sqrt{-106}) \) |
$2$ |
$[0, 1]$ |
55.3 |
\( 5 \cdot 11 \) |
\( 5^{10} \cdot 11^{14} \) |
$5.01086$ |
$(5,a+3), (11,a+2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2^{2} \) |
$1$ |
$1.084708409$ |
0.421424777 |
\( \frac{2734676695743488}{1181640625} a + \frac{17162649294593856}{1181640625} \) |
\( \bigl[a\) , \( -1\) , \( a + 1\) , \( 160 a - 24501\) , \( -16065 a + 1727907\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^3-{x}^2+\left(160a-24501\right){x}-16065a+1727907$ |
| 55.3-b1 |
55.3-b |
$1$ |
$1$ |
\(\Q(\sqrt{-106}) \) |
$2$ |
$[0, 1]$ |
55.3 |
\( 5 \cdot 11 \) |
\( 5^{22} \cdot 11^{2} \) |
$5.01086$ |
$(5,a+3), (11,a+2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2^{2} \cdot 5 \) |
$1.346990674$ |
$1.084708409$ |
5.676552447 |
\( \frac{2734676695743488}{1181640625} a + \frac{17162649294593856}{1181640625} \) |
\( \bigl[a\) , \( a + 1\) , \( a + 1\) , \( 352 a - 3217\) , \( -17288 a + 60545\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^3+\left(a+1\right){x}^2+\left(352a-3217\right){x}-17288a+60545$ |
| 55.4-a1 |
55.4-a |
$2$ |
$3$ |
\(\Q(\sqrt{-106}) \) |
$2$ |
$[0, 1]$ |
55.4 |
\( 5 \cdot 11 \) |
\( 5^{2} \cdot 11^{14} \) |
$5.01086$ |
$(5,a+3), (11,a+9)$ |
$0 \le r \le 1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1 |
|
\( 2^{2} \) |
$1$ |
$5.531032214$ |
4.785098045 |
\( -\frac{24059392}{3025} a - \frac{7360704}{3025} \) |
\( \bigl[a\) , \( a + 1\) , \( a + 1\) , \( 18 a + 35\) , \( 17 a + 306\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^3+\left(a+1\right){x}^2+\left(18a+35\right){x}+17a+306$ |
| 55.4-a2 |
55.4-a |
$2$ |
$3$ |
\(\Q(\sqrt{-106}) \) |
$2$ |
$[0, 1]$ |
55.4 |
\( 5 \cdot 11 \) |
\( 5^{6} \cdot 11^{18} \) |
$5.01086$ |
$(5,a+3), (11,a+9)$ |
$0 \le r \le 1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1 |
|
\( 2^{2} \) |
$1$ |
$1.843677404$ |
4.785098045 |
\( -\frac{2541855346688}{27680640625} a + \frac{27390419367744}{27680640625} \) |
\( \bigl[a\) , \( a + 1\) , \( a + 1\) , \( -167 a + 215\) , \( 3445 a + 4489\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^3+\left(a+1\right){x}^2+\left(-167a+215\right){x}+3445a+4489$ |
| 55.4-b1 |
55.4-b |
$2$ |
$3$ |
\(\Q(\sqrt{-106}) \) |
$2$ |
$[0, 1]$ |
55.4 |
\( 5 \cdot 11 \) |
\( 5^{14} \cdot 11^{2} \) |
$5.01086$ |
$(5,a+3), (11,a+9)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 2^{2} \) |
$1$ |
$5.531032214$ |
2.148885357 |
\( -\frac{24059392}{3025} a - \frac{7360704}{3025} \) |
\( \bigl[a\) , \( -1\) , \( a + 1\) , \( 2 a + 223\) , \( -10 a - 266\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^3-{x}^2+\left(2a+223\right){x}-10a-266$ |
| 55.4-b2 |
55.4-b |
$2$ |
$3$ |
\(\Q(\sqrt{-106}) \) |
$2$ |
$[0, 1]$ |
55.4 |
\( 5 \cdot 11 \) |
\( 5^{18} \cdot 11^{6} \) |
$5.01086$ |
$(5,a+3), (11,a+9)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$1.843677404$ |
2.148885357 |
\( -\frac{2541855346688}{27680640625} a + \frac{27390419367744}{27680640625} \) |
\( \bigl[a\) , \( -1\) , \( a + 1\) , \( -23 a + 523\) , \( 281 a - 4633\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^3-{x}^2+\left(-23a+523\right){x}+281a-4633$ |
| 72.1-a1 |
72.1-a |
$6$ |
$8$ |
\(\Q(\sqrt{-106}) \) |
$2$ |
$[0, 1]$ |
72.1 |
\( 2^{3} \cdot 3^{2} \) |
\( 2^{22} \cdot 3^{16} \) |
