| 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 |
| 9.1-CMa1 |
9.1-CMa |
$1$ |
$1$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
9.1 |
\( 3^{2} \) |
\( 3^{6} \) |
$0.51333$ |
$(-a)$ |
$0$ |
$\Z/3\Z$ |
$\textsf{yes}$ |
$-11$ |
$\mathrm{U}(1)$ |
✓ |
|
|
✓ |
$3$ |
3Cs.1.1 |
$1$ |
\( 1 \) |
$1$ |
$6.657786957$ |
0.446088510 |
\( -32768 \) |
\( \bigl[0\) , \( a\) , \( 1\) , \( a - 3\) , \( -2\bigr] \) |
${y}^2+{y}={x}^{3}+a{x}^{2}+\left(a-3\right){x}-2$ |
| 9.3-CMa1 |
9.3-CMa |
$1$ |
$1$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
9.3 |
\( 3^{2} \) |
\( 3^{6} \) |
$0.51333$ |
$(a-1)$ |
$0$ |
$\Z/3\Z$ |
$\textsf{yes}$ |
$-11$ |
$\mathrm{U}(1)$ |
✓ |
|
|
✓ |
$3$ |
3Cs.1.1 |
$1$ |
\( 1 \) |
$1$ |
$6.657786957$ |
0.446088510 |
\( -32768 \) |
\( \bigl[0\) , \( -a + 1\) , \( 1\) , \( -a - 2\) , \( -2\bigr] \) |
${y}^2+{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-a-2\right){x}-2$ |
| 11.1-a1 |
11.1-a |
$3$ |
$25$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
11.1 |
\( 11 \) |
\( 11^{2} \) |
$0.53974$ |
$(-2a+1)$ |
$0$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 5$ |
2Cn, 5B.1.2 |
$1$ |
\( 2 \) |
$1$ |
$0.370308724$ |
0.446609125 |
\( -\frac{52893159101157376}{11} \) |
\( \bigl[0\) , \( -1\) , \( 1\) , \( -7820\) , \( -263580\bigr] \) |
${y}^2+{y}={x}^{3}-{x}^{2}-7820{x}-263580$ |
| 11.1-a2 |
11.1-a |
$3$ |
$25$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
11.1 |
\( 11 \) |
\( 11^{10} \) |
$0.53974$ |
$(-2a+1)$ |
$0$ |
$\Z/5\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 5$ |
2Cn, 5Cs.1.1 |
$1$ |
\( 2 \cdot 5 \) |
$1$ |
$1.851543623$ |
0.446609125 |
\( -\frac{122023936}{161051} \) |
\( \bigl[0\) , \( -1\) , \( 1\) , \( -10\) , \( -20\bigr] \) |
${y}^2+{y}={x}^{3}-{x}^{2}-10{x}-20$ |
| 11.1-a3 |
11.1-a |
$3$ |
$25$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
11.1 |
\( 11 \) |
\( 11^{2} \) |
$0.53974$ |
$(-2a+1)$ |
$0$ |
$\Z/5\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 5$ |
2Cn, 5B.1.1 |
$1$ |
\( 2 \) |
$1$ |
$9.257718117$ |
0.446609125 |
\( -\frac{4096}{11} \) |
\( \bigl[0\) , \( -1\) , \( 1\) , \( 0\) , \( 0\bigr] \) |
${y}^2+{y}={x}^{3}-{x}^{2}$ |
| 27.2-a1 |
27.2-a |
$8$ |
$20$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
27.2 |
\( 3^{3} \) |
\( 3^{18} \) |
$0.67558$ |
$(-a), (a-1)$ |
$0$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 5$ |
2Cs, 5B |
$1$ |
\( 2^{3} \) |
$1$ |
$2.289634401$ |
0.690350747 |
\( -\frac{349209575}{59049} a - \frac{298597801}{19683} \) |
\( \bigl[a\) , \( a\) , \( a + 1\) , \( -7 a + 15\) , \( -3 a - 13\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(-7a+15\right){x}-3a-13$ |
| 27.2-a2 |
27.2-a |
$8$ |
$20$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
27.2 |
\( 3^{3} \) |
\( 3^{18} \) |
$0.67558$ |
$(-a), (a-1)$ |
$0$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 5$ |
2Cs, 5B |
$1$ |
\( 2^{3} \) |
$1$ |
$2.289634401$ |
0.690350747 |
\( \frac{349209575}{59049} a - \frac{1245002978}{59049} \) |
\( \bigl[1\) , \( -a - 1\) , \( a\) , \( -4 a + 15\) , \( 8 a + 3\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-4a+15\right){x}+8a+3$ |
| 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 |
