| 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 |
| 196.1-a1 |
196.1-a |
$1$ |
$1$ |
\(\Q(\sqrt{93}) \) |
$2$ |
$[2, 0]$ |
196.1 |
\( 2^{2} \cdot 7^{2} \) |
\( 2^{2} \cdot 7^{5} \) |
$3.22436$ |
$(-a+6), (a+5), (2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2^{2} \) |
$1$ |
$3.259127486$ |
1.351823108 |
\( \frac{3534334150509}{4802} a - \frac{9408921892079}{2401} \) |
\( \bigl[a + 1\) , \( -1\) , \( 0\) , \( 66 a - 331\) , \( 651 a - 3451\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}-{x}^{2}+\left(66a-331\right){x}+651a-3451$ |
| 196.1-b1 |
196.1-b |
$6$ |
$18$ |
\(\Q(\sqrt{93}) \) |
$2$ |
$[2, 0]$ |
196.1 |
\( 2^{2} \cdot 7^{2} \) |
\( 2^{36} \cdot 7^{2} \) |
$3.22436$ |
$(-a+6), (a+5), (2)$ |
$0 \le r \le 1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
|
\( 2 \cdot 3^{2} \) |
$1$ |
$7.027708105$ |
7.987769023 |
\( -\frac{548347731625}{1835008} \) |
\( \bigl[a\) , \( -a\) , \( a + 1\) , \( -14839 a - 64112\) , \( 2157342 a + 9323679\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(-14839a-64112\right){x}+2157342a+9323679$ |
| 196.1-b2 |
196.1-b |
$6$ |
$18$ |
\(\Q(\sqrt{93}) \) |
$2$ |
$[2, 0]$ |
196.1 |
\( 2^{2} \cdot 7^{2} \) |
\( 2^{4} \cdot 7^{2} \) |
$3.22436$ |
$(-a+6), (a+5), (2)$ |
$0 \le r \le 1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
|
\( 2 \) |
$1$ |
$7.027708105$ |
7.987769023 |
\( -\frac{15625}{28} \) |
\( \bigl[a\) , \( -a\) , \( a + 1\) , \( -49 a - 192\) , \( -768 a - 3295\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(-49a-192\right){x}-768a-3295$ |
| 196.1-b3 |
196.1-b |
$6$ |
$18$ |
\(\Q(\sqrt{93}) \) |
$2$ |
$[2, 0]$ |
196.1 |
\( 2^{2} \cdot 7^{2} \) |
\( 2^{12} \cdot 7^{6} \) |
$3.22436$ |
$(-a+6), (a+5), (2)$ |
$0 \le r \le 1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3Cs.1.1 |
|
\( 2 \cdot 3^{3} \) |
$1$ |
$7.027708105$ |
7.987769023 |
\( \frac{9938375}{21952} \) |
\( \bigl[a\) , \( -a\) , \( a + 1\) , \( 386 a + 1688\) , \( 15657 a + 67691\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(386a+1688\right){x}+15657a+67691$ |
| 196.1-b4 |
196.1-b |
$6$ |
$18$ |
\(\Q(\sqrt{93}) \) |
$2$ |
$[2, 0]$ |
196.1 |
\( 2^{2} \cdot 7^{2} \) |
\( 2^{6} \cdot 7^{12} \) |
$3.22436$ |
$(-a+6), (a+5), (2)$ |
$0 \le r \le 1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3Cs.1.1 |
|
\( 2^{2} \cdot 3^{3} \) |
$1$ |
$7.027708105$ |
7.987769023 |
\( \frac{4956477625}{941192} \) |
\( \bigl[a\) , \( -a\) , \( a + 1\) , \( -3094 a - 13352\) , \( 166497 a + 719595\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(-3094a-13352\right){x}+166497a+719595$ |
| 196.1-b5 |
196.1-b |
$6$ |
$18$ |
\(\Q(\sqrt{93}) \) |
$2$ |
$[2, 0]$ |
196.1 |
\( 2^{2} \cdot 7^{2} \) |
\( 2^{2} \cdot 7^{4} \) |
$3.22436$ |
$(-a+6), (a+5), (2)$ |
$0 \le r \le 1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
|
\( 2^{2} \) |
$1$ |
$7.027708105$ |
7.987769023 |
\( \frac{128787625}{98} \) |
\( \bigl[a + 1\) , \( -1\) , \( a\) , \( 917 a - 4870\) , \( 33617 a - 178884\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}-{x}^{2}+\left(917a-4870\right){x}+33617a-178884$ |
