| 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 |
| 588.2-a3 |
588.2-a |
$6$ |
$8$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
588.2 |
\( 2^{2} \cdot 3 \cdot 7^{2} \) |
\( 2^{4} \cdot 3^{16} \cdot 7^{8} \) |
$0.76216$ |
$(-2a+1), (-3a+1), (3a-2), (2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$1$ |
$0.685091833$ |
0.791075908 |
\( \frac{124475734657}{63011844} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -104\) , \( 101\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-104{x}+101$ |
| 882.1-a3 |
882.1-a |
$6$ |
$8$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
882.1 |
\( 2 \cdot 3^{2} \cdot 7^{2} \) |
\( 2^{4} \cdot 3^{16} \cdot 7^{8} \) |
$0.97395$ |
$(a+1), (3), (7)$ |
0 |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{7} \) |
$1$ |
$0.685091833$ |
1.370183666 |
\( \frac{124475734657}{63011844} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -104\) , \( 101\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-104{x}+101$ |
| 252.2-a5 |
252.2-a |
$8$ |
$16$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
252.2 |
\( 2^{2} \cdot 3^{2} \cdot 7 \) |
\( 2^{4} \cdot 3^{16} \cdot 7^{8} \) |
$0.94197$ |
$(a), (-a+1), (-2a+1), (3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{6} \) |
$1$ |
$0.685091833$ |
2.071522989 |
\( \frac{124475734657}{63011844} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -104\) , \( 101\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-104{x}+101$ |
| 882.2-a3 |
882.2-a |
$8$ |
$16$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
882.2 |
\( 2 \cdot 3^{2} \cdot 7^{2} \) |
\( 2^{4} \cdot 3^{16} \cdot 7^{8} \) |
$1.37737$ |
$(a), (-a-1), (a-1), (7)$ |
$1$ |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{6} \) |
$2.283039317$ |
$0.685091833$ |
2.211959540 |
\( \frac{124475734657}{63011844} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -104\) , \( 101\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-104{x}+101$ |
| 1764.2-a3 |
1764.2-a |
$6$ |
$8$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
1764.2 |
\( 2^{2} \cdot 3^{2} \cdot 7^{2} \) |
\( 2^{4} \cdot 3^{16} \cdot 7^{8} \) |
$1.92070$ |
$(-a), (a-1), (2), (7)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$1.057617394$ |
$0.685091833$ |
1.747716634 |
\( \frac{124475734657}{63011844} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -104\) , \( 101\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-104{x}+101$ |
| 588.2-b3 |
588.2-b |
$6$ |
$8$ |
\(\Q(\sqrt{-15}) \) |
$2$ |
$[0, 1]$ |
588.2 |
\( 2^{2} \cdot 3 \cdot 7^{2} \) |
\( 2^{4} \cdot 3^{16} \cdot 7^{8} \) |
$1.70423$ |
$(2,a), (2,a+1), (3,a+1), (7)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$4$ |
\( 2^{5} \) |
$1$ |
$0.685091833$ |
2.830239210 |
\( \frac{124475734657}{63011844} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -104\) , \( 101\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3+{x}^2-104{x}+101$ |
| 1764.2-a3 |
1764.2-a |
$6$ |
$8$ |
\(\Q(\sqrt{-19}) \) |
$2$ |
$[0, 1]$ |
1764.2 |
\( 2^{2} \cdot 3^{2} \cdot 7^{2} \) |
\( 2^{4} \cdot 3^{16} \cdot 7^{8} \) |
$2.52429$ |
$(-a-1), (a-2), (2), (3)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{6} \) |
$1.056927538$ |
$0.685091833$ |
2.657891120 |
\( \frac{124475734657}{63011844} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -104\) , \( 101\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3+{x}^2-104{x}+101$ |
| 882.5-b3 |
882.5-b |
