| 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 |
| 4.2-a1 |
4.2-a |
$2$ |
$3$ |
\(\Q(\sqrt{201}) \) |
$2$ |
$[2, 0]$ |
4.2 |
\( 2^{2} \) |
\( 2^{8} \) |
$1.79164$ |
$(-17a+129)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{potential}$ |
$-3$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$67$ |
67Ns.4.1 |
$1$ |
\( 1 \) |
$0.919143165$ |
$17.69503190$ |
2.294385976 |
\( 0 \) |
\( \bigl[0\) , \( -a - 1\) , \( a + 1\) , \( a + 17\) , \( 17333 a + 114201\bigr] \) |
${y}^2+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(a+17\right){x}+17333a+114201$ |
| 4.2-a2 |
4.2-a |
$2$ |
$3$ |
\(\Q(\sqrt{201}) \) |
$2$ |
$[2, 0]$ |
4.2 |
\( 2^{2} \) |
\( 2^{8} \) |
$1.79164$ |
$(-17a+129)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{potential}$ |
$-3$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$67$ |
67Ns.4.1 |
$1$ |
\( 3 \) |
$0.306381055$ |
$17.69503190$ |
2.294385976 |
\( 0 \) |
\( \bigl[0\) , \( a + 1\) , \( a + 1\) , \( a + 17\) , \( -11621086910 a + 88189214630\bigr] \) |
${y}^2+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(a+17\right){x}-11621086910a+88189214630$ |
| 4.3-a1 |
4.3-a |
$2$ |
$3$ |
\(\Q(\sqrt{201}) \) |
$2$ |
$[2, 0]$ |
4.3 |
\( 2^{2} \) |
\( 2^{8} \) |
$1.79164$ |
$(-17a-112)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{potential}$ |
$-3$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$67$ |
67Ns.4.1 |
$1$ |
\( 1 \) |
$0.919143165$ |
$17.69503190$ |
2.294385976 |
\( 0 \) |
\( \bigl[0\) , \( a + 1\) , \( a\) , \( a + 17\) , \( -17334 a + 131552\bigr] \) |
${y}^2+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(a+17\right){x}-17334a+131552$ |
| 4.3-a2 |
4.3-a |
$2$ |
$3$ |
\(\Q(\sqrt{201}) \) |
$2$ |
$[2, 0]$ |
4.3 |
\( 2^{2} \) |
\( 2^{8} \) |
$1.79164$ |
$(-17a-112)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{potential}$ |
$-3$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$67$ |
67Ns.4.1 |
$1$ |
\( 3 \) |
$0.306381055$ |
$17.69503190$ |
2.294385976 |
\( 0 \) |
\( \bigl[0\) , \( -a - 1\) , \( a\) , \( a + 17\) , \( 11621086909 a + 76568127704\bigr] \) |
${y}^2+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(a+17\right){x}+11621086909a+76568127704$ |
| 6.1-a1 |
6.1-a |
$1$ |
$1$ |
\(\Q(\sqrt{201}) \) |
$2$ |
$[2, 0]$ |
6.1 |
\( 2 \cdot 3 \) |
\( 2^{4} \cdot 3^{2} \) |
$1.98278$ |
$(-17a+129), (-124a+941)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2^{3} \) |
$1$ |
$10.12498409$ |
5.713290511 |
\( \frac{78761}{48} a - \frac{267337}{24} \) |
\( \bigl[1\) , \( a + 1\) , \( 0\) , \( 91686871 a - 695786281\) , \( 1321324052350 a - 10027162807058\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(91686871a-695786281\right){x}+1321324052350a-10027162807058$ |
| 6.1-b1 |
6.1-b |
$1$ |
$1$ |
\(\Q(\sqrt{201}) \) |
$2$ |
$[2, 0]$ |
6.1 |
\( 2 \cdot 3 \) |
\( 2^{4} \cdot 3^{2} \) |
$1.98278$ |
$(-17a+129), (-124a+941)$ |
$2$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2^{2} \) |
$0.045395480$ |
$28.18391405$ |
1.443895878 |
\( \frac{78761}{48} a - \frac{267337}{24} \) |
\( \bigl[1\) , \( a - 1\) , \( 1\) , \( 40 a + 281\) , \( -114 a - 766\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(40a+281\right){x}-114a-766$ |
| 6.2-a1 |
6.2-a |
$1$ |
$1$ |
\(\Q(\sqrt{201}) \) |
$2$ |
$[2, 0]$ |
6.2 |
\( 2 \cdot 3 \) |
