| 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 |
| 27.2-a3 |
27.2-a |
$8$ |
$20$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
27.2 |
\( 3^{3} \) |
\( 3^{12} \) |
$0.67558$ |
$(-a), (a-1)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 5$ |
2B, 5B |
$1$ |
\( 2^{2} \) |
$1$ |
$4.579268803$ |
0.690350747 |
\( -\frac{77935}{243} a - \frac{11594}{81} \) |
\( \bigl[a\) , \( a\) , \( a + 1\) , \( -2 a\) , \( -2 a + 2\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}-2a{x}-2a+2$ |
| 27.3-a3 |
27.3-a |
$8$ |
$20$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
27.3 |
\( 3^{3} \) |
\( 3^{12} \) |
$0.67558$ |
$(-a), (a-1)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 5$ |
2B, 5B |
$1$ |
\( 2^{2} \) |
$1$ |
$4.579268803$ |
0.690350747 |
\( -\frac{77935}{243} a - \frac{11594}{81} \) |
\( \bigl[1\) , \( a + 1\) , \( a\) , \( 1\) , \( 3\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+{x}+3$ |
| 675.4-c3 |
675.4-c |
$8$ |
$20$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
675.4 |
\( 3^{3} \cdot 5^{2} \) |
\( 3^{12} \cdot 5^{6} \) |
$1.51064$ |
$(-a), (a-1), (-a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 5$ |
2B, 5B |
$1$ |
\( 2^{3} \cdot 5 \) |
$0.093030027$ |
$2.047911266$ |
2.297724390 |
\( -\frac{77935}{243} a - \frac{11594}{81} \) |
\( \bigl[a + 1\) , \( a - 1\) , \( 0\) , \( -2 a + 6\) , \( 11 a + 7\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-2a+6\right){x}+11a+7$ |
| 675.6-a3 |
675.6-a |
$8$ |
$20$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
675.6 |
\( 3^{3} \cdot 5^{2} \) |
\( 3^{12} \cdot 5^{6} \) |
$1.51064$ |
$(-a), (a-1), (a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 5$ |
2B, 5B |
$1$ |
\( 2^{2} \) |
$1$ |
$2.047911266$ |
1.234936958 |
\( -\frac{77935}{243} a - \frac{11594}{81} \) |
\( \bigl[1\) , \( -a - 1\) , \( 0\) , \( 3 a - 9\) , \( 10 a - 7\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(3a-9\right){x}+10a-7$ |
| 675.7-a3 |
675.7-a |
$8$ |
$20$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
675.7 |
\( 3^{3} \cdot 5^{2} \) |
\( 3^{12} \cdot 5^{6} \) |
$1.51064$ |
$(-a), (a-1), (-a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 5$ |
2B, 5B |
$1$ |
\( 2^{2} \) |
$1$ |
$2.047911266$ |
1.234936958 |
\( -\frac{77935}{243} a - \frac{11594}{81} \) |
\( \bigl[a\) , \( -1\) , \( 1\) , \( 3 a + 4\) , \( 4 a - 19\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}-{x}^{2}+\left(3a+4\right){x}+4a-19$ |
| 675.9-c3 |
675.9-c |
$8$ |
$20$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
675.9 |
\( 3^{3} \cdot 5^{2} \) |
\( 3^{12} \cdot 5^{6} \) |
$1.51064$ |
$(-a), (a-1), (a-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 5$ |
2B, 5B |
$1$ |
\( 2^{3} \) |
$0.465150138$ |
$2.047911266$ |
2.297724390 |
\( -\frac{77935}{243} a - \frac{11594}{81} \) |
\( \bigl[a + 1\) , \( -a\) , \( a\) , \( -4 a - 3\) , \( -5 a - 9\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}-a{x}^{2}+\left(-4a-3\right){x}-5a-9$ |
| 1089.2-c3 |
1089.2-c |
$8$ |
$20$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
1089.2 |
\( 3^{2} \cdot 11^{2} \) |
\( 3^{6} \cdot 11^{6} \) |
$1.70252$ |
$(-a), (a-1), (-2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 5$ |
2B, 5B |
$1$ |
\( 2 \cdot 5 \) |
$1$ |
$2.391445137$ |
3.605239194 |
