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 |
2.1-a1 |
2.1-a |
$2$ |
$5$ |
3.3.940.1 |
$3$ |
$[3, 0]$ |
2.1 |
\( 2 \) |
\( - 2^{2} \) |
$3.07521$ |
$(-a-2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.4.2 |
$1$ |
\( 2 \) |
$0.009848962$ |
$265.3922715$ |
0.511524064 |
\( -\frac{1897}{4} a^{2} - 353 a + \frac{6735}{4} \) |
\( \bigl[a^{2} - 5\) , \( a^{2} - a - 5\) , \( a\) , \( -2 a - 2\) , \( 0\bigr] \) |
${y}^2+\left(a^{2}-5\right){x}{y}+a{y}={x}^{3}+\left(a^{2}-a-5\right){x}^{2}+\left(-2a-2\right){x}$ |
2.1-a2 |
2.1-a |
$2$ |
$5$ |
3.3.940.1 |
$3$ |
$[3, 0]$ |
2.1 |
\( 2 \) |
\( - 2^{10} \) |
$3.07521$ |
$(-a-2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.4.1 |
$1$ |
\( 2 \) |
$0.049244811$ |
$53.07845431$ |
0.511524064 |
\( \frac{947071607}{1024} a^{2} - \frac{142177921}{256} a - \frac{6291555537}{1024} \) |
\( \bigl[a^{2} - 5\) , \( 1\) , \( a^{2} - 4\) , \( -36 a^{2} + 83 a + 59\) , \( -284 a^{2} + 651 a + 493\bigr] \) |
${y}^2+\left(a^{2}-5\right){x}{y}+\left(a^{2}-4\right){y}={x}^{3}+{x}^{2}+\left(-36a^{2}+83a+59\right){x}-284a^{2}+651a+493$ |
4.1-a1 |
4.1-a |
$4$ |
$10$ |
3.3.940.1 |
$3$ |
$[3, 0]$ |
4.1 |
\( 2^{2} \) |
\( 2^{15} \) |
$3.45180$ |
$(-a-2), (a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B.4.1 |
$1$ |
\( 2 \cdot 5 \) |
$1$ |
$25.56327504$ |
2.084455243 |
\( \frac{5682805}{32} a^{2} + \frac{17340215}{32} a + \frac{8387901}{32} \) |
\( \bigl[a^{2} - a - 5\) , \( a^{2} - a - 4\) , \( a + 1\) , \( -47 a^{2} + 107 a + 84\) , \( -466 a^{2} + 1066 a + 816\bigr] \) |
${y}^2+\left(a^{2}-a-5\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a^{2}-a-4\right){x}^{2}+\left(-47a^{2}+107a+84\right){x}-466a^{2}+1066a+816$ |
4.1-a2 |
4.1-a |
$4$ |
$10$ |
3.3.940.1 |
$3$ |
$[3, 0]$ |
4.1 |
\( 2^{2} \) |
\( - 2^{3} \) |
$3.45180$ |
$(-a-2), (a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B.4.2 |
$1$ |
\( 2 \) |
$1$ |
$127.8163752$ |
2.084455243 |
\( -\frac{398753577}{4} a^{2} + \frac{120161319}{2} a + \frac{2646449161}{4} \) |
\( \bigl[a^{2} - a - 5\) , \( a - 1\) , \( 0\) , \( -117 a^{2} + 268 a + 206\) , \( 1378 a^{2} - 3159 a - 2404\bigr] \) |
${y}^2+\left(a^{2}-a-5\right){x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-117a^{2}+268a+206\right){x}+1378a^{2}-3159a-2404$ |
4.1-a3 |
4.1-a |
$4$ |
$10$ |
3.3.940.1 |
$3$ |
$[3, 0]$ |
4.1 |
\( 2^{2} \) |
\( 2^{3} \) |
$3.45180$ |
$(-a-2), (a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B.4.2 |
$1$ |
\( 2 \) |
$1$ |
$127.8163752$ |
2.084455243 |
\( \frac{64525}{2} a^{2} + \frac{158775}{2} a + \frac{25181}{2} \) |
\( \bigl[1\) , \( a^{2} - a - 4\) , \( a^{2} - 5\) , \( -2 a^{2} - 6 a + 2\) , \( 4 a^{2} + 6 a - 4\bigr] \) |
