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 |
$1$ |
$1$ |
\(\Q(\sqrt{73}) \) |
$2$ |
$[2, 0]$ |
2.1 |
\( 2 \) |
\( 2^{5} \) |
$0.90794$ |
$(a+4)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$1$ |
$14.01215728$ |
1.639998963 |
\( -\frac{1081}{32} a + \frac{5527}{32} \) |
\( \bigl[a + 1\) , \( -a\) , \( 1\) , \( 5650 a + 21324\) , \( -5829019 a - 21987064\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}-a{x}^{2}+\left(5650a+21324\right){x}-5829019a-21987064$ |
2.2-a1 |
2.2-a |
$1$ |
$1$ |
\(\Q(\sqrt{73}) \) |
$2$ |
$[2, 0]$ |
2.2 |
\( 2 \) |
\( 2^{5} \) |
$0.90794$ |
$(-a+5)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$1$ |
$14.01215728$ |
1.639998963 |
\( \frac{1081}{32} a + \frac{2223}{16} \) |
\( \bigl[a\) , \( 0\) , \( 1\) , \( -5651 a + 26975\) , \( 5829019 a - 27816083\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+\left(-5651a+26975\right){x}+5829019a-27816083$ |
4.1-a1 |
4.1-a |
$4$ |
$6$ |
\(\Q(\sqrt{73}) \) |
$2$ |
$[2, 0]$ |
4.1 |
\( 2^{2} \) |
\( - 2^{7} \) |
$1.07973$ |
$(a+4), (-a+5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$1$ |
$21.45043377$ |
1.255291688 |
\( -\frac{100491}{64} a + \frac{236995}{32} \) |
\( \bigl[1\) , \( 1\) , \( 0\) , \( -410 a - 1546\) , \( -42886 a - 161766\bigr] \) |
${y}^2+{x}{y}={x}^{3}+{x}^{2}+\left(-410a-1546\right){x}-42886a-161766$ |
4.1-a2 |
4.1-a |
$4$ |
$6$ |
\(\Q(\sqrt{73}) \) |
$2$ |
$[2, 0]$ |
4.1 |
\( 2^{2} \) |
\( - 2^{5} \) |
$1.07973$ |
$(a+4), (-a+5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$1$ |
$21.45043377$ |
1.255291688 |
\( -\frac{264081}{8} a + \frac{1260865}{8} \) |
\( \bigl[1\) , \( 1\) , \( 0\) , \( 2 a - 9\) , \( 4 a - 19\bigr] \) |
${y}^2+{x}{y}={x}^{3}+{x}^{2}+\left(2a-9\right){x}+4a-19$ |
4.1-a3 |
4.1-a |
$4$ |
$6$ |
\(\Q(\sqrt{73}) \) |
$2$ |
$[2, 0]$ |
4.1 |
\( 2^{2} \) |
\( - 2^{7} \) |
$1.07973$ |
$(a+4), (-a+5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$1$ |
$21.45043377$ |
1.255291688 |
\( \frac{100491}{64} a + \frac{373499}{64} \) |
\( \bigl[1\) , \( 1\) , \( 0\) , \( 410 a - 1956\) , \( 42886 a - 204652\bigr] \) |
${y}^2+{x}{y}={x}^{3}+{x}^{2}+\left(410a-1956\right){x}+42886a-204652$ |
4.1-a4 |
4.1-a |
$4$ |
$6$ |
\(\Q(\sqrt{73}) \) |
$2$ |
$[2, 0]$ |
4.1 |
\( 2^{2} \) |
\( - 2^{5} \) |
$1.07973$ |
$(a+4), (-a+5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$1$ |
$21.45043377$ |
1.255291688 |
\( \frac{264081}{8} a + 124598 \) |
\( \bigl[1\) , \( 1\) , \( 0\) , \( -2 a - 7\) , \( -4 a - 15\bigr] \) |
${y}^2+{x}{y}={x}^{3}+{x}^{2}+\left(-2a-7\right){x}-4a-15$ |
4.1-b1 |
4.1-b |
$4$ |
$6$ |
\(\Q(\sqrt{73}) \) |
$2$ |
$[2, 0]$ |
4.1 |
\( 2^{2} \) |
\( - 2^{15} \) |
$1.07973$ |
$(a+4), (-a+5)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2 \) |
$1$ |
$27.60123454$ |
0.179471119 |
\( -\frac{59103316107}{1024} a + \frac{141009574339}{512} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( 487414 a - 2325941\) , \( -382806222 a + 1826752008\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(487414a-2325941\right){x}-382806222a+1826752008$ |
