| 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 |
| 57600.1-a1 |
57600.1-a |
$8$ |
$12$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
57600.1 |
\( 2^{8} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{48} \cdot 3^{8} \cdot 5^{6} \) |
$2.39775$ |
$(-2a+1), (2), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B[2] |
$1$ |
\( 2^{3} \) |
$4.281418887$ |
$0.186814690$ |
3.694265501 |
\( -\frac{273359449}{1536000} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -648 a\) , \( 24480 a - 12240\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}-648a{x}+24480a-12240$ |
| 57600.1-a2 |
57600.1-a |
$8$ |
$12$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
57600.1 |
\( 2^{8} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{32} \cdot 3^{12} \cdot 5^{2} \) |
$2.39775$ |
$(-2a+1), (2), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B[2] |
$1$ |
\( 2^{3} \) |
$1.427139629$ |
$0.560444070$ |
3.694265501 |
\( \frac{357911}{2160} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 72 a\) , \( -864 a + 432\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+72a{x}-864a+432$ |
| 57600.1-a3 |
57600.1-a |
$8$ |
$12$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
57600.1 |
\( 2^{8} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{30} \cdot 3^{8} \cdot 5^{24} \) |
$2.39775$ |
$(-2a+1), (2), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B[2] |
$1$ |
\( 2^{5} \) |
$4.281418887$ |
$0.046703672$ |
3.694265501 |
\( \frac{10316097499609}{5859375000} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -21768 a\) , \( 208800 a - 104400\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}-21768a{x}+208800a-104400$ |
| 57600.1-a4 |
57600.1-a |
$8$ |
$12$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
57600.1 |
\( 2^{8} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{26} \cdot 3^{30} \cdot 5^{2} \) |
$2.39775$ |
$(-2a+1), (2), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B[2] |
$1$ |
\( 2^{3} \) |
$5.708558516$ |
$0.140111017$ |
3.694265501 |
\( \frac{35578826569}{5314410} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -3288 a\) , \( 74400 a - 37200\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}-3288a{x}+74400a-37200$ |
| 57600.1-a5 |
57600.1-a |
$8$ |
$12$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
57600.1 |
\( 2^{8} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{28} \cdot 3^{18} \cdot 5^{4} \) |
$2.39775$ |
$(-2a+1), (2), (5)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2Cs, 3B[2] |
$1$ |
\( 2^{5} \) |
$2.854279258$ |
$0.280222035$ |
3.694265501 |
\( \frac{702595369}{72900} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -888 a\) , \( -10080 a + 5040\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}-888a{x}-10080a+5040$ |
| 57600.1-a6 |
57600.1-a |
$8$ |
$12$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
57600.1 |
\( 2^{8} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{36} \cdot 3^{10} \cdot 5^{12} \) |
$2.39775$ |
$(-2a+1), (2), (5)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2Cs, 3B[2] |
$1$ |
\( 2^{5} \) |
$8.562837774$ |
$0.093407345$ |
3.694265501 |
\( \frac{4102915888729}{9000000} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -16008 a\) , \( 909216 a - 454608\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}-16008a{x}+909216a-454608$ |
| 57600.1-a7 |
57600.1-a |
$8$ |
$12$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
57600.1 |
\( 2^{8} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{26} \cdot 3^{12} \cdot 5^{8} \) |
$2.39775$ |
$(-2a+1), (2), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B[2] |
$1$ |
\( 2^{5} \) |
$1.427139629$ |
$0.140111017$ |
3.694265501 |
\( \frac{2656166199049}{33750} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -13848 a\) , \( -715104 a + 357552\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}-13848a{x}-715104a+357552$ |
| 57600.1-a8 |
57600.1-a |
$8$ |
$12$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
57600.1 |
\( 2^{8} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{30} \cdot 3^{14} \cdot 5^{6} \) |
$2.39775$ |
$(-2a+1), (2), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B[2] |
$1$ |
\( 2^{3} \) |
$17.12567554$ |
$0.046703672$ |
3.694265501 |
\( \frac{16778985534208729}{81000} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -256008 a\) , \( 57741216 a - 28870608\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}-256008a{x}+57741216a-28870608$ |
| 57600.1-b1 |
57600.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
57600.1 |
\( 2^{8} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{20} \cdot 3^{6} \cdot 5^{8} \) |
$2.39775$ |
$(-2a+1), (2), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$0.865127330$ |
1.997925987 |
\( \frac{237276}{625} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 39 a\) , \( 204 a - 102\bigr] \) |
${y}^2={x}^{3}+39a{x}+204a-102$ |
| 57600.1-b2 |
57600.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
57600.1 |