\( -\frac{77935}{243} a - \frac{11594}{81} \) |
\( \bigl[a + 1\) , \( 0\) , \( 1\) , \( -4 a + 2\) , \( 5 a - 7\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(-4a+2\right){x}+5a-7$ |
| 2304.2-d3 |
2304.2-d |
$8$ |
$20$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
2304.2 |
\( 2^{8} \cdot 3^{2} \) |
\( 2^{24} \cdot 3^{6} \) |
$2.05331$ |
$(-a), (a-1), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 5$ |
2B, 5B |
$1$ |
\( 2^{2} \cdot 5 \) |
$0.211352803$ |
$1.982881557$ |
2.527193171 |
\( -\frac{77935}{243} a - \frac{11594}{81} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 6 a - 5\) , \( -9 a - 3\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(6a-5\right){x}-9a-3$ |
| 2304.2-h3 |
2304.2-h |
$8$ |
$20$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
2304.2 |
\( 2^{8} \cdot 3^{2} \) |
\( 2^{24} \cdot 3^{6} \) |
$2.05331$ |
$(-a), (a-1), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 5$ |
2B, 5B |
$1$ |
\( 2^{2} \) |
$1.056764017$ |
$1.982881557$ |
2.527193171 |
\( -\frac{77935}{243} a - \frac{11594}{81} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 6 a - 5\) , \( 9 a + 3\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(6a-5\right){x}+9a+3$ |
| 4761.4-b3 |
4761.4-b |
$8$ |
$20$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
4761.4 |
\( 3^{2} \cdot 23^{2} \) |
\( 3^{6} \cdot 23^{6} \) |
$2.46184$ |
$(-a), (a-1), (a+4)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 5$ |
2B, 5B |
$1$ |
\( 2 \cdot 5 \) |
$1$ |
$1.653837544$ |
2.493253908 |
\( -\frac{77935}{243} a - \frac{11594}{81} \) |
\( \bigl[a\) , \( -a + 1\) , \( a\) , \( 4 a - 11\) , \( 20 a - 12\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(4a-11\right){x}+20a-12$ |
| 4761.6-b3 |
4761.6-b |
$8$ |
$20$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
4761.6 |
\( 3^{2} \cdot 23^{2} \) |
\( 3^{6} \cdot 23^{6} \) |
$2.46184$ |
$(-a), (a-1), (a-5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 5$ |
2B, 5B |
$1$ |
\( 2 \cdot 5 \) |
$1$ |
$1.653837544$ |
2.493253908 |
\( -\frac{77935}{243} a - \frac{11594}{81} \) |
\( \bigl[1\) , \( 0\) , \( a + 1\) , \( 6 a + 2\) , \( 6 a - 31\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(6a+2\right){x}+6a-31$ |
| 6912.2-n3 |
6912.2-n |
$8$ |
$20$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
6912.2 |
\( 2^{8} \cdot 3^{3} \) |
\( 2^{24} \cdot 3^{12} \) |
$2.70231$ |
$(-a), (a-1), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 5$ |
2B, 5B |
$1$ |
\( 2^{3} \cdot 5 \) |
$0.371638034$ |
$1.144817200$ |
5.131211894 |
\( -\frac{77935}{243} a - \frac{11594}{81} \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( -14 a - 3\) , \( 49 a + 2\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(-14a-3\right){x}+49a+2$ |
| 6912.3-r3 |
6912.3-r |
$8$ |
$20$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
6912.3 |
\( 2^{8} \cdot 3^{3} \) |
\( 2^{24} \cdot 3^{12} \) |
$2.70231$ |
$(-a), (a-1), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 5$ |
2B, 5B |
$1$ |
\( 2^{3} \) |
$1.858190172$ |
$1.144817200$ |
5.131211894 |
\( -\frac{77935}{243} a - \frac{11594}{81} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -11 a + 23\) , \( -9 a - 94\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(-11a+23\right){x}-9a-94$ |
| 8649.4-c3 |