4.1-b2 |
4.1-b |
$4$ |
$6$ |
\(\Q(\sqrt{73}) \) |
$2$ |
$[2, 0]$ |
4.1 |
\( 2^{2} \) |
\( - 2^{45} \) |
$1.07973$ |
$(a+4), (-a+5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2 \) |
$1$ |
$3.066803838$ |
0.179471119 |
\( -\frac{22499709675}{1073741824} a + \frac{934397801011}{536870912} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( 637174 a - 3040596\) , \( -128263298 a + 612072698\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(637174a-3040596\right){x}-128263298a+612072698$ |
4.1-b3 |
4.1-b |
$4$ |
$6$ |
\(\Q(\sqrt{73}) \) |
$2$ |
$[2, 0]$ |
4.1 |
\( 2^{2} \) |
\( - 2^{45} \) |
$1.07973$ |
$(a+4), (-a+5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2 \) |
$1$ |
$3.066803838$ |
0.179471119 |
\( \frac{22499709675}{1073741824} a + \frac{1846295892347}{1073741824} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -637174 a - 2403422\) , \( 128263298 a + 483809400\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(-637174a-2403422\right){x}+128263298a+483809400$ |
4.1-b4 |
4.1-b |
$4$ |
$6$ |
\(\Q(\sqrt{73}) \) |
$2$ |
$[2, 0]$ |
4.1 |
\( 2^{2} \) |
\( - 2^{15} \) |
$1.07973$ |
$(a+4), (-a+5)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2 \) |
$1$ |
$27.60123454$ |
0.179471119 |
\( \frac{59103316107}{1024} a + \frac{222915832571}{1024} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -487414 a - 1838527\) , \( 382806222 a + 1443945786\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(-487414a-1838527\right){x}+382806222a+1443945786$ |
6.1-a1 |
6.1-a |
$2$ |
$3$ |
\(\Q(\sqrt{73}) \) |
$2$ |
$[2, 0]$ |
6.1 |
\( 2 \cdot 3 \) |
\( 2^{5} \cdot 3^{6} \) |
$1.19492$ |
$(a+4), (-4a-15)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 2 \cdot 5 \) |
$0.050185898$ |
$13.89342905$ |
1.632148693 |
\( -\frac{1507745137}{23328} a - \frac{5691580961}{23328} \) |
\( \bigl[a + 1\) , \( 1\) , \( 1\) , \( -1438638 a - 5426541\) , \( 1939925739 a + 7317403521\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+{x}^{2}+\left(-1438638a-5426541\right){x}+1939925739a+7317403521$ |
6.1-a2 |
6.1-a |
$2$ |
$3$ |
\(\Q(\sqrt{73}) \) |
$2$ |
$[2, 0]$ |
6.1 |
\( 2 \cdot 3 \) |
\( 2^{15} \cdot 3^{2} \) |
$1.19492$ |
$(a+4), (-4a-15)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 2 \cdot 3 \cdot 5 \) |
$0.016728632$ |
$13.89342905$ |
1.632148693 |
\( \frac{2965031}{294912} a + \frac{62364151}{294912} \) |
\( \bigl[a + 1\) , \( 1\) , \( 1\) , \( -5 a + 50\) , \( -74 a + 383\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+{x}^{2}+\left(-5a+50\right){x}-74a+383$ |
6.1-b1 |
6.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{73}) \) |
$2$ |
$[2, 0]$ |
6.1 |
\( 2 \cdot 3 \) |
\( - 2^{4} \cdot 3^{3} \) |
$1.19492$ |
$(a+4), (-4a-15)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \cdot 3 \) |
$0.119321614$ |
$24.55457373$ |
1.028753542 |
\( -\frac{19452727}{432} a + \frac{93088873}{432} \) |
