| 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 |
| 6.1-a1 |
6.1-a |
$2$ |
$7$ |
\(\Q(\sqrt{10}) \) |
$2$ |
$[2, 0]$ |
6.1 |
\( 2 \cdot 3 \) |
\( 2^{13} \cdot 3 \) |
$0.88452$ |
$(2,a), (3,a+2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$7$ |
7B.6.3 |
$49$ |
\( 1 \) |
$1$ |
$0.136429462$ |
1.056998213 |
\( \frac{574055084970269951}{6} a - \frac{907661070264560078}{3} \) |
\( \bigl[a\) , \( a\) , \( 0\) , \( 1263 a - 8032\) , \( 62956 a - 305877\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+a{x}^{2}+\left(1263a-8032\right){x}+62956a-305877$ |
| 6.1-a2 |
6.1-a |
$2$ |
$7$ |
\(\Q(\sqrt{10}) \) |
$2$ |
$[2, 0]$ |
6.1 |
\( 2 \cdot 3 \) |
\( 2^{19} \cdot 3^{7} \) |
$0.88452$ |
$(2,a), (3,a+2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$7$ |
7B.6.1 |
$1$ |
\( 1 \) |
$1$ |
$6.685043672$ |
1.056998213 |
\( \frac{7261339}{34992} a + \frac{5642407}{8748} \) |
\( \bigl[a\) , \( a\) , \( 0\) , \( 3 a + 8\) , \( 4 a + 3\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+a{x}^{2}+\left(3a+8\right){x}+4a+3$ |
| 6.1-b1 |
6.1-b |
$2$ |
$7$ |
\(\Q(\sqrt{10}) \) |
$2$ |
$[2, 0]$ |
6.1 |
\( 2 \cdot 3 \) |
\( 2 \cdot 3 \) |
$0.88452$ |
$(2,a), (3,a+2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$7$ |
7B.1.3 |
$49$ |
\( 1 \) |
$1$ |
$0.136429462$ |
1.056998213 |
\( \frac{574055084970269951}{6} a - \frac{907661070264560078}{3} \) |
\( \bigl[1\) , \( -a + 1\) , \( a + 1\) , \( 314 a - 2006\) , \( 8873 a - 39813\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(314a-2006\right){x}+8873a-39813$ |
| 6.1-b2 |
6.1-b |
$2$ |
$7$ |
\(\Q(\sqrt{10}) \) |
$2$ |
$[2, 0]$ |
6.1 |
\( 2 \cdot 3 \) |
\( 2^{7} \cdot 3^{7} \) |
$0.88452$ |
$(2,a), (3,a+2)$ |
0 |
$\Z/7\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$7$ |
7B.1.1 |
$1$ |
\( 7^{2} \) |
$1$ |
$6.685043672$ |
1.056998213 |
\( \frac{7261339}{34992} a + \frac{5642407}{8748} \) |
\( \bigl[1\) , \( -a + 1\) , \( a + 1\) , \( -a + 4\) , \( -a - 3\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-a+4\right){x}-a-3$ |
| 6.2-a1 |
6.2-a |
$2$ |
$7$ |
\(\Q(\sqrt{10}) \) |
$2$ |
$[2, 0]$ |
6.2 |
\( 2 \cdot 3 \) |
\( 2^{13} \cdot 3 \) |
$0.88452$ |
$(2,a), (3,a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$7$ |
7B.6.3 |
$49$ |
\( 1 \) |
$1$ |
$0.136429462$ |
1.056998213 |
\( -\frac{574055084970269951}{6} a - \frac{907661070264560078}{3} \) |
\( \bigl[a\) , \( -a\) , \( a\) , \( -2741954 a - 8670817\) , \( -4394335877 a - 13896110178\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}-a{x}^{2}+\left(-2741954a-8670817\right){x}-4394335877a-13896110178$ |
| 6.2-a2 |
6.2-a |
$2$ |
$7$ |
\(\Q(\sqrt{10}) \) |
$2$ |
$[2, 0]$ |
6.2 |
\( 2 \cdot 3 \) |
\( 2^{19} \cdot 3^{7} \) |
$0.88452$ |
$(2,a), (3,a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$7$ |
7B.6.1 |
$1$ |
\( 1 \) |
$1$ |
$6.685043672$ |
1.056998213 |
\( -\frac{7261339}{34992} a + \frac{5642407}{8748} \) |
\( \bigl[a\) , \( -a\) , \( a\) , \( -374 a - 1177\) , \( -86489 a - 273498\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}-a{x}^{2}+\left(-374a-1177\right){x}-86489a-273498$ |
| 6.2-b1 |
6.2-b |
$2$ |
$7$ |
\(\Q(\sqrt{10}) \) |