\( 2^{8} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{16} \cdot 3^{6} \cdot 5^{4} \) |
$2.39775$ |
$(-2a+1), (2), (5)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$1$ |
$1.730254660$ |
1.997925987 |
\( \frac{148176}{25} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -21 a\) , \( 36 a - 18\bigr] \) |
${y}^2={x}^{3}-21a{x}+36a-18$ |
| 57600.1-b3 |
57600.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
57600.1 |
\( 2^{8} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{8} \cdot 3^{6} \cdot 5^{2} \) |
$2.39775$ |
$(-2a+1), (2), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$3.460509320$ |
1.997925987 |
\( \frac{55296}{5} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -6 a\) , \( -6 a + 3\bigr] \) |
${y}^2={x}^{3}-6a{x}-6a+3$ |
| 57600.1-b4 |
57600.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
57600.1 |
\( 2^{8} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{20} \cdot 3^{6} \cdot 5^{2} \) |
$2.39775$ |
$(-2a+1), (2), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$0.865127330$ |
1.997925987 |
\( \frac{132304644}{5} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -321 a\) , \( 2556 a - 1278\bigr] \) |
${y}^2={x}^{3}-321a{x}+2556a-1278$ |
| 57600.1-c1 |
57600.1-c |
$4$ |
$4$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
57600.1 |
\( 2^{8} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{16} \cdot 3^{8} \cdot 5^{2} \) |
$2.39775$ |
$(-2a+1), (2), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$2.010095125$ |
2.321057923 |
\( \frac{21296}{15} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 12 a\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+12a{x}$ |
| 57600.1-c2 |
57600.1-c |
$4$ |
$4$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
57600.1 |
\( 2^{8} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{20} \cdot 3^{10} \cdot 5^{4} \) |
$2.39775$ |
$(-2a+1), (2), (5)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$1$ |
$1.005047562$ |
2.321057923 |
\( \frac{470596}{225} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -48 a\) , \( -96 a + 48\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}-48a{x}-96a+48$ |
| 57600.1-c3 |
57600.1-c |
$4$ |
$4$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
57600.1 |
\( 2^{8} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{22} \cdot 3^{8} \cdot 5^{8} \) |
$2.39775$ |
$(-2a+1), (2), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$0.502523781$ |
2.321057923 |
\( \frac{136835858}{1875} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -408 a\) , \( 3360 a - 1680\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}-408a{x}+3360a-1680$ |
| 57600.1-c4 |
57600.1-c |
$4$ |
$4$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
57600.1 |
\( 2^{8} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{22} \cdot 3^{14} \cdot 5^{2} \) |
$2.39775$ |
$(-2a+1), (2), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$0.502523781$ |
2.321057923 |
\( \frac{546718898}{405} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -648 a\) , \( -7776 a + 3888\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}-648a{x}-7776a+3888$ |
| 57600.1-d1 |
57600.1-d |
$4$ |
$6$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
57600.1 |
\( 2^{8} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{36} \cdot 3^{6} \cdot 5^{2} \) |
$2.39775$ |
$(-2a+1), (2), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B[2] |
$1$ |
\( 2^{3} \) |
$0.949584851$ |
$0.704990522$ |
3.092049343 |
\( -\frac{1860867}{320} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -123\) , \( -598\bigr] \) |
${y}^2={x}^{3}-123{x}-598$ |
| 57600.1-d2 |
57600.1-d |
$4$ |
$6$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
57600.1 |
\( 2^{8} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{28} \cdot 3^{6} \cdot 5^{6} \) |
$2.39775$ |
$(-2a+1), (2), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B[2] |
$1$ |
\( 2^{3} \cdot 3 \) |
$0.316528283$ |
$0.704990522$ |
3.092049343 |
\( \frac{804357}{500} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 93\) , \( -94\bigr] \) |
${y}^2={x}^{3}+93{x}-94$ |
| 57600.1-d3 |
57600.1-d |
$4$ |
$6$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
57600.1 |
\( 2^{8} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{26} \cdot 3^{6} \cdot 5^{12} \) |
$2.39775$ |
$(-2a+1), (2), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B[2] |
$1$ |
\( 2^{5} \cdot 3 \) |
$0.158264141$ |
$0.352495261$ |
3.092049343 |
\( \frac{57960603}{31250} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -387\) , \( -766\bigr] \) |
${y}^2={x}^{3}-387{x}-766$ |
| 57600.1-d4 |
57600.1-d |
$4$ |
$6$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
57600.1 |
\( 2^{8} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{30} \cdot 3^{6} \cdot 5^{4} \) |
$2.39775$ |
$(-2a+1), (2), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B[2] |
$1$ |
\( 2^{5} \) |
$0.474792425$ |
$0.352495261$ |
3.092049343 |
\( \frac{8527173507}{200} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -2043\) , \( -35542\bigr] \) |
${y}^2={x}^{3}-2043{x}-35542$ |