${y}^2+{x}{y}+\left(a^{2}-5\right){y}={x}^{3}+\left(a^{2}-a-4\right){x}^{2}+\left(-2a^{2}-6a+2\right){x}+4a^{2}+6a-4$ |
4.1-a4 |
4.1-a |
$4$ |
$10$ |
3.3.940.1 |
$3$ |
$[3, 0]$ |
4.1 |
\( 2^{2} \) |
\( - 2^{15} \) |
$3.45180$ |
$(-a-2), (a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B.4.1 |
$1$ |
\( 2 \cdot 5 \) |
$1$ |
$25.56327504$ |
2.084455243 |
\( \frac{264544214121}{1024} a^{2} - \frac{151611822399}{256} a - \frac{461586534863}{1024} \) |
\( \bigl[1\) , \( a^{2} - 4\) , \( 1\) , \( -105115 a^{2} + 240969 a + 183412\) , \( -38888874 a^{2} + 89148913 a + 67857014\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(a^{2}-4\right){x}^{2}+\left(-105115a^{2}+240969a+183412\right){x}-38888874a^{2}+89148913a+67857014$ |
5.1-a1 |
5.1-a |
$4$ |
$4$ |
3.3.940.1 |
$3$ |
$[3, 0]$ |
5.1 |
\( 5 \) |
\( 5 \) |
$3.58259$ |
$(a^2-a-7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$183.1922990$ |
1.493768493 |
\( -\frac{8468}{5} a^{2} + \frac{4144}{5} a + \frac{57849}{5} \) |
\( \bigl[a^{2} - a - 5\) , \( -a\) , \( a^{2} - 5\) , \( -a^{2} - 7 a - 6\) , \( 16 a^{2} + 44 a + 19\bigr] \) |
${y}^2+\left(a^{2}-a-5\right){x}{y}+\left(a^{2}-5\right){y}={x}^{3}-a{x}^{2}+\left(-a^{2}-7a-6\right){x}+16a^{2}+44a+19$ |
5.1-a2 |
5.1-a |
$4$ |
$4$ |
3.3.940.1 |
$3$ |
$[3, 0]$ |
5.1 |
\( 5 \) |
\( 5 \) |
$3.58259$ |
$(a^2-a-7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$183.1922990$ |
1.493768493 |
\( -\frac{20786237}{5} a^{2} + \frac{5310351}{5} a + \frac{158857721}{5} \) |
\( \bigl[a^{2} - a - 5\) , \( -a^{2} + 2 a + 4\) , \( a + 1\) , \( -1533 a^{2} + 3510 a + 2687\) , \( -66131 a^{2} + 151595 a + 115399\bigr] \) |
${y}^2+\left(a^{2}-a-5\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a^{2}+2a+4\right){x}^{2}+\left(-1533a^{2}+3510a+2687\right){x}-66131a^{2}+151595a+115399$ |
5.1-a3 |
5.1-a |
$4$ |
$4$ |
3.3.940.1 |
$3$ |
$[3, 0]$ |
5.1 |
\( 5 \) |
\( 5^{2} \) |
$3.58259$ |
$(a^2-a-7)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2 \) |
$1$ |
$366.3845981$ |
1.493768493 |
\( \frac{148422}{5} a^{2} + \frac{437592}{5} a + \frac{240941}{5} \) |
\( \bigl[1\) , \( -a^{2} + a + 4\) , \( 1\) , \( -a^{2} + a + 4\) , \( 1\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(-a^{2}+a+4\right){x}^{2}+\left(-a^{2}+a+4\right){x}+1$ |
5.1-a4 |
5.1-a |
$4$ |
$4$ |
3.3.940.1 |
$3$ |
$[3, 0]$ |
5.1 |
\( 5 \) |
\( - 5^{4} \) |
$3.58259$ |
$(a^2-a-7)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$183.1922990$ |
1.493768493 |
\( \frac{416211993101}{25} a^{2} + \frac{1204977729061}{25} a + \frac{575055675183}{25} \) |