\( -\frac{77935}{243} a - \frac{11594}{81} \) |
\( \bigl[a\) , \( a\) , \( a + 1\) , \( -2 a\) , \( -2 a + 2\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}-2a{x}-2a+2$ |
| 27.2-a4 |
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 |
\( \frac{77935}{243} a - \frac{112717}{243} \) |
\( \bigl[1\) , \( -a - 1\) , \( a\) , \( a\) , \( -a + 3\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+a{x}-a+3$ |
| 27.2-a5 |
27.2-a |
$8$ |
$20$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
27.2 |
\( 3^{3} \) |
\( 3^{27} \) |
$0.67558$ |
$(-a), (a-1)$ |
$0$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 5$ |
2B, 5B |
$1$ |
\( 2^{2} \) |
$1$ |
$1.144817200$ |
0.690350747 |
\( -\frac{2927543402641}{3486784401} a + \frac{1635099303025}{3486784401} \) |
\( \bigl[1\) , \( -a - 1\) , \( a\) , \( -19 a + 15\) , \( 50 a - 96\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-19a+15\right){x}+50a-96$ |
| 27.2-a6 |
27.2-a |
$8$ |
$20$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
27.2 |
\( 3^{3} \) |
\( 3^{27} \) |
$0.67558$ |
$(-a), (a-1)$ |
$0$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 5$ |
2B, 5B |
$1$ |
\( 2^{2} \) |
$1$ |
$1.144817200$ |
0.690350747 |
\( \frac{2927543402641}{3486784401} a - \frac{430814699872}{1162261467} \) |
\( \bigl[a\) , \( a\) , \( a + 1\) , \( 3 a + 30\) , \( 51 a - 94\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(3a+30\right){x}+51a-94$ |
| 27.2-a7 |
27.2-a |
$8$ |
$20$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
27.2 |
\( 3^{3} \) |
\( 3^{15} \) |
$0.67558$ |
$(-a), (a-1)$ |
$0$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 5$ |
2B, 5B |
$1$ |
\( 2^{2} \) |
$1$ |
$1.144817200$ |
0.690350747 |
\( -\frac{54238838797}{243} a + \frac{90191354077}{243} \) |
\( \bigl[1\) , \( -a - 1\) , \( a\) , \( -69 a + 255\) , \( 642 a + 522\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-69a+255\right){x}+642a+522$ |
| 27.2-a8 |
27.2-a |
$8$ |
$20$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
27.2 |
\( 3^{3} \) |
\( 3^{15} \) |
$0.67558$ |
$(-a), (a-1)$ |
$0$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 5$ |
2B, 5B |
$1$ |
\( 2^{2} \) |
$1$ |
$1.144817200$ |
0.690350747 |
\( \frac{54238838797}{243} a + \frac{1331574640}{9} \) |
\( \bigl[a\) , \( a\) , \( a + 1\) , \( -97 a + 240\) , \( -381 a - 1012\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(-97a+240\right){x}-381a-1012$ |
| 27.3-a1 |
27.3-a |
$8$ |
$20$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
27.3 |
\( 3^{3} \) |
\( 3^{18} \) |
$0.67558$ |
$(-a), (a-1)$ |
$0$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 5$ |
2Cs, 5B |
$1$ |
\( 2^{3} \) |
$1$ |
$2.289634401$ |
0.690350747 |
\( -\frac{349209575}{59049} a - \frac{298597801}{19683} \) |
\( \bigl[1\) , \( a + 1\) , \( a\) , \( 5 a + 11\) , \( -4 a + 22\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(5a+11\right){x}-4a+22$ |
| 27.3-a2 |
27.3-a |
$8$ |
$20$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
27.3 |
\( 3^{3} \) |
\( 3^{18} \) |
$0.67558$ |
$(-a), (a-1)$ |
$0$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 5$ |
2Cs, 5B |
$1$ |
\( 2^{3} \) |
$1$ |
$2.289634401$ |
0.690350747 |