| 57600.1-e1 |
57600.1-e |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
57600.1 |
\( 2^{8} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{20} \cdot 3^{6} \cdot 5^{2} \) |
$2.39775$ |
$(-2a+1), (2), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.381839169$ |
$1.948709202$ |
3.436820672 |
\( -\frac{108}{5} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -3\) , \( 18\bigr] \) |
${y}^2={x}^{3}-3{x}+18$ |
| 57600.1-e2 |
57600.1-e |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
57600.1 |
\( 2^{8} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{22} \cdot 3^{6} \cdot 5^{4} \) |
$2.39775$ |
$(-2a+1), (2), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$0.190919584$ |
$0.974354601$ |
3.436820672 |
\( \frac{3721734}{25} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -123\) , \( 522\bigr] \) |
${y}^2={x}^{3}-123{x}+522$ |
| 57600.1-f1 |
57600.1-f |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
57600.1 |
\( 2^{8} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{16} \cdot 3^{6} \cdot 5^{2} \) |
$2.39775$ |
$(-2a+1), (2), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.670659947$ |
$2.391071723$ |
3.703346414 |
\( \frac{5776}{5} a + \frac{2864}{5} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -3 a + 9\) , \( -9 a\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(-3a+9\right){x}-9a$ |
| 57600.1-f2 |
57600.1-f |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
57600.1 |
\( 2^{8} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{20} \cdot 3^{6} \cdot 5^{4} \) |
$2.39775$ |
$(-2a+1), (2), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$0.335329973$ |
$1.195535861$ |
3.703346414 |
\( -\frac{1293836}{25} a + \frac{52992}{5} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -63 a + 69\) , \( 39 a + 156\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(-63a+69\right){x}+39a+156$ |
| 57600.1-g1 |
57600.1-g |
$4$ |
$6$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
57600.1 |
\( 2^{8} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{16} \cdot 3^{6} \cdot 5^{12} \) |
$2.39775$ |
$(-2a+1), (2), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B[2] |
$1$ |
\( 2^{3} \) |
$1.293210583$ |
$0.618062667$ |
3.691740124 |
\( -\frac{20720464}{15625} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( a + 109\) , \( -731 a + 420\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(a+109\right){x}-731a+420$ |
| 57600.1-g2 |
57600.1-g |
$4$ |
$6$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
57600.1 |
\( 2^{8} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{16} \cdot 3^{6} \cdot 5^{4} \) |
$2.39775$ |
$(-2a+1), (2), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B[2] |
$1$ |
\( 2^{3} \) |
$0.431070194$ |
$1.854188003$ |
3.691740124 |
\( \frac{21296}{25} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( a - 11\) , \( 13 a - 12\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(a-11\right){x}+13a-12$ |
| 57600.1-g3 |
57600.1-g |
$4$ |
$6$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
57600.1 |
\( 2^{8} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{8} \cdot 3^{6} \cdot 5^{2} \) |
$2.39775$ |
$(-2a+1), (2), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B[2] |
$1$ |
\( 2 \) |
$0.862140388$ |
$3.708376006$ |
3.691740124 |
\( \frac{16384}{5} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( a + 4\) , \( 4 a\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(a+4\right){x}+4a$ |
| 57600.1-g4 |
57600.1-g |
$4$ |
$6$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
57600.1 |
\( 2^{8} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{8} \cdot 3^{6} \cdot 5^{6} \) |
$2.39775$ |
$(-2a+1), (2), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B[2] |
$1$ |
\( 2 \) |
$2.586421166$ |
$1.236125335$ |
3.691740124 |
\( \frac{488095744}{125} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( a + 124\) , \( -572 a + 348\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(a+124\right){x}-572a+348$ |
| 57600.1-h1 |
57600.1-h |
$6$ |
$8$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
57600.1 |
\( 2^{8} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{22} \cdot 3^{8} \cdot 5^{16} \) |
$2.39775$ |
$(-2a+1), (2), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$0.221063812$ |
1.021050013 |
\( -\frac{27995042}{1171875} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 242 a - 241\) , \( 14159 a - 6959\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(242a-241\right){x}+14159a-6959$ |
| 57600.1-h2 |
57600.1-h |
$6$ |
$8$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
57600.1 |
\( 2^{8} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{20} \cdot 3^{22} \cdot 5^{2} \) |
$2.39775$ |
$(-2a+1), (2), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$0.442127625$ |
1.021050013 |
\( \frac{54607676}{32805} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -238 a + 239\) , \( -241 a + 1\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(-238a+239\right){x}-241a+1$ |
| 57600.1-h3 |
