| 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 |
| 1.1-a1 |
1.1-a |
$2$ |
$11$ |
\(\Q(\sqrt{165}) \) |
$2$ |
$[2, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$1.14784$ |
$\textsf{none}$ |
0 |
$\mathsf{trivial}$ |
$\textsf{potential}$ |
$-11$ |
$N(\mathrm{U}(1))$ |
✓ |
|
✓ |
✓ |
|
|
$1$ |
\( 1 \) |
$1$ |
$23.06325055$ |
1.795471620 |
\( -32768 \) |
\( \bigl[0\) , \( -1\) , \( 1\) , \( 112 a - 775\) , \( -1715 a + 11872\bigr] \) |
${y}^2+{y}={x}^{3}-{x}^{2}+\left(112a-775\right){x}-1715a+11872$ |
| 1.1-a2 |
1.1-a |
$2$ |
$11$ |
\(\Q(\sqrt{165}) \) |
$2$ |
$[2, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$1.14784$ |
$\textsf{none}$ |
0 |
$\mathsf{trivial}$ |
$\textsf{potential}$ |
$-11$ |
$N(\mathrm{U}(1))$ |
✓ |
|
✓ |
✓ |
|
|
$1$ |
\( 1 \) |
$1$ |
$23.06325055$ |
1.795471620 |
\( -32768 \) |
\( \bigl[0\) , \( a\) , \( 1\) , \( a + 9\) , \( a + 5\bigr] \) |
${y}^2+{y}={x}^{3}+a{x}^{2}+\left(a+9\right){x}+a+5$ |
| 1.1-b1 |
1.1-b |
$2$ |
$11$ |
\(\Q(\sqrt{165}) \) |
$2$ |
$[2, 0]$ |
1.1 |
\( 1 \) |
\( 3^{12} \) |
$1.14784$ |
$\textsf{none}$ |
0 |
$\mathsf{trivial}$ |
$\textsf{potential}$ |
$-11$ |
$N(\mathrm{U}(1))$ |
✓ |
|
✓ |
✓ |
|
|
$1$ |
\( 1 \) |
$1$ |
$23.06325055$ |
1.795471620 |
\( -32768 \) |
\( \bigl[0\) , \( 0\) , \( 1\) , \( 1008 a - 6978\) , \( 45297 a - 313574\bigr] \) |
${y}^2+{y}={x}^{3}+\left(1008a-6978\right){x}+45297a-313574$ |
| 1.1-b2 |
1.1-b |
$2$ |
$11$ |
\(\Q(\sqrt{165}) \) |
$2$ |
$[2, 0]$ |
1.1 |
\( 1 \) |
\( 3^{12} \) |
$1.14784$ |
$\textsf{none}$ |
0 |
$\mathsf{trivial}$ |
$\textsf{potential}$ |
$-11$ |
$N(\mathrm{U}(1))$ |
✓ |
|
✓ |
✓ |
|
|
$1$ |
\( 1 \) |
$1$ |
$23.06325055$ |
1.795471620 |
\( -32768 \) |
\( \bigl[0\) , \( 0\) , \( 1\) , \( 6 a - 42\) , \( -21 a + 145\bigr] \) |
${y}^2+{y}={x}^{3}+\left(6a-42\right){x}-21a+145$ |
| 7.1-a1 |
7.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{165}) \) |
$2$ |
$[2, 0]$ |
7.1 |
\( 7 \) |
\( 7^{2} \) |
$1.86705$ |
$(7,a+2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$2.595777089$ |
$14.31145301$ |
2.892072341 |
\( -\frac{11259}{49} a - \frac{50139}{49} \) |
\( \bigl[a\) , \( -1\) , \( a\) , \( a + 9\) , \( 2 a + 22\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(a+9\right){x}+2a+22$ |
| 7.1-a2 |
7.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{165}) \) |
$2$ |
$[2, 0]$ |
7.1 |
\( 7 \) |
\( 7^{8} \) |
$1.86705$ |
$(7,a+2)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$2.595777089$ |
$14.31145301$ |
2.892072341 |
\( -\frac{14138533098945}{5764801} a + \frac{97899308888103}{5764801} \) |
\( \bigl[a\) , \( -1\) , \( a\) , \( 6 a - 31\) , \( -3 a + 33\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(6a-31\right){x}-3a+33$ |
| 7.1-a3 |
7.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{165}) \) |
$2$ |
$[2, 0]$ |
7.1 |
\( 7 \) |
\( 7^{4} \) |