\( \bigl[1\) , \( -a^{2} + a + 4\) , \( 1\) , \( -6 a^{2} + 6 a + 9\) , \( 18 a^{2} - 26 a - 21\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(-a^{2}+a+4\right){x}^{2}+\left(-6a^{2}+6a+9\right){x}+18a^{2}-26a-21$ |
5.2-a1 |
5.2-a |
$6$ |
$8$ |
3.3.940.1 |
$3$ |
$[3, 0]$ |
5.2 |
\( 5 \) |
\( 5 \) |
$3.58259$ |
$(-a^2+a+5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 1 \) |
$1$ |
$20.50717563$ |
0.668870318 |
\( -\frac{199332986876}{5} a^{2} + \frac{120136663044}{5} a + \frac{1322930343681}{5} \) |
\( \bigl[a^{2} - a - 5\) , \( -a - 1\) , \( 1\) , \( 106 a^{2} - 63 a - 702\) , \( 1165 a^{2} - 702 a - 7734\bigr] \) |
${y}^2+\left(a^{2}-a-5\right){x}{y}+{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(106a^{2}-63a-702\right){x}+1165a^{2}-702a-7734$ |
5.2-a2 |
5.2-a |
$6$ |
$8$ |
3.3.940.1 |
$3$ |
$[3, 0]$ |
5.2 |
\( 5 \) |
\( 5^{2} \) |
$3.58259$ |
$(-a^2+a+5)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2 \) |
$1$ |
$164.0574050$ |
0.668870318 |
\( -\frac{2046904}{25} a^{2} + \frac{1230056}{25} a + \frac{13638769}{25} \) |
\( \bigl[a^{2} - a - 5\) , \( -a - 1\) , \( 1\) , \( 6 a^{2} - 3 a - 37\) , \( 24 a^{2} - 15 a - 160\bigr] \) |
${y}^2+\left(a^{2}-a-5\right){x}{y}+{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(6a^{2}-3a-37\right){x}+24a^{2}-15a-160$ |
5.2-a3 |
5.2-a |
$6$ |
$8$ |
3.3.940.1 |
$3$ |
$[3, 0]$ |
5.2 |
\( 5 \) |
\( 5^{2} \) |
$3.58259$ |
$(-a^2+a+5)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$164.0574050$ |
0.668870318 |
\( \frac{197192105429}{25} a^{2} + \frac{570892174269}{25} a + \frac{272448900581}{25} \) |
\( \bigl[a^{2} - a - 5\) , \( -a^{2} + a + 6\) , \( a^{2} - 4\) , \( 225 a^{2} - 526 a - 364\) , \( 392426 a^{2} - 899618 a - 684689\bigr] \) |
${y}^2+\left(a^{2}-a-5\right){x}{y}+\left(a^{2}-4\right){y}={x}^{3}+\left(-a^{2}+a+6\right){x}^{2}+\left(225a^{2}-526a-364\right){x}+392426a^{2}-899618a-684689$ |
5.2-a4 |
5.2-a |
$6$ |
$8$ |
3.3.940.1 |
$3$ |
$[3, 0]$ |
5.2 |
\( 5 \) |
\( 5^{4} \) |
$3.58259$ |
$(-a^2+a+5)$ |
0 |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$1$ |
$328.1148101$ |
0.668870318 |
\( \frac{16042346}{625} a^{2} + \frac{30639556}{625} a + \frac{13745569}{625} \) |
\( \bigl[1\) , \( a - 1\) , \( a^{2} - a - 5\) , \( -15 a^{2} + 38 a + 17\) , \( 97 a^{2} - 222 a - 170\bigr] \) |
${y}^2+{x}{y}+\left(a^{2}-a-5\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-15a^{2}+38a+17\right){x}+97a^{2}-222a-170$ |
5.2-a5 |
5.2-a |
$6$ |
$8$ |
3.3.940.1 |
$3$ |
$[3, 0]$ |
5.2 |
\( 5 \) |
\( - 5^{8} \) |
$3.58259$ |
$(-a^2+a+5)$ |
0 |
$\Z/8\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$164.0574050$ |
0.668870318 |
\( \frac{85288749659771}{390625} a^{2} - \frac{195535485731269}{390625} a - \frac{148763739022981}{390625} \) |