$6$ |
$8$ |
\(\Q(\sqrt{-5}) \) |
$2$ |
$[0, 1]$ |
882.5 |
\( 2 \cdot 3^{2} \cdot 7^{2} \) |
\( 2^{4} \cdot 3^{16} \cdot 7^{8} \) |
$2.17781$ |
$(2,a+1), (3,a+1), (3,a+2), (7,a+3), (7,a+4)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{6} \) |
$1$ |
$0.685091833$ |
1.225529527 |
\( \frac{124475734657}{63011844} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -104\) , \( 101\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3+{x}^2-104{x}+101$ |
| 1764.5-c3 |
1764.5-c |
$6$ |
$8$ |
\(\Q(\sqrt{-23}) \) |
$2$ |
$[0, 1]$ |
1764.5 |
\( 2^{2} \cdot 3^{2} \cdot 7^{2} \) |
\( 2^{4} \cdot 3^{16} \cdot 7^{8} \) |
$2.77733$ |
$(2,a), (2,a+1), (3,a), (3,a+2), (7)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$4$ |
\( 2^{6} \) |
$1$ |
$0.685091833$ |
4.571248708 |
\( \frac{124475734657}{63011844} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -104\) , \( 101\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3+{x}^2-104{x}+101$ |
| 294.2-b3 |
294.2-b |
$6$ |
$8$ |
\(\Q(\sqrt{-6}) \) |
$2$ |
$[0, 1]$ |
294.2 |
\( 2 \cdot 3 \cdot 7^{2} \) |
\( 2^{4} \cdot 3^{16} \cdot 7^{8} \) |
$1.81272$ |
$(2,a), (3,a), (a+1), (a-1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$1$ |
$0.685091833$ |
0.559375139 |
\( \frac{124475734657}{63011844} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -104\) , \( 101\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3+{x}^2-104{x}+101$ |
| 1764.5-g3 |
1764.5-g |
$6$ |
$8$ |
\(\Q(\sqrt{-31}) \) |
$2$ |
$[0, 1]$ |
1764.5 |
\( 2^{2} \cdot 3^{2} \cdot 7^{2} \) |
\( 2^{4} \cdot 3^{16} \cdot 7^{8} \) |
$3.22436$ |
$(2,a), (2,a+1), (7,a+2), (7,a+4), (3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{7} \) |
$1$ |
$0.685091833$ |
1.968738009 |
\( \frac{124475734657}{63011844} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -104\) , \( 101\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3+{x}^2-104{x}+101$ |
| 252.2-a3 |
252.2-a |
$6$ |
$8$ |
\(\Q(\sqrt{-35}) \) |
$2$ |
$[0, 1]$ |
252.2 |
\( 2^{2} \cdot 3^{2} \cdot 7 \) |
\( 2^{4} \cdot 3^{16} \cdot 7^{8} \) |
$2.10631$ |
$(3,a), (3,a+2), (7,a+3), (2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$4$ |
\( 2^{4} \) |
$1$ |
$0.685091833$ |
0.926413244 |
\( \frac{124475734657}{63011844} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -104\) , \( 101\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3+{x}^2-104{x}+101$ |
| 588.2-j3 |
588.2-j |
$6$ |
$8$ |
\(\Q(\sqrt{-39}) \) |
$2$ |
$[0, 1]$ |
588.2 |
\( 2^{2} \cdot 3 \cdot 7^{2} \) |
\( 2^{4} \cdot 3^{16} \cdot 7^{8} \) |
$2.74799$ |
$(2,a), (2,a+1), (3,a+1), (7)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$4$ |
\( 2^{5} \) |
$1$ |
$0.685091833$ |
1.755239846 |
\( \frac{124475734657}{63011844} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -104\) , \( 101\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3+{x}^2-104{x}+101$ |
| 882.2-b3 |
882.2-b |
$6$ |
$8$ |
\(\Q(\sqrt{-10}) \) |
$2$ |
$[0, 1]$ |
882.2 |
\( 2 \cdot 3^{2} \cdot 7^{2} \) |
\( 2^{4} \cdot 3^{16} \cdot 7^{8} \) |
$3.07989$ |
$(2,a), (7,a+2), (7,a+5), (3)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{7} \) |
$1.665006708$ |
$0.685091833$ |
5.771447647 |
\( \frac{124475734657}{63011844} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -104\) , \( 101\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3+{x}^2-104{x}+101$ |
| 1764.1-a3 |
1764.1-a |
$6$ |
$8$ |
\(\Q(\sqrt{-43}) \) |
$2$ |
$[0, 1]$ |
