| 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 |
| 2.1-a1 |
2.1-a |
$1$ |
$1$ |
\(\Q(\sqrt{145}) \) |
$2$ |
$[2, 0]$ |
2.1 |
\( 2 \) |
\( 2^{20} \) |
$1.27962$ |
$(2,a)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \) |
$1$ |
$10.98033663$ |
1.823734648 |
\( \frac{69373}{256} a - \frac{10305}{256} \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( 0\) , \( 462 a - 2998\) , \( 20904 a - 136300\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(462a-2998\right){x}+20904a-136300$ |
| 2.1-b1 |
2.1-b |
$1$ |
$1$ |
\(\Q(\sqrt{145}) \) |
$2$ |
$[2, 0]$ |
2.1 |
\( 2 \) |
\( 2^{20} \) |
$1.27962$ |
$(2,a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2^{3} \) |
$0.098634177$ |
$10.98033663$ |
1.439060535 |
\( \frac{69373}{256} a - \frac{10305}{256} \) |
\( \bigl[a\) , \( 0\) , \( 0\) , \( 2 a + 29\) , \( 4 a + 34\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(2a+29\right){x}+4a+34$ |
| 2.2-a1 |
2.2-a |
$1$ |
$1$ |
\(\Q(\sqrt{145}) \) |
$2$ |
$[2, 0]$ |
2.2 |
\( 2 \) |
\( 2^{20} \) |
$1.27962$ |
$(2,a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \) |
$1$ |
$10.98033663$ |
1.823734648 |
\( -\frac{69373}{256} a + \frac{14767}{64} \) |
\( \bigl[a\) , \( -1\) , \( 0\) , \( -462 a - 2536\) , \( -20904 a - 115396\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-{x}^{2}+\left(-462a-2536\right){x}-20904a-115396$ |
| 2.2-b1 |
2.2-b |
$1$ |
$1$ |
\(\Q(\sqrt{145}) \) |
$2$ |
$[2, 0]$ |
2.2 |
\( 2 \) |
\( 2^{20} \) |
$1.27962$ |
$(2,a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2^{3} \) |
$0.098634177$ |
$10.98033663$ |
1.439060535 |
\( -\frac{69373}{256} a + \frac{14767}{64} \) |
\( \bigl[a + 1\) , \( -a\) , \( 0\) , \( -2 a + 31\) , \( -4 a + 38\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}-a{x}^{2}+\left(-2a+31\right){x}-4a+38$ |
| 4.1-a1 |
4.1-a |
$2$ |
$5$ |
\(\Q(\sqrt{145}) \) |
$2$ |
$[2, 0]$ |
4.1 |
\( 2^{2} \) |
\( 2^{20} \) |
$1.52173$ |
$(2,a), (2,a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$5$ |
5B.4.2 |
$1$ |
\( 2^{3} \) |
$0.036167522$ |
$48.80986873$ |
2.345645522 |
\( -\frac{1030301}{16} \) |
\( \bigl[a\) , \( 1\) , \( a\) , \( -43 a - 228\) , \( 229 a + 1280\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}+\left(-43a-228\right){x}+229a+1280$ |
| 4.1-a2 |
4.1-a |
$2$ |
$5$ |
\(\Q(\sqrt{145}) \) |
$2$ |
$[2, 0]$ |
4.1 |
\( 2^{2} \) |
\( 2^{52} \) |
$1.52173$ |
$(2,a), (2,a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$5$ |
5B.4.1 |
$1$ |
\( 2^{3} \cdot 5 \) |
$0.180837612$ |
$1.952394749$ |
2.345645522 |
\( \frac{237176659}{1048576} \) |
\( \bigl[a\) , \( 1\) , \( a\) , \( 272 a + 1512\) , \( -14291 a - 78880\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}+\left(272a+1512\right){x}-14291a-78880$ |
| 4.1-b1 |
4.1-b |
$2$ |
$5$ |
\(\Q(\sqrt{145}) \) |
$2$ |
$[2, 0]$ |
4.1 |
\( 2^{2} \) |
\( 2^{20} \) |
$1.52173$ |
$(2,a), (2,a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$5$ |
5B.4.2 |
$1$ |
\( 2^{3} \) |
$0.036167522$ |
$48.80986873$ |
2.345645522 |
\( -\frac{1030301}{16} \) |