\( \frac{349209575}{59049} a - \frac{1245002978}{59049} \) |
\( \bigl[a + 1\) , \( a + 1\) , \( a + 1\) , \( 6 a + 7\) , \( 16 a - 34\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(6a+7\right){x}+16a-34$ |
| 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 |
\( -\frac{77935}{243} a - \frac{11594}{81} \) |
\( \bigl[1\) , \( a + 1\) , \( a\) , \( 1\) , \( 3\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+{x}+3$ |
| 27.3-a4 |
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 |
\( \frac{77935}{243} a - \frac{112717}{243} \) |
\( \bigl[a + 1\) , \( a + 1\) , \( a + 1\) , \( a - 3\) , \( -3\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(a-3\right){x}-3$ |
| 27.3-a5 |
27.3-a |
$8$ |
$20$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
27.3 |
\( 3^{3} \) |
\( 3^{27} \) |
$0.67558$ |
$(-a), (a-1)$ |
$0$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 5$ |
2B, 5B |
$1$ |
\( 2^{2} \) |
$1$ |
$1.144817200$ |
0.690350747 |
\( -\frac{2927543402641}{3486784401} a + \frac{1635099303025}{3486784401} \) |
\( \bigl[a + 1\) , \( a + 1\) , \( a + 1\) , \( -4 a + 32\) , \( -23 a - 31\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-4a+32\right){x}-23a-31$ |
| 27.3-a6 |
27.3-a |
$8$ |
$20$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
27.3 |
\( 3^{3} \) |
\( 3^{27} \) |
$0.67558$ |
$(-a), (a-1)$ |
$0$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 5$ |
2B, 5B |
$1$ |
\( 2^{2} \) |
$1$ |
$1.144817200$ |
0.690350747 |
\( \frac{2927543402641}{3486784401} a - \frac{430814699872}{1162261467} \) |
\( \bigl[1\) , \( a + 1\) , \( a\) , \( 20 a - 4\) , \( -31 a - 50\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(20a-4\right){x}-31a-50$ |
| 27.3-a7 |
27.3-a |
$8$ |
$20$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
27.3 |
\( 3^{3} \) |
\( 3^{15} \) |
$0.67558$ |
$(-a), (a-1)$ |
$0$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 5$ |
2B, 5B |
$1$ |
\( 2^{2} \) |
$1$ |
$1.144817200$ |
0.690350747 |
\( -\frac{54238838797}{243} a + \frac{90191354077}{243} \) |
\( \bigl[a + 1\) , \( a + 1\) , \( a + 1\) , \( 96 a + 142\) , \( 619 a - 1681\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(96a+142\right){x}+619a-1681$ |
| 27.3-a8 |
27.3-a |
$8$ |
$20$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
27.3 |
\( 3^{3} \) |
\( 3^{15} \) |
$0.67558$ |
$(-a), (a-1)$ |
$0$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 5$ |
2B, 5B |
$1$ |
\( 2^{2} \) |
$1$ |
$1.144817200$ |
0.690350747 |
\( \frac{54238838797}{243} a + \frac{1331574640}{9} \) |
\( \bigl[1\) , \( a + 1\) , \( a\) , \( 70 a + 186\) , \( -573 a + 1350\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(70a+186\right){x}-573a+1350$ |
| 47.1-a1 |
47.1-a |
$1$ |
$1$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
47.1 |
\( 47 \) |
\( 47^{2} \) |
$0.77600$ |
$(-2a+7)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cn |
$1$ |
\( 2 \) |
$0.037922542$ |
$7.280811841$ |
0.665994884 |
\( -\frac{598016}{2209} a + \frac{430080}{2209} \) |
\( \bigl[0\) , \( a\) , \( 1\) , \( -1\) , \( 0\bigr] \) |
${y}^2+{y}={x}^{3}+a{x}^{2}-{x}$ |
| 47.2-a1 |
47.2-a |
$1$ |
$1$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
47.2 |