1764.1 |
\( 2^{2} \cdot 3^{2} \cdot 7^{2} \) |
\( 2^{4} \cdot 3^{16} \cdot 7^{8} \) |
$3.79750$ |
$(2), (3), (7)$ |
$0 \le r \le 2$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$4$ |
\( 2^{6} \) |
$1$ |
$0.685091833$ |
3.343216802 |
\( \frac{124475734657}{63011844} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -104\) , \( 101\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3+{x}^2-104{x}+101$ |
| 588.1-a3 |
588.1-a |
$6$ |
$8$ |
\(\Q(\sqrt{-51}) \) |
$2$ |
$[0, 1]$ |
588.1 |
\( 2^{2} \cdot 3 \cdot 7^{2} \) |
\( 2^{4} \cdot 3^{16} \cdot 7^{8} \) |
$3.14245$ |
$(3,a+1), (2), (7)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$4$ |
\( 2^{4} \) |
$2.015272456$ |
$0.685091833$ |
3.093267326 |
\( \frac{124475734657}{63011844} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -104\) , \( 101\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3+{x}^2-104{x}+101$ |
| 882.2-b3 |
882.2-b |
$6$ |
$8$ |
\(\Q(\sqrt{-13}) \) |
$2$ |
$[0, 1]$ |
882.2 |
\( 2 \cdot 3^{2} \cdot 7^{2} \) |
\( 2^{4} \cdot 3^{16} \cdot 7^{8} \) |
$3.51162$ |
$(2,a+1), (7,a+1), (7,a+6), (3)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{7} \) |
$2.235137593$ |
$0.685091833$ |
6.795186172 |
\( \frac{124475734657}{63011844} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -104\) , \( 101\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3+{x}^2-104{x}+101$ |
| 126.2-a3 |
126.2-a |
$6$ |
$8$ |
\(\Q(\sqrt{-14}) \) |
$2$ |
$[0, 1]$ |
126.2 |
\( 2 \cdot 3^{2} \cdot 7 \) |
\( 2^{4} \cdot 3^{16} \cdot 7^{8} \) |
$2.24040$ |
$(2,a), (3,a+1), (3,a+2), (7,a)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$4$ |
\( 2^{5} \) |
$1$ |
$0.685091833$ |
1.464787953 |
\( \frac{124475734657}{63011844} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -104\) , \( 101\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3+{x}^2-104{x}+101$ |
| 1764.1-a3 |
1764.1-a |
$6$ |
$8$ |
\(\Q(\sqrt{-67}) \) |
$2$ |
$[0, 1]$ |
1764.1 |
\( 2^{2} \cdot 3^{2} \cdot 7^{2} \) |
\( 2^{4} \cdot 3^{16} \cdot 7^{8} \) |
$4.74024$ |
$(2), (3), (7)$ |
$0 \le r \le 2$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$4$ |
\( 2^{6} \) |
$1$ |
$0.685091833$ |
2.678313234 |
\( \frac{124475734657}{63011844} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -104\) , \( 101\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3+{x}^2-104{x}+101$ |
| 882.5-i3 |
882.5-i |
$6$ |
$8$ |
\(\Q(\sqrt{-17}) \) |
$2$ |
$[0, 1]$ |
882.5 |
\( 2 \cdot 3^{2} \cdot 7^{2} \) |
\( 2^{4} \cdot 3^{16} \cdot 7^{8} \) |
$4.01569$ |
$(2,a+1), (3,a+1), (3,a+2), (7,a+2), (7,a+5)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$4$ |
\( 2^{6} \) |
$1$ |
$0.685091833$ |
2.658546815 |
\( \frac{124475734657}{63011844} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -104\) , \( 101\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3+{x}^2-104{x}+101$ |
| 42.1-c3 |
42.1-c |
$6$ |
$8$ |
\(\Q(\sqrt{-21}) \) |
$2$ |
$[0, 1]$ |
42.1 |
\( 2 \cdot 3 \cdot 7 \) |
\( 2^{4} \cdot 3^{16} \cdot 7^{8} \) |
$2.08493$ |
$(2,a+1), (3,a), (7,a)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$4$ |
\( 2^{4} \) |
$1$ |
$0.685091833$ |
0.597997177 |
\( \frac{124475734657}{63011844} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -104\) , \( 101\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3+{x}^2-104{x}+101$ |
| 588.5-l3 |
588.5-l |
$6$ |
$8$ |
\(\Q(\sqrt{-87}) \) |
$2$ |
$[0, 1]$ |
588.5 |
\( 2^{2} \cdot 3 \cdot 7^{2} \) |