$1.86705$ |
$(7,a+2)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$5.191554178$ |
$14.31145301$ |
2.892072341 |
\( \frac{2034703395}{2401} a + \frac{12066116778}{2401} \) |
\( \bigl[a\) , \( -1\) , \( a\) , \( a + 4\) , \( a + 6\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(a+4\right){x}+a+6$ |
| 7.1-a4 |
7.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{165}) \) |
$2$ |
$[2, 0]$ |
7.1 |
\( 7 \) |
\( 7^{2} \) |
$1.86705$ |
$(7,a+2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$10.38310835$ |
$3.577863254$ |
2.892072341 |
\( \frac{452487485914929}{49} a + \frac{2679909755295897}{49} \) |
\( \bigl[a\) , \( -1\) , \( a\) , \( -4 a - 41\) , \( -39 a - 305\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(-4a-41\right){x}-39a-305$ |
| 7.1-b1 |
7.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{165}) \) |
$2$ |
$[2, 0]$ |
7.1 |
\( 7 \) |
\( 3^{12} \cdot 7^{2} \) |
$1.86705$ |
$(7,a+2)$ |
$0 \le r \le 2$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$16$ |
\( 2 \) |
$1$ |
$14.31145301$ |
2.228290212 |
\( -\frac{11259}{49} a - \frac{50139}{49} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -36 a - 213\) , \( -375 a - 2221\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}+\left(-36a-213\right){x}-375a-2221$ |
| 7.1-b2 |
7.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{165}) \) |
$2$ |
$[2, 0]$ |
7.1 |
\( 7 \) |
\( 3^{12} \cdot 7^{8} \) |
$1.86705$ |
$(7,a+2)$ |
$0 \le r \le 2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 2 \) |
$1$ |
$14.31145301$ |
2.228290212 |
\( -\frac{14138533098945}{5764801} a + \frac{97899308888103}{5764801} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -666 a - 3948\) , \( -17889 a - 105946\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}+\left(-666a-3948\right){x}-17889a-105946$ |
| 7.1-b3 |
7.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{165}) \) |
$2$ |
$[2, 0]$ |
7.1 |
\( 7 \) |
\( 3^{12} \cdot 7^{4} \) |
$1.86705$ |
$(7,a+2)$ |
$0 \le r \le 2$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$16$ |
\( 2 \) |
$1$ |
$14.31145301$ |
2.228290212 |
\( \frac{2034703395}{2401} a + \frac{12066116778}{2401} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -621 a - 3678\) , \( -21192 a - 125512\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}+\left(-621a-3678\right){x}-21192a-125512$ |
| 7.1-b4 |
7.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{165}) \) |
$2$ |
$[2, 0]$ |
7.1 |
\( 7 \) |
\( 3^{12} \cdot 7^{2} \) |
$1.86705$ |
$(7,a+2)$ |
$0 \le r \le 2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$16$ |
\( 2 \) |
$1$ |
$3.577863254$ |
2.228290212 |
\( \frac{452487485914929}{49} a + \frac{2679909755295897}{49} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -9936 a - 58848\) , \( -1363803 a - 8077282\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}+\left(-9936a-58848\right){x}-1363803a-8077282$ |