\( \bigl[a + 1\) , \( -a + 1\) , \( a + 1\) , \( 41 a - 271\) , \( -230 a + 1509\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(41a-271\right){x}-230a+1509$ |
| 4.1-b2 |
4.1-b |
$2$ |
$5$ |
\(\Q(\sqrt{145}) \) |
$2$ |
$[2, 0]$ |
4.1 |
\( 2^{2} \) |
\( 2^{52} \) |
$1.52173$ |
$(2,a), (2,a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$5$ |
5B.4.1 |
$1$ |
\( 2^{3} \cdot 5 \) |
$0.180837612$ |
$1.952394749$ |
2.345645522 |
\( \frac{237176659}{1048576} \) |
\( \bigl[a + 1\) , \( -a + 1\) , \( a + 1\) , \( -274 a + 1784\) , \( 14290 a - 93171\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-274a+1784\right){x}+14290a-93171$ |
| 4.2-a1 |
4.2-a |
$2$ |
$2$ |
\(\Q(\sqrt{145}) \) |
$2$ |
$[2, 0]$ |
4.2 |
\( 2^{2} \) |
\( - 2^{20} \) |
$1.52173$ |
$(2,a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2, 5$ |
2B, 5Nn |
$1$ |
\( 3 \) |
$0.952650991$ |
$27.80637502$ |
3.299783584 |
\( 65 a + 1476 \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( -a + 5\) , \( 2 a + 18\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(-a+5\right){x}+2a+18$ |
| 4.2-a2 |
4.2-a |
$2$ |
$2$ |
\(\Q(\sqrt{145}) \) |
$2$ |
$[2, 0]$ |
4.2 |
\( 2^{2} \) |
\( 2^{4} \) |
$1.52173$ |
$(2,a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2, 5$ |
2B, 5Nn |
$1$ |
\( 3 \) |
$0.476325495$ |
$55.61275005$ |
3.299783584 |
\( 69125 a + 384228 \) |
\( \bigl[a\) , \( a\) , \( 0\) , \( 7 a + 40\) , \( 11 a + 61\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+a{x}^{2}+\left(7a+40\right){x}+11a+61$ |
| 4.2-b1 |
4.2-b |
$2$ |
$2$ |
\(\Q(\sqrt{145}) \) |
$2$ |
$[2, 0]$ |
4.2 |
\( 2^{2} \) |
\( - 2^{20} \) |
$1.52173$ |
$(2,a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2, 5$ |
2B, 5Nn |
$1$ |
\( 1 \) |
$0.740300779$ |
$27.80637502$ |
0.854748968 |
\( 65 a + 1476 \) |
\( \bigl[a\) , \( 0\) , \( 0\) , \( -a + 44\) , \( -8 a + 96\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-a+44\right){x}-8a+96$ |
| 4.2-b2 |
4.2-b |
$2$ |
$2$ |
\(\Q(\sqrt{145}) \) |
$2$ |
$[2, 0]$ |
4.2 |
\( 2^{2} \) |
\( 2^{4} \cdot 5^{12} \) |
$1.52173$ |
$(2,a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2, 5$ |
2B, 5Nn |
$1$ |
\( 1 \) |
$0.370150389$ |
$55.61275005$ |
0.854748968 |
\( 69125 a + 384228 \) |
\( \bigl[a\) , \( 0\) , \( 0\) , \( -24 a - 116\) , \( 86 a + 485\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-24a-116\right){x}+86a+485$ |
| 4.3-a1 |
4.3-a |
$2$ |
$2$ |
\(\Q(\sqrt{145}) \) |
$2$ |
$[2, 0]$ |
4.3 |
\( 2^{2} \) |
\( - 2^{20} \) |
$1.52173$ |
$(2,a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2, 5$ |
2B, 5Nn |
$1$ |
\( 3 \) |
$0.952650991$ |
$27.80637502$ |
3.299783584 |
\( -65 a + 1541 \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( a + 4\) , \( -2 a + 20\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(a+4\right){x}-2a+20$ |
| 4.3-a2 |
4.3-a |
$2$ |
$2$ |
\(\Q(\sqrt{145}) \) |
$2$ |
$[2, 0]$ |
4.3 |
\( 2^{2} \) |
\( 2^{4} \) |
$1.52173$ |
$(2,a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2, 5$ |
2B, 5Nn |
$1$ |
\( 3 \) |