$5.35987$ |
$(2,a), (3)$ |
$0 \le r \le 1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
|
\( 2^{4} \) |
$1$ |
$1.817673508$ |
5.617857955 |
\( \frac{207646}{6561} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( 16\) , \( -180\bigr] \) |
${y}^2={x}^3-{x}^2+16{x}-180$ |
| 72.1-a2 |
72.1-a |
$6$ |
$8$ |
\(\Q(\sqrt{-106}) \) |
$2$ |
$[0, 1]$ |
72.1 |
\( 2^{3} \cdot 3^{2} \) |
\( 2^{8} \cdot 3^{2} \) |
$5.35987$ |
$(2,a), (3)$ |
$0 \le r \le 1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
|
\( 2 \) |
$1$ |
$7.270694035$ |
5.617857955 |
\( \frac{2048}{3} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( 1\) , \( 0\bigr] \) |
${y}^2={x}^3-{x}^2+{x}$ |
| 72.1-a3 |
72.1-a |
$6$ |
$8$ |
\(\Q(\sqrt{-106}) \) |
$2$ |
$[0, 1]$ |
72.1 |
\( 2^{3} \cdot 3^{2} \) |
\( 2^{16} \cdot 3^{4} \) |
$5.35987$ |
$(2,a), (3)$ |
$0 \le r \le 1$ |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
|
\( 2^{2} \) |
$1$ |
$7.270694035$ |
5.617857955 |
\( \frac{35152}{9} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -4\) , \( 4\bigr] \) |
${y}^2={x}^3-{x}^2-4{x}+4$ |
| 72.1-a4 |
72.1-a |
$6$ |
$8$ |
\(\Q(\sqrt{-106}) \) |
$2$ |
$[0, 1]$ |
72.1 |
\( 2^{3} \cdot 3^{2} \) |
\( 2^{20} \cdot 3^{8} \) |
$5.35987$ |
$(2,a), (3)$ |
$0 \le r \le 1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
|
\( 2^{4} \) |
$1$ |
$3.635347017$ |
5.617857955 |
\( \frac{1556068}{81} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -24\) , \( -36\bigr] \) |
${y}^2={x}^3-{x}^2-24{x}-36$ |
| 72.1-a5 |
72.1-a |
$6$ |
$8$ |
\(\Q(\sqrt{-106}) \) |
$2$ |
$[0, 1]$ |
72.1 |
\( 2^{3} \cdot 3^{2} \) |
\( 2^{20} \cdot 3^{2} \) |
$5.35987$ |
$(2,a), (3)$ |
$0 \le r \le 1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
|
\( 2^{2} \) |
$1$ |
$3.635347017$ |
5.617857955 |
\( \frac{28756228}{3} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -64\) , \( 220\bigr] \) |
${y}^2={x}^3-{x}^2-64{x}+220$ |
| 72.1-a6 |
72.1-a |
$6$ |
$8$ |
\(\Q(\sqrt{-106}) \) |
$2$ |
$[0, 1]$ |
72.1 |
\( 2^{3} \cdot 3^{2} \) |
\( 2^{22} \cdot 3^{4} \) |
$5.35987$ |
$(2,a), (3)$ |
$0 \le r \le 1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
|
\( 2^{2} \) |
$1$ |
$1.817673508$ |
5.617857955 |
\( \frac{3065617154}{9} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -384\) , \( -2772\bigr] \) |
${y}^2={x}^3-{x}^2-384{x}-2772$ |
| 72.1-b1 |
72.1-b |
$6$ |
$8$ |
\(\Q(\sqrt{-106}) \) |
$2$ |
$[0, 1]$ |
72.1 |
\( 2^{3} \cdot 3^{2} \) |
\( 2^{10} \cdot 3^{16} \) |
$5.35987$ |
$(2,a), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$9$ |
\( 2^{4} \) |
$1$ |
$1.817673508$ |
6.355730093 |
\( \frac{207646}{6561} \) |
\( \bigl[a\) , \( 0\) , \( 0\) , \( 238\) , \( -702\bigr] \) |
${y}^2+a{x}{y}={x}^3+238{x}-702$ |
| 72.1-b2 |
72.1-b |
$6$ |
$8$ |
\(\Q(\sqrt{-106}) \) |
$2$ |
$[0, 1]$ |
72.1 |
\( 2^{3} \cdot 3^{2} \) |
\( 2^{20} \cdot 3^{2} \) |
$5.35987$ |
$(2,a), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$9$ |
\( 2^{2} \) |
$1$ |
$7.270694035$ |
6.355730093 |
\( \frac{2048}{3} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( 3\) , \( -3\bigr] \) |
${y}^2={x}^3-{x}^2+3{x}-3$ |
| 72.1-b3 |
72.1-b |
$6$ |
$8$ |
\(\Q(\sqrt{-106}) \) |
$2$ |
$[0, 1]$ |
72.1 |
\( 2^{3} \cdot 3^{2} \) |
\( 2^{4} \cdot 3^{4} \) |