\( 2^{4} \cdot 3^{16} \cdot 7^{8} \) |
$4.10433$ |
$(2,a), (2,a+1), (3,a+1), (7,a+2), (7,a+4)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$18.80524959$ |
$0.685091833$ |
11.04989759 |
\( \frac{124475734657}{63011844} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -104\) , \( 101\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3+{x}^2-104{x}+101$ |
| 882.1-b3 |
882.1-b |
$6$ |
$8$ |
\(\Q(\sqrt{-22}) \) |
$2$ |
$[0, 1]$ |
882.1 |
\( 2 \cdot 3^{2} \cdot 7^{2} \) |
\( 2^{4} \cdot 3^{16} \cdot 7^{8} \) |
$4.56822$ |
$(2,a), (3), (7)$ |
$0 \le r \le 2$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$4$ |
\( 2^{7} \) |
$1$ |
$0.685091833$ |
4.673986226 |
\( \frac{124475734657}{63011844} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -104\) , \( 101\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3+{x}^2-104{x}+101$ |
| 252.1-a3 |
252.1-a |
$6$ |
$8$ |
\(\Q(\sqrt{-91}) \) |
$2$ |
$[0, 1]$ |
252.1 |
\( 2^{2} \cdot 3^{2} \cdot 7 \) |
\( 2^{4} \cdot 3^{16} \cdot 7^{8} \) |
$3.39633$ |
$(7,a+3), (2), (3)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$4$ |
\( 2^{5} \) |
$1.842761269$ |
$0.685091833$ |
4.234938894 |
\( \frac{124475734657}{63011844} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -104\) , \( 101\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3+{x}^2-104{x}+101$ |
| 882.5-b3 |
882.5-b |
$6$ |
$8$ |
\(\Q(\sqrt{-26}) \) |
$2$ |
$[0, 1]$ |
882.5 |
\( 2 \cdot 3^{2} \cdot 7^{2} \) |
\( 2^{4} \cdot 3^{16} \cdot 7^{8} \) |
$4.96618$ |
$(2,a), (3,a+1), (3,a+2), (7,a+3), (7,a+4)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{6} \) |
$1$ |
$0.685091833$ |
0.537430250 |
\( \frac{124475734657}{63011844} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -104\) , \( 101\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3+{x}^2-104{x}+101$ |
| 588.5-f3 |
588.5-f |
$6$ |
$8$ |
\(\Q(\sqrt{-111}) \) |
$2$ |
$[0, 1]$ |
588.5 |
\( 2^{2} \cdot 3 \cdot 7^{2} \) |
\( 2^{4} \cdot 3^{16} \cdot 7^{8} \) |
$4.63601$ |
$(2,a), (2,a+1), (3,a+1), (7,a), (7,a+6)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$16.81608932$ |
$1.370183666$ |
8.747869457 |
\( \frac{124475734657}{63011844} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -104\) , \( 101\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3+{x}^2-104{x}+101$ |
| 252.5-e3 |
252.5-e |
$6$ |
$8$ |
\(\Q(\sqrt{-119}) \) |
$2$ |
$[0, 1]$ |
252.5 |
\( 2^{2} \cdot 3^{2} \cdot 7 \) |
\( 2^{4} \cdot 3^{16} \cdot 7^{8} \) |
$3.88385$ |
$(2,a), (2,a+1), (3,a), (3,a+2), (7,a+3)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$4$ |
\( 2^{5} \) |
$2.967424456$ |
$1.370183666$ |
5.963551302 |
\( \frac{124475734657}{63011844} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -104\) , \( 101\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3+{x}^2-104{x}+101$ |
| 294.1-c3 |
294.1-c |
$6$ |
$8$ |
\(\Q(\sqrt{-30}) \) |
$2$ |
$[0, 1]$ |
294.1 |
\( 2 \cdot 3 \cdot 7^{2} \) |
\( 2^{4} \cdot 3^{16} \cdot 7^{8} \) |
$4.05337$ |
$(2,a), (3,a), (7)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$4$ |
\( 2^{5} \) |
$3.431705475$ |
$0.685091833$ |
6.867808126 |
\( \frac{124475734657}{63011844} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -104\) , \( 101\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3+{x}^2-104{x}+101$ |
| 1764.1-a3 |
1764.1-a |
$6$ |
$8$ |
\(\Q(\sqrt{-163}) \) |
$2$ |
$[0, 1]$ |
1764.1 |
\( 2^{2} \cdot 3^{2} \cdot 7^{2} \) |