\( \bigl[1\) , \( -a\) , \( 1\) , \( 60 a - 280\) , \( -440 a + 2096\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-a{x}^{2}+\left(60a-280\right){x}-440a+2096$ |
6.1-b2 |
6.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{73}) \) |
$2$ |
$[2, 0]$ |
6.1 |
\( 2 \cdot 3 \) |
\( 2^{2} \cdot 3^{6} \) |
$1.19492$ |
$(a+4), (-4a-15)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \cdot 3 \) |
$0.238643228$ |
$24.55457373$ |
1.028753542 |
\( \frac{870191}{2916} a + \frac{8359939}{2916} \) |
\( \bigl[1\) , \( -a\) , \( 1\) , \( -a + 1\) , \( 2\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-a{x}^{2}+\left(-a+1\right){x}+2$ |
6.1-b3 |
6.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{73}) \) |
$2$ |
$[2, 0]$ |
6.1 |
\( 2 \cdot 3 \) |
\( 2 \cdot 3^{12} \) |
$1.19492$ |
$(a+4), (-4a-15)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \cdot 3 \) |
$0.119321614$ |
$12.27728686$ |
1.028753542 |
\( -\frac{24786320489}{1062882} a + \frac{136072433501}{1062882} \) |
\( \bigl[1\) , \( -a\) , \( 1\) , \( -6 a - 19\) , \( 26 a + 98\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-a{x}^{2}+\left(-6a-19\right){x}+26a+98$ |
6.1-b4 |
6.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{73}) \) |
$2$ |
$[2, 0]$ |
6.1 |
\( 2 \cdot 3 \) |
\( - 2 \cdot 3^{3} \) |
$1.19492$ |
$(a+4), (-4a-15)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 3 \) |
$0.477286456$ |
$12.27728686$ |
1.028753542 |
\( \frac{76920011}{54} a + \frac{290235025}{54} \) |
\( \bigl[1\) , \( -a\) , \( 1\) , \( -6540 a - 24664\) , \( -585162 a - 2207230\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-a{x}^{2}+\left(-6540a-24664\right){x}-585162a-2207230$ |
6.4-a1 |
6.4-a |
$2$ |
$3$ |
\(\Q(\sqrt{73}) \) |
$2$ |
$[2, 0]$ |
6.4 |
\( 2 \cdot 3 \) |
\( 2^{5} \cdot 3^{6} \) |
$1.19492$ |
$(-a+5), (4a-19)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 2 \cdot 5 \) |
$0.050185898$ |
$13.89342905$ |
1.632148693 |
\( \frac{1507745137}{23328} a - \frac{399962561}{1296} \) |
\( \bigl[a\) , \( -a - 1\) , \( a + 1\) , \( 1438638 a - 6865197\) , \( -1941364378 a + 9264194439\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(1438638a-6865197\right){x}-1941364378a+9264194439$ |
6.4-a2 |
6.4-a |
$2$ |
$3$ |
\(\Q(\sqrt{73}) \) |
$2$ |
$[2, 0]$ |
6.4 |
\( 2 \cdot 3 \) |
\( 2^{15} \cdot 3^{2} \) |
$1.19492$ |
$(-a+5), (4a-19)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 2 \cdot 3 \cdot 5 \) |
$0.016728632$ |
$13.89342905$ |
1.632148693 |
\( -\frac{2965031}{294912} a + \frac{3629399}{16384} \) |
\( \bigl[a\) , \( -a - 1\) , \( a + 1\) , \( 5 a + 27\) , \( 68 a + 264\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(5a+27\right){x}+68a+264$ |
6.4-b1 |
6.4-b |
$4$ |
$4$ |
\(\Q(\sqrt{73}) \) |
$2$ |
$[2, 0]$ |
6.4 |
\( 2 \cdot 3 \) |
\( - 2 \cdot 3^{3} \) |
$1.19492$ |
$(-a+5), (4a-19)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 3 \) |
$0.477286456$ |
$12.27728686$ |
1.028753542 |
\( -\frac{76920011}{54} a + \frac{20397502}{3} \) |
\( \bigl[1\) , \( a - 1\) , \( 1\) , \( 6540 a - 31204\) , \( 585162 a - 2792392\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(6540a-31204\right){x}+585162a-2792392$ |