\( 47 \) |
\( 47^{2} \) |
$0.77600$ |
$(2a+5)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cn |
$1$ |
\( 2 \) |
$0.037922542$ |
$7.280811841$ |
0.665994884 |
\( \frac{598016}{2209} a - \frac{167936}{2209} \) |
\( \bigl[0\) , \( -a + 1\) , \( 1\) , \( -1\) , \( 0\bigr] \) |
${y}^2+{y}={x}^{3}+\left(-a+1\right){x}^{2}-{x}$ |
| 89.1-a1 |
89.1-a |
$2$ |
$2$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
89.1 |
\( 89 \) |
\( 89^{2} \) |
$0.91030$ |
$(5a+2)$ |
$0$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$4.747780797$ |
1.431509771 |
\( -\frac{842425675}{7921} a - \frac{307621662}{7921} \) |
\( \bigl[a\) , \( a\) , \( 0\) , \( 4\) , \( 5 a - 3\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+a{x}^{2}+4{x}+5a-3$ |
| 89.1-a2 |
89.1-a |
$2$ |
$2$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
89.1 |
\( 89 \) |
\( 89 \) |
$0.91030$ |
$(5a+2)$ |
$0$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$9.495561594$ |
1.431509771 |
\( \frac{4885}{89} a + \frac{99249}{89} \) |
\( \bigl[a\) , \( a\) , \( 0\) , \( -1\) , \( 0\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+a{x}^{2}-{x}$ |
| 89.2-a1 |
89.2-a |
$2$ |
$2$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
89.2 |
\( 89 \) |
\( 89^{2} \) |
$0.91030$ |
$(5a-7)$ |
$0$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$4.747780797$ |
1.431509771 |
\( \frac{842425675}{7921} a - \frac{1150047337}{7921} \) |
\( \bigl[a + 1\) , \( a + 1\) , \( 1\) , \( a + 2\) , \( 1\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(a+2\right){x}+1$ |
| 89.2-a2 |
89.2-a |
$2$ |
$2$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
89.2 |
\( 89 \) |
\( 89 \) |
$0.91030$ |
$(5a-7)$ |
$0$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$9.495561594$ |
1.431509771 |
\( -\frac{4885}{89} a + \frac{104134}{89} \) |
\( \bigl[a + 1\) , \( a + 1\) , \( 1\) , \( a - 3\) , \( -1\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(a-3\right){x}-1$ |
| 92.1-a1 |
92.1-a |
$3$ |
$9$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
92.1 |
\( 2^{2} \cdot 23 \) |
\( 2^{4} \cdot 23 \) |
$0.91787$ |
$(a+4), (2)$ |
$0$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1 |
$1$ |
\( 2 \) |
$1$ |
$8.238724756$ |
1.104030657 |
\( \frac{36793}{92} a + \frac{210163}{92} \) |
\( \bigl[a + 1\) , \( 0\) , \( 1\) , \( -a - 1\) , \( 0\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(-a-1\right){x}$ |
| 92.1-a2 |
92.1-a |
$3$ |
$9$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
92.1 |
\( 2^{2} \cdot 23 \) |
\( 2^{4} \cdot 23^{9} \) |
$0.91787$ |
$(a+4), (2)$ |
$0$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.2 |
$1$ |
\( 2 \) |
$1$ |
$0.915413861$ |
1.104030657 |
\( -\frac{34638770834904571}{3602305322926} a + \frac{53455263008615953}{7204610645852} \) |
\( \bigl[a + 1\) , \( 0\) , \( 1\) , \( 24 a - 96\) , \( 116 a - 322\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(24a-96\right){x}+116a-322$ |
| 92.1-a3 |
92.1-a |
$3$ |
$9$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
92.1 |
\( 2^{2} \cdot 23 \) |
\( 2^{12} \cdot 23^{3} \) |
$0.91787$ |
$(a+4), (2)$ |
$0$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3Cs.1.1 |