| 196.1-b6 |
196.1-b |
$6$ |
$18$ |
\(\Q(\sqrt{93}) \) |
$2$ |
$[2, 0]$ |
196.1 |
\( 2^{2} \cdot 7^{2} \) |
\( 2^{18} \cdot 7^{4} \) |
$3.22436$ |
$(-a+6), (a+5), (2)$ |
$0 \le r \le 1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
|
\( 2^{2} \cdot 3^{2} \) |
$1$ |
$7.027708105$ |
7.987769023 |
\( \frac{2251439055699625}{25088} \) |
\( \bigl[a\) , \( -a\) , \( a + 1\) , \( -237559 a - 1026672\) , \( 138254622 a + 597512351\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(-237559a-1026672\right){x}+138254622a+597512351$ |
| 196.1-c1 |
196.1-c |
$2$ |
$2$ |
\(\Q(\sqrt{93}) \) |
$2$ |
$[2, 0]$ |
196.1 |
\( 2^{2} \cdot 7^{2} \) |
\( 2^{4} \cdot 7^{16} \) |
$3.22436$ |
$(-a+6), (a+5), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \cdot 7 \) |
$0.538642987$ |
$3.147932770$ |
4.923149403 |
\( \frac{534704152736331}{2712892291396} a - \frac{663232495122864}{678223072849} \) |
\( \bigl[1\) , \( -a + 1\) , \( a\) , \( 28 a + 127\) , \( 831 a + 3590\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(28a+127\right){x}+831a+3590$ |
| 196.1-c2 |
196.1-c |
$2$ |
$2$ |
\(\Q(\sqrt{93}) \) |
$2$ |
$[2, 0]$ |
196.1 |
\( 2^{2} \cdot 7^{2} \) |
\( 2^{8} \cdot 7^{8} \) |
$3.22436$ |
$(-a+6), (a+5), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \cdot 7 \) |
$0.269321493$ |
$12.59173108$ |
4.923149403 |
\( -\frac{8509626897633}{13176688} a + \frac{45474992833545}{13176688} \) |
\( \bigl[1\) , \( -a + 1\) , \( a\) , \( -32 a - 133\) , \( 243 a + 1046\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-32a-133\right){x}+243a+1046$ |
| 196.1-d1 |
196.1-d |
$1$ |
$1$ |
\(\Q(\sqrt{93}) \) |
$2$ |
$[2, 0]$ |
196.1 |
\( 2^{2} \cdot 7^{2} \) |
\( 2^{2} \cdot 7^{5} \) |
$3.22436$ |
$(-a+6), (a+5), (2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2^{2} \) |
$1$ |
$5.128825823$ |
2.127337851 |
\( -\frac{3534334150509}{4802} a - \frac{15283509633649}{4802} \) |
\( \bigl[1\) , \( 0\) , \( a\) , \( 583 a - 3106\) , \( 16907 a - 89983\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(583a-3106\right){x}+16907a-89983$ |
| 196.1-e1 |
196.1-e |
$2$ |
$2$ |
\(\Q(\sqrt{93}) \) |
$2$ |
$[2, 0]$ |
196.1 |
\( 2^{2} \cdot 7^{2} \) |
\( 2^{4} \cdot 7^{16} \) |
$3.22436$ |
$(-a+6), (a+5), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \cdot 7 \) |
$2.385367945$ |
$0.834964112$ |
5.782820946 |
\( -\frac{534704152736331}{2712892291396} a - \frac{2118225827755125}{2712892291396} \) |
\( \bigl[a\) , \( a\) , \( a + 1\) , \( -563 a - 2440\) , \( -24858 a - 107435\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(-563a-2440\right){x}-24858a-107435$ |
| 196.1-e2 |
196.1-e |
$2$ |
$2$ |
\(\Q(\sqrt{93}) \) |
$2$ |
$[2, 0]$ |
196.1 |
\( 2^{2} \cdot 7^{2} \) |
\( 2^{8} \cdot 7^{8} \) |
$3.22436$ |
$(-a+6), (a+5), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \cdot 7 \) |
$1.192683972$ |
$3.339856449$ |
5.782820946 |
\( \frac{8509626897633}{13176688} a + \frac{4620670741989}{1647086} \) |