6.4-b2 |
6.4-b |
$4$ |
$4$ |
\(\Q(\sqrt{73}) \) |
$2$ |
$[2, 0]$ |
6.4 |
\( 2 \cdot 3 \) |
\( 2^{2} \cdot 3^{6} \) |
$1.19492$ |
$(-a+5), (4a-19)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \cdot 3 \) |
$0.238643228$ |
$24.55457373$ |
1.028753542 |
\( -\frac{870191}{2916} a + \frac{512785}{162} \) |
\( \bigl[1\) , \( a - 1\) , \( 1\) , \( a\) , \( 2\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(a-1\right){x}^{2}+a{x}+2$ |
6.4-b3 |
6.4-b |
$4$ |
$4$ |
\(\Q(\sqrt{73}) \) |
$2$ |
$[2, 0]$ |
6.4 |
\( 2 \cdot 3 \) |
\( 2 \cdot 3^{12} \) |
$1.19492$ |
$(-a+5), (4a-19)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \cdot 3 \) |
$0.119321614$ |
$12.27728686$ |
1.028753542 |
\( \frac{24786320489}{1062882} a + \frac{6182561834}{59049} \) |
\( \bigl[1\) , \( a - 1\) , \( 1\) , \( 6 a - 25\) , \( -26 a + 124\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(6a-25\right){x}-26a+124$ |
6.4-b4 |
6.4-b |
$4$ |
$4$ |
\(\Q(\sqrt{73}) \) |
$2$ |
$[2, 0]$ |
6.4 |
\( 2 \cdot 3 \) |
\( - 2^{4} \cdot 3^{3} \) |
$1.19492$ |
$(-a+5), (4a-19)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \cdot 3 \) |
$0.119321614$ |
$24.55457373$ |
1.028753542 |
\( \frac{19452727}{432} a + \frac{4090897}{24} \) |
\( \bigl[1\) , \( a - 1\) , \( 1\) , \( -60 a - 220\) , \( 440 a + 1656\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-60a-220\right){x}+440a+1656$ |
8.1-a1 |
8.1-a |
$2$ |
$3$ |
\(\Q(\sqrt{73}) \) |
$2$ |
$[2, 0]$ |
8.1 |
\( 2^{3} \) |
\( 2^{9} \) |
$1.28402$ |
$(a+4), (-a+5)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B |
$1$ |
\( 3 \) |
$1$ |
$6.805173064$ |
2.389455786 |
\( -\frac{66199}{2} a - 123137 \) |
\( \bigl[a\) , \( -a - 1\) , \( 0\) , \( -5329 a + 25430\) , \( 27759 a - 132466\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-5329a+25430\right){x}+27759a-132466$ |
8.1-a2 |
8.1-a |
$2$ |
$3$ |
\(\Q(\sqrt{73}) \) |
$2$ |
$[2, 0]$ |
8.1 |
\( 2^{3} \) |
\( 2^{11} \) |
$1.28402$ |
$(a+4), (-a+5)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B |
$1$ |
\( 3 \) |
$1$ |
$6.805173064$ |
2.389455786 |
\( \frac{14273}{8} a - \frac{32153}{4} \) |
\( \bigl[a\) , \( -a - 1\) , \( 0\) , \( 234 a + 896\) , \( -6608 a - 24916\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(234a+896\right){x}-6608a-24916$ |
8.2-a1 |
8.2-a |
$2$ |
$3$ |
\(\Q(\sqrt{73}) \) |
$2$ |
$[2, 0]$ |
8.2 |
\( 2^{3} \) |
\( 2^{11} \) |
$1.28402$ |
$(a+4), (-a+5)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B |
$1$ |
\( 3 \) |
$1$ |
$6.805173064$ |
2.389455786 |
\( -\frac{14273}{8} a - \frac{50033}{8} \) |
\( \bigl[a + 1\) , \( 1\) , \( a + 1\) , \( -234 a + 1129\) , \( 6374 a - 30395\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(-234a+1129\right){x}+6374a-30395$ |
8.2-a2 |
8.2-a |
$2$ |
$3$ |
\(\Q(\sqrt{73}) \) |
$2$ |
$[2, 0]$ |
8.2 |
\( 2^{3} \) |
\( 2^{9} \) |
$1.28402$ |
$(a+4), (-a+5)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B |
$1$ |