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$2.746241585$ |
1.104030657 |
\( \frac{4146024701}{389344} a - \frac{1186600043}{778688} \) |
\( \bigl[a + 1\) , \( 0\) , \( 1\) , \( 4 a + 4\) , \( 4 a - 18\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(4a+4\right){x}+4a-18$ |
| 92.2-a1 |
92.2-a |
$3$ |
$9$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
92.2 |
\( 2^{2} \cdot 23 \) |
\( 2^{4} \cdot 23 \) |
$0.91787$ |
$(a-5), (2)$ |
$0$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1 |
$1$ |
\( 2 \) |
$1$ |
$8.238724756$ |
1.104030657 |
\( -\frac{36793}{92} a + \frac{61739}{23} \) |
\( \bigl[a\) , \( -a + 1\) , \( 1\) , \( -1\) , \( 0\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+\left(-a+1\right){x}^{2}-{x}$ |
| 92.2-a2 |
92.2-a |
$3$ |
$9$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
92.2 |
\( 2^{2} \cdot 23 \) |
\( 2^{4} \cdot 23^{9} \) |
$0.91787$ |
$(a-5), (2)$ |
$0$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.2 |
$1$ |
\( 2 \) |
$1$ |
$0.915413861$ |
1.104030657 |
\( \frac{34638770834904571}{3602305322926} a - \frac{15822278661193189}{7204610645852} \) |
\( \bigl[a\) , \( -a + 1\) , \( 1\) , \( -25 a - 71\) , \( -116 a - 206\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-25a-71\right){x}-116a-206$ |
| 92.2-a3 |
92.2-a |
$3$ |
$9$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
92.2 |
\( 2^{2} \cdot 23 \) |
\( 2^{12} \cdot 23^{3} \) |
$0.91787$ |
$(a-5), (2)$ |
$0$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3Cs.1.1 |
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$2.746241585$ |
1.104030657 |
\( -\frac{4146024701}{389344} a + \frac{7105449359}{778688} \) |
\( \bigl[a\) , \( -a + 1\) , \( 1\) , \( -5 a + 9\) , \( -4 a - 14\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-5a+9\right){x}-4a-14$ |
| 99.1-a1 |
99.1-a |
$2$ |
$2$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
99.1 |
\( 3^{2} \cdot 11 \) |
\( 3^{9} \cdot 11^{2} \) |
$0.93485$ |
$(-a), (-2a+1)$ |
$0$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$2.452601877$ |
1.478974579 |
\( -\frac{393194}{11} a - 1506561 \) |
\( \bigl[1\) , \( -a - 1\) , \( 1\) , \( -10 a - 17\) , \( 41 a + 6\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-10a-17\right){x}+41a+6$ |
| 99.1-a2 |
99.1-a |
$2$ |
$2$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
99.1 |
\( 3^{2} \cdot 11 \) |
\( 3^{9} \cdot 11 \) |
$0.93485$ |
$(-a), (-2a+1)$ |
$0$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$4.905203755$ |
1.478974579 |
\( -\frac{7136}{11} a + \frac{11895}{11} \) |
\( \bigl[1\) , \( -a - 1\) , \( 1\) , \( -2\) , \( a\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(-a-1\right){x}^{2}-2{x}+a$ |
| 99.2-a1 |
99.2-a |
$6$ |
$8$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
99.2 |
\( 3^{2} \cdot 11 \) |
\( 3^{24} \cdot 11^{2} \) |
$0.93485$ |
$(-a), (a-1), (-2a+1)$ |
$0$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1$ |
$1.025585977$ |
0.309225806 |
\( \frac{9090072503}{5845851} \) |
\( \bigl[1\) , \( 1\) , \( 0\) , \( 44\) , \( 55\bigr] \) |
${y}^2+{x}{y}={x}^{3}+{x}^{2}+44{x}+55$ |
| 99.2-a2 |
99.2-a |
$6$ |
$8$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
99.2 |