8649.4-c |
$8$ |
$20$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
8649.4 |
\( 3^{2} \cdot 31^{2} \) |
\( 3^{6} \cdot 31^{6} \) |
$2.85809$ |
$(-a), (a-1), (-3a+4)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 5$ |
2B, 5B |
$1$ |
\( 2^{2} \) |
$3.111678720$ |
$1.424544163$ |
5.346066004 |
\( -\frac{77935}{243} a - \frac{11594}{81} \) |
\( \bigl[a\) , \( 1\) , \( 0\) , \( -4 a + 17\) , \( -14 a - 31\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+{x}^{2}+\left(-4a+17\right){x}-14a-31$ |
| 8649.6-c3 |
8649.6-c |
$8$ |
$20$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
8649.6 |
\( 3^{2} \cdot 31^{2} \) |
\( 3^{6} \cdot 31^{6} \) |
$2.85809$ |
$(-a), (a-1), (3a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 5$ |
2B, 5B |
$1$ |
\( 2^{2} \cdot 5 \) |
$0.622335744$ |
$1.424544163$ |
5.346066004 |
\( -\frac{77935}{243} a - \frac{11594}{81} \) |
\( \bigl[1\) , \( -a + 1\) , \( 1\) , \( -8 a - 8\) , \( 24 a + 8\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-8a-8\right){x}+24a+8$ |
| 9801.3-l3 |
9801.3-l |
$8$ |
$20$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
9801.3 |
\( 3^{4} \cdot 11^{2} \) |
\( 3^{18} \cdot 11^{6} \) |
$2.94885$ |
$(-a), (a-1), (-2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 5$ |
2B, 5B |
$1$ |
\( 2^{3} \) |
$1$ |
$0.797148379$ |
0.961397118 |
\( -\frac{77935}{243} a - \frac{11594}{81} \) |
\( \bigl[a + 1\) , \( -1\) , \( a + 1\) , \( -33 a + 28\) , \( -110 a + 250\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(-33a+28\right){x}-110a+250$ |
| 16875.13-bc5 |
16875.13-bc |
$8$ |
$20$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
16875.13 |
\( 3^{3} \cdot 5^{4} \) |
\( 3^{12} \cdot 5^{12} \) |
$3.37789$ |
$(-a), (a-1), (-a-1), (a-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 5$ |
2B, 5B |
$1$ |
\( 2^{3} \) |
$3.119933717$ |
$0.915853760$ |
6.892315432 |
\( -\frac{77935}{243} a - \frac{11594}{81} \) |
\( \bigl[1\) , \( -a\) , \( a\) , \( -17 a + 36\) , \( -6 a + 165\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}-a{x}^{2}+\left(-17a+36\right){x}-6a+165$ |
| 16875.8-ba5 |
16875.8-ba |
$8$ |
$20$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
16875.8 |
\( 3^{3} \cdot 5^{4} \) |
\( 3^{12} \cdot 5^{12} \) |
$3.37789$ |
$(-a), (a-1), (-a-1), (a-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 5$ |
2B, 5B |
$1$ |
\( 2^{3} \cdot 5 \) |
$0.623986743$ |
$0.915853760$ |
6.892315432 |
\( -\frac{77935}{243} a - \frac{11594}{81} \) |
\( \bigl[a\) , \( 0\) , \( 1\) , \( -23 a - 3\) , \( -103 a + 30\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+\left(-23a-3\right){x}-103a+30$ |
| 19881.4-a5 |
19881.4-a |
$8$ |
$20$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
19881.4 |
\( 3^{2} \cdot 47^{2} \) |
\( 3^{6} \cdot 47^{6} \) |
$3.51920$ |
$(-a), (a-1), (-2a+7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 5$ |
2B, 5B |
$1$ |
\( 2 \) |
$1$ |
$1.156932005$ |
0.348828124 |
\( -\frac{77935}{243} a - \frac{11594}{81} \) |
\( \bigl[a + 1\) , \( 1\) , \( 0\) , \( 11 a + 12\) , \( 46 a - 87\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+{x}^{2}+\left(11a+12\right){x}+46a-87$ |
| 19881.6-b5 |
19881.6-b |
$8$ |
$20$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
19881.6 |
\( 3^{2} \cdot 47^{2} \) |