\( 3 \) |
$1$ |
$6.805173064$ |
2.389455786 |
\( \frac{66199}{2} a - \frac{312473}{2} \) |
\( \bigl[a + 1\) , \( 1\) , \( a + 1\) , \( 5329 a + 20100\) , \( -22430 a - 84607\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(5329a+20100\right){x}-22430a-84607$ |
9.1-a1 |
9.1-a |
$6$ |
$8$ |
\(\Q(\sqrt{73}) \) |
$2$ |
$[2, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{9} \) |
$1.32239$ |
$(-4a-15), (4a-19)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$19.82686912$ |
1.160279753 |
\( -\frac{1626482}{6561} a + \frac{208967}{729} \) |
\( \bigl[1\) , \( 1\) , \( 0\) , \( -11 a + 53\) , \( -31 a + 148\bigr] \) |
${y}^2+{x}{y}={x}^{3}+{x}^{2}+\left(-11a+53\right){x}-31a+148$ |
9.1-a2 |
9.1-a |
$6$ |
$8$ |
\(\Q(\sqrt{73}) \) |
$2$ |
$[2, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{9} \) |
$1.32239$ |
$(-4a-15), (4a-19)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$19.82686912$ |
1.160279753 |
\( \frac{1626482}{6561} a + \frac{254221}{6561} \) |
\( \bigl[1\) , \( 1\) , \( 0\) , \( 11 a + 42\) , \( 31 a + 117\bigr] \) |
${y}^2+{x}{y}={x}^{3}+{x}^{2}+\left(11a+42\right){x}+31a+117$ |
9.1-a3 |
9.1-a |
$6$ |
$8$ |
\(\Q(\sqrt{73}) \) |
$2$ |
$[2, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{6} \) |
$1.32239$ |
$(-4a-15), (4a-19)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$1$ |
$39.65373825$ |
1.160279753 |
\( -\frac{21883576}{81} a + \frac{104623105}{81} \) |
\( \bigl[1\) , \( 1\) , \( 0\) , \( -19647 a - 74108\) , \( 1633869 a + 6162957\bigr] \) |
${y}^2+{x}{y}={x}^{3}+{x}^{2}+\left(-19647a-74108\right){x}+1633869a+6162957$ |
9.1-a4 |
9.1-a |
$6$ |
$8$ |
\(\Q(\sqrt{73}) \) |
$2$ |
$[2, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{3} \) |
$1.32239$ |
$(-4a-15), (4a-19)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$19.82686912$ |
1.160279753 |
\( -\frac{5620752580586}{9} a + \frac{26822242278227}{9} \) |
\( \bigl[1\) , \( 1\) , \( 0\) , \( -147477 a - 556283\) , \( -62638251 a - 236271600\bigr] \) |
${y}^2+{x}{y}={x}^{3}+{x}^{2}+\left(-147477a-556283\right){x}-62638251a-236271600$ |
9.1-a5 |
9.1-a |
$6$ |
$8$ |
\(\Q(\sqrt{73}) \) |
$2$ |
$[2, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{6} \) |
$1.32239$ |
$(-4a-15), (4a-19)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$1$ |
$39.65373825$ |
1.160279753 |
\( \frac{21883576}{81} a + \frac{3064427}{3} \) |
\( \bigl[1\) , \( 1\) , \( 0\) , \( 19647 a - 93755\) , \( -1633869 a + 7796826\bigr] \) |
${y}^2+{x}{y}={x}^{3}+{x}^{2}+\left(19647a-93755\right){x}-1633869a+7796826$ |
9.1-a6 |
9.1-a |
$6$ |
$8$ |
\(\Q(\sqrt{73}) \) |
$2$ |
$[2, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{3} \) |
$1.32239$ |
$(-4a-15), (4a-19)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$19.82686912$ |
1.160279753 |
\( \frac{5620752580586}{9} a + \frac{7067163232547}{3} \) |
\( \bigl[1\) , \( 1\) , \( 0\) , \( 147477 a - 703760\) , \( 62638251 a - 298909851\bigr] \) |
${y}^2+{x}{y}={x}^{3}+{x}^{2}+\left(147477a-703760\right){x}+62638251a-298909851$ |