\( 2^{4} \cdot 3^{2} \) |
$1.98278$ |
$(-17a-112), (-124a+941)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2^{3} \) |
$1$ |
$10.12498409$ |
5.713290511 |
\( -\frac{78761}{48} a - \frac{151971}{16} \) |
\( \bigl[1\) , \( -a - 1\) , \( 1\) , \( -91686869 a - 604099412\) , \( -1321232365480 a - 8705234655297\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-91686869a-604099412\right){x}-1321232365480a-8705234655297$ |
| 6.2-b1 |
6.2-b |
$1$ |
$1$ |
\(\Q(\sqrt{201}) \) |
$2$ |
$[2, 0]$ |
6.2 |
\( 2 \cdot 3 \) |
\( 2^{4} \cdot 3^{2} \) |
$1.98278$ |
$(-17a-112), (-124a+941)$ |
$2$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2^{2} \) |
$0.045395480$ |
$28.18391405$ |
1.443895878 |
\( -\frac{78761}{48} a - \frac{151971}{16} \) |
\( \bigl[1\) , \( -a\) , \( 1\) , \( -40 a + 321\) , \( 114 a - 880\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-a{x}^{2}+\left(-40a+321\right){x}+114a-880$ |
| 8.1-a1 |
8.1-a |
$1$ |
$1$ |
\(\Q(\sqrt{201}) \) |
$2$ |
$[2, 0]$ |
8.1 |
\( 2^{3} \) |
\( 2^{12} \) |
$2.13064$ |
$(-17a-112), (-17a+129)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2^{2} \) |
$1$ |
$18.88411150$ |
5.327930103 |
\( -\frac{111605}{16} a - \frac{367203}{8} \) |
\( \bigl[a\) , \( 1\) , \( a\) , \( -255 a - 1655\) , \( 4702 a + 31031\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}+\left(-255a-1655\right){x}+4702a+31031$ |
| 8.1-b1 |
8.1-b |
$1$ |
$1$ |
\(\Q(\sqrt{201}) \) |
$2$ |
$[2, 0]$ |
8.1 |
\( 2^{3} \) |
\( 2^{12} \) |
$2.13064$ |
$(-17a-112), (-17a+129)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2 \cdot 3 \) |
$0.203460626$ |
$7.874121406$ |
1.356018769 |
\( -\frac{111605}{16} a - \frac{367203}{8} \) |
\( \bigl[a\) , \( 0\) , \( a\) , \( -25561331 a + 193977912\) , \( -1004825194159 a + 7625340503489\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-25561331a+193977912\right){x}-1004825194159a+7625340503489$ |
| 8.2-a1 |
8.2-a |
$1$ |
$1$ |
\(\Q(\sqrt{201}) \) |
$2$ |
$[2, 0]$ |
8.2 |
\( 2^{3} \) |
\( 2^{12} \) |
$2.13064$ |
$(-17a-112), (-17a+129)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2^{2} \) |
$1$ |
$18.88411150$ |
5.327930103 |
\( \frac{111605}{16} a - \frac{846011}{16} \) |
\( \bigl[a + 1\) , \( -a + 1\) , \( a + 1\) , \( 253 a - 1910\) , \( -4703 a + 35733\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(253a-1910\right){x}-4703a+35733$ |
| 8.2-b1 |
8.2-b |
$1$ |
$1$ |
\(\Q(\sqrt{201}) \) |
$2$ |
$[2, 0]$ |
8.2 |
\( 2^{3} \) |
\( 2^{12} \) |
$2.13064$ |
$(-17a-112), (-17a+129)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2 \cdot 3 \) |
$0.203460626$ |
$7.874121406$ |
1.356018769 |
\( \frac{111605}{16} a - \frac{846011}{16} \) |
\( \bigl[a + 1\) , \( -a\) , \( a + 1\) , \( 25561329 a + 168416581\) , \( 1004825194158 a + 6620515309330\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(25561329a+168416581\right){x}+1004825194158a+6620515309330$ |
| 10.2-a1 |
10.2-a |
$1$ |
$1$ |
\(\Q(\sqrt{201}) \) |
$2$ |
$[2, 0]$ |
10.2 |
\( 2 \cdot 5 \) |
\( - 2^{2} \cdot 5 \) |
$2.25287$ |
$(-17a-112), (-2a-13)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \) |
$1.643351567$ |
$21.86480122$ |
10.13766602 |
\( -\frac{26063}{20} a + \frac{31245}{4} \) |
\( \bigl[a + 1\) , \( a - 1\) , \( 1\) , \( 23 a + 30\) , \( 6 a + 535\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(23a+30\right){x}+6a+535$ |