| 7.1-c1 |
7.1-c |
$4$ |
$4$ |
\(\Q(\sqrt{165}) \) |
$2$ |
$[2, 0]$ |
7.1 |
\( 7 \) |
\( 7^{2} \) |
$1.86705$ |
$(7,a+2)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 2 \) |
$1$ |
$26.86191021$ |
1.045598437 |
\( -\frac{11259}{49} a - \frac{50139}{49} \) |
\( \bigl[1\) , \( a\) , \( a\) , \( -4 a - 10\) , \( 6 a + 20\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+a{x}^{2}+\left(-4a-10\right){x}+6a+20$ |
| 7.1-c2 |
7.1-c |
$4$ |
$4$ |
\(\Q(\sqrt{165}) \) |
$2$ |
$[2, 0]$ |
7.1 |
\( 7 \) |
\( 7^{8} \) |
$1.86705$ |
$(7,a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 2 \) |
$1$ |
$6.715477554$ |
1.045598437 |
\( -\frac{14138533098945}{5764801} a + \frac{97899308888103}{5764801} \) |
\( \bigl[1\) , \( a\) , \( a\) , \( -74 a - 425\) , \( 493 a + 2905\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+a{x}^{2}+\left(-74a-425\right){x}+493a+2905$ |
| 7.1-c3 |
7.1-c |
$4$ |
$4$ |
\(\Q(\sqrt{165}) \) |
$2$ |
$[2, 0]$ |
7.1 |
\( 7 \) |
\( 7^{4} \) |
$1.86705$ |
$(7,a+2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$4$ |
\( 2 \) |
$1$ |
$26.86191021$ |
1.045598437 |
\( \frac{2034703395}{2401} a + \frac{12066116778}{2401} \) |
\( \bigl[1\) , \( a\) , \( a\) , \( -69 a - 395\) , \( 627 a + 3698\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+a{x}^{2}+\left(-69a-395\right){x}+627a+3698$ |
| 7.1-c4 |
7.1-c |
$4$ |
$4$ |
\(\Q(\sqrt{165}) \) |
$2$ |
$[2, 0]$ |
7.1 |
\( 7 \) |
\( 7^{2} \) |
$1.86705$ |
$(7,a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$26.86191021$ |
1.045598437 |
\( \frac{452487485914929}{49} a + \frac{2679909755295897}{49} \) |
\( \bigl[1\) , \( a\) , \( a\) , \( -1104 a - 6525\) , \( 47965 a + 284063\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+a{x}^{2}+\left(-1104a-6525\right){x}+47965a+284063$ |
| 7.1-d1 |
7.1-d |
$4$ |
$4$ |
\(\Q(\sqrt{165}) \) |
$2$ |
$[2, 0]$ |
7.1 |
\( 7 \) |
\( 3^{12} \cdot 7^{2} \) |
$1.86705$ |
$(7,a+2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1.632402031$ |
$26.86191021$ |
3.413674026 |
\( -\frac{11259}{49} a - \frac{50139}{49} \) |
\( \bigl[a\) , \( -a + 1\) , \( 0\) , \( -6 a + 51\) , \( -12 a + 88\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-6a+51\right){x}-12a+88$ |
| 7.1-d2 |
7.1-d |
$4$ |
$4$ |
\(\Q(\sqrt{165}) \) |
$2$ |
$[2, 0]$ |
7.1 |
\( 7 \) |
\( 3^{12} \cdot 7^{8} \) |
$1.86705$ |
$(7,a+2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1.632402031$ |
$6.715477554$ |
3.413674026 |
\( -\frac{14138533098945}{5764801} a + \frac{97899308888103}{5764801} \) |
\( \bigl[a\) , \( -a + 1\) , \( 0\) , \( 39 a - 309\) , \( 708 a - 4889\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(39a-309\right){x}+708a-4889$ |
| 7.1-d3 |
7.1-d |
$4$ |
$4$ |
\(\Q(\sqrt{165}) \) |
$2$ |
$[2, 0]$ |
7.1 |
\( 7 \) |
\( 3^{12} \cdot 7^{4} \) |