9.1-b1 |
9.1-b |
$1$ |
$1$ |
\(\Q(\sqrt{73}) \) |
$2$ |
$[2, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{6} \) |
$1.32239$ |
$(-4a-15), (4a-19)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 5 \) |
$0.026837949$ |
$29.96854929$ |
0.941355393 |
\( \frac{45056}{243} a - \frac{20480}{27} \) |
\( \bigl[0\) , \( -a - 1\) , \( 1\) , \( 732 a - 3482\) , \( -32196 a + 153632\bigr] \) |
${y}^2+{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(732a-3482\right){x}-32196a+153632$ |
9.1-c1 |
9.1-c |
$6$ |
$8$ |
\(\Q(\sqrt{73}) \) |
$2$ |
$[2, 0]$ |
9.1 |
\( 3^{2} \) |
\( - 3^{10} \) |
$1.32239$ |
$(-4a-15), (4a-19)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$2.426410428$ |
0.283989860 |
\( -\frac{40271074813250}{6561} a + \frac{21352627114625}{729} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -1495635 a - 5641538\) , \( -11268678906 a - 42505477936\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}+\left(-1495635a-5641538\right){x}-11268678906a-42505477936$ |
9.1-c2 |
9.1-c |
$6$ |
$8$ |
\(\Q(\sqrt{73}) \) |
$2$ |
$[2, 0]$ |
9.1 |
\( 3^{2} \) |
\( - 3^{2} \) |
$1.32239$ |
$(-4a-15), (4a-19)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$38.82256685$ |
0.283989860 |
\( -\frac{126250}{3} a + \frac{607625}{3} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( 535 a - 2553\) , \( -13666 a + 65214\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}+\left(535a-2553\right){x}-13666a+65214$ |
9.1-c3 |
9.1-c |
$6$ |
$8$ |
\(\Q(\sqrt{73}) \) |
$2$ |
$[2, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{4} \) |
$1.32239$ |
$(-4a-15), (4a-19)$ |
0 |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$1$ |
$38.82256685$ |
0.283989860 |
\( \frac{15625}{9} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( 278125 a - 1327213\) , \( -11163626 a + 53272844\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}+\left(278125a-1327213\right){x}-11163626a+53272844$ |
9.1-c4 |
9.1-c |
$6$ |
$8$ |
\(\Q(\sqrt{73}) \) |
$2$ |
$[2, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{8} \) |
$1.32239$ |
$(-4a-15), (4a-19)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$1$ |
$9.705641713$ |
0.283989860 |
\( \frac{18609625}{81} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( 2948125 a - 14068458\) , \( 5674822628 a - 27080264208\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}+\left(2948125a-14068458\right){x}+5674822628a-27080264208$ |
9.1-c5 |
9.1-c |
$6$ |
$8$ |
\(\Q(\sqrt{73}) \) |
$2$ |
$[2, 0]$ |
9.1 |
\( 3^{2} \) |
\( - 3^{2} \) |
$1.32239$ |
$(-4a-15), (4a-19)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$38.82256685$ |
0.283989860 |
\( \frac{126250}{3} a + \frac{481375}{3} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -535 a - 2018\) , \( 13666 a + 51548\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}+\left(-535a-2018\right){x}+13666a+51548$ |
9.1-c6 |
9.1-c |
$6$ |
$8$ |
\(\Q(\sqrt{73}) \) |
$2$ |
$[2, 0]$ |
9.1 |
\( 3^{2} \) |
\( - 3^{10} \) |
$1.32239$ |