\( 3^{2} \cdot 11 \) |
\( 3^{12} \cdot 11^{4} \) |
$0.93485$ |
$(-a), (a-1), (-2a+1)$ |
$0$ |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$1$ |
$2.051171954$ |
0.309225806 |
\( \frac{169112377}{88209} \) |
\( \bigl[1\) , \( 1\) , \( 0\) , \( -11\) , \( 0\bigr] \) |
${y}^2+{x}{y}={x}^{3}+{x}^{2}-11{x}$ |
| 99.2-a3 |
99.2-a |
$6$ |
$8$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
99.2 |
\( 3^{2} \cdot 11 \) |
\( 3^{6} \cdot 11^{2} \) |
$0.93485$ |
$(-a), (a-1), (-2a+1)$ |
$0$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$4.102343908$ |
0.309225806 |
\( \frac{30664297}{297} \) |
\( \bigl[1\) , \( 1\) , \( 0\) , \( -6\) , \( -9\bigr] \) |
${y}^2+{x}{y}={x}^{3}+{x}^{2}-6{x}-9$ |
| 99.2-a4 |
99.2-a |
$6$ |
$8$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
99.2 |
\( 3^{2} \cdot 11 \) |
\( 3^{30} \cdot 11 \) |
$0.93485$ |
$(-a), (a-1), (-2a+1)$ |
$0$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$0.512792988$ |
0.309225806 |
\( -\frac{450360153235512010}{3106724901291} a + \frac{211862156595042847}{1035574967097} \) |
\( \bigl[1\) , \( 1\) , \( 0\) , \( -50 a + 509\) , \( 2414 a + 58\bigr] \) |
${y}^2+{x}{y}={x}^{3}+{x}^{2}+\left(-50a+509\right){x}+2414a+58$ |
| 99.2-a5 |
99.2-a |
$6$ |
$8$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
99.2 |
\( 3^{2} \cdot 11 \) |
\( 3^{30} \cdot 11 \) |
$0.93485$ |
$(-a), (a-1), (-2a+1)$ |
$0$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$0.512792988$ |
0.309225806 |
\( \frac{450360153235512010}{3106724901291} a + \frac{185226316549616531}{3106724901291} \) |
\( \bigl[1\) , \( 1\) , \( 0\) , \( 50 a + 459\) , \( -2414 a + 2472\bigr] \) |
${y}^2+{x}{y}={x}^{3}+{x}^{2}+\left(50a+459\right){x}-2414a+2472$ |
| 99.2-a6 |
99.2-a |
$6$ |
$8$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
99.2 |
\( 3^{2} \cdot 11 \) |
\( 3^{6} \cdot 11^{8} \) |
$0.93485$ |
$(-a), (a-1), (-2a+1)$ |
$0$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$1.025585977$ |
0.309225806 |
\( \frac{347873904937}{395307} \) |
\( \bigl[1\) , \( 1\) , \( 0\) , \( -146\) , \( 621\bigr] \) |
${y}^2+{x}{y}={x}^{3}+{x}^{2}-146{x}+621$ |
| 99.3-a1 |
99.3-a |
$2$ |
$2$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
99.3 |
\( 3^{2} \cdot 11 \) |
\( 3^{9} \cdot 11^{2} \) |
$0.93485$ |
$(a-1), (-2a+1)$ |
$0$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$2.452601877$ |
1.478974579 |
\( \frac{393194}{11} a - \frac{16965365}{11} \) |
\( \bigl[1\) , \( a + 1\) , \( 0\) , \( 12 a - 27\) , \( -30 a + 20\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(12a-27\right){x}-30a+20$ |
| 99.3-a2 |
99.3-a |
$2$ |
$2$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
99.3 |
\( 3^{2} \cdot 11 \) |
\( 3^{9} \cdot 11 \) |
$0.93485$ |
$(a-1), (-2a+1)$ |
$0$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$4.905203755$ |
1.478974579 |
\( \frac{7136}{11} a + \frac{4759}{11} \) |
\( \bigl[1\) , \( a + 1\) , \( 0\) , \( 2 a - 2\) , \( -1\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(2a-2\right){x}-1$ |
| 108.1-a1 |
108.1-a |
$4$ |
$27$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
108.1 |
\( 2^{2} \cdot 3^{3} \) |
\( 2^{6} \cdot 3^{11} \) |
$0.95541$ |