\( \bigl[a\) , \( a\) , \( a + 1\) , \( -623 a - 2700\) , \( -21366 a - 92343\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(-623a-2700\right){x}-21366a-92343$ |
| 196.1-f1 |
196.1-f |
$2$ |
$2$ |
\(\Q(\sqrt{93}) \) |
$2$ |
$[2, 0]$ |
196.1 |
\( 2^{2} \cdot 7^{2} \) |
\( 2^{4} \cdot 7^{16} \) |
$3.22436$ |
$(-a+6), (a+5), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \cdot 7 \) |
$0.538642987$ |
$3.147932770$ |
4.923149403 |
\( -\frac{534704152736331}{2712892291396} a - \frac{2118225827755125}{2712892291396} \) |
\( \bigl[1\) , \( a\) , \( a + 1\) , \( -29 a + 155\) , \( -832 a + 4421\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(-29a+155\right){x}-832a+4421$ |
| 196.1-f2 |
196.1-f |
$2$ |
$2$ |
\(\Q(\sqrt{93}) \) |
$2$ |
$[2, 0]$ |
196.1 |
\( 2^{2} \cdot 7^{2} \) |
\( 2^{8} \cdot 7^{8} \) |
$3.22436$ |
$(-a+6), (a+5), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \cdot 7 \) |
$0.269321493$ |
$12.59173108$ |
4.923149403 |
\( \frac{8509626897633}{13176688} a + \frac{4620670741989}{1647086} \) |
\( \bigl[1\) , \( a\) , \( a + 1\) , \( 31 a - 165\) , \( -244 a + 1289\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(31a-165\right){x}-244a+1289$ |
| 196.1-g1 |
196.1-g |
$1$ |
$1$ |
\(\Q(\sqrt{93}) \) |
$2$ |
$[2, 0]$ |
196.1 |
\( 2^{2} \cdot 7^{2} \) |
\( 2^{2} \cdot 7^{5} \) |
$3.22436$ |
$(-a+6), (a+5), (2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2^{2} \) |
$1$ |
$3.259127486$ |
1.351823108 |
\( -\frac{3534334150509}{4802} a - \frac{15283509633649}{4802} \) |
\( \bigl[a\) , \( -a\) , \( 0\) , \( -66 a - 265\) , \( -651 a - 2800\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-a{x}^{2}+\left(-66a-265\right){x}-651a-2800$ |
| 196.1-h1 |
196.1-h |
$2$ |
$2$ |
\(\Q(\sqrt{93}) \) |
$2$ |
$[2, 0]$ |
196.1 |
\( 2^{2} \cdot 7^{2} \) |
\( 2^{4} \cdot 7^{16} \) |
$3.22436$ |
$(-a+6), (a+5), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \cdot 7 \) |
$2.385367945$ |
$0.834964112$ |
5.782820946 |
\( \frac{534704152736331}{2712892291396} a - \frac{663232495122864}{678223072849} \) |
\( \bigl[a + 1\) , \( a + 1\) , \( a + 1\) , \( 575 a - 2991\) , \( 22429 a - 119211\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(575a-2991\right){x}+22429a-119211$ |
| 196.1-h2 |
196.1-h |
$2$ |
$2$ |
\(\Q(\sqrt{93}) \) |
$2$ |
$[2, 0]$ |
196.1 |
\( 2^{2} \cdot 7^{2} \) |
\( 2^{8} \cdot 7^{8} \) |
$3.22436$ |
$(-a+6), (a+5), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \cdot 7 \) |
$1.192683972$ |
$3.339856449$ |
5.782820946 |
\( -\frac{8509626897633}{13176688} a + \frac{45474992833545}{13176688} \) |
\( \bigl[a + 1\) , \( a + 1\) , \( a + 1\) , \( 635 a - 3311\) , \( 18677 a - 99247\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(635a-3311\right){x}+18677a-99247$ |
| 196.1-i1 |
196.1-i |
$6$ |
$18$ |
\(\Q(\sqrt{93}) \) |
$2$ |
$[2, 0]$ |
196.1 |
\( 2^{2} \cdot 7^{2} \) |
\( 2^{36} \cdot 7^{2} \) |
$3.22436$ |
$(-a+6), (a+5), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2 \cdot 3^{2} \) |