$2$ |
$[2, 0]$ |
6.2 |
\( 2 \cdot 3 \) |
\( 2 \cdot 3 \) |
$0.88452$ |
$(2,a), (3,a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$7$ |
7B.1.3 |
$49$ |
\( 1 \) |
$1$ |
$0.136429462$ |
1.056998213 |
\( -\frac{574055084970269951}{6} a - \frac{907661070264560078}{3} \) |
\( \bigl[1\) , \( a + 1\) , \( a + 1\) , \( -315 a - 2006\) , \( -8874 a - 39813\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-315a-2006\right){x}-8874a-39813$ |
| 6.2-b2 |
6.2-b |
$2$ |
$7$ |
\(\Q(\sqrt{10}) \) |
$2$ |
$[2, 0]$ |
6.2 |
\( 2 \cdot 3 \) |
\( 2^{7} \cdot 3^{7} \) |
$0.88452$ |
$(2,a), (3,a+1)$ |
0 |
$\Z/7\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$7$ |
7B.1.1 |
$1$ |
\( 7^{2} \) |
$1$ |
$6.685043672$ |
1.056998213 |
\( -\frac{7261339}{34992} a + \frac{5642407}{8748} \) |
\( \bigl[1\) , \( a + 1\) , \( a + 1\) , \( 4\) , \( -3\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+4{x}-3$ |
| 12.1-a1 |
12.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{10}) \) |
$2$ |
$[2, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( - 2^{20} \cdot 3^{8} \) |
$1.05187$ |
$(2,a), (3,a+1)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$19.19785289$ |
1.517723533 |
\( -\frac{1957662404}{6561} a + \frac{6190492076}{6561} \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( -14 a - 42\) , \( 390 a + 1238\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(-14a-42\right){x}+390a+1238$ |
| 12.1-a2 |
12.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{10}) \) |
$2$ |
$[2, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( 2^{8} \cdot 3^{2} \) |
$1.05187$ |
$(2,a), (3,a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$19.19785289$ |
1.517723533 |
\( -\frac{77824}{9} a + \frac{262144}{9} \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( -4 a - 7\) , \( -3 a - 12\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(-4a-7\right){x}-3a-12$ |
| 12.1-a3 |
12.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{10}) \) |
$2$ |
$[2, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( 2^{16} \cdot 3^{4} \) |
$1.05187$ |
$(2,a), (3,a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$1$ |
$38.39570578$ |
1.517723533 |
\( \frac{2053600}{81} a + \frac{6678128}{81} \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( -34 a - 102\) , \( 162 a + 510\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(-34a-102\right){x}+162a+510$ |
| 12.1-a4 |
12.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{10}) \) |
$2$ |
$[2, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( - 2^{20} \cdot 3^{2} \) |
$1.05187$ |
$(2,a), (3,a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$19.19785289$ |
1.517723533 |
\( \frac{37287936100}{9} a + \frac{117914819012}{9} \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( -534 a - 1682\) , \( 11534 a + 36470\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(-534a-1682\right){x}+11534a+36470$ |
| 12.1-b1 |
12.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{10}) \) |
$2$ |
$[2, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( - 2^{8} \cdot 3^{8} \) |
$1.05187$ |