\( \bigl[1\) , \( a - 1\) , \( a^{2} - a - 5\) , \( -250 a^{2} + 613 a + 322\) , \( 5318 a^{2} - 12391 a - 8700\bigr] \) |
${y}^2+{x}{y}+\left(a^{2}-a-5\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-250a^{2}+613a+322\right){x}+5318a^{2}-12391a-8700$ |
5.2-a6 |
5.2-a |
$6$ |
$8$ |
3.3.940.1 |
$3$ |
$[3, 0]$ |
5.2 |
\( 5 \) |
\( -5 \) |
$3.58259$ |
$(-a^2+a+5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$82.02870253$ |
0.668870318 |
\( \frac{1306}{5} a^{2} - \frac{264}{5} a - \frac{1601}{5} \) |
\( \bigl[1\) , \( -a^{2} + a + 6\) , \( a\) , \( a + 4\) , \( 4 a^{2} - 2 a - 27\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a^{2}+a+6\right){x}^{2}+\left(a+4\right){x}+4a^{2}-2a-27$ |
8.1-a1 |
8.1-a |
$4$ |
$4$ |
3.3.940.1 |
$3$ |
$[3, 0]$ |
8.1 |
\( 2^{3} \) |
\( - 2^{15} \) |
$3.87452$ |
$(-a-2), (a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$116.1061059$ |
0.946740904 |
\( -\frac{411926287272281}{128} a^{2} + \frac{62067501092911}{32} a + \frac{2733850455242975}{128} \) |
\( \bigl[a^{2} - 5\) , \( -a^{2} + 2 a + 4\) , \( a^{2} - 5\) , \( 513 a^{2} - 316 a - 3409\) , \( -9574 a^{2} + 5824 a + 63656\bigr] \) |
${y}^2+\left(a^{2}-5\right){x}{y}+\left(a^{2}-5\right){y}={x}^{3}+\left(-a^{2}+2a+4\right){x}^{2}+\left(513a^{2}-316a-3409\right){x}-9574a^{2}+5824a+63656$ |
8.1-a2 |
8.1-a |
$4$ |
$4$ |
3.3.940.1 |
$3$ |
$[3, 0]$ |
8.1 |
\( 2^{3} \) |
\( 2^{15} \) |
$3.87452$ |
$(-a-2), (a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$116.1061059$ |
0.946740904 |
\( \frac{31029133791577}{128} a^{2} - \frac{17449377850799}{32} a - \frac{53338737080543}{128} \) |
\( \bigl[a + 1\) , \( -1\) , \( a^{2} - a - 4\) , \( 6039 a^{2} - 3631 a - 40105\) , \( -283676 a^{2} + 170947 a + 1882761\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{2}-a-4\right){y}={x}^{3}-{x}^{2}+\left(6039a^{2}-3631a-40105\right){x}-283676a^{2}+170947a+1882761$ |
8.1-a3 |
8.1-a |
$4$ |
$4$ |
3.3.940.1 |
$3$ |
$[3, 0]$ |
8.1 |
\( 2^{3} \) |
\( 2^{18} \) |
$3.87452$ |
$(-a-2), (a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2 \) |
$1$ |
$232.2122118$ |
0.946740904 |
\( -\frac{9204129895}{16384} a^{2} + \frac{391390225}{4096} a + \frac{75753312097}{16384} \) |
\( \bigl[a + 1\) , \( -1\) , \( a^{2} - a - 4\) , \( 5419 a^{2} - 3266 a - 35965\) , \( -374961 a^{2} + 225991 a + 2488521\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{2}-a-4\right){y}={x}^{3}-{x}^{2}+\left(5419a^{2}-3266a-35965\right){x}-374961a^{2}+225991a+2488521$ |
8.1-a4 |
8.1-a |
$4$ |
$4$ |
3.3.940.1 |
$3$ |
$[3, 0]$ |
8.1 |
\( 2^{3} \) |
\( 2^{36} \) |
$3.87452$ |
$(-a-2), (a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$58.05305296$ |
0.946740904 |