57600.1-h |
$6$ |
$8$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
57600.1 |
\( 2^{8} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{16} \cdot 3^{14} \cdot 5^{4} \) |
$2.39775$ |
$(-2a+1), (2), (5)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$1$ |
$0.884255250$ |
1.021050013 |
\( \frac{3631696}{2025} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 62 a - 61\) , \( -61 a + 61\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(62a-61\right){x}-61a+61$ |
| 57600.1-h4 |
57600.1-h |
$6$ |
$8$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
57600.1 |
\( 2^{8} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{20} \cdot 3^{10} \cdot 5^{8} \) |
$2.39775$ |
$(-2a+1), (2), (5)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$1$ |
$0.442127625$ |
1.021050013 |
\( \frac{868327204}{5625} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 602 a - 601\) , \( 6311 a - 2855\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(602a-601\right){x}+6311a-2855$ |
| 57600.1-h5 |
57600.1-h |
$6$ |
$8$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
57600.1 |
\( 2^{8} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{8} \cdot 3^{10} \cdot 5^{2} \) |
$2.39775$ |
$(-2a+1), (2), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$1.768510500$ |
1.021050013 |
\( \frac{24918016}{45} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 47 a - 46\) , \( -154 a + 100\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(47a-46\right){x}-154a+100$ |
| 57600.1-h6 |
57600.1-h |
$6$ |
$8$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
57600.1 |
\( 2^{8} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{22} \cdot 3^{8} \cdot 5^{4} \) |
$2.39775$ |
$(-2a+1), (2), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$0.221063812$ |
1.021050013 |
\( \frac{1770025017602}{75} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 9602 a - 9601\) , \( 414911 a - 202655\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(9602a-9601\right){x}+414911a-202655$ |
| 57600.1-i1 |
57600.1-i |
$6$ |
$8$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
57600.1 |
\( 2^{8} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{22} \cdot 3^{8} \cdot 5^{16} \) |
$2.39775$ |
$(-2a+1), (2), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$0.221063812$ |
1.021050013 |
\( -\frac{27995042}{1171875} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -240 a\) , \( -14400 a + 7200\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}-240a{x}-14400a+7200$ |
| 57600.1-i2 |
57600.1-i |
$6$ |
$8$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
57600.1 |
\( 2^{8} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{20} \cdot 3^{22} \cdot 5^{2} \) |
$2.39775$ |
$(-2a+1), (2), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$0.442127625$ |
1.021050013 |
\( \frac{54607676}{32805} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 240 a\) , \( 480 a - 240\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+240a{x}+480a-240$ |
| 57600.1-i3 |
57600.1-i |
$6$ |
$8$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
57600.1 |
\( 2^{8} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{16} \cdot 3^{14} \cdot 5^{4} \) |
$2.39775$ |
$(-2a+1), (2), (5)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$1$ |
$0.884255250$ |
1.021050013 |
\( \frac{3631696}{2025} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -60 a\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}-60a{x}$ |
| 57600.1-i4 |
57600.1-i |
$6$ |
$8$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
57600.1 |
\( 2^{8} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{20} \cdot 3^{10} \cdot 5^{8} \) |
$2.39775$ |
$(-2a+1), (2), (5)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$1$ |
$0.442127625$ |
1.021050013 |
\( \frac{868327204}{5625} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -600 a\) , \( -6912 a + 3456\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}-600a{x}-6912a+3456$ |
| 57600.1-i5 |
57600.1-i |
$6$ |
$8$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
57600.1 |
\( 2^{8} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{8} \cdot 3^{10} \cdot 5^{2} \) |
$2.39775$ |
$(-2a+1), (2), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$1.768510500$ |
1.021050013 |
\( \frac{24918016}{45} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -45 a\) , \( 108 a - 54\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}-45a{x}+108a-54$ |
| 57600.1-i6 |
57600.1-i |
$6$ |
$8$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
57600.1 |
\( 2^{8} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{22} \cdot 3^{8} \cdot 5^{4} \) |
$2.39775$ |
$(-2a+1), (2), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$0.221063812$ |
1.021050013 |
\( \frac{1770025017602}{75} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -9600 a\) , \( -424512 a + 212256\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}-9600a{x}-424512a+212256$ |
| 57600.1-j1 |
57600.1-j |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