$(-4a-15), (4a-19)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$2.426410428$ |
0.283989860 |
\( \frac{40271074813250}{6561} a + \frac{151902569218375}{6561} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( 1495635 a - 7137173\) , \( 11268678906 a - 53774156842\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}+\left(1495635a-7137173\right){x}+11268678906a-53774156842$ |
9.1-d1 |
9.1-d |
$1$ |
$1$ |
\(\Q(\sqrt{73}) \) |
$2$ |
$[2, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{6} \) |
$1.32239$ |
$(-4a-15), (4a-19)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 5 \) |
$0.026837949$ |
$29.96854929$ |
0.941355393 |
\( -\frac{45056}{243} a - \frac{139264}{243} \) |
\( \bigl[0\) , \( a + 1\) , \( 1\) , \( -730 a - 2751\) , \( 31465 a + 118685\bigr] \) |
${y}^2+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-730a-2751\right){x}+31465a+118685$ |
12.1-a1 |
12.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{73}) \) |
$2$ |
$[2, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( - 2^{24} \cdot 3 \) |
$1.42100$ |
$(a+4), (-a+5), (-4a-15)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$8.192371235$ |
1.917689055 |
\( -\frac{205759183}{3145728} a + \frac{6415562209}{3145728} \) |
\( \bigl[1\) , \( -a\) , \( 1\) , \( 25605 a + 96587\) , \( -130053 a - 490558\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-a{x}^{2}+\left(25605a+96587\right){x}-130053a-490558$ |
12.1-a2 |
12.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{73}) \) |
$2$ |
$[2, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( 2^{18} \cdot 3^{2} \) |
$1.42100$ |
$(a+4), (-a+5), (-4a-15)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$1$ |
$8.192371235$ |
1.917689055 |
\( -\frac{2079872305}{9216} a + \frac{9941086051}{9216} \) |
\( \bigl[1\) , \( -a\) , \( 1\) , \( 649425 a - 3099051\) , \( 589412923 a - 2812679576\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-a{x}^{2}+\left(649425a-3099051\right){x}+589412923a-2812679576$ |
12.1-a3 |
12.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{73}) \) |
$2$ |
$[2, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( 2^{9} \cdot 3^{4} \) |
$1.42100$ |
$(a+4), (-a+5), (-4a-15)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$4.096185617$ |
1.917689055 |
\( -\frac{1129089087829553}{2592} a + \frac{5388015939519749}{2592} \) |
\( \bigl[1\) , \( -a\) , \( 1\) , \( 10389505 a - 49578731\) , \( 37690476667 a - 179859025240\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-a{x}^{2}+\left(10389505a-49578731\right){x}+37690476667a-179859025240$ |
12.1-a4 |
12.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{73}) \) |
$2$ |
$[2, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( - 2^{21} \cdot 3 \) |
$1.42100$ |
$(a+4), (-a+5), (-4a-15)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$4.096185617$ |
1.917689055 |
\( \frac{7083271375}{196608} a + \frac{13282784137}{98304} \) |
\( \bigl[1\) , \( -a\) , \( 1\) , \( 91 a - 428\) , \( 1871 a - 8932\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-a{x}^{2}+\left(91a-428\right){x}+1871a-8932$ |