$0.476325495$ |
$55.61275005$ |
3.299783584 |
\( -69125 a + 453353 \) |
\( \bigl[a + 1\) , \( a + 1\) , \( 0\) , \( 14 a + 65\) , \( 30 a + 180\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(14a+65\right){x}+30a+180$ |
| 4.3-b1 |
4.3-b |
$2$ |
$2$ |
\(\Q(\sqrt{145}) \) |
$2$ |
$[2, 0]$ |
4.3 |
\( 2^{2} \) |
\( - 2^{20} \) |
$1.52173$ |
$(2,a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2, 5$ |
2B, 5Nn |
$1$ |
\( 1 \) |
$0.740300779$ |
$27.80637502$ |
0.854748968 |
\( -65 a + 1541 \) |
\( \bigl[a + 1\) , \( -a\) , \( 0\) , \( a + 43\) , \( 8 a + 88\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}-a{x}^{2}+\left(a+43\right){x}+8a+88$ |
| 4.3-b2 |
4.3-b |
$2$ |
$2$ |
\(\Q(\sqrt{145}) \) |
$2$ |
$[2, 0]$ |
4.3 |
\( 2^{2} \) |
\( 2^{4} \cdot 5^{12} \) |
$1.52173$ |
$(2,a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2, 5$ |
2B, 5Nn |
$1$ |
\( 1 \) |
$0.370150389$ |
$55.61275005$ |
0.854748968 |
\( -69125 a + 453353 \) |
\( \bigl[a + 1\) , \( -a\) , \( 0\) , \( 24 a - 140\) , \( -86 a + 571\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}-a{x}^{2}+\left(24a-140\right){x}-86a+571$ |
| 6.2-a1 |
6.2-a |
$2$ |
$2$ |
\(\Q(\sqrt{145}) \) |
$2$ |
$[2, 0]$ |
6.2 |
\( 2 \cdot 3 \) |
\( - 2^{18} \cdot 3^{2} \) |
$1.68407$ |
$(2,a), (3,a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$11.19770184$ |
2.789755568 |
\( -\frac{576713}{576} a + \frac{274965}{64} \) |
\( \bigl[a\) , \( -a + 1\) , \( a\) , \( 141 a - 932\) , \( 2827 a - 18440\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(141a-932\right){x}+2827a-18440$ |
| 6.2-a2 |
6.2-a |
$2$ |
$2$ |
\(\Q(\sqrt{145}) \) |
$2$ |
$[2, 0]$ |
6.2 |
\( 2 \cdot 3 \) |
\( - 2^{3} \cdot 3 \) |
$1.68407$ |
$(2,a), (3,a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 3 \) |
$1$ |
$11.19770184$ |
2.789755568 |
\( \frac{16895305}{24} a + \frac{31093129}{8} \) |
\( \bigl[1\) , \( 0\) , \( a\) , \( -12 a + 75\) , \( 162 a - 1067\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(-12a+75\right){x}+162a-1067$ |
| 6.2-b1 |
6.2-b |
$2$ |
$5$ |
\(\Q(\sqrt{145}) \) |
$2$ |
$[2, 0]$ |
6.2 |
\( 2 \cdot 3 \) |
\( - 2^{15} \cdot 3 \) |
$1.68407$ |
$(2,a), (3,a+2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.4.2 |
$1$ |
\( 3 \) |
$0.209797355$ |
$46.53464872$ |
4.864561506 |
\( \frac{38645}{24} a + \frac{71117}{8} \) |
\( \bigl[a + 1\) , \( 1\) , \( a + 1\) , \( 4 a + 22\) , \( -40 a + 375\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(4a+22\right){x}-40a+375$ |
| 6.2-b2 |
6.2-b |
$2$ |
$5$ |
\(\Q(\sqrt{145}) \) |
$2$ |
$[2, 0]$ |
6.2 |
\( 2 \cdot 3 \) |
\( - 2^{27} \cdot 3^{5} \) |
$1.68407$ |
$(2,a), (3,a+2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.4.1 |
$1$ |
\( 3 \cdot 5 \) |
$1.048986777$ |
$1.861385948$ |
4.864561506 |
\( \frac{345772615815749}{7962624} a + \frac{212097907422431}{884736} \) |
\( \bigl[a + 1\) , \( 1\) , \( a + 1\) , \( 369 a - 2363\) , \( 11114 a - 72387\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(369a-2363\right){x}+11114a-72387$ |
| 6.2-c1 |
6.2-c |