\( 3^{6} \cdot 47^{6} \) |
$3.51920$ |
$(-a), (a-1), (2a+5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 5$ |
2B, 5B |
$1$ |
\( 2 \) |
$1$ |
$1.156932005$ |
0.348828124 |
\( -\frac{77935}{243} a - \frac{11594}{81} \) |
\( \bigl[a + 1\) , \( 1\) , \( 1\) , \( 5 a - 27\) , \( 38 a - 84\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+{x}^{2}+\left(5a-27\right){x}+38a-84$ |
| 20736.3-bi5 |
20736.3-bi |
$8$ |
$20$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
20736.3 |
\( 2^{8} \cdot 3^{4} \) |
\( 2^{24} \cdot 3^{18} \) |
$3.55645$ |
$(-a), (a-1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 5$ |
2B, 5B |
$1$ |
\( 2^{5} \) |
$1$ |
$0.660960519$ |
3.188593517 |
\( -\frac{77935}{243} a - \frac{11594}{81} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 45 a - 39\) , \( 188 a + 266\bigr] \) |
${y}^2={x}^{3}+\left(45a-39\right){x}+188a+266$ |
| 20736.3-bl5 |
20736.3-bl |
$8$ |
$20$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
20736.3 |
\( 2^{8} \cdot 3^{4} \) |
\( 2^{24} \cdot 3^{18} \) |
$3.55645$ |
$(-a), (a-1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 5$ |
2B, 5B |
$1$ |
\( 2^{5} \) |
$1$ |
$0.660960519$ |
3.188593517 |
\( -\frac{77935}{243} a - \frac{11594}{81} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 45 a - 39\) , \( -188 a - 266\bigr] \) |
${y}^2={x}^{3}+\left(45a-39\right){x}-188a-266$ |
| 27225.4-f5 |
27225.4-f |
$8$ |
$20$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
27225.4 |
\( 3^{2} \cdot 5^{2} \cdot 11^{2} \) |
\( 3^{6} \cdot 5^{6} \cdot 11^{6} \) |
$3.80695$ |
$(-a), (a-1), (-a-1), (-2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 5$ |
2B, 5B |
$1$ |
\( 2^{2} \) |
$2.844226804$ |
$1.069486778$ |
3.668624767 |
\( -\frac{77935}{243} a - \frac{11594}{81} \) |
\( \bigl[1\) , \( a\) , \( 0\) , \( 6 a + 24\) , \( -57 a + 39\bigr] \) |
${y}^2+{x}{y}={x}^{3}+a{x}^{2}+\left(6a+24\right){x}-57a+39$ |
| 27225.6-c5 |
27225.6-c |
$8$ |
$20$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
27225.6 |
\( 3^{2} \cdot 5^{2} \cdot 11^{2} \) |
\( 3^{6} \cdot 5^{6} \cdot 11^{6} \) |
$3.80695$ |
$(-a), (a-1), (a-2), (-2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 5$ |
2B, 5B |
$1$ |
\( 2^{2} \cdot 5 \) |
$0.568845360$ |
$1.069486778$ |
3.668624767 |
\( -\frac{77935}{243} a - \frac{11594}{81} \) |
\( \bigl[a\) , \( a - 1\) , \( a + 1\) , \( -4 a - 27\) , \( -27 a + 137\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-4a-27\right){x}-27a+137$ |
| 31329.4-b5 |
31329.4-b |
$8$ |
$20$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
31329.4 |
\( 3^{2} \cdot 59^{2} \) |
\( 3^{6} \cdot 59^{6} \) |
$3.94295$ |
$(-a), (a-1), (a+7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 5$ |
2B, 5B |
$1$ |
\( 2 \cdot 5 \) |
$1$ |
$1.032596762$ |
1.556698190 |
\( -\frac{77935}{243} a - \frac{11594}{81} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( 15 a - 27\) , \( 75 a - 14\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(15a-27\right){x}+75a-14$ |
| 31329.6-b5 |
31329.6-b |
$8$ |
$20$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
31329.6 |
\( 3^{2} \cdot 59^{2} \) |
\( 3^{6} \cdot 59^{6} \) |
$3.94295$ |
$(-a), (a-1), (a-8)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 5$ |
2B, 5B |
$1$ |
\( 2 \cdot 5 \) |
$1$ |