$(2,a), (3,a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \cdot 3 \) |
$0.131320837$ |
$19.19785289$ |
1.195852355 |
\( -\frac{1957662404}{6561} a + \frac{6190492076}{6561} \) |
\( \bigl[a\) , \( -a\) , \( a\) , \( -5 a - 11\) , \( 50 a + 161\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}-a{x}^{2}+\left(-5a-11\right){x}+50a+161$ |
| 12.1-b2 |
12.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{10}) \) |
$2$ |
$[2, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( 2^{20} \cdot 3^{2} \) |
$1.05187$ |
$(2,a), (3,a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \cdot 3 \) |
$0.131320837$ |
$19.19785289$ |
1.195852355 |
\( -\frac{77824}{9} a + \frac{262144}{9} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -14 a - 39\) , \( a + 5\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(-14a-39\right){x}+a+5$ |
| 12.1-b3 |
12.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{10}) \) |
$2$ |
$[2, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( 2^{4} \cdot 3^{4} \) |
$1.05187$ |
$(2,a), (3,a+1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2 \cdot 3 \) |
$0.262641675$ |
$38.39570578$ |
1.195852355 |
\( \frac{2053600}{81} a + \frac{6678128}{81} \) |
\( \bigl[a\) , \( -a\) , \( a\) , \( -10 a - 26\) , \( 24 a + 80\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}-a{x}^{2}+\left(-10a-26\right){x}+24a+80$ |
| 12.1-b4 |
12.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{10}) \) |
$2$ |
$[2, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( - 2^{8} \cdot 3^{2} \) |
$1.05187$ |
$(2,a), (3,a+1)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \cdot 3 \) |
$0.525283350$ |
$19.19785289$ |
1.195852355 |
\( \frac{37287936100}{9} a + \frac{117914819012}{9} \) |
\( \bigl[a\) , \( -a\) , \( a\) , \( -135 a - 421\) , \( 1518 a + 4805\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}-a{x}^{2}+\left(-135a-421\right){x}+1518a+4805$ |
| 12.2-a1 |
12.2-a |
$4$ |
$4$ |
\(\Q(\sqrt{10}) \) |
$2$ |
$[2, 0]$ |
12.2 |
\( 2^{2} \cdot 3 \) |
\( - 2^{20} \cdot 3^{2} \) |
$1.05187$ |
$(2,a), (3,a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$19.19785289$ |
1.517723533 |
\( -\frac{37287936100}{9} a + \frac{117914819012}{9} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 202 a + 638\) , \( 1306 a + 4130\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(202a+638\right){x}+1306a+4130$ |
| 12.2-a2 |
12.2-a |
$4$ |
$4$ |
\(\Q(\sqrt{10}) \) |
$2$ |
$[2, 0]$ |
12.2 |
\( 2^{2} \cdot 3 \) |
\( 2^{16} \cdot 3^{4} \) |
$1.05187$ |
$(2,a), (3,a+2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$1$ |
$38.39570578$ |
1.517723533 |
\( -\frac{2053600}{81} a + \frac{6678128}{81} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -58 a - 182\) , \( 294 a + 930\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(-58a-182\right){x}+294a+930$ |
| 12.2-a3 |
12.2-a |
$4$ |
$4$ |
\(\Q(\sqrt{10}) \) |
$2$ |
$[2, 0]$ |
12.2 |
\( 2^{2} \cdot 3 \) |
\( 2^{8} \cdot 3^{2} \) |
$1.05187$ |
$(2,a), (3,a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$19.19785289$ |
1.517723533 |