$1.86705$ |
$(7,a+2)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$3.264804063$ |
$26.86191021$ |
3.413674026 |
\( \frac{2034703395}{2401} a + \frac{12066116778}{2401} \) |
\( \bigl[a\) , \( -a + 1\) , \( 0\) , \( -6 a + 6\) , \( 15 a - 65\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-6a+6\right){x}+15a-65$ |
| 7.1-d4 |
7.1-d |
$4$ |
$4$ |
\(\Q(\sqrt{165}) \) |
$2$ |
$[2, 0]$ |
7.1 |
\( 7 \) |
\( 3^{12} \cdot 7^{2} \) |
$1.86705$ |
$(7,a+2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1.632402031$ |
$26.86191021$ |
3.413674026 |
\( \frac{452487485914929}{49} a + \frac{2679909755295897}{49} \) |
\( \bigl[a\) , \( -a + 1\) , \( 0\) , \( -51 a - 399\) , \( 510 a + 3067\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-51a-399\right){x}+510a+3067$ |
| 7.2-a1 |
7.2-a |
$4$ |
$4$ |
\(\Q(\sqrt{165}) \) |
$2$ |
$[2, 0]$ |
7.2 |
\( 7 \) |
\( 7^{2} \) |
$1.86705$ |
$(7,a+4)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$2.595777089$ |
$14.31145301$ |
2.892072341 |
\( \frac{11259}{49} a - \frac{61398}{49} \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( -3 a + 10\) , \( -3 a + 24\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-3a+10\right){x}-3a+24$ |
| 7.2-a2 |
7.2-a |
$4$ |
$4$ |
\(\Q(\sqrt{165}) \) |
$2$ |
$[2, 0]$ |
7.2 |
\( 7 \) |
\( 7^{4} \) |
$1.86705$ |
$(7,a+4)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$5.191554178$ |
$14.31145301$ |
2.892072341 |
\( -\frac{2034703395}{2401} a + \frac{14100820173}{2401} \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( -3 a + 5\) , \( -2 a + 7\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-3a+5\right){x}-2a+7$ |
| 7.2-a3 |
7.2-a |
$4$ |
$4$ |
\(\Q(\sqrt{165}) \) |
$2$ |
$[2, 0]$ |
7.2 |
\( 7 \) |
\( 7^{2} \) |
$1.86705$ |
$(7,a+4)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$10.38310835$ |
$3.577863254$ |
2.892072341 |
\( -\frac{452487485914929}{49} a + \frac{3132397241210826}{49} \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( 2 a - 45\) , \( 38 a - 344\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(2a-45\right){x}+38a-344$ |
| 7.2-a4 |
7.2-a |
$4$ |
$4$ |
\(\Q(\sqrt{165}) \) |
$2$ |
$[2, 0]$ |
7.2 |
\( 7 \) |
\( 7^{8} \) |
$1.86705$ |
$(7,a+4)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$2.595777089$ |
$14.31145301$ |
2.892072341 |
\( \frac{14138533098945}{5764801} a + \frac{83760775789158}{5764801} \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( -8 a - 25\) , \( 2 a + 30\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-8a-25\right){x}+2a+30$ |
| 7.2-b1 |
7.2-b |
$4$ |
$4$ |
\(\Q(\sqrt{165}) \) |
$2$ |
$[2, 0]$ |
7.2 |
\( 7 \) |
\( 3^{12} \cdot 7^{2} \) |
$1.86705$ |
$(7,a+4)$ |
$0 \le r \le 2$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$16$ |
\( 2 \) |
$1$ |
$14.31145301$ |
2.228290212 |