$2$ |
$2$ |
\(\Q(\sqrt{145}) \) |
$2$ |
$[2, 0]$ |
6.2 |
\( 2 \cdot 3 \) |
\( - 2^{18} \cdot 3^{10} \) |
$1.68407$ |
$(2,a), (3,a+2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \cdot 5 \) |
$0.115113349$ |
$15.39291078$ |
1.471507366 |
\( -\frac{24682058105}{3779136} a + \frac{18031607557}{419904} \) |
\( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( 1228 a + 6778\) , \( 118559 a + 654540\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(1228a+6778\right){x}+118559a+654540$ |
| 6.2-c2 |
6.2-c |
$2$ |
$2$ |
\(\Q(\sqrt{145}) \) |
$2$ |
$[2, 0]$ |
6.2 |
\( 2 \cdot 3 \) |
\( 2^{3} \cdot 3^{5} \cdot 5^{12} \) |
$1.68407$ |
$(2,a), (3,a+2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 5 \) |
$0.230226698$ |
$30.78582157$ |
1.471507366 |
\( -\frac{988579167505}{1944} a + \frac{716259601493}{216} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -200 a - 1151\) , \( 3275 a + 18198\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(-200a-1151\right){x}+3275a+18198$ |
| 6.2-d1 |
6.2-d |
$4$ |
$4$ |
\(\Q(\sqrt{145}) \) |
$2$ |
$[2, 0]$ |
6.2 |
\( 2 \cdot 3 \) |
\( - 2^{16} \cdot 3^{12} \) |
$1.68407$ |
$(2,a), (3,a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$5.349208508$ |
0.444227587 |
\( -\frac{10742434793}{8503056} a - \frac{4822222235}{944784} \) |
\( \bigl[a\) , \( a\) , \( 0\) , \( 419336 a - 2734307\) , \( 100467076 a - 655125250\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+a{x}^{2}+\left(419336a-2734307\right){x}+100467076a-655125250$ |
| 6.2-d2 |
6.2-d |
$4$ |
$4$ |
\(\Q(\sqrt{145}) \) |
$2$ |
$[2, 0]$ |
6.2 |
\( 2 \cdot 3 \) |
\( 2^{13} \cdot 3^{3} \) |
$1.68407$ |
$(2,a), (3,a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 1 \) |
$1$ |
$5.349208508$ |
0.444227587 |
\( -\frac{2580910083523}{54} a + \frac{1869954697517}{6} \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( 0\) , \( 5248141 a - 34222049\) , \( 16075108293 a - 104822522573\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(5248141a-34222049\right){x}+16075108293a-104822522573$ |
| 6.2-d3 |
6.2-d |
$4$ |
$4$ |
\(\Q(\sqrt{145}) \) |
$2$ |
$[2, 0]$ |
6.2 |
\( 2 \cdot 3 \) |
\( 2^{2} \cdot 3^{6} \) |
$1.68407$ |
$(2,a), (3,a+2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$4$ |
\( 2^{2} \) |
$1$ |
$5.349208508$ |
0.444227587 |
\( \frac{47771196715}{2916} a + \frac{29549937397}{324} \) |
\( \bigl[1\) , \( -a - 1\) , \( a\) , \( 328113 a - 2139544\) , \( 251265419 a - 1638450888\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(328113a-2139544\right){x}+251265419a-1638450888$ |
| 6.2-d4 |
6.2-d |
$4$ |
$4$ |
\(\Q(\sqrt{145}) \) |
$2$ |
$[2, 0]$ |
6.2 |
\( 2 \cdot 3 \) |
\( - 2 \cdot 3^{3} \) |
$1.68407$ |
$(2,a), (3,a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$16$ |
\( 1 \) |
$1$ |
$1.337302127$ |
0.444227587 |
\( \frac{175860717738397615}{54} a + \frac{107876819311265443}{6} \) |
\( \bigl[1\) , \( -a - 1\) , \( a\) , \( 238558 a - 1555574\) , \( 391024161 a - 2549789314\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(238558a-1555574\right){x}+391024161a-2549789314$ |