\( \frac{77824}{9} a + \frac{262144}{9} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -28 a - 87\) , \( -107 a - 338\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(-28a-87\right){x}-107a-338$ |
| 12.2-a4 |
12.2-a |
$4$ |
$4$ |
\(\Q(\sqrt{10}) \) |
$2$ |
$[2, 0]$ |
12.2 |
\( 2^{2} \cdot 3 \) |
\( - 2^{20} \cdot 3^{8} \) |
$1.05187$ |
$(2,a), (3,a+2)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$19.19785289$ |
1.517723533 |
\( \frac{1957662404}{6561} a + \frac{6190492076}{6561} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -798 a - 2522\) , \( 22946 a + 72562\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(-798a-2522\right){x}+22946a+72562$ |
| 12.2-b1 |
12.2-b |
$4$ |
$4$ |
\(\Q(\sqrt{10}) \) |
$2$ |
$[2, 0]$ |
12.2 |
\( 2^{2} \cdot 3 \) |
\( - 2^{8} \cdot 3^{2} \) |
$1.05187$ |
$(2,a), (3,a+2)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \cdot 3 \) |
$0.525283350$ |
$19.19785289$ |
1.195852355 |
\( -\frac{37287936100}{9} a + \frac{117914819012}{9} \) |
\( \bigl[a\) , \( a\) , \( a\) , \( 135 a - 421\) , \( -1518 a + 4805\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+a{x}^{2}+\left(135a-421\right){x}-1518a+4805$ |
| 12.2-b2 |
12.2-b |
$4$ |
$4$ |
\(\Q(\sqrt{10}) \) |
$2$ |
$[2, 0]$ |
12.2 |
\( 2^{2} \cdot 3 \) |
\( 2^{4} \cdot 3^{4} \) |
$1.05187$ |
$(2,a), (3,a+2)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2 \cdot 3 \) |
$0.262641675$ |
$38.39570578$ |
1.195852355 |
\( -\frac{2053600}{81} a + \frac{6678128}{81} \) |
\( \bigl[a\) , \( a\) , \( a\) , \( 10 a - 26\) , \( -24 a + 80\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+a{x}^{2}+\left(10a-26\right){x}-24a+80$ |
| 12.2-b3 |
12.2-b |
$4$ |
$4$ |
\(\Q(\sqrt{10}) \) |
$2$ |
$[2, 0]$ |
12.2 |
\( 2^{2} \cdot 3 \) |
\( 2^{20} \cdot 3^{2} \) |
$1.05187$ |
$(2,a), (3,a+2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \cdot 3 \) |
$0.131320837$ |
$19.19785289$ |
1.195852355 |
\( \frac{77824}{9} a + \frac{262144}{9} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 14 a - 39\) , \( -a + 5\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(14a-39\right){x}-a+5$ |
| 12.2-b4 |
12.2-b |
$4$ |
$4$ |
\(\Q(\sqrt{10}) \) |
$2$ |
$[2, 0]$ |
12.2 |
\( 2^{2} \cdot 3 \) |
\( - 2^{8} \cdot 3^{8} \) |
$1.05187$ |
$(2,a), (3,a+2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \cdot 3 \) |
$0.131320837$ |
$19.19785289$ |
1.195852355 |
\( \frac{1957662404}{6561} a + \frac{6190492076}{6561} \) |
\( \bigl[a\) , \( a\) , \( a\) , \( 5 a - 11\) , \( -50 a + 161\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+a{x}^{2}+\left(5a-11\right){x}-50a+161$ |
| 18.2-a1 |
18.2-a |
$2$ |
$3$ |
\(\Q(\sqrt{10}) \) |
$2$ |
$[2, 0]$ |
18.2 |
\( 2 \cdot 3^{2} \) |
\( 2^{7} \cdot 3^{3} \) |
$1.16409$ |
$(2,a), (3,a+2)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.1 |
$1$ |
\( 2 \) |
$1$ |
$38.48760139$ |
1.352316467 |
\( -\frac{1099493}{16} a - \frac{462131}{2} \) |
\( \bigl[1\) , \( a + 1\) , \( 0\) , \( -143 a - 451\) , \( 1462 a + 4623\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-143a-451\right){x}+1462a+4623$ |
| 18.2-a2 |
18.2-a |
$2$ |
$3$ |
\(\Q(\sqrt{10}) \) |
$2$ |
$[2, 0]$ |
18.2 |
\( 2 \cdot 3^{2} \) |
\( 2^{21} \cdot 3^{9} \) |
$1.16409$ |