\( 2^{4} \cdot 3^{16} \cdot 7^{8} \) |
$7.39362$ |
$(2), (3), (7)$ |
$0 \le r \le 2$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$4$ |
\( 2^{6} \) |
$1$ |
$0.685091833$ |
1.717137079 |
\( \frac{124475734657}{63011844} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -104\) , \( 101\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3+{x}^2-104{x}+101$ |
| 42.1-a3 |
42.1-a |
$6$ |
$8$ |
\(\Q(\sqrt{-42}) \) |
$2$ |
$[0, 1]$ |
42.1 |
\( 2 \cdot 3 \cdot 7 \) |
\( 2^{4} \cdot 3^{16} \cdot 7^{8} \) |
$2.94853$ |
$(2,a), (3,a), (7,a)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$36$ |
\( 2^{4} \) |
$1$ |
$0.685091833$ |
3.805630735 |
\( \frac{124475734657}{63011844} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -104\) , \( 101\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3+{x}^2-104{x}+101$ |
| 84.2-b3 |
84.2-b |
$6$ |
$8$ |
\(\Q(\sqrt{-231}) \) |
$2$ |
$[0, 1]$ |
84.2 |
\( 2^{2} \cdot 3 \cdot 7 \) |
\( 2^{4} \cdot 3^{16} \cdot 7^{8} \) |
$4.11163$ |
$(2,a), (2,a+1), (3,a+1), (7,a+3)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$4$ |
\( 2^{4} \) |
$10.59071639$ |
$0.685091833$ |
7.638148921 |
\( \frac{124475734657}{63011844} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -104\) , \( 101\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3+{x}^2-104{x}+101$ |
| 84.2-c3 |
84.2-c |
$6$ |
$8$ |
\(\Q(\sqrt{-399}) \) |
$2$ |
$[0, 1]$ |
84.2 |
\( 2^{2} \cdot 3 \cdot 7 \) |
\( 2^{4} \cdot 3^{16} \cdot 7^{8} \) |
$5.40374$ |
$(2,a), (2,a+1), (3,a+1), (7,a+3)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$4$ |
\( 2^{4} \) |
$20.96087473$ |
$0.685091833$ |
11.50248637 |
\( \frac{124475734657}{63011844} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -104\) , \( 101\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3+{x}^2-104{x}+101$ |
| 42.1-e3 |
42.1-e |
$6$ |
$8$ |
\(\Q(\sqrt{-105}) \) |
$2$ |
$[0, 1]$ |
42.1 |
\( 2 \cdot 3 \cdot 7 \) |
\( 2^{4} \cdot 3^{16} \cdot 7^{8} \) |
$4.66203$ |
$(2,a+1), (3,a), (7,a)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$16$ |
\( 2^{4} \) |
$1$ |
$0.685091833$ |
1.069729871 |
\( \frac{124475734657}{63011844} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -104\) , \( 101\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3+{x}^2-104{x}+101$ |
| 84.1-a3 |
84.1-a |
$6$ |
$8$ |
\(\Q(\sqrt{-483}) \) |
$2$ |
$[0, 1]$ |
84.1 |
\( 2^{2} \cdot 3 \cdot 7 \) |
\( 2^{4} \cdot 3^{16} \cdot 7^{8} \) |
$5.94541$ |
$(3,a+1), (7,a+3), (2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$16$ |
\( 2^{3} \) |
$1$ |
$0.685091833$ |
0.498764124 |
\( \frac{124475734657}{63011844} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -104\) , \( 101\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3+{x}^2-104{x}+101$ |
| 84.1-a3 |
84.1-a |
$6$ |
$8$ |
\(\Q(\sqrt{-651}) \) |
$2$ |
$[0, 1]$ |
84.1 |
\( 2^{2} \cdot 3 \cdot 7 \) |
\( 2^{4} \cdot 3^{16} \cdot 7^{8} \) |
$6.90238$ |
$(3,a+1), (7,a+3), (2)$ |
$0 \le r \le 2$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$64$ |
\( 2^{3} \) |
$1$ |
$1.370183666$ |
1.718455419 |
\( \frac{124475734657}{63011844} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -104\) , \( 101\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3+{x}^2-104{x}+101$ |
| 42.1-e3 |
42.1-e |
$6$ |
$8$ |
\(\Q(\sqrt{-210}) \) |
$2$ |
$[0, 1]$ |
42.1 |
\( 2 \cdot 3 \cdot 7 \) |
\( 2^{4} \cdot 3^{16} \cdot 7^{8} \) |
$6.59311$ |