$1.032596762$ |
1.556698190 |
\( -\frac{77935}{243} a - \frac{11594}{81} \) |
\( \bigl[a\) , \( -a + 1\) , \( 1\) , \( 18 a - 3\) , \( -7 a - 109\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(18a-3\right){x}-7a-109$ |
| 36864.2-t5 |
36864.2-t |
$8$ |
$20$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
36864.2 |
\( 2^{12} \cdot 3^{2} \) |
\( 2^{36} \cdot 3^{6} \) |
$4.10663$ |
$(-a), (a-1), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 5$ |
2B, 5B |
$1$ |
\( 2^{2} \cdot 5 \) |
$1.399529155$ |
$0.991440778$ |
8.367242985 |
\( -\frac{77935}{243} a - \frac{11594}{81} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 21 a - 18\) , \( 48 a + 105\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(21a-18\right){x}+48a+105$ |
| 36864.2-bg5 |
36864.2-bg |
$8$ |
$20$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
36864.2 |
\( 2^{12} \cdot 3^{2} \) |
\( 2^{36} \cdot 3^{6} \) |
$4.10663$ |
$(-a), (a-1), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 5$ |
2B, 5B |
$1$ |
\( 2^{2} \) |
$6.997645777$ |
$0.991440778$ |
8.367242985 |
\( -\frac{77935}{243} a - \frac{11594}{81} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 21 a - 18\) , \( -48 a - 105\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(21a-18\right){x}-48a-105$ |
| 36963.4-a5 |
36963.4-a |
$8$ |
$20$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
36963.4 |
\( 3^{3} \cdot 37^{2} \) |
\( 3^{12} \cdot 37^{6} \) |
$4.10938$ |
$(-a), (a-1), (-3a-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 5$ |
2B, 5B |
$1$ |
\( 2^{3} \cdot 5 \) |
$0.433988200$ |
$0.752827153$ |
3.940368569 |
\( -\frac{77935}{243} a - \frac{11594}{81} \) |
\( \bigl[1\) , \( a - 1\) , \( 1\) , \( -a + 58\) , \( 196 a + 33\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-a+58\right){x}+196a+33$ |
| 36963.6-a5 |
36963.6-a |
$8$ |
$20$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
36963.6 |
\( 3^{3} \cdot 37^{2} \) |
\( 3^{12} \cdot 37^{6} \) |
$4.10938$ |
$(-a), (a-1), (3a-5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 5$ |
2B, 5B |
$1$ |
\( 2^{3} \cdot 5 \) |
$0.920908287$ |
$0.752827153$ |
8.361328871 |
\( -\frac{77935}{243} a - \frac{11594}{81} \) |
\( \bigl[a + 1\) , \( a - 1\) , \( 1\) , \( 22 a - 59\) , \( 162 a - 142\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(22a-59\right){x}+162a-142$ |
| 36963.7-a5 |
36963.7-a |
$8$ |
$20$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
36963.7 |
\( 3^{3} \cdot 37^{2} \) |
\( 3^{12} \cdot 37^{6} \) |
$4.10938$ |
$(-a), (a-1), (-3a-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 5$ |
2B, 5B |
$1$ |
\( 2^{3} \) |
$4.604541439$ |
$0.752827153$ |
8.361328871 |
\( -\frac{77935}{243} a - \frac{11594}{81} \) |
\( \bigl[a + 1\) , \( -a\) , \( a + 1\) , \( 31 a + 9\) , \( 38 a - 329\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(31a+9\right){x}+38a-329$ |
| 36963.9-a5 |
36963.9-a |
$8$ |
$20$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
36963.9 |
\( 3^{3} \cdot 37^{2} \) |
\( 3^{12} \cdot 37^{6} \) |
$4.10938$ |
$(-a), (a-1), (3a-5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 5$ |
2B, 5B |
$1$ |
\( 2^{3} \) |
$2.169941003$ |
$0.752827153$ |
3.940368569 |
\( -\frac{77935}{243} a - \frac{11594}{81} \) |