$(2,a), (3,a+2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.2 |
$1$ |
\( 2 \) |
$1$ |
$4.276400154$ |
1.352316467 |
\( -\frac{454513}{2048} a + \frac{260987}{256} \) |
\( \bigl[1\) , \( a + 1\) , \( 0\) , \( 257 a + 814\) , \( 8740 a + 27638\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(257a+814\right){x}+8740a+27638$ |
| 18.2-b1 |
18.2-b |
$4$ |
$15$ |
\(\Q(\sqrt{10}) \) |
$2$ |
$[2, 0]$ |
18.2 |
\( 2 \cdot 3^{2} \) |
\( 2^{15} \cdot 3^{11} \) |
$1.16409$ |
$(2,a), (3,a+2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3, 5$ |
3B, 5B.4.1 |
$1$ |
\( 2^{2} \) |
$0.167148684$ |
$4.709278832$ |
0.995674444 |
\( -\frac{14810400553709}{62208} a - \frac{11708649294791}{15552} \) |
\( \bigl[a + 1\) , \( -1\) , \( a\) , \( -4515 a - 14281\) , \( 288657 a + 912811\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}-{x}^{2}+\left(-4515a-14281\right){x}+288657a+912811$ |
| 18.2-b2 |
18.2-b |
$4$ |
$15$ |
\(\Q(\sqrt{10}) \) |
$2$ |
$[2, 0]$ |
18.2 |
\( 2 \cdot 3^{2} \) |
\( 2^{17} \cdot 3^{21} \) |
$1.16409$ |
$(2,a), (3,a+2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3, 5$ |
3B, 5B.4.1 |
$1$ |
\( 2^{2} \) |
$0.501446054$ |
$1.569759610$ |
0.995674444 |
\( \frac{49923068043119}{114791256} a - \frac{39483668375137}{28697814} \) |
\( \bigl[a\) , \( -a\) , \( 0\) , \( -65 a - 304\) , \( 1536 a + 4219\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-a{x}^{2}+\left(-65a-304\right){x}+1536a+4219$ |
| 18.2-b3 |
18.2-b |
$4$ |
$15$ |
\(\Q(\sqrt{10}) \) |
$2$ |
$[2, 0]$ |
18.2 |
\( 2 \cdot 3^{2} \) |
\( 2^{13} \cdot 3^{9} \) |
$1.16409$ |
$(2,a), (3,a+2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3, 5$ |
3B, 5B.4.2 |
$1$ |
\( 2^{2} \) |
$0.100289210$ |
$7.848798054$ |
0.995674444 |
\( -\frac{18505}{54} a + \frac{15214}{27} \) |
\( \bigl[a\) , \( -a\) , \( 0\) , \( -5 a - 4\) , \( -12 a - 29\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-a{x}^{2}+\left(-5a-4\right){x}-12a-29$ |
| 18.2-b4 |
18.2-b |
$4$ |
$15$ |
\(\Q(\sqrt{10}) \) |
$2$ |
$[2, 0]$ |
18.2 |
\( 2 \cdot 3^{2} \) |
\( 2^{3} \cdot 3^{7} \) |
$1.16409$ |
$(2,a), (3,a+2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3, 5$ |
3B, 5B.4.2 |
$1$ |
\( 2^{2} \) |
$0.033429736$ |
$23.54639416$ |
0.995674444 |
\( \frac{40555}{12} a - \frac{30779}{3} \) |
\( \bigl[a + 1\) , \( -1\) , \( a\) , \( 15 a + 44\) , \( 114 a + 358\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}-{x}^{2}+\left(15a+44\right){x}+114a+358$ |
| 18.2-c1 |
18.2-c |
$4$ |
$15$ |
\(\Q(\sqrt{10}) \) |
$2$ |
$[2, 0]$ |
18.2 |
\( 2 \cdot 3^{2} \) |
\( 2^{27} \cdot 3^{11} \) |
$1.16409$ |
$(2,a), (3,a+2)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3, 5$ |
3B.1.1, 5B.4.1 |
$1$ |
\( 2 \cdot 3 \cdot 5 \) |
$1$ |
$4.709278832$ |
2.482007874 |
\( -\frac{14810400553709}{62208} a - \frac{11708649294791}{15552} \) |
\( \bigl[a\) , \( a + 1\) , \( a\) , \( -95 a + 231\) , \( 6100 a - 19186\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-95a+231\right){x}+6100a-19186$ |
| 18.2-c2 |
18.2-c |
$4$ |
$15$ |
\(\Q(\sqrt{10}) \) |
$2$ |
$[2, 0]$ |
18.2 |
\( 2 \cdot 3^{2} \) |
\( 2^{5} \cdot 3^{21} \) |
$1.16409$ |