12.2-a1 |
12.2-a |
$4$ |
$4$ |
\(\Q(\sqrt{73}) \) |
$2$ |
$[2, 0]$ |
12.2 |
\( 2^{2} \cdot 3 \) |
\( - 2^{21} \cdot 3 \) |
$1.42100$ |
$(a+4), (-a+5), (4a-19)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$4.096185617$ |
1.917689055 |
\( -\frac{7083271375}{196608} a + \frac{11216279883}{65536} \) |
\( \bigl[1\) , \( a - 1\) , \( 1\) , \( -91 a - 337\) , \( -1871 a - 7061\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-91a-337\right){x}-1871a-7061$ |
12.2-a2 |
12.2-a |
$4$ |
$4$ |
\(\Q(\sqrt{73}) \) |
$2$ |
$[2, 0]$ |
12.2 |
\( 2^{2} \cdot 3 \) |
\( - 2^{24} \cdot 3 \) |
$1.42100$ |
$(a+4), (-a+5), (4a-19)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$8.192371235$ |
1.917689055 |
\( \frac{205759183}{3145728} a + \frac{1034967171}{524288} \) |
\( \bigl[1\) , \( a - 1\) , \( 1\) , \( -25605 a + 122192\) , \( 130053 a - 620611\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-25605a+122192\right){x}+130053a-620611$ |
12.2-a3 |
12.2-a |
$4$ |
$4$ |
\(\Q(\sqrt{73}) \) |
$2$ |
$[2, 0]$ |
12.2 |
\( 2^{2} \cdot 3 \) |
\( 2^{18} \cdot 3^{2} \) |
$1.42100$ |
$(a+4), (-a+5), (4a-19)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$1$ |
$8.192371235$ |
1.917689055 |
\( \frac{2079872305}{9216} a + \frac{436734097}{512} \) |
\( \bigl[1\) , \( a - 1\) , \( 1\) , \( -649425 a - 2449626\) , \( -589412923 a - 2223266653\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-649425a-2449626\right){x}-589412923a-2223266653$ |
12.2-a4 |
12.2-a |
$4$ |
$4$ |
\(\Q(\sqrt{73}) \) |
$2$ |
$[2, 0]$ |
12.2 |
\( 2^{2} \cdot 3 \) |
\( 2^{9} \cdot 3^{4} \) |
$1.42100$ |
$(a+4), (-a+5), (4a-19)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$4.096185617$ |
1.917689055 |
\( \frac{1129089087829553}{2592} a + \frac{118303523658061}{72} \) |
\( \bigl[1\) , \( a - 1\) , \( 1\) , \( -10389505 a - 39189226\) , \( -37690476667 a - 142168548573\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-10389505a-39189226\right){x}-37690476667a-142168548573$ |
16.2-a1 |
16.2-a |
$4$ |
$4$ |
\(\Q(\sqrt{73}) \) |
$2$ |
$[2, 0]$ |
16.2 |
\( 2^{4} \) |
\( - 2^{9} \) |
$1.52697$ |
$(a+4), (-a+5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$14.07794017$ |
0.823849134 |
\( -\frac{2702403}{2} a + \frac{12895821}{2} \) |
\( \bigl[a + 1\) , \( -1\) , \( 0\) , \( 235362 a - 1123130\) , \( 128525518 a - 613323998\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}-{x}^{2}+\left(235362a-1123130\right){x}+128525518a-613323998$ |
16.2-a2 |
16.2-a |
$4$ |
$4$ |
\(\Q(\sqrt{73}) \) |
$2$ |
$[2, 0]$ |
16.2 |
\( 2^{4} \) |
\( - 2^{15} \) |
$1.52697$ |
$(a+4), (-a+5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$14.07794017$ |
0.823849134 |
\( \frac{2187}{16} a + \frac{18171}{16} \) |
\( \bigl[a + 1\) , \( -1\) , \( 0\) , \( -3 a - 11\) , \( -13 a - 49\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}-{x}^{2}+\left(-3a-11\right){x}-13a-49$ |
*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.