| 10.2-b1 |
10.2-b |
$1$ |
$1$ |
\(\Q(\sqrt{201}) \) |
$2$ |
$[2, 0]$ |
10.2 |
\( 2 \cdot 5 \) |
\( - 2^{2} \cdot 5 \) |
$2.25287$ |
$(-17a-112), (-2a-13)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \) |
$0.108189977$ |
$35.86412383$ |
1.094735542 |
\( -\frac{26063}{20} a + \frac{31245}{4} \) |
\( \bigl[a + 1\) , \( a\) , \( 1\) , \( -229925524 a - 1514915686\) , \( 6836173662496 a + 45041657645752\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+a{x}^{2}+\left(-229925524a-1514915686\right){x}+6836173662496a+45041657645752$ |
| 10.3-a1 |
10.3-a |
$1$ |
$1$ |
\(\Q(\sqrt{201}) \) |
$2$ |
$[2, 0]$ |
10.3 |
\( 2 \cdot 5 \) |
\( - 2^{2} \cdot 5 \) |
$2.25287$ |
$(-17a+129), (-2a+15)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \) |
$1.643351567$ |
$21.86480122$ |
10.13766602 |
\( \frac{26063}{20} a + \frac{65081}{10} \) |
\( \bigl[a\) , \( a + 1\) , \( a + 1\) , \( 2 a + 4\) , \( -a - 9\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(2a+4\right){x}-a-9$ |
| 10.3-b1 |
10.3-b |
$1$ |
$1$ |
\(\Q(\sqrt{201}) \) |
$2$ |
$[2, 0]$ |
10.3 |
\( 2 \cdot 5 \) |
\( - 2^{2} \cdot 5 \) |
$2.25287$ |
$(-17a+129), (-2a+15)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \) |
$0.108189977$ |
$35.86412383$ |
1.094735542 |
\( \frac{26063}{20} a + \frac{65081}{10} \) |
\( \bigl[a\) , \( a - 1\) , \( 1\) , \( 229925549 a - 1744841260\) , \( -6837918503756 a + 51891072426358\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(229925549a-1744841260\right){x}-6837918503756a+51891072426358$ |
| 12.1-a1 |
12.1-a |
$2$ |
$2$ |
\(\Q(\sqrt{201}) \) |
$2$ |
$[2, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( - 2^{9} \cdot 3^{6} \) |
$2.35794$ |
$(-17a-112), (-17a+129), (-124a+941)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \cdot 7 \) |
$1$ |
$10.53468068$ |
5.201413584 |
\( -\frac{23814025}{3456} a + \frac{181283143}{3456} \) |
\( \bigl[1\) , \( -a\) , \( a\) , \( 367949415 a + 2424316954\) , \( 31639530031843 a + 208464113131738\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}-a{x}^{2}+\left(367949415a+2424316954\right){x}+31639530031843a+208464113131738$ |
| 12.1-a2 |
12.1-a |
$2$ |
$2$ |
\(\Q(\sqrt{201}) \) |
$2$ |
$[2, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( 2^{15} \cdot 3^{3} \) |
$2.35794$ |
$(-17a-112), (-17a+129), (-124a+941)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \cdot 7 \) |
$1$ |
$21.06936136$ |
5.201413584 |
\( \frac{80764003}{147456} a + \frac{818135443}{147456} \) |
\( \bigl[1\) , \( a - 1\) , \( a + 1\) , \( -2 a + 7\) , \( -21\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-2a+7\right){x}-21$ |
| 12.1-b1 |
12.1-b |
$2$ |
$2$ |
\(\Q(\sqrt{201}) \) |
$2$ |
$[2, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( 2^{15} \cdot 3^{3} \) |
$2.35794$ |
$(-17a-112), (-17a+129), (-124a+941)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \cdot 3 \) |
$0.725963699$ |
$13.29680258$ |
2.042609520 |
\( -\frac{80764003}{147456} a + \frac{449449723}{73728} \) |
\( \bigl[1\) , \( -a - 1\) , \( a\) , \( -42609173496 a - 280740060131\) , \( -4209975559945543 a - 27738364651025565\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-42609173496a-280740060131\right){x}-4209975559945543a-27738364651025565$ |