\( \frac{11259}{49} a - \frac{61398}{49} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( 36 a - 249\) , \( 375 a - 2596\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}+\left(36a-249\right){x}+375a-2596$ |
| 7.2-b2 |
7.2-b |
$4$ |
$4$ |
\(\Q(\sqrt{165}) \) |
$2$ |
$[2, 0]$ |
7.2 |
\( 7 \) |
\( 3^{12} \cdot 7^{4} \) |
$1.86705$ |
$(7,a+4)$ |
$0 \le r \le 2$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$16$ |
\( 2 \) |
$1$ |
$14.31145301$ |
2.228290212 |
\( -\frac{2034703395}{2401} a + \frac{14100820173}{2401} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( 621 a - 4299\) , \( 21192 a - 146704\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}+\left(621a-4299\right){x}+21192a-146704$ |
| 7.2-b3 |
7.2-b |
$4$ |
$4$ |
\(\Q(\sqrt{165}) \) |
$2$ |
$[2, 0]$ |
7.2 |
\( 7 \) |
\( 3^{12} \cdot 7^{2} \) |
$1.86705$ |
$(7,a+4)$ |
$0 \le r \le 2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$16$ |
\( 2 \) |
$1$ |
$3.577863254$ |
2.228290212 |
\( -\frac{452487485914929}{49} a + \frac{3132397241210826}{49} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( 9936 a - 68784\) , \( 1363803 a - 9441085\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}+\left(9936a-68784\right){x}+1363803a-9441085$ |
| 7.2-b4 |
7.2-b |
$4$ |
$4$ |
\(\Q(\sqrt{165}) \) |
$2$ |
$[2, 0]$ |
7.2 |
\( 7 \) |
\( 3^{12} \cdot 7^{8} \) |
$1.86705$ |
$(7,a+4)$ |
$0 \le r \le 2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 2 \) |
$1$ |
$14.31145301$ |
2.228290212 |
\( \frac{14138533098945}{5764801} a + \frac{83760775789158}{5764801} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( 666 a - 4614\) , \( 17889 a - 123835\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}+\left(666a-4614\right){x}+17889a-123835$ |
| 7.2-c1 |
7.2-c |
$4$ |
$4$ |
\(\Q(\sqrt{165}) \) |
$2$ |
$[2, 0]$ |
7.2 |
\( 7 \) |
\( 7^{2} \) |
$1.86705$ |
$(7,a+4)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 2 \) |
$1$ |
$26.86191021$ |
1.045598437 |
\( \frac{11259}{49} a - \frac{61398}{49} \) |
\( \bigl[1\) , \( -a + 1\) , \( a + 1\) , \( 3 a - 14\) , \( -7 a + 26\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(3a-14\right){x}-7a+26$ |
| 7.2-c2 |
7.2-c |
$4$ |
$4$ |
\(\Q(\sqrt{165}) \) |
$2$ |
$[2, 0]$ |
7.2 |
\( 7 \) |
\( 7^{4} \) |
$1.86705$ |
$(7,a+4)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$4$ |
\( 2 \) |
$1$ |
$26.86191021$ |
1.045598437 |
\( -\frac{2034703395}{2401} a + \frac{14100820173}{2401} \) |
\( \bigl[1\) , \( -a + 1\) , \( a + 1\) , \( 68 a - 464\) , \( -628 a + 4325\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(68a-464\right){x}-628a+4325$ |
| 7.2-c3 |
7.2-c |
$4$ |
$4$ |
\(\Q(\sqrt{165}) \) |
$2$ |
$[2, 0]$ |
7.2 |
\( 7 \) |
\( 7^{2} \) |
$1.86705$ |
$(7,a+4)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$26.86191021$ |
1.045598437 |