$10.62213171$ |
$0.436190660$ |
4.324033801 |
\( -\frac{548347731625}{1835008} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -171\) , \( -874\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-171{x}-874$ |
| 196.1-i2 |
196.1-i |
$6$ |
$18$ |
\(\Q(\sqrt{93}) \) |
$2$ |
$[2, 0]$ |
196.1 |
\( 2^{2} \cdot 7^{2} \) |
\( 2^{4} \cdot 7^{2} \) |
$3.22436$ |
$(-a+6), (a+5), (2)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2 \) |
$10.62213171$ |
$35.33144352$ |
4.324033801 |
\( -\frac{15625}{28} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -1\) , \( 0\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}$ |
| 196.1-i3 |
196.1-i |
$6$ |
$18$ |
\(\Q(\sqrt{93}) \) |
$2$ |
$[2, 0]$ |
196.1 |
\( 2^{2} \cdot 7^{2} \) |
\( 2^{12} \cdot 7^{6} \) |
$3.22436$ |
$(-a+6), (a+5), (2)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3Cs.1.1 |
$1$ |
\( 2 \cdot 3^{3} \) |
$3.540710571$ |
$3.925715946$ |
4.324033801 |
\( \frac{9938375}{21952} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( 4\) , \( -6\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+4{x}-6$ |
| 196.1-i4 |
196.1-i |
$6$ |
$18$ |
\(\Q(\sqrt{93}) \) |
$2$ |
$[2, 0]$ |
196.1 |
\( 2^{2} \cdot 7^{2} \) |
\( 2^{6} \cdot 7^{12} \) |
$3.22436$ |
$(-a+6), (a+5), (2)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3Cs.1.1 |
$1$ |
\( 2^{2} \cdot 3^{3} \) |
$1.770355285$ |
$3.925715946$ |
4.324033801 |
\( \frac{4956477625}{941192} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -36\) , \( -70\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-36{x}-70$ |
| 196.1-i5 |
196.1-i |
$6$ |
$18$ |
\(\Q(\sqrt{93}) \) |
$2$ |
$[2, 0]$ |
196.1 |
\( 2^{2} \cdot 7^{2} \) |
\( 2^{2} \cdot 7^{4} \) |
$3.22436$ |
$(-a+6), (a+5), (2)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{2} \) |
$5.311065857$ |
$35.33144352$ |
4.324033801 |
\( \frac{128787625}{98} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -11\) , \( 12\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-11{x}+12$ |
| 196.1-i6 |
196.1-i |
$6$ |
$18$ |
\(\Q(\sqrt{93}) \) |
$2$ |
$[2, 0]$ |
196.1 |
\( 2^{2} \cdot 7^{2} \) |
\( 2^{18} \cdot 7^{4} \) |
$3.22436$ |
$(-a+6), (a+5), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2^{2} \cdot 3^{2} \) |
$5.311065857$ |
$0.436190660$ |
4.324033801 |
\( \frac{2251439055699625}{25088} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -2731\) , \( -55146\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-2731{x}-55146$ |
| 196.1-j1 |
196.1-j |
$1$ |
$1$ |
\(\Q(\sqrt{93}) \) |
$2$ |
$[2, 0]$ |
196.1 |
\( 2^{2} \cdot 7^{2} \) |
\( 2^{2} \cdot 7^{5} \) |
$3.22436$ |
$(-a+6), (a+5), (2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2^{2} \) |
$1$ |
$5.128825823$ |
2.127337851 |
\( \frac{3534334150509}{4802} a - \frac{9408921892079}{2401} \) |
\( \bigl[1\) , \( 0\) , \( a + 1\) , \( -584 a - 2523\) , \( -16908 a - 73076\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-584a-2523\right){x}-16908a-73076$ |
*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.