$(2,a), (3,a+2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3, 5$ |
3B.1.2, 5B.4.1 |
$1$ |
\( 2 \cdot 5 \) |
$1$ |
$1.569759610$ |
2.482007874 |
\( \frac{49923068043119}{114791256} a - \frac{39483668375137}{28697814} \) |
\( \bigl[a + 1\) , \( -a\) , \( 0\) , \( 6220 a - 19669\) , \( 484078 a - 1530789\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}-a{x}^{2}+\left(6220a-19669\right){x}+484078a-1530789$ |
| 18.2-c3 |
18.2-c |
$4$ |
$15$ |
\(\Q(\sqrt{10}) \) |
$2$ |
$[2, 0]$ |
18.2 |
\( 2 \cdot 3^{2} \) |
\( 2 \cdot 3^{9} \) |
$1.16409$ |
$(2,a), (3,a+2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3, 5$ |
3B.1.2, 5B.4.2 |
$1$ |
\( 2 \) |
$1$ |
$7.848798054$ |
2.482007874 |
\( -\frac{18505}{54} a + \frac{15214}{27} \) |
\( \bigl[a + 1\) , \( -a\) , \( 0\) , \( -65 a + 206\) , \( -203 a + 642\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}-a{x}^{2}+\left(-65a+206\right){x}-203a+642$ |
| 18.2-c4 |
18.2-c |
$4$ |
$15$ |
\(\Q(\sqrt{10}) \) |
$2$ |
$[2, 0]$ |
18.2 |
\( 2 \cdot 3^{2} \) |
\( 2^{15} \cdot 3^{7} \) |
$1.16409$ |
$(2,a), (3,a+2)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3, 5$ |
3B.1.1, 5B.4.2 |
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$23.54639416$ |
2.482007874 |
\( \frac{40555}{12} a - \frac{30779}{3} \) |
\( \bigl[a\) , \( a + 1\) , \( a\) , \( 25 a - 69\) , \( -104 a + 338\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(25a-69\right){x}-104a+338$ |
| 18.2-d1 |
18.2-d |
$2$ |
$3$ |
\(\Q(\sqrt{10}) \) |
$2$ |
$[2, 0]$ |
18.2 |
\( 2 \cdot 3^{2} \) |
\( 2^{19} \cdot 3^{3} \) |
$1.16409$ |
$(2,a), (3,a+2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B |
$1$ |
\( 2 \cdot 7 \) |
$0.010597633$ |
$38.48760139$ |
1.805750669 |
\( -\frac{1099493}{16} a - \frac{462131}{2} \) |
\( \bigl[a\) , \( -a\) , \( a\) , \( 10 a - 39\) , \( -21 a + 66\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}-a{x}^{2}+\left(10a-39\right){x}-21a+66$ |
| 18.2-d2 |
18.2-d |
$2$ |
$3$ |
\(\Q(\sqrt{10}) \) |
$2$ |
$[2, 0]$ |
18.2 |
\( 2 \cdot 3^{2} \) |
\( 2^{33} \cdot 3^{9} \) |
$1.16409$ |
$(2,a), (3,a+2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B |
$1$ |
\( 2 \cdot 3 \cdot 7 \) |
$0.031792900$ |
$4.276400154$ |
1.805750669 |
\( -\frac{454513}{2048} a + \frac{260987}{256} \) |
\( \bigl[a\) , \( -a\) , \( a\) , \( -70 a + 221\) , \( -165 a + 526\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}-a{x}^{2}+\left(-70a+221\right){x}-165a+526$ |
| 18.3-a1 |
18.3-a |
$2$ |
$3$ |
\(\Q(\sqrt{10}) \) |
$2$ |
$[2, 0]$ |
18.3 |
\( 2 \cdot 3^{2} \) |
\( 2^{7} \cdot 3^{3} \) |
$1.16409$ |
$(2,a), (3,a+1)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.1 |
$1$ |
\( 2 \) |
$1$ |
$38.48760139$ |
1.352316467 |
\( \frac{1099493}{16} a - \frac{462131}{2} \) |
\( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( -3 a - 12\) , \( a + 2\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-3a-12\right){x}+a+2$ |
| 18.3-a2 |
18.3-a |
$2$ |
$3$ |
\(\Q(\sqrt{10}) \) |
$2$ |
$[2, 0]$ |
18.3 |
\( 2 \cdot 3^{2} \) |
\( 2^{21} \cdot 3^{9} \) |
$1.16409$ |
$(2,a), (3,a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.2 |
$1$ |
\( 2 \) |