\( \bigl[a\) , \( a + 1\) , \( a + 1\) , \( -16 a - 45\) , \( -83 a - 265\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-16a-45\right){x}-83a-265$ |
| 40401.4-a5 |
40401.4-a |
$8$ |
$20$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
40401.4 |
\( 3^{2} \cdot 67^{2} \) |
\( 3^{6} \cdot 67^{6} \) |
$4.20178$ |
$(-a), (a-1), (-3a-5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 5$ |
2B, 5B |
$1$ |
\( 2^{2} \) |
$5.828122650$ |
$0.968990152$ |
6.811012775 |
\( -\frac{77935}{243} a - \frac{11594}{81} \) |
\( \bigl[1\) , \( a\) , \( a\) , \( a - 37\) , \( -53 a + 152\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+a{x}^{2}+\left(a-37\right){x}-53a+152$ |
| 40401.6-a5 |
40401.6-a |
$8$ |
$20$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
40401.6 |
\( 3^{2} \cdot 67^{2} \) |
\( 3^{6} \cdot 67^{6} \) |
$4.20178$ |
$(-a), (a-1), (3a-8)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 5$ |
2B, 5B |
$1$ |
\( 2^{2} \cdot 5 \) |
$1.165624530$ |
$0.968990152$ |
6.811012775 |
\( -\frac{77935}{243} a - \frac{11594}{81} \) |
\( \bigl[a\) , \( a - 1\) , \( 0\) , \( 9 a + 26\) , \( -77 a + 64\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(9a+26\right){x}-77a+64$ |
| 42849.7-c5 |
42849.7-c |
$8$ |
$20$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
42849.7 |
\( 3^{4} \cdot 23^{2} \) |
\( 3^{18} \cdot 23^{6} \) |
$4.26403$ |
$(-a), (a-1), (a+4)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 5$ |
2B, 5B |
$1$ |
\( 2^{3} \) |
$1$ |
$0.551279181$ |
0.664867708 |
\( -\frac{77935}{243} a - \frac{11594}{81} \) |
\( \bigl[a\) , \( -a\) , \( 1\) , \( 40 a - 108\) , \( -478 a + 464\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}-a{x}^{2}+\left(40a-108\right){x}-478a+464$ |
| 42849.9-d5 |
42849.9-d |
$8$ |
$20$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
42849.9 |
\( 3^{4} \cdot 23^{2} \) |
\( 3^{18} \cdot 23^{6} \) |
$4.26403$ |
$(-a), (a-1), (a-5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 5$ |
2B, 5B |
$1$ |
\( 2^{3} \) |
$1$ |
$0.551279181$ |
0.664867708 |
\( -\frac{77935}{243} a - \frac{11594}{81} \) |
\( \bigl[1\) , \( -1\) , \( a + 1\) , \( 58 a + 22\) , \( -183 a + 851\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(58a+22\right){x}-183a+851$ |
| 45369.4-a5 |
45369.4-a |
$8$ |
$20$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
45369.4 |
\( 3^{2} \cdot 71^{2} \) |
\( 3^{6} \cdot 71^{6} \) |
$4.32538$ |
$(-a), (a-1), (-5a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 5$ |
2B, 5B |
$1$ |
\( 2 \) |
$1$ |
$0.941298984$ |
0.283812322 |
\( -\frac{77935}{243} a - \frac{11594}{81} \) |
\( \bigl[1\) , \( 1\) , \( a + 1\) , \( -23 a + 6\) , \( -108 a + 81\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(-23a+6\right){x}-108a+81$ |
| 45369.6-a5 |
45369.6-a |
$8$ |
$20$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
45369.6 |
\( 3^{2} \cdot 71^{2} \) |
\( 3^{6} \cdot 71^{6} \) |
$4.32538$ |
$(-a), (a-1), (5a-4)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 5$ |
2B, 5B |
$1$ |
\( 2 \) |
$1$ |
$0.941298984$ |
0.283812322 |
\( -\frac{77935}{243} a - \frac{11594}{81} \) |
\( \bigl[a\) , \( -a - 1\) , \( a + 1\) , \( -19 a + 32\) , \( -24 a + 141\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-19a+32\right){x}-24a+141$ |
*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.