| 12.1-b2 |
12.1-b |
$2$ |
$2$ |
\(\Q(\sqrt{201}) \) |
$2$ |
$[2, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( - 2^{9} \cdot 3^{6} \) |
$2.35794$ |
$(-17a-112), (-17a+129), (-124a+941)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \cdot 3 \) |
$0.362981849$ |
$13.29680258$ |
2.042609520 |
\( \frac{23814025}{3456} a + \frac{26244853}{576} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -113 a - 745\) , \( 1716 a + 11306\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(-113a-745\right){x}+1716a+11306$ |
| 12.1-c1 |
12.1-c |
$2$ |
$2$ |
\(\Q(\sqrt{201}) \) |
$2$ |
$[2, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( 2^{15} \cdot 3^{3} \) |
$2.35794$ |
$(-17a-112), (-17a+129), (-124a+941)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \cdot 7 \) |
$1$ |
$21.06936136$ |
5.201413584 |
\( -\frac{80764003}{147456} a + \frac{449449723}{73728} \) |
\( \bigl[1\) , \( -a\) , \( a\) , \( a + 6\) , \( -a - 20\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}-a{x}^{2}+\left(a+6\right){x}-a-20$ |
| 12.1-c2 |
12.1-c |
$2$ |
$2$ |
\(\Q(\sqrt{201}) \) |
$2$ |
$[2, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( - 2^{9} \cdot 3^{6} \) |
$2.35794$ |
$(-17a-112), (-17a+129), (-124a+941)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \cdot 7 \) |
$1$ |
$10.53468068$ |
5.201413584 |
\( \frac{23814025}{3456} a + \frac{26244853}{576} \) |
\( \bigl[1\) , \( a - 1\) , \( a + 1\) , \( -367949416 a + 2792266369\) , \( -31639530031844 a + 240103643163581\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-367949416a+2792266369\right){x}-31639530031844a+240103643163581$ |
| 12.1-d1 |
12.1-d |
$2$ |
$2$ |
\(\Q(\sqrt{201}) \) |
$2$ |
$[2, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( - 2^{9} \cdot 3^{6} \) |
$2.35794$ |
$(-17a-112), (-17a+129), (-124a+941)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \cdot 3 \) |
$0.362981849$ |
$13.29680258$ |
2.042609520 |
\( -\frac{23814025}{3456} a + \frac{181283143}{3456} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( 113 a - 858\) , \( -1716 a + 13022\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(113a-858\right){x}-1716a+13022$ |
| 12.1-d2 |
12.1-d |
$2$ |
$2$ |
\(\Q(\sqrt{201}) \) |
$2$ |
$[2, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( 2^{15} \cdot 3^{3} \) |
$2.35794$ |
$(-17a-112), (-17a+129), (-124a+941)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \cdot 3 \) |
$0.725963699$ |
$13.29680258$ |
2.042609520 |
\( \frac{80764003}{147456} a + \frac{818135443}{147456} \) |
\( \bigl[1\) , \( a + 1\) , \( a\) , \( 42609173497 a - 323349233627\) , \( 4210018169119039 a - 31948663560204735\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(42609173497a-323349233627\right){x}+4210018169119039a-31948663560204735$ |
| 12.2-a1 |
12.2-a |
$2$ |
$2$ |
\(\Q(\sqrt{201}) \) |
$2$ |
$[2, 0]$ |
12.2 |
\( 2^{2} \cdot 3 \) |
\( 2^{8} \cdot 3^{10} \) |
$2.35794$ |
$(-17a+129), (-124a+941)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \cdot 5 \) |
$1$ |
$12.63209841$ |
2.227498808 |
\( \frac{47243}{243} a + \frac{127475}{27} \) |
\( \bigl[a + 1\) , \( -a\) , \( a + 1\) , \( -504562 a - 3324366\) , \( -442912183 a - 2918225779\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(-504562a-3324366\right){x}-442912183a-2918225779$ |