$(-a), (2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.2 |
$1$ |
\( 3 \) |
$0.392228249$ |
$0.681207479$ |
0.966725513 |
\( \frac{116453655937}{8} a - 37004774076 \) |
\( \bigl[a + 1\) , \( a - 1\) , \( a + 1\) , \( 443 a - 974\) , \( 6754 a - 9107\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(443a-974\right){x}+6754a-9107$ |
| 108.1-a2 |
108.1-a |
$4$ |
$27$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
108.1 |
\( 2^{2} \cdot 3^{3} \) |
\( 2^{18} \cdot 3^{9} \) |
$0.95541$ |
$(-a), (2)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3Cs.1.1 |
$1$ |
\( 3^{3} \) |
$0.130742749$ |
$2.043622437$ |
0.966725513 |
\( -\frac{488881}{256} a + \frac{1381533}{512} \) |
\( \bigl[a + 1\) , \( a - 1\) , \( a + 1\) , \( 3 a - 14\) , \( 2 a - 11\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(3a-14\right){x}+2a-11$ |
| 108.1-a3 |
108.1-a |
$4$ |
$27$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
108.1 |
\( 2^{2} \cdot 3^{3} \) |
\( 2^{6} \cdot 3^{3} \) |
$0.95541$ |
$(-a), (2)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3Cs.1.1 |
$1$ |
\( 3 \) |
$0.392228249$ |
$6.130867313$ |
0.966725513 |
\( -\frac{21349}{4} a + \frac{328857}{8} \) |
\( \bigl[a + 1\) , \( a - 1\) , \( a + 1\) , \( -2 a + 1\) , \( a - 1\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-2a+1\right){x}+a-1$ |
| 108.1-a4 |
108.1-a |
$4$ |
$27$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
108.1 |
\( 2^{2} \cdot 3^{3} \) |
\( 2^{2} \cdot 3^{5} \) |
$0.95541$ |
$(-a), (2)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.1 |
$1$ |
\( 1 \) |
$1.176684747$ |
$6.130867313$ |
0.966725513 |
\( \frac{21493}{2} a + 66744 \) |
\( \bigl[1\) , \( a - 1\) , \( a + 1\) , \( -2 a + 1\) , \( 3\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-2a+1\right){x}+3$ |
| 108.1-b1 |
108.1-b |
$3$ |
$9$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
108.1 |
\( 2^{2} \cdot 3^{3} \) |
\( 2^{2} \cdot 3^{9} \) |
$0.95541$ |
$(-a), (2)$ |
$0$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.2 |
$1$ |
\( 1 \) |
$1$ |
$2.453117830$ |
1.479285710 |
\( -13361111 a - \frac{6886077}{2} \) |
\( \bigl[1\) , \( a - 1\) , \( a\) , \( -21 a + 30\) , \( 6 a - 81\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-21a+30\right){x}+6a-81$ |
| 108.1-b2 |
108.1-b |
$3$ |
$9$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
108.1 |
\( 2^{2} \cdot 3^{3} \) |
\( 2^{2} \cdot 3^{5} \) |
$0.95541$ |
$(-a), (2)$ |
$0$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.1 |
$1$ |
\( 3 \) |
$1$ |
$7.359353490$ |
1.479285710 |
\( -\frac{3637}{2} a - 1296 \) |
\( \bigl[a\) , \( 0\) , \( 1\) , \( 0\) , \( 0\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}$ |
| 108.1-b3 |
108.1-b |
$3$ |
$9$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
108.1 |
\( 2^{2} \cdot 3^{3} \) |
\( 2^{6} \cdot 3^{3} \) |
$0.95541$ |
$(-a), (2)$ |
$0$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3Cs.1.1 |
$1$ |
\( 3 \) |
$1$ |
$7.359353490$ |
1.479285710 |
\( \frac{1261}{4} a + \frac{11127}{8} \) |
\( \bigl[1\) , \( a - 1\) , \( a\) , \( -a\) , \( 1\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}-a{x}+1$ |
*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.