| 6.2-e1 |
6.2-e |
$4$ |
$4$ |
\(\Q(\sqrt{145}) \) |
$2$ |
$[2, 0]$ |
6.2 |
\( 2 \cdot 3 \) |
\( - 2^{16} \cdot 3^{12} \) |
$1.68407$ |
$(2,a), (3,a+2)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{4} \cdot 3 \) |
$1$ |
$5.349208508$ |
1.332682762 |
\( -\frac{10742434793}{8503056} a - \frac{4822222235}{944784} \) |
\( \bigl[a + 1\) , \( a - 1\) , \( a + 1\) , \( -181 a - 1009\) , \( -4946 a - 27311\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-181a-1009\right){x}-4946a-27311$ |
| 6.2-e2 |
6.2-e |
$4$ |
$4$ |
\(\Q(\sqrt{145}) \) |
$2$ |
$[2, 0]$ |
6.2 |
\( 2 \cdot 3 \) |
\( 2^{13} \cdot 3^{3} \) |
$1.68407$ |
$(2,a), (3,a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 3 \) |
$1$ |
$5.349208508$ |
1.332682762 |
\( -\frac{2580910083523}{54} a + \frac{1869954697517}{6} \) |
\( \bigl[a\) , \( 0\) , \( 0\) , \( -9415 a - 51959\) , \( -1180527 a - 6517434\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-9415a-51959\right){x}-1180527a-6517434$ |
| 6.2-e3 |
6.2-e |
$4$ |
$4$ |
\(\Q(\sqrt{145}) \) |
$2$ |
$[2, 0]$ |
6.2 |
\( 2 \cdot 3 \) |
\( 2^{2} \cdot 3^{6} \cdot 5^{12} \) |
$1.68407$ |
$(2,a), (3,a+2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$4$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$5.349208508$ |
1.332682762 |
\( \frac{47771196715}{2916} a + \frac{29549937397}{324} \) |
\( \bigl[1\) , \( a - 1\) , \( a + 1\) , \( -34 a - 468\) , \( -588 a - 4597\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-34a-468\right){x}-588a-4597$ |
| 6.2-e4 |
6.2-e |
$4$ |
$4$ |
\(\Q(\sqrt{145}) \) |
$2$ |
$[2, 0]$ |
6.2 |
\( 2 \cdot 3 \) |
\( - 2 \cdot 3^{3} \cdot 5^{12} \) |
$1.68407$ |
$(2,a), (3,a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$16$ |
\( 3 \) |
$1$ |
$1.337302127$ |
1.332682762 |
\( \frac{175860717738397615}{54} a + \frac{107876819311265443}{6} \) |
\( \bigl[1\) , \( a - 1\) , \( a + 1\) , \( -909 a - 5218\) , \( -39213 a - 219097\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-909a-5218\right){x}-39213a-219097$ |
| 6.2-f1 |
6.2-f |
$2$ |
$2$ |
\(\Q(\sqrt{145}) \) |
$2$ |
$[2, 0]$ |
6.2 |
\( 2 \cdot 3 \) |
\( - 2^{18} \cdot 3^{2} \) |
$1.68407$ |
$(2,a), (3,a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$11.19770184$ |
0.929918522 |
\( -\frac{576713}{576} a + \frac{274965}{64} \) |
\( \bigl[a + 1\) , \( 1\) , \( 0\) , \( 7 a + 30\) , \( 16 a + 20\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+{x}^{2}+\left(7a+30\right){x}+16a+20$ |
| 6.2-f2 |
6.2-f |
$2$ |
$2$ |
\(\Q(\sqrt{145}) \) |
$2$ |
$[2, 0]$ |
6.2 |
\( 2 \cdot 3 \) |
\( - 2^{3} \cdot 3 \cdot 5^{12} \) |
$1.68407$ |
$(2,a), (3,a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 1 \) |
$1$ |
$11.19770184$ |
0.929918522 |
\( \frac{16895305}{24} a + \frac{31093129}{8} \) |
\( \bigl[1\) , \( 1\) , \( a\) , \( -288 a + 1875\) , \( 20281 a - 132259\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+{x}^{2}+\left(-288a+1875\right){x}+20281a-132259$ |
| 6.2-g1 |
6.2-g |
$2$ |
$5$ |