| 12.2-a2 |
12.2-a |
$2$ |
$2$ |
\(\Q(\sqrt{201}) \) |
$2$ |
$[2, 0]$ |
12.2 |
\( 2^{2} \cdot 3 \) |
\( - 2^{4} \cdot 3^{5} \) |
$2.35794$ |
$(-17a+129), (-124a+941)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 5 \) |
$1$ |
$25.26419682$ |
2.227498808 |
\( \frac{18481}{27} a + \frac{143425}{27} \) |
\( \bigl[a + 1\) , \( -a\) , \( a + 1\) , \( -141242 a - 930551\) , \( 69805497 a + 459929217\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(-141242a-930551\right){x}+69805497a+459929217$ |
| 12.2-b1 |
12.2-b |
$2$ |
$2$ |
\(\Q(\sqrt{201}) \) |
$2$ |
$[2, 0]$ |
12.2 |
\( 2^{2} \cdot 3 \) |
\( 2^{8} \cdot 3^{10} \) |
$2.35794$ |
$(-17a+129), (-124a+941)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \cdot 3 \) |
$0.736731914$ |
$13.79879482$ |
2.151165712 |
\( \frac{47243}{243} a + \frac{127475}{27} \) |
\( \bigl[a + 1\) , \( -a + 1\) , \( a + 1\) , \( 311394 a - 2363073\) , \( 179268594 a - 1360419738\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(311394a-2363073\right){x}+179268594a-1360419738$ |
| 12.2-b2 |
12.2-b |
$2$ |
$2$ |
\(\Q(\sqrt{201}) \) |
$2$ |
$[2, 0]$ |
12.2 |
\( 2^{2} \cdot 3 \) |
\( - 2^{4} \cdot 3^{5} \) |
$2.35794$ |
$(-17a+129), (-124a+941)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 3 \) |
$1.473463829$ |
$13.79879482$ |
2.151165712 |
\( \frac{18481}{27} a + \frac{143425}{27} \) |
\( \bigl[a + 1\) , \( -a + 1\) , \( a + 1\) , \( -51926 a + 394062\) , \( 18154185 a - 137767046\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-51926a+394062\right){x}+18154185a-137767046$ |
| 12.3-a1 |
12.3-a |
$2$ |
$2$ |
\(\Q(\sqrt{201}) \) |
$2$ |
$[2, 0]$ |
12.3 |
\( 2^{2} \cdot 3 \) |
\( - 2^{4} \cdot 3^{5} \) |
$2.35794$ |
$(-17a-112), (-124a+941)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 5 \) |
$1$ |
$25.26419682$ |
2.227498808 |
\( -\frac{18481}{27} a + \frac{161906}{27} \) |
\( \bigl[a\) , \( 0\) , \( a\) , \( 141240 a - 1071791\) , \( -69805498 a + 529734715\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(141240a-1071791\right){x}-69805498a+529734715$ |
| 12.3-a2 |
12.3-a |
$2$ |
$2$ |
\(\Q(\sqrt{201}) \) |
$2$ |
$[2, 0]$ |
12.3 |
\( 2^{2} \cdot 3 \) |
\( 2^{8} \cdot 3^{10} \) |
$2.35794$ |
$(-17a-112), (-124a+941)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \cdot 5 \) |
$1$ |
$12.63209841$ |
2.227498808 |
\( -\frac{47243}{243} a + \frac{1194518}{243} \) |
\( \bigl[a\) , \( 0\) , \( a\) , \( 504560 a - 3828926\) , \( 442912182 a - 3361137961\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(504560a-3828926\right){x}+442912182a-3361137961$ |
| 12.3-b1 |
12.3-b |
$2$ |
$2$ |
\(\Q(\sqrt{201}) \) |
$2$ |
$[2, 0]$ |
12.3 |
\( 2^{2} \cdot 3 \) |
\( - 2^{4} \cdot 3^{5} \) |
$2.35794$ |
$(-17a-112), (-124a+941)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 3 \) |
$1.473463829$ |
$13.79879482$ |
2.151165712 |
\( -\frac{18481}{27} a + \frac{161906}{27} \) |
\( \bigl[a\) , \( 1\) , \( a\) , \( 51924 a + 342138\) , \( -18154186 a - 119612860\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}+\left(51924a+342138\right){x}-18154186a-119612860$ |
| 12.3-b2 |
12.3-b |
$2$ |
$2$ |
\(\Q(\sqrt{201}) \) |
$2$ |
$[2, 0]$ |
12.3 |
\( 2^{2} \cdot 3 \) |
\( 2^{8} \cdot 3^{10} \) |
$2.35794$ |