57600.1 |
\( 2^{8} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{24} \cdot 3^{38} \cdot 5^{2} \) |
$2.39775$ |
$(-2a+1), (2), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$10.65864296$ |
$0.080673936$ |
3.971591054 |
\( -\frac{147281603041}{215233605} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -5280 a\) , \( -316728 a + 158364\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}-5280a{x}-316728a+158364$ |
| 57600.1-j2 |
57600.1-j |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
57600.1 |
\( 2^{8} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{24} \cdot 3^{8} \cdot 5^{2} \) |
$2.39775$ |
$(-2a+1), (2), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.666165185$ |
$1.290782985$ |
3.971591054 |
\( -\frac{1}{15} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 0\) , \( 72 a - 36\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+72a-36$ |
| 57600.1-j3 |
57600.1-j |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
57600.1 |
\( 2^{8} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{24} \cdot 3^{10} \cdot 5^{16} \) |
$2.39775$ |
$(-2a+1), (2), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$5.329321481$ |
$0.161347873$ |
3.971591054 |
\( \frac{4733169839}{3515625} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 1680 a\) , \( -17400 a + 8700\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+1680a{x}-17400a+8700$ |
| 57600.1-j4 |
57600.1-j |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
57600.1 |
\( 2^{8} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{24} \cdot 3^{14} \cdot 5^{8} \) |
$2.39775$ |
$(-2a+1), (2), (5)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$2.664660740$ |
$0.322695746$ |
3.971591054 |
\( \frac{111284641}{50625} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -480 a\) , \( -1848 a + 924\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}-480a{x}-1848a+924$ |
| 57600.1-j5 |
57600.1-j |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
57600.1 |
\( 2^{8} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{24} \cdot 3^{10} \cdot 5^{4} \) |
$2.39775$ |
$(-2a+1), (2), (5)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$1.332330370$ |
$0.645391492$ |
3.971591054 |
\( \frac{13997521}{225} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -240 a\) , \( 1800 a - 900\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}-240a{x}+1800a-900$ |
| 57600.1-j6 |
57600.1-j |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
57600.1 |
\( 2^{8} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{24} \cdot 3^{22} \cdot 5^{4} \) |
$2.39775$ |
$(-2a+1), (2), (5)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$5.329321481$ |
$0.161347873$ |
3.971591054 |
\( \frac{272223782641}{164025} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -6480 a\) , \( -227448 a + 113724\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}-6480a{x}-227448a+113724$ |
| 57600.1-j7 |
57600.1-j |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
57600.1 |
\( 2^{8} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{24} \cdot 3^{8} \cdot 5^{2} \) |
$2.39775$ |
$(-2a+1), (2), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$2.664660740$ |
$0.322695746$ |
3.971591054 |
\( \frac{56667352321}{15} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -3840 a\) , \( 108360 a - 54180\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}-3840a{x}+108360a-54180$ |
| 57600.1-j8 |
57600.1-j |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
57600.1 |
\( 2^{8} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{24} \cdot 3^{14} \cdot 5^{2} \) |
$2.39775$ |
$(-2a+1), (2), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$10.65864296$ |
$0.080673936$ |
3.971591054 |
\( \frac{1114544804970241}{405} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -103680 a\) , \( -14768568 a + 7384284\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}-103680a{x}-14768568a+7384284$ |
| 57600.1-k1 |
57600.1-k |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
57600.1 |
\( 2^{8} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{24} \cdot 3^{38} \cdot 5^{2} \) |
$2.39775$ |
$(-2a+1), (2), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$10.65864296$ |
$0.080673936$ |
3.971591054 |
\( -\frac{147281603041}{215233605} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 5282 a - 5281\) , \( 322009 a - 163645\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(5282a-5281\right){x}+322009a-163645$ |
| 57600.1-k2 |
57600.1-k |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
57600.1 |
\( 2^{8} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{24} \cdot 3^{8} \cdot 5^{2} \) |
$2.39775$ |
$(-2a+1), (2), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.666165185$ |
$1.290782985$ |
3.971591054 |
\( -\frac{1}{15} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 2 a - 1\) , \( -71 a + 35\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(2a-1\right){x}-71a+35$ |
*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.