$1$ |
$4.276400154$ |
1.352316467 |
\( \frac{454513}{2048} a + \frac{260987}{256} \) |
\( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( 17 a + 53\) , \( 29 a + 92\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(17a+53\right){x}+29a+92$ |
| 18.3-b1 |
18.3-b |
$4$ |
$15$ |
\(\Q(\sqrt{10}) \) |
$2$ |
$[2, 0]$ |
18.3 |
\( 2 \cdot 3^{2} \) |
\( 2^{17} \cdot 3^{21} \) |
$1.16409$ |
$(2,a), (3,a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3, 5$ |
3B, 5B.4.1 |
$1$ |
\( 2^{2} \) |
$0.501446054$ |
$1.569759610$ |
0.995674444 |
\( -\frac{49923068043119}{114791256} a - \frac{39483668375137}{28697814} \) |
\( \bigl[a\) , \( a\) , \( a\) , \( -24882 a - 78689\) , \( -3847743 a - 12167634\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+a{x}^{2}+\left(-24882a-78689\right){x}-3847743a-12167634$ |
| 18.3-b2 |
18.3-b |
$4$ |
$15$ |
\(\Q(\sqrt{10}) \) |
$2$ |
$[2, 0]$ |
18.3 |
\( 2 \cdot 3^{2} \) |
\( 2^{3} \cdot 3^{7} \) |
$1.16409$ |
$(2,a), (3,a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3, 5$ |
3B, 5B.4.2 |
$1$ |
\( 2^{2} \) |
$0.033429736$ |
$23.54639416$ |
0.995674444 |
\( -\frac{40555}{12} a - \frac{30779}{3} \) |
\( \bigl[1\) , \( a\) , \( a + 1\) , \( -6 a - 15\) , \( 7 a + 20\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(-6a-15\right){x}+7a+20$ |
| 18.3-b3 |
18.3-b |
$4$ |
$15$ |
\(\Q(\sqrt{10}) \) |
$2$ |
$[2, 0]$ |
18.3 |
\( 2 \cdot 3^{2} \) |
\( 2^{15} \cdot 3^{11} \) |
$1.16409$ |
$(2,a), (3,a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3, 5$ |
3B, 5B.4.1 |
$1$ |
\( 2^{2} \) |
$0.167148684$ |
$4.709278832$ |
0.995674444 |
\( \frac{14810400553709}{62208} a - \frac{11708649294791}{15552} \) |
\( \bigl[1\) , \( a\) , \( a + 1\) , \( 24 a + 60\) , \( -746 a - 2308\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(24a+60\right){x}-746a-2308$ |
| 18.3-b4 |
18.3-b |
$4$ |
$15$ |
\(\Q(\sqrt{10}) \) |
$2$ |
$[2, 0]$ |
18.3 |
\( 2 \cdot 3^{2} \) |
\( 2^{13} \cdot 3^{9} \) |
$1.16409$ |
$(2,a), (3,a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3, 5$ |
3B, 5B.4.2 |
$1$ |
\( 2^{2} \) |
$0.100289210$ |
$7.848798054$ |
0.995674444 |
\( \frac{18505}{54} a + \frac{15214}{27} \) |
\( \bigl[a\) , \( a\) , \( a\) , \( 258 a + 811\) , \( 1365 a + 4314\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+a{x}^{2}+\left(258a+811\right){x}+1365a+4314$ |
| 18.3-c1 |
18.3-c |
$4$ |
$15$ |
\(\Q(\sqrt{10}) \) |
$2$ |
$[2, 0]$ |
18.3 |
\( 2 \cdot 3^{2} \) |
\( 2^{5} \cdot 3^{21} \) |
$1.16409$ |
$(2,a), (3,a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3, 5$ |
3B.1.2, 5B.4.1 |
$1$ |
\( 2 \cdot 5 \) |
$1$ |
$1.569759610$ |
2.482007874 |
\( -\frac{49923068043119}{114791256} a - \frac{39483668375137}{28697814} \) |
\( \bigl[a + 1\) , \( 0\) , \( 0\) , \( -6220 a - 19669\) , \( -484078 a - 1530789\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-6220a-19669\right){x}-484078a-1530789$ |
| 18.3-c2 |
18.3-c |
$4$ |
$15$ |
\(\Q(\sqrt{10}) \) |
$2$ |
$[2, 0]$ |
18.3 |
\( 2 \cdot 3^{2} \) |
\( 2^{15} \cdot 3^{7} \) |
$1.16409$ |
$(2,a), (3,a+1)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3, 5$ |
3B.1.1, 5B.4.2 |