\( \frac{72406586393}{268435456} a^{2} + \frac{19685037201}{67108864} a - \frac{363726133279}{268435456} \) |
\( \bigl[a + 1\) , \( -a\) , \( a^{2} - 5\) , \( 1221 a^{2} - 674 a - 8289\) , \( -61314 a^{2} + 36140 a + 409280\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{2}-5\right){y}={x}^{3}-a{x}^{2}+\left(1221a^{2}-674a-8289\right){x}-61314a^{2}+36140a+409280$ |
8.1-b1 |
8.1-b |
$2$ |
$3$ |
3.3.940.1 |
$3$ |
$[3, 0]$ |
8.1 |
\( 2^{3} \) |
\( - 2^{10} \) |
$3.87452$ |
$(-a-2), (a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.2 |
$9$ |
\( 2 \) |
$1$ |
$1.706913567$ |
1.002120874 |
\( -\frac{4506419129977}{64} a^{2} + \frac{2582846188559}{16} a + \frac{7860731202239}{64} \) |
\( \bigl[a^{2} - 5\) , \( -a^{2} + 6\) , \( a + 1\) , \( 58 a^{2} - 37 a - 391\) , \( 732 a^{2} - 443 a - 4864\bigr] \) |
${y}^2+\left(a^{2}-5\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a^{2}+6\right){x}^{2}+\left(58a^{2}-37a-391\right){x}+732a^{2}-443a-4864$ |
8.1-b2 |
8.1-b |
$2$ |
$3$ |
3.3.940.1 |
$3$ |
$[3, 0]$ |
8.1 |
\( 2^{3} \) |
\( - 2^{6} \) |
$3.87452$ |
$(-a-2), (a+1)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.1 |
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$46.08666632$ |
1.002120874 |
\( -\frac{3289}{4} a^{2} + 2223 a + \frac{6495}{4} \) |
\( \bigl[a^{2} - 5\) , \( -a^{2} + 6\) , \( a + 1\) , \( -7 a^{2} + 3 a + 44\) , \( -6 a^{2} + 3 a + 38\bigr] \) |
${y}^2+\left(a^{2}-5\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a^{2}+6\right){x}^{2}+\left(-7a^{2}+3a+44\right){x}-6a^{2}+3a+38$ |
8.2-a1 |
8.2-a |
$1$ |
$1$ |
3.3.940.1 |
$3$ |
$[3, 0]$ |
8.2 |
\( 2^{3} \) |
\( - 2^{27} \) |
$3.87452$ |
$(-a-2), (a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 3 \cdot 23 \) |
$0.007144739$ |
$58.16900756$ |
2.805979536 |
\( \frac{757971727}{4096} a^{2} - \frac{456662163}{4096} a - \frac{1257523137}{1024} \) |
\( \bigl[a\) , \( a\) , \( a\) , \( 2 a - 1\) , \( 5 a^{2} - 11 a - 7\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+a{x}^{2}+\left(2a-1\right){x}+5a^{2}-11a-7$ |
8.2-b1 |
8.2-b |
$2$ |
$3$ |
3.3.940.1 |
$3$ |
$[3, 0]$ |
8.2 |
\( 2^{3} \) |
\( - 2^{37} \) |
$3.87452$ |
$(-a-2), (a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.2 |
$9$ |
\( 1 \) |
$1$ |
$2.425628142$ |
0.712037399 |
\( -\frac{85276761673}{131072} a^{2} - \frac{246981661297}{131072} a - \frac{29512153075}{32768} \) |
\( \bigl[a\) , \( a + 1\) , \( a\) , \( -5 a^{2} - 18 a - 18\) , \( -38 a^{2} - 119 a - 75\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-5a^{2}-18a-18\right){x}-38a^{2}-119a-75$ |
8.2-b2 |
8.2-b |
$2$ |
$3$ |
3.3.940.1 |
$3$ |
$[3, 0]$ |
8.2 |
\( 2^{3} \) |
\( - 2^{15} \) |
$3.87452$ |