$(2,a), (3,a), (7,a)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$16$ |
\( 2^{4} \) |
$1$ |
$1.370183666$ |
0.756413246 |
\( \frac{124475734657}{63011844} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -104\) , \( 101\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3+{x}^2-104{x}+101$ |
| 84.2-c3 |
84.2-c |
$6$ |
$8$ |
\(\Q(\sqrt{-903}) \) |
$2$ |
$[0, 1]$ |
84.2 |
\( 2^{2} \cdot 3 \cdot 7 \) |
\( 2^{4} \cdot 3^{16} \cdot 7^{8} \) |
$8.12928$ |
$(2,a), (2,a+1), (3,a+1), (7,a+3)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$4$ |
\( 2^{4} \) |
$42.90162872$ |
$1.370183666$ |
15.64943555 |
\( \frac{124475734657}{63011844} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -104\) , \( 101\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3+{x}^2-104{x}+101$ |
| 84.1-a3 |
84.1-a |
$6$ |
$8$ |
\(\Q(\sqrt{-987}) \) |
$2$ |
$[0, 1]$ |
84.1 |
\( 2^{2} \cdot 3 \cdot 7 \) |
\( 2^{4} \cdot 3^{16} \cdot 7^{8} \) |
$8.49898$ |
$(3,a+1), (7,a+3), (2)$ |
$0 \le r \le 2$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$64$ |
\( 2^{3} \) |
$1$ |
$1.370183666$ |
1.395629651 |
\( \frac{124475734657}{63011844} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -104\) , \( 101\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3+{x}^2-104{x}+101$ |
| 1764.1-e3 |
1764.1-e |
$6$ |
$8$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
1764.1 |
\( 2^{2} \cdot 3^{2} \cdot 7^{2} \) |
\( 2^{4} \cdot 3^{16} \cdot 7^{8} \) |
$1.29494$ |
$(2), (3), (7)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{6} \) |
$0.174386829$ |
$3.019683757$ |
1.883996662 |
\( \frac{124475734657}{63011844} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -104\) , \( 101\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-104{x}+101$ |
| 882.1-a4 |
882.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
882.1 |
\( 2 \cdot 3^{2} \cdot 7^{2} \) |
\( 2^{4} \cdot 3^{16} \cdot 7^{8} \) |
$1.37737$ |
$(a), (-2a+1), (2a+1), (3)$ |
0 |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{7} \) |
$1$ |
$3.019683757$ |
2.135238861 |
\( \frac{124475734657}{63011844} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -104\) , \( 101\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-104{x}+101$ |
| 294.1-f3 |
294.1-f |
$6$ |
$8$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
294.1 |
\( 2 \cdot 3 \cdot 7^{2} \) |
\( 2^{4} \cdot 3^{16} \cdot 7^{8} \) |
$1.28179$ |
$(a+1), (a), (7)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$1$ |
$3.019683757$ |
1.743415230 |
\( \frac{124475734657}{63011844} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -104\) , \( 101\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-104{x}+101$ |
| 1764.1-b3 |
1764.1-b |
$6$ |
$8$ |
\(\Q(\sqrt{13}) \) |
$2$ |
$[2, 0]$ |
1764.1 |
\( 2^{2} \cdot 3^{2} \cdot 7^{2} \) |
\( 2^{4} \cdot 3^{16} \cdot 7^{8} \) |
$2.08802$ |
$(-a), (-a+1), (2), (7)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$1$ |
$3.019683757$ |
1.675019172 |
\( \frac{124475734657}{63011844} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -104\) , \( 101\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-104{x}+101$ |
| 84.1-b3 |
84.1-b |
$6$ |
$8$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
84.1 |
\( 2^{2} \cdot 3 \cdot 7 \) |
\( 2^{4} \cdot 3^{16} \cdot 7^{8} \) |
$1.23970$ |
$(-a+2), (a+3), (2)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$2.212924023$ |
$3.019683757$ |
1.458204113 |