\(\Q(\sqrt{145}) \) |
$2$ |
$[2, 0]$ |
6.2 |
\( 2 \cdot 3 \) |
\( - 2^{15} \cdot 3 \) |
$1.68407$ |
$(2,a), (3,a+2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.4.2 |
$1$ |
\( 1 \) |
$0.175813208$ |
$46.53464872$ |
1.358857554 |
\( \frac{38645}{24} a + \frac{71117}{8} \) |
\( \bigl[0\) , \( 1\) , \( a\) , \( 16 a - 104\) , \( -37870 a + 246932\bigr] \) |
${y}^2+a{y}={x}^{3}+{x}^{2}+\left(16a-104\right){x}-37870a+246932$ |
| 6.2-g2 |
6.2-g |
$2$ |
$5$ |
\(\Q(\sqrt{145}) \) |
$2$ |
$[2, 0]$ |
6.2 |
\( 2 \cdot 3 \) |
\( - 2^{27} \cdot 3^{5} \) |
$1.68407$ |
$(2,a), (3,a+2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.4.1 |
$1$ |
\( 5 \) |
$0.879066040$ |
$1.861385948$ |
1.358857554 |
\( \frac{345772615815749}{7962624} a + \frac{212097907422431}{884736} \) |
\( \bigl[0\) , \( 1\) , \( a\) , \( 30546 a - 199184\) , \( 7924176 a - 51671956\bigr] \) |
${y}^2+a{y}={x}^{3}+{x}^{2}+\left(30546a-199184\right){x}+7924176a-51671956$ |
| 6.2-h1 |
6.2-h |
$2$ |
$2$ |
\(\Q(\sqrt{145}) \) |
$2$ |
$[2, 0]$ |
6.2 |
\( 2 \cdot 3 \) |
\( - 2^{18} \cdot 3^{10} \) |
$1.68407$ |
$(2,a), (3,a+2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \cdot 3 \) |
$0.308413437$ |
$15.39291078$ |
2.365490964 |
\( -\frac{24682058105}{3779136} a + \frac{18031607557}{419904} \) |
\( \bigl[a\) , \( -a - 1\) , \( 0\) , \( 51604 a - 336496\) , \( -15277923 a + 99624240\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(51604a-336496\right){x}-15277923a+99624240$ |
| 6.2-h2 |
6.2-h |
$2$ |
$2$ |
\(\Q(\sqrt{145}) \) |
$2$ |
$[2, 0]$ |
6.2 |
\( 2 \cdot 3 \) |
\( 2^{3} \cdot 3^{5} \) |
$1.68407$ |
$(2,a), (3,a+2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 3 \) |
$0.616826874$ |
$30.78582157$ |
2.365490964 |
\( -\frac{988579167505}{1944} a + \frac{716259601493}{216} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( 51450 a - 335495\) , \( -15565763 a + 101501185\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}+\left(51450a-335495\right){x}-15565763a+101501185$ |
| 6.3-a1 |
6.3-a |
$2$ |
$2$ |
\(\Q(\sqrt{145}) \) |
$2$ |
$[2, 0]$ |
6.3 |
\( 2 \cdot 3 \) |
\( - 2^{3} \cdot 3 \) |
$1.68407$ |
$(2,a+1), (3,a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 3 \) |
$1$ |
$11.19770184$ |
2.789755568 |
\( -\frac{16895305}{24} a + \frac{27543673}{6} \) |
\( \bigl[1\) , \( 0\) , \( a + 1\) , \( 11 a + 63\) , \( -163 a - 905\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(11a+63\right){x}-163a-905$ |
| 6.3-a2 |
6.3-a |
$2$ |
$2$ |
\(\Q(\sqrt{145}) \) |
$2$ |
$[2, 0]$ |
6.3 |
\( 2 \cdot 3 \) |
\( - 2^{18} \cdot 3^{2} \) |
$1.68407$ |
$(2,a+1), (3,a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$11.19770184$ |
2.789755568 |
\( \frac{576713}{576} a + \frac{474493}{144} \) |
\( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( -143 a - 791\) , \( -2828 a - 15613\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-143a-791\right){x}-2828a-15613$ |
| 6.3-b1 |
6.3-b |
$2$ |
$5$ |
\(\Q(\sqrt{145}) \) |
$2$ |
$[2, 0]$ |
6.3 |
\( 2 \cdot 3 \) |
\( - 2^{27} \cdot 3^{5} \) |