$(-17a-112), (-124a+941)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \cdot 3 \) |
$0.736731914$ |
$13.79879482$ |
2.151165712 |
\( -\frac{47243}{243} a + \frac{1194518}{243} \) |
\( \bigl[a\) , \( 1\) , \( a\) , \( -311396 a - 2051677\) , \( -179268595 a - 1181151143\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}+\left(-311396a-2051677\right){x}-179268595a-1181151143$ |
| 15.1-a1 |
15.1-a |
$1$ |
$1$ |
\(\Q(\sqrt{201}) \) |
$2$ |
$[2, 0]$ |
15.1 |
\( 3 \cdot 5 \) |
\( 3^{11} \cdot 5^{5} \) |
$2.49321$ |
$(-124a+941), (-2a-13)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 11 \) |
$1.270794236$ |
$2.378830149$ |
4.690977206 |
\( \frac{615021539}{2278125} a - \frac{186622822}{91125} \) |
\( \bigl[a\) , \( 0\) , \( 1\) , \( 264935 a + 1745626\) , \( -9627100173 a - 63430300516\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+\left(264935a+1745626\right){x}-9627100173a-63430300516$ |
| 15.1-b1 |
15.1-b |
$1$ |
$1$ |
\(\Q(\sqrt{201}) \) |
$2$ |
$[2, 0]$ |
15.1 |
\( 3 \cdot 5 \) |
\( 3^{11} \cdot 5^{5} \) |
$2.49321$ |
$(-124a+941), (-2a-13)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 5 \) |
$0.169226185$ |
$10.72443788$ |
1.280100526 |
\( \frac{615021539}{2278125} a - \frac{186622822}{91125} \) |
\( \bigl[a\) , \( -a\) , \( 1\) , \( 99919 a - 758246\) , \( -54573381 a + 414142307\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}-a{x}^{2}+\left(99919a-758246\right){x}-54573381a+414142307$ |
| 15.2-a1 |
15.2-a |
$1$ |
$1$ |
\(\Q(\sqrt{201}) \) |
$2$ |
$[2, 0]$ |
15.2 |
\( 3 \cdot 5 \) |
\( 3^{11} \cdot 5^{5} \) |
$2.49321$ |
$(-124a+941), (-2a+15)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 11 \) |
$1.270794236$ |
$2.378830149$ |
4.690977206 |
\( -\frac{615021539}{2278125} a - \frac{4050549011}{2278125} \) |
\( \bigl[a + 1\) , \( -a\) , \( 1\) , \( -264936 a + 2010561\) , \( 9627100173 a - 73057400689\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}-a{x}^{2}+\left(-264936a+2010561\right){x}+9627100173a-73057400689$ |
| 15.2-b1 |
15.2-b |
$1$ |
$1$ |
\(\Q(\sqrt{201}) \) |
$2$ |
$[2, 0]$ |
15.2 |
\( 3 \cdot 5 \) |
\( 3^{11} \cdot 5^{5} \) |
$2.49321$ |
$(-124a+941), (-2a+15)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 5 \) |
$0.169226185$ |
$10.72443788$ |
1.280100526 |
\( -\frac{615021539}{2278125} a - \frac{4050549011}{2278125} \) |
\( \bigl[a + 1\) , \( -1\) , \( 1\) , \( -99920 a - 658327\) , \( 54573381 a + 359568926\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}-{x}^{2}+\left(-99920a-658327\right){x}+54573381a+359568926$ |
| 16.1-a1 |
16.1-a |
$4$ |
$6$ |
\(\Q(\sqrt{201}) \) |
$2$ |
$[2, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{8} \) |
$2.53377$ |
$(-17a-112), (-17a+129)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-3$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$2, 67$ |
2B, 67Ns.4.1 |
$1$ |
\( 3 \) |
$1$ |
$17.69503190$ |
0.936083488 |
\( 0 \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( a + 17\) , \( 14193713 a - 107712186\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(a+17\right){x}+14193713a-107712186$ |
| 16.1-a2 |
16.1-a |
$4$ |
$6$ |
\(\Q(\sqrt{201}) \) |
$2$ |
$[2, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{8} \) |
$2.53377$ |
$(-17a-112), (-17a+129)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-3$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$2, 67$ |