$(-a-2), (a+1)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.1 |
$1$ |
\( 3 \) |
$1$ |
$65.49195985$ |
0.712037399 |
\( -\frac{8729}{64} a^{2} + \frac{4725}{64} a + \frac{14871}{16} \) |
\( \bigl[a\) , \( a + 1\) , \( a\) , \( 2 a + 2\) , \( a + 1\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(2a+2\right){x}+a+1$ |
8.4-a1 |
8.4-a |
$1$ |
$1$ |
3.3.940.1 |
$3$ |
$[3, 0]$ |
8.4 |
\( 2^{3} \) |
\( - 2^{10} \) |
$3.87452$ |
$(-a-2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
|
|
$1$ |
\( 2 \) |
$1$ |
$15.69521707$ |
1.023843070 |
\( -14596 a^{2} + 34928 a + 21212 \) |
\( \bigl[0\) , \( -a\) , \( a^{2} - 4\) , \( 2 a - 3\) , \( -a^{2} + 3 a - 6\bigr] \) |
${y}^2+\left(a^{2}-4\right){y}={x}^{3}-a{x}^{2}+\left(2a-3\right){x}-a^{2}+3a-6$ |
10.2-a1 |
10.2-a |
$2$ |
$2$ |
3.3.940.1 |
$3$ |
$[3, 0]$ |
10.2 |
\( 2 \cdot 5 \) |
\( 2^{2} \cdot 5^{2} \) |
$4.02132$ |
$(-a-2), (-a^2+a+5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.173638506$ |
$87.03496867$ |
1.478758139 |
\( \frac{1176761}{100} a^{2} + \frac{847874}{25} a + \frac{1736929}{100} \) |
\( \bigl[a^{2} - a - 5\) , \( -a^{2} + 2 a + 5\) , \( a^{2} - 4\) , \( 13396 a^{2} - 30712 a - 23365\) , \( -767129 a^{2} + 1758563 a + 1338569\bigr] \) |
${y}^2+\left(a^{2}-a-5\right){x}{y}+\left(a^{2}-4\right){y}={x}^{3}+\left(-a^{2}+2a+5\right){x}^{2}+\left(13396a^{2}-30712a-23365\right){x}-767129a^{2}+1758563a+1338569$ |
10.2-a2 |
10.2-a |
$2$ |
$2$ |
3.3.940.1 |
$3$ |
$[3, 0]$ |
10.2 |
\( 2 \cdot 5 \) |
\( - 2 \cdot 5 \) |
$4.02132$ |
$(-a-2), (-a^2+a+5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$0.347277013$ |
$174.0699373$ |
1.478758139 |
\( -\frac{1831}{10} a^{2} - \frac{1458}{5} a + \frac{23271}{10} \) |
\( \bigl[1\) , \( -a - 1\) , \( a^{2} - 4\) , \( -27 a^{2} + 62 a + 49\) , \( -75 a^{2} + 171 a + 127\bigr] \) |
${y}^2+{x}{y}+\left(a^{2}-4\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-27a^{2}+62a+49\right){x}-75a^{2}+171a+127$ |
10.2-b1 |
10.2-b |
$4$ |
$10$ |
3.3.940.1 |
$3$ |
$[3, 0]$ |
10.2 |
\( 2 \cdot 5 \) |
\( - 2^{10} \cdot 5^{10} \) |
$4.02132$ |
$(-a-2), (-a^2+a+5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B.4.1 |
$1$ |
\( 2^{2} \) |
$0.309868878$ |
$33.61809242$ |
1.019314858 |
\( -\frac{7820493189972621}{10000000000} a^{2} + \frac{1180705834842011}{2500000000} a + \frac{51924634646264331}{10000000000} \) |
\( \bigl[a + 1\) , \( a^{2} - 5\) , \( a^{2} - 4\) , \( 277223 a^{2} - 167091 a - 1839829\) , \( -136978402 a^{2} + 82557689 a + 909090597\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{2}-4\right){y}={x}^{3}+\left(a^{2}-5\right){x}^{2}+\left(277223a^{2}-167091a-1839829\right){x}-136978402a^{2}+82557689a+909090597$ |