\( -\frac{452487485914929}{49} a + \frac{3132397241210826}{49} \) |
\( \bigl[1\) , \( -a + 1\) , \( a + 1\) , \( 1103 a - 7629\) , \( -47966 a + 332028\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(1103a-7629\right){x}-47966a+332028$ |
| 7.2-c4 |
7.2-c |
$4$ |
$4$ |
\(\Q(\sqrt{165}) \) |
$2$ |
$[2, 0]$ |
7.2 |
\( 7 \) |
\( 7^{8} \) |
$1.86705$ |
$(7,a+4)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 2 \) |
$1$ |
$6.715477554$ |
1.045598437 |
\( \frac{14138533098945}{5764801} a + \frac{83760775789158}{5764801} \) |
\( \bigl[1\) , \( -a + 1\) , \( a + 1\) , \( 73 a - 499\) , \( -494 a + 3398\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(73a-499\right){x}-494a+3398$ |
| 7.2-d1 |
7.2-d |
$4$ |
$4$ |
\(\Q(\sqrt{165}) \) |
$2$ |
$[2, 0]$ |
7.2 |
\( 7 \) |
\( 3^{12} \cdot 7^{2} \) |
$1.86705$ |
$(7,a+4)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1.632402031$ |
$26.86191021$ |
3.413674026 |
\( \frac{11259}{49} a - \frac{61398}{49} \) |
\( \bigl[a + 1\) , \( 0\) , \( 0\) , \( 6 a + 45\) , \( 12 a + 76\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(6a+45\right){x}+12a+76$ |
| 7.2-d2 |
7.2-d |
$4$ |
$4$ |
\(\Q(\sqrt{165}) \) |
$2$ |
$[2, 0]$ |
7.2 |
\( 7 \) |
\( 3^{12} \cdot 7^{4} \) |
$1.86705$ |
$(7,a+4)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$3.264804063$ |
$26.86191021$ |
3.413674026 |
\( -\frac{2034703395}{2401} a + \frac{14100820173}{2401} \) |
\( \bigl[a + 1\) , \( 0\) , \( 0\) , \( 6 a\) , \( -15 a - 50\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+6a{x}-15a-50$ |
| 7.2-d3 |
7.2-d |
$4$ |
$4$ |
\(\Q(\sqrt{165}) \) |
$2$ |
$[2, 0]$ |
7.2 |
\( 7 \) |
\( 3^{12} \cdot 7^{2} \) |
$1.86705$ |
$(7,a+4)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1.632402031$ |
$26.86191021$ |
3.413674026 |
\( -\frac{452487485914929}{49} a + \frac{3132397241210826}{49} \) |
\( \bigl[a + 1\) , \( 0\) , \( 0\) , \( 51 a - 450\) , \( -510 a + 3577\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(51a-450\right){x}-510a+3577$ |
| 7.2-d4 |
7.2-d |
$4$ |
$4$ |
\(\Q(\sqrt{165}) \) |
$2$ |
$[2, 0]$ |
7.2 |
\( 7 \) |
\( 3^{12} \cdot 7^{8} \) |
$1.86705$ |
$(7,a+4)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1.632402031$ |
$6.715477554$ |
3.413674026 |
\( \frac{14138533098945}{5764801} a + \frac{83760775789158}{5764801} \) |
\( \bigl[a + 1\) , \( 0\) , \( 0\) , \( -39 a - 270\) , \( -708 a - 4181\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-39a-270\right){x}-708a-4181$ |
| 11.1-a1 |
11.1-a |
$3$ |
$25$ |
\(\Q(\sqrt{165}) \) |
$2$ |
$[2, 0]$ |
11.1 |
\( 11 \) |
\( 11^{2} \) |
$2.09040$ |
$(a+5)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$5$ |
5B.1.2 |
$1$ |
\( 2 \) |
$131.8741668$ |
$0.064435690$ |
2.646087697 |
\( -\frac{52893159101157376}{11} \) |
\( \bigl[0\) , \( -1\) , \( 1\) , \( -7820\) , \( -263580\bigr] \) |
${y}^2+{y}={x}^{3}-{x}^{2}-7820{x}-263580$ |