2B, 67Ns.4.1 |
$1$ |
\( 3 \) |
$1$ |
$17.69503190$ |
0.936083488 |
\( 0 \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( a + 17\) , \( -14193713 a - 93518456\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(a+17\right){x}-14193713a-93518456$ |
| 16.1-a3 |
16.1-a |
$4$ |
$6$ |
\(\Q(\sqrt{201}) \) |
$2$ |
$[2, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{16} \) |
$2.53377$ |
$(-17a-112), (-17a+129)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-12$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$67$ |
67Ns.4.1 |
$1$ |
\( 3 \) |
$1$ |
$17.69503190$ |
0.936083488 |
\( 54000 \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 363321 a - 2757118\) , \( 312938562 a - 2374804224\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(363321a-2757118\right){x}+312938562a-2374804224$ |
| 16.1-a4 |
16.1-a |
$4$ |
$6$ |
\(\Q(\sqrt{201}) \) |
$2$ |
$[2, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{16} \) |
$2.53377$ |
$(-17a-112), (-17a+129)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-12$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$67$ |
67Ns.4.1 |
$1$ |
\( 3 \) |
$1$ |
$17.69503190$ |
0.936083488 |
\( 54000 \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -363319 a - 2393798\) , \( -313301882 a - 2064259460\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(-363319a-2393798\right){x}-313301882a-2064259460$ |
| 16.4-a1 |
16.4-a |
$1$ |
$1$ |
\(\Q(\sqrt{201}) \) |
$2$ |
$[2, 0]$ |
16.4 |
\( 2^{4} \) |
\( 2^{8} \) |
$2.53377$ |
$(-17a+129)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
|
|
$1$ |
\( 1 \) |
$3.597665179$ |
$14.32560224$ |
7.270522090 |
\( 53 a + 949 \) |
\( \bigl[a + 1\) , \( -1\) , \( 0\) , \( -284353901 a + 2157883215\) , \( 9530103912546 a - 72321322940658\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}-{x}^{2}+\left(-284353901a+2157883215\right){x}+9530103912546a-72321322940658$ |
| 16.4-b1 |
16.4-b |
$2$ |
$67$ |
\(\Q(\sqrt{201}) \) |
$2$ |
$[2, 0]$ |
16.4 |
\( 2^{4} \) |
\( 2^{12} \) |
$2.53377$ |
$(-17a+129)$ |
$0 \le r \le 1$ |
$\mathsf{trivial}$ |
$\textsf{potential}$ |
$-67$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
|
\( 1 \) |
$1$ |
$18.20067866$ |
2.878048675 |
\( -147197952000 \) |
\( \bigl[0\) , \( 0\) , \( a + 1\) , \( -40228944910 a - 265057392270\) , \( 11693784714885414 a + 77047113446016374\bigr] \) |
${y}^2+\left(a+1\right){y}={x}^{3}+\left(-40228944910a-265057392270\right){x}+11693784714885414a+77047113446016374$ |
| 16.4-b2 |
16.4-b |
$2$ |
$67$ |
\(\Q(\sqrt{201}) \) |
$2$ |
$[2, 0]$ |
16.4 |
\( 2^{4} \) |
\( 2^{12} \) |
$2.53377$ |
$(-17a+129)$ |
$0 \le r \le 1$ |
$\mathsf{trivial}$ |
$\textsf{potential}$ |
$-67$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
|
\( 1 \) |
$1$ |
$0.271651920$ |
2.878048675 |
\( -147197952000 \) |
\( \bigl[0\) , \( 0\) , \( a + 1\) , \( 25410 a - 192830\) , \( 5870229 a - 44547563\bigr] \) |
${y}^2+\left(a+1\right){y}={x}^{3}+\left(25410a-192830\right){x}+5870229a-44547563$ |
| 16.4-c1 |
16.4-c |
$1$ |
$1$ |
\(\Q(\sqrt{201}) \) |
$2$ |
$[2, 0]$ |
16.4 |
\( 2^{4} \) |
\( 2^{8} \) |
$2.53377$ |
$(-17a+129)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
|
|
$1$ |
\( 1 \) |
$0.298679995$ |