\( \frac{124475734657}{63011844} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -104\) , \( 101\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-104{x}+101$ |
| 294.1-h3 |
294.1-h |
$6$ |
$8$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
294.1 |
\( 2 \cdot 3 \cdot 7^{2} \) |
\( 2^{4} \cdot 3^{16} \cdot 7^{8} \) |
$1.81272$ |
$(-a+2), (a+3), (7)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$1$ |
$3.019683757$ |
1.232780731 |
\( \frac{124475734657}{63011844} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -104\) , \( 101\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-104{x}+101$ |
| 126.1-f4 |
126.1-f |
$8$ |
$16$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
126.1 |
\( 2 \cdot 3^{2} \cdot 7 \) |
\( 2^{4} \cdot 3^{16} \cdot 7^{8} \) |
$1.58420$ |
$(a+3), (-a+2), (-a-2), (a)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$1.155405907$ |
$3.019683757$ |
2.637406196 |
\( \frac{124475734657}{63011844} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -104\) , \( 101\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-104{x}+101$ |
| 588.1-e3 |
588.1-e |
$6$ |
$8$ |
\(\Q(\sqrt{33}) \) |
$2$ |
$[2, 0]$ |
588.1 |
\( 2^{2} \cdot 3 \cdot 7^{2} \) |
\( 2^{4} \cdot 3^{16} \cdot 7^{8} \) |
$2.52778$ |
$(-a-2), (-a+3), (-2a+7), (7)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$3.493772007$ |
$3.019683757$ |
7.346137370 |
\( \frac{124475734657}{63011844} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -104\) , \( 101\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-104{x}+101$ |
| 1764.1-c3 |
1764.1-c |
$6$ |
$8$ |
\(\Q(\sqrt{53}) \) |
$2$ |
$[2, 0]$ |
1764.1 |
\( 2^{2} \cdot 3^{2} \cdot 7^{2} \) |
\( 2^{4} \cdot 3^{16} \cdot 7^{8} \) |
$4.21601$ |
$(-a-2), (-a+3), (2), (3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{6} \) |
$1$ |
$3.019683757$ |
1.659141855 |
\( \frac{124475734657}{63011844} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -104\) , \( 101\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-104{x}+101$ |
| 126.1-b3 |
126.1-b |
$6$ |
$8$ |
\(\Q(\sqrt{14}) \) |
$2$ |
$[2, 0]$ |
126.1 |
\( 2 \cdot 3^{2} \cdot 7 \) |
\( 2^{4} \cdot 3^{16} \cdot 7^{8} \) |
$2.24040$ |
$(-a+4), (-2a+7), (3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{6} \) |
$1$ |
$3.019683757$ |
1.614088862 |
\( \frac{124475734657}{63011844} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -104\) , \( 101\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-104{x}+101$ |
| 252.1-b3 |
252.1-b |
$6$ |
$8$ |
\(\Q(\sqrt{77}) \) |
$2$ |
$[2, 0]$ |
252.1 |
\( 2^{2} \cdot 3^{2} \cdot 7 \) |
\( 2^{4} \cdot 3^{16} \cdot 7^{8} \) |
$3.12417$ |
$(a+3), (2), (3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$4$ |
\( 2^{5} \) |
$1$ |
$3.019683757$ |
2.752999213 |
\( \frac{124475734657}{63011844} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -104\) , \( 101\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-104{x}+101$ |
| 42.1-a3 |
42.1-a |
$6$ |
$8$ |
\(\Q(\sqrt{42}) \) |
$2$ |
$[2, 0]$ |
42.1 |
\( 2 \cdot 3 \cdot 7 \) |
\( 2^{4} \cdot 3^{16} \cdot 7^{8} \) |
$2.94853$ |
$(2,a), (3,a), (a+7)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$11.75931960$ |
$3.019683757$ |
5.479223448 |
\( \frac{124475734657}{63011844} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -104\) , \( 101\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-104{x}+101$ |
*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.