$1.68407$ |
$(2,a+1), (3,a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.4.1 |
$1$ |
\( 3 \cdot 5 \) |
$1.048986777$ |
$1.861385948$ |
4.864561506 |
\( -\frac{345772615815749}{7962624} a + \frac{563663445654407}{1990656} \) |
\( \bigl[a\) , \( -a - 1\) , \( 0\) , \( -369 a - 1993\) , \( -10745 a - 59279\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-369a-1993\right){x}-10745a-59279$ |
| 6.3-b2 |
6.3-b |
$2$ |
$5$ |
\(\Q(\sqrt{145}) \) |
$2$ |
$[2, 0]$ |
6.3 |
\( 2 \cdot 3 \) |
\( - 2^{15} \cdot 3 \) |
$1.68407$ |
$(2,a+1), (3,a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.4.2 |
$1$ |
\( 3 \) |
$0.209797355$ |
$46.53464872$ |
4.864561506 |
\( -\frac{38645}{24} a + \frac{62999}{6} \) |
\( \bigl[a\) , \( -a - 1\) , \( 0\) , \( -4 a + 27\) , \( 44 a + 309\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-4a+27\right){x}+44a+309$ |
| 6.3-c1 |
6.3-c |
$2$ |
$2$ |
\(\Q(\sqrt{145}) \) |
$2$ |
$[2, 0]$ |
6.3 |
\( 2 \cdot 3 \) |
\( - 2^{18} \cdot 3^{10} \) |
$1.68407$ |
$(2,a+1), (3,a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \cdot 5 \) |
$0.115113349$ |
$15.39291078$ |
1.471507366 |
\( \frac{24682058105}{3779136} a + \frac{34400602477}{944784} \) |
\( \bigl[a\) , \( -a + 1\) , \( a\) , \( -1230 a + 8008\) , \( -118560 a + 773100\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-1230a+8008\right){x}-118560a+773100$ |
| 6.3-c2 |
6.3-c |
$2$ |
$2$ |
\(\Q(\sqrt{145}) \) |
$2$ |
$[2, 0]$ |
6.3 |
\( 2 \cdot 3 \) |
\( 2^{3} \cdot 3^{5} \cdot 5^{12} \) |
$1.68407$ |
$(2,a+1), (3,a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 5 \) |
$0.230226698$ |
$30.78582157$ |
1.471507366 |
\( \frac{988579167505}{1944} a + \frac{1364439311483}{486} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( 200 a - 1351\) , \( -3275 a + 21473\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(200a-1351\right){x}-3275a+21473$ |
| 6.3-d1 |
6.3-d |
$4$ |
$4$ |
\(\Q(\sqrt{145}) \) |
$2$ |
$[2, 0]$ |
6.3 |
\( 2 \cdot 3 \) |
\( - 2 \cdot 3^{3} \) |
$1.68407$ |
$(2,a+1), (3,a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$16$ |
\( 1 \) |
$1$ |
$1.337302127$ |
0.444227587 |
\( -\frac{175860717738397615}{54} a + \frac{573376045769893301}{27} \) |
\( \bigl[1\) , \( a + 1\) , \( a\) , \( -238557 a - 1317016\) , \( -391262719 a - 2160082169\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-238557a-1317016\right){x}-391262719a-2160082169$ |
| 6.3-d2 |
6.3-d |
$4$ |
$4$ |
\(\Q(\sqrt{145}) \) |
$2$ |
$[2, 0]$ |
6.3 |
\( 2 \cdot 3 \) |
\( - 2^{16} \cdot 3^{12} \) |
$1.68407$ |
$(2,a+1), (3,a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$5.349208508$ |
0.444227587 |
\( \frac{10742434793}{8503056} a - \frac{13535608727}{2125764} \) |
\( \bigl[a + 1\) , \( a + 1\) , \( 0\) , \( -419315 a - 2314953\) , \( -103201382 a - 569753910\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-419315a-2314953\right){x}-103201382a-569753910$ |
| 6.3-d3 |
6.3-d |
$4$ |
$4$ |
\(\Q(\sqrt{145}) \) |
$2$ |
$[2, 0]$ |
6.3 |
\( 2 \cdot 3 \) |
\( 2^{2} \cdot 3^{6} \) |