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$23.54639416$ |
2.482007874 |
\( -\frac{40555}{12} a - \frac{30779}{3} \) |
\( \bigl[a\) , \( -a + 1\) , \( a\) , \( -25 a - 69\) , \( 104 a + 338\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-25a-69\right){x}+104a+338$ |
| 18.3-c3 |
18.3-c |
$4$ |
$15$ |
\(\Q(\sqrt{10}) \) |
$2$ |
$[2, 0]$ |
18.3 |
\( 2 \cdot 3^{2} \) |
\( 2^{27} \cdot 3^{11} \) |
$1.16409$ |
$(2,a), (3,a+1)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3, 5$ |
3B.1.1, 5B.4.1 |
$1$ |
\( 2 \cdot 3 \cdot 5 \) |
$1$ |
$4.709278832$ |
2.482007874 |
\( \frac{14810400553709}{62208} a - \frac{11708649294791}{15552} \) |
\( \bigl[a\) , \( -a + 1\) , \( a\) , \( 95 a + 231\) , \( -6100 a - 19186\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(95a+231\right){x}-6100a-19186$ |
| 18.3-c4 |
18.3-c |
$4$ |
$15$ |
\(\Q(\sqrt{10}) \) |
$2$ |
$[2, 0]$ |
18.3 |
\( 2 \cdot 3^{2} \) |
\( 2 \cdot 3^{9} \) |
$1.16409$ |
$(2,a), (3,a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3, 5$ |
3B.1.2, 5B.4.2 |
$1$ |
\( 2 \) |
$1$ |
$7.848798054$ |
2.482007874 |
\( \frac{18505}{54} a + \frac{15214}{27} \) |
\( \bigl[a + 1\) , \( 0\) , \( 0\) , \( 65 a + 206\) , \( 203 a + 642\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(65a+206\right){x}+203a+642$ |
| 18.3-d1 |
18.3-d |
$2$ |
$3$ |
\(\Q(\sqrt{10}) \) |
$2$ |
$[2, 0]$ |
18.3 |
\( 2 \cdot 3^{2} \) |
\( 2^{19} \cdot 3^{3} \) |
$1.16409$ |
$(2,a), (3,a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B |
$1$ |
\( 2 \cdot 7 \) |
$0.010597633$ |
$38.48760139$ |
1.805750669 |
\( \frac{1099493}{16} a - \frac{462131}{2} \) |
\( \bigl[a\) , \( a\) , \( a\) , \( -10 a - 39\) , \( 21 a + 66\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+a{x}^{2}+\left(-10a-39\right){x}+21a+66$ |
| 18.3-d2 |
18.3-d |
$2$ |
$3$ |
\(\Q(\sqrt{10}) \) |
$2$ |
$[2, 0]$ |
18.3 |
\( 2 \cdot 3^{2} \) |
\( 2^{33} \cdot 3^{9} \) |
$1.16409$ |
$(2,a), (3,a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B |
$1$ |
\( 2 \cdot 3 \cdot 7 \) |
$0.031792900$ |
$4.276400154$ |
1.805750669 |
\( \frac{454513}{2048} a + \frac{260987}{256} \) |
\( \bigl[a\) , \( a\) , \( a\) , \( 70 a + 221\) , \( 165 a + 526\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+a{x}^{2}+\left(70a+221\right){x}+165a+526$ |
| 20.1-a1 |
20.1-a |
$4$ |
$6$ |
\(\Q(\sqrt{10}) \) |
$2$ |
$[2, 0]$ |
20.1 |
\( 2^{2} \cdot 5 \) |
\( 2^{4} \cdot 5^{12} \) |
$1.19516$ |
$(2,a), (5,a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \cdot 3^{2} \) |
$1$ |
$1.772687765$ |
2.522578912 |
\( -\frac{20720464}{15625} \) |
\( \bigl[a\) , \( 1\) , \( 0\) , \( -5\) , \( -25\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+{x}^{2}-5{x}-25$ |
| 20.1-a2 |
20.1-a |
$4$ |
$6$ |
\(\Q(\sqrt{10}) \) |
$2$ |
$[2, 0]$ |
20.1 |
\( 2^{2} \cdot 5 \) |
\( 2^{4} \cdot 5^{4} \) |
$1.19516$ |
$(2,a), (5,a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \) |
$1$ |
$15.95418988$ |
2.522578912 |
\( \frac{21296}{25} \) |
\( \bigl[a\) , \( 1\) , \( 0\) , \( 5\) , \( 3\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+{x}^{2}+5{x}+3$ |
*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.