$21.18880991$ |
0.892780442 |
\( 53 a + 949 \) |
\( \bigl[a + 1\) , \( a - 1\) , \( a + 1\) , \( 18 a + 103\) , \( 88 a + 572\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(18a+103\right){x}+88a+572$ |
| 16.5-a1 |
16.5-a |
$1$ |
$1$ |
\(\Q(\sqrt{201}) \) |
$2$ |
$[2, 0]$ |
16.5 |
\( 2^{4} \) |
\( 2^{8} \) |
$2.53377$ |
$(-17a-112)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
|
|
$1$ |
\( 1 \) |
$3.597665179$ |
$14.32560224$ |
7.270522090 |
\( -53 a + 1002 \) |
\( \bigl[a\) , \( -a\) , \( 0\) , \( 284353901 a + 1873529314\) , \( -9530103912546 a - 62791219028112\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-a{x}^{2}+\left(284353901a+1873529314\right){x}-9530103912546a-62791219028112$ |
| 16.5-b1 |
16.5-b |
$2$ |
$67$ |
\(\Q(\sqrt{201}) \) |
$2$ |
$[2, 0]$ |
16.5 |
\( 2^{4} \) |
\( 2^{12} \) |
$2.53377$ |
$(-17a-112)$ |
$0 \le r \le 1$ |
$\mathsf{trivial}$ |
$\textsf{potential}$ |
$-67$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
|
\( 1 \) |
$1$ |
$18.20067866$ |
2.878048675 |
\( -147197952000 \) |
\( \bigl[0\) , \( 0\) , \( a\) , \( 40228944910 a - 305286337180\) , \( -11693784714885415 a + 88740898160901789\bigr] \) |
${y}^2+a{y}={x}^{3}+\left(40228944910a-305286337180\right){x}-11693784714885415a+88740898160901789$ |
| 16.5-b2 |
16.5-b |
$2$ |
$67$ |
\(\Q(\sqrt{201}) \) |
$2$ |
$[2, 0]$ |
16.5 |
\( 2^{4} \) |
\( 2^{12} \) |
$2.53377$ |
$(-17a-112)$ |
$0 \le r \le 1$ |
$\mathsf{trivial}$ |
$\textsf{potential}$ |
$-67$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
|
\( 1 \) |
$1$ |
$0.271651920$ |
2.878048675 |
\( -147197952000 \) |
\( \bigl[0\) , \( 0\) , \( a\) , \( -25410 a - 167420\) , \( -5870230 a - 38677333\bigr] \) |
${y}^2+a{y}={x}^{3}+\left(-25410a-167420\right){x}-5870230a-38677333$ |
| 16.5-c1 |
16.5-c |
$1$ |
$1$ |
\(\Q(\sqrt{201}) \) |
$2$ |
$[2, 0]$ |
16.5 |
\( 2^{4} \) |
\( 2^{8} \) |
$2.53377$ |
$(-17a-112)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
|
|
$1$ |
\( 1 \) |
$0.298679995$ |
$21.18880991$ |
0.892780442 |
\( -53 a + 1002 \) |
\( \bigl[a\) , \( a + 1\) , \( 0\) , \( 7 a + 123\) , \( 15 a + 336\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(7a+123\right){x}+15a+336$ |
| 18.1-a1 |
18.1-a |
$1$ |
$1$ |
\(\Q(\sqrt{201}) \) |
$2$ |
$[2, 0]$ |
18.1 |
\( 2 \cdot 3^{2} \) |
\( 2^{4} \cdot 3^{8} \) |
$2.60948$ |
$(-17a-112), (-124a+941)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2^{3} \) |
$1$ |
$5.096969173$ |
2.876099888 |
\( -\frac{78761}{48} a - \frac{151971}{16} \) |
\( \bigl[1\) , \( a\) , \( a\) , \( -124137628 a + 942046144\) , \( 1127279649150 a - 8554613496236\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+a{x}^{2}+\left(-124137628a+942046144\right){x}+1127279649150a-8554613496236$ |
| 18.1-b1 |
18.1-b |
$1$ |
$1$ |
\(\Q(\sqrt{201}) \) |
$2$ |
$[2, 0]$ |
18.1 |
\( 2 \cdot 3^{2} \) |
\( 2^{4} \cdot 3^{8} \) |
$2.60948$ |
$(-17a-112), (-124a+941)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2^{2} \) |
$0.226863617$ |
$18.66218084$ |
2.389016808 |
\( -\frac{78761}{48} a - \frac{151971}{16} \) |
\( \bigl[1\) , \( -a + 1\) , \( a\) , \( -268 a - 1742\) , \( 7129 a + 46978\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-268a-1742\right){x}+7129a+46978$ |
*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.