$1.68407$ |
$(2,a+1), (3,a)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$4$ |
\( 2^{2} \) |
$1$ |
$5.349208508$ |
0.444227587 |
\( -\frac{47771196715}{2916} a + \frac{78430158322}{729} \) |
\( \bigl[1\) , \( a + 1\) , \( a\) , \( -328112 a - 1811431\) , \( -251593532 a - 1388996900\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-328112a-1811431\right){x}-251593532a-1388996900$ |
| 6.3-d4 |
6.3-d |
$4$ |
$4$ |
\(\Q(\sqrt{145}) \) |
$2$ |
$[2, 0]$ |
6.3 |
\( 2 \cdot 3 \) |
\( 2^{13} \cdot 3^{3} \) |
$1.68407$ |
$(2,a+1), (3,a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 1 \) |
$1$ |
$5.349208508$ |
0.444227587 |
\( \frac{2580910083523}{54} a + \frac{7124341097065}{27} \) |
\( \bigl[a\) , \( -1\) , \( 0\) , \( -5248141 a - 28973908\) , \( -16075108293 a - 88747414280\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-{x}^{2}+\left(-5248141a-28973908\right){x}-16075108293a-88747414280$ |
| 6.3-e1 |
6.3-e |
$4$ |
$4$ |
\(\Q(\sqrt{145}) \) |
$2$ |
$[2, 0]$ |
6.3 |
\( 2 \cdot 3 \) |
\( - 2 \cdot 3^{3} \cdot 5^{12} \) |
$1.68407$ |
$(2,a+1), (3,a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$16$ |
\( 3 \) |
$1$ |
$1.337302127$ |
1.332682762 |
\( -\frac{175860717738397615}{54} a + \frac{573376045769893301}{27} \) |
\( \bigl[1\) , \( -a\) , \( a\) , \( 908 a - 6126\) , \( 39212 a - 258309\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}-a{x}^{2}+\left(908a-6126\right){x}+39212a-258309$ |
| 6.3-e2 |
6.3-e |
$4$ |
$4$ |
\(\Q(\sqrt{145}) \) |
$2$ |
$[2, 0]$ |
6.3 |
\( 2 \cdot 3 \) |
\( - 2^{16} \cdot 3^{12} \) |
$1.68407$ |
$(2,a+1), (3,a)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{4} \cdot 3 \) |
$1$ |
$5.349208508$ |
1.332682762 |
\( \frac{10742434793}{8503056} a - \frac{13535608727}{2125764} \) |
\( \bigl[a\) , \( a + 1\) , \( 0\) , \( 199 a - 1188\) , \( 3937 a - 25452\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(199a-1188\right){x}+3937a-25452$ |
| 6.3-e3 |
6.3-e |
$4$ |
$4$ |
\(\Q(\sqrt{145}) \) |
$2$ |
$[2, 0]$ |
6.3 |
\( 2 \cdot 3 \) |
\( 2^{2} \cdot 3^{6} \cdot 5^{12} \) |
$1.68407$ |
$(2,a+1), (3,a)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$4$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$5.349208508$ |
1.332682762 |
\( -\frac{47771196715}{2916} a + \frac{78430158322}{729} \) |
\( \bigl[1\) , \( -a\) , \( a\) , \( 33 a - 501\) , \( 587 a - 5184\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}-a{x}^{2}+\left(33a-501\right){x}+587a-5184$ |
| 6.3-e4 |
6.3-e |
$4$ |
$4$ |
\(\Q(\sqrt{145}) \) |
$2$ |
$[2, 0]$ |
6.3 |
\( 2 \cdot 3 \) |
\( 2^{13} \cdot 3^{3} \) |
$1.68407$ |
$(2,a+1), (3,a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 3 \) |
$1$ |
$5.349208508$ |
1.332682762 |
\( \frac{2580910083523}{54} a + \frac{7124341097065}{27} \) |
\( \bigl[a + 1\) , \( -a\) , \( 0\) , \( -1314 a - 7217\) , \( -66846 a - 369000\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}-a{x}^{2}+\left(-1314a-7217\right){x}-66846a-369000$ |
*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.