$5.35987$ |
$(2,a), (3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$36$ |
\( 2^{2} \) |
$1$ |
$7.270694035$ |
6.355730093 |
\( \frac{35152}{9} \) |
\( \bigl[a\) , \( 0\) , \( 0\) , \( 233\) , \( -680\bigr] \) |
${y}^2+a{x}{y}={x}^3+233{x}-680$ |
| 72.1-b4 |
72.1-b |
$6$ |
$8$ |
\(\Q(\sqrt{-106}) \) |
$2$ |
$[0, 1]$ |
72.1 |
\( 2^{3} \cdot 3^{2} \) |
\( 2^{8} \cdot 3^{8} \) |
$5.35987$ |
$(2,a), (3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$36$ |
\( 2^{3} \) |
$1$ |
$3.635347017$ |
6.355730093 |
\( \frac{1556068}{81} \) |
\( \bigl[a\) , \( 0\) , \( 0\) , \( 228\) , \( -630\bigr] \) |
${y}^2+a{x}{y}={x}^3+228{x}-630$ |
| 72.1-b5 |
72.1-b |
$6$ |
$8$ |
\(\Q(\sqrt{-106}) \) |
$2$ |
$[0, 1]$ |
72.1 |
\( 2^{3} \cdot 3^{2} \) |
\( 2^{8} \cdot 3^{2} \) |
$5.35987$ |
$(2,a), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$36$ |
\( 2 \) |
$1$ |
$3.635347017$ |
6.355730093 |
\( \frac{28756228}{3} \) |
\( \bigl[a\) , \( 0\) , \( 0\) , \( 218\) , \( -572\bigr] \) |
${y}^2+a{x}{y}={x}^3+218{x}-572$ |
| 72.1-b6 |
72.1-b |
$6$ |
$8$ |
\(\Q(\sqrt{-106}) \) |
$2$ |
$[0, 1]$ |
72.1 |
\( 2^{3} \cdot 3^{2} \) |
\( 2^{10} \cdot 3^{4} \) |
$5.35987$ |
$(2,a), (3)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$144$ |
\( 2^{2} \) |
$1$ |
$1.817673508$ |
6.355730093 |
\( \frac{3065617154}{9} \) |
\( \bigl[a\) , \( 0\) , \( 0\) , \( 138\) , \( 522\bigr] \) |
${y}^2+a{x}{y}={x}^3+138{x}+522$ |
| 98.1-a1 |
98.1-a |
$6$ |
$18$ |
\(\Q(\sqrt{-106}) \) |
$2$ |
$[0, 1]$ |
98.1 |
\( 2 \cdot 7^{2} \) |
\( 2^{36} \cdot 7^{2} \) |
$5.78933$ |
$(2,a), (7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3Cs.1.1 |
$36$ |
\( 2 \) |
$1$ |
$0.875417135$ |
1.530504516 |
\( -\frac{548347731625}{1835008} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -171\) , \( -874\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3-171{x}-874$ |
| 98.1-a2 |
98.1-a |
$6$ |
$18$ |
\(\Q(\sqrt{-106}) \) |
$2$ |
$[0, 1]$ |
98.1 |
\( 2 \cdot 7^{2} \) |
\( 2^{4} \cdot 7^{2} \) |
$5.78933$ |
$(2,a), (7)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3Cs.1.1 |
$36$ |
\( 2 \) |
$1$ |
$7.878754216$ |
1.530504516 |
\( -\frac{15625}{28} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -1\) , \( 0\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3-{x}$ |
| 98.1-a3 |
98.1-a |
$6$ |
$18$ |
\(\Q(\sqrt{-106}) \) |
$2$ |
$[0, 1]$ |
98.1 |
\( 2 \cdot 7^{2} \) |
\( 2^{12} \cdot 7^{6} \) |
$5.78933$ |
$(2,a), (7)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3Cs.1.1 |
$36$ |
\( 2 \cdot 3 \) |
$1$ |
$2.626251405$ |
1.530504516 |
\( \frac{9938375}{21952} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( 4\) , \( -6\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3+4{x}-6$ |
| 98.1-a4 |
98.1-a |
$6$ |
$18$ |
\(\Q(\sqrt{-106}) \) |
$2$ |
$[0, 1]$ |
98.1 |
\( 2 \cdot 7^{2} \) |
\( 2^{6} \cdot 7^{12} \) |
$5.78933$ |
$(2,a), (7)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3Cs.1.1 |
$36$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$1.313125702$ |
1.530504516 |
\( \frac{4956477625}{941192} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -36\) , \( -70\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3-36{x}-70$ |
*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.