| 11.1-a2 |
11.1-a |
$3$ |
$25$ |
\(\Q(\sqrt{165}) \) |
$2$ |
$[2, 0]$ |
11.1 |
\( 11 \) |
\( 11^{10} \) |
$2.09040$ |
$(a+5)$ |
$1$ |
$\Z/5\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$5$ |
5Cs.1.1 |
$1$ |
\( 2 \cdot 5 \) |
$26.37483336$ |
$1.610892258$ |
2.646087697 |
\( -\frac{122023936}{161051} \) |
\( \bigl[0\) , \( -1\) , \( 1\) , \( -10\) , \( -20\bigr] \) |
${y}^2+{y}={x}^{3}-{x}^{2}-10{x}-20$ |
| 11.1-a3 |
11.1-a |
$3$ |
$25$ |
\(\Q(\sqrt{165}) \) |
$2$ |
$[2, 0]$ |
11.1 |
\( 11 \) |
\( 11^{2} \) |
$2.09040$ |
$(a+5)$ |
$1$ |
$\Z/5\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$5$ |
5B.1.1 |
$1$ |
\( 2 \) |
$5.274966672$ |
$40.27230645$ |
2.646087697 |
\( -\frac{4096}{11} \) |
\( \bigl[0\) , \( -1\) , \( 1\) , \( 0\) , \( 0\bigr] \) |
${y}^2+{y}={x}^{3}-{x}^{2}$ |
| 11.1-b1 |
11.1-b |
$3$ |
$25$ |
\(\Q(\sqrt{165}) \) |
$2$ |
$[2, 0]$ |
11.1 |
\( 11 \) |
\( 3^{12} \cdot 11^{2} \) |
$2.09040$ |
$(a+5)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$5$ |
5B.4.2 |
$1$ |
\( 2 \) |
$1$ |
$8.512583687$ |
1.325407482 |
\( -\frac{52893159101157376}{11} \) |
\( \bigl[0\) , \( 0\) , \( 1\) , \( -70383\) , \( 7187035\bigr] \) |
${y}^2+{y}={x}^{3}-70383{x}+7187035$ |
| 11.1-b2 |
11.1-b |
$3$ |
$25$ |
\(\Q(\sqrt{165}) \) |
$2$ |
$[2, 0]$ |
11.1 |
\( 11 \) |
\( 3^{12} \cdot 11^{10} \) |
$2.09040$ |
$(a+5)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$5$ |
5Cs.4.1 |
$1$ |
\( 2 \) |
$1$ |
$8.512583687$ |
1.325407482 |
\( -\frac{122023936}{161051} \) |
\( \bigl[0\) , \( 0\) , \( 1\) , \( -93\) , \( 625\bigr] \) |
${y}^2+{y}={x}^{3}-93{x}+625$ |
| 11.1-b3 |
11.1-b |
$3$ |
$25$ |
\(\Q(\sqrt{165}) \) |
$2$ |
$[2, 0]$ |
11.1 |
\( 11 \) |
\( 3^{12} \cdot 11^{2} \) |
$2.09040$ |
$(a+5)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$5$ |
5B.4.1 |
$1$ |
\( 2 \) |
$1$ |
$8.512583687$ |
1.325407482 |
\( -\frac{4096}{11} \) |
\( \bigl[0\) , \( 0\) , \( 1\) , \( -3\) , \( -5\bigr] \) |
${y}^2+{y}={x}^{3}-3{x}-5$ |
| 11.1-c1 |
11.1-c |
$3$ |
$25$ |
\(\Q(\sqrt{165}) \) |
$2$ |
$[2, 0]$ |
11.1 |
\( 11 \) |
\( 11^{2} \) |
$2.09040$ |
$(a+5)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$5$ |
5B.4.2 |
$1$ |
\( 2 \) |
$1$ |
$8.512583687$ |
1.325407482 |
\( -\frac{52893159101157376}{11} \) |
\( \bigl[0\) , \( a\) , \( 1\) , \( -101664 a - 602152\) , \( 44484722 a + 263466147\bigr] \) |
${y}^2+{y}={x}^{3}+a{x}^{2}+\left(-101664a-602152\right){x}+44484722a+263466147$ |
| 11.1-c2 |
11.1-c |
$3$ |
$25$ |
\(\Q(\sqrt{165}) \) |
$2$ |
$[2, 0]$ |
11.1 |
\( 11 \) |
\( 11^{10} \) |
$2.09040$ |
$(a+5)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$5$ |
5Cs.4.1 |
$1$ |
\( 2 \) |
$1$ |
$8.512583687$ |
1.325407482 |
\( -\frac{122023936}{161051} \) |
\( \bigl[0\) , \( a\) , \( 1\) , \( -134 a - 782\) , \( 3582 a + 21207\bigr] \) |
${y}^2+{y}={x}^{3}+a{x}^{2}+\left(-134a-782\right){x}+3582a+21207$ |
| 11.1-c3 |
11.1-c |
$3$ |
$25$ |
\(\Q(\sqrt{165}) \) |
$2$ |
$[2, 0]$ |
11.1 |
\( 11 \) |
\( 11^{2} \) |
$2.09040$ |
$(a+5)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$5$ |
5B.4.1 |
$1$ |
\( 2 \) |
$1$ |
$8.512583687$ |
1.325407482 |
\( -\frac{4096}{11} \) |
\( \bigl[0\) , \( a\) , \( 1\) , \( -4 a - 12\) , \( -38 a - 233\bigr] \) |
${y}^2+{y}={x}^{3}+a{x}^{2}+\left(-4a-12\right){x}-38a-233$ |
| 11.1-d1 |
11.1-d |
$3$ |
$25$ |
\(\Q(\sqrt{165}) \) |
$2$ |
$[2, 0]$ |
11.1 |
\( 11 \) |
\( 3^{12} \cdot 11^{2} \) |
$2.09040$ |
$(a+5)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$5$ |
5B.1.3 |
$25$ |
\( 2 \) |
$7.655751664$ |
$0.064435690$ |
3.840363655 |
\( -\frac{52893159101157376}{11} \) |
\( \bigl[0\) , \( 0\) , \( 1\) , \( 914979 a - 6334470\) , \( 1207421922 a - 8358521996\bigr] \) |
${y}^2+{y}={x}^{3}+\left(914979a-6334470\right){x}+1207421922a-8358521996$ |
| 11.1-d2 |
11.1-d |
$3$ |
$25$ |
\(\Q(\sqrt{165}) \) |
$2$ |
$[2, 0]$ |
11.1 |
\( 11 \) |
\( 3^{12} \cdot 11^{10} \) |
$2.09040$ |
$(a+5)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$5$ |
5Cs.1.3 |
$1$ |
\( 2 \cdot 5 \) |
$1.531150332$ |
$1.610892258$ |
3.840363655 |
\( -\frac{122023936}{161051} \) |
\( \bigl[0\) , \( 0\) , \( 1\) , \( 1209 a - 8370\) , \( 105042 a - 727166\bigr] \) |
${y}^2+{y}={x}^{3}+\left(1209a-8370\right){x}+105042a-727166$ |
| 11.1-d3 |
11.1-d |
$3$ |
$25$ |
\(\Q(\sqrt{165}) \) |
$2$ |
$[2, 0]$ |
11.1 |
\( 11 \) |
\( 3^{12} \cdot 11^{2} \) |
$2.09040$ |
$(a+5)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$5$ |
5B.1.4 |
$1$ |
\( 2 \) |
$0.306230066$ |
$40.27230645$ |
3.840363655 |
\( -\frac{4096}{11} \) |
\( \bigl[0\) , \( 0\) , \( 1\) , \( 39 a - 270\) , \( -798 a + 5524\bigr] \) |
${y}^2+{y}={x}^{3}+\left(39a-270\right){x}-798a+5524$ |
| 12.1-a1 |
12.1-a |
$2$ |
$2$ |
\(\Q(\sqrt{165}) \) |
$2$ |
$[2, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( 2^{12} \cdot 3^{6} \) |
$2.13637$ |
$(3,a+1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 3$ |
2B, 3Ns |
$1$ |
\( 2^{2} \) |
$1$ |
$15.71636264$ |
1.223517172 |
\( \frac{3723875}{1728} \) |
\( \bigl[a + 1\) , \( a\) , \( a + 1\) , \( 15 a + 35\) , \( 29 a + 210\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(15a+35\right){x}+29a+210$ |
| 12.1-a2 |
12.1-a |
$2$ |
$2$ |
\(\Q(\sqrt{165}) \) |
$2$ |
$[2, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( 2^{6} \cdot 3^{12} \) |
$2.13637$ |
$(3,a+1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 3$ |
2B, 3Ns |
$4$ |
\( 2 \) |
$1$ |
$7.858181321$ |
1.223517172 |
\( \frac{8934171875}{5832} \) |
\( \bigl[a + 1\) , \( a\) , \( a + 1\) , \( 55 a - 245\) , \( -363 a + 2898\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(55a-245\right){x}-363a+2898$ |
*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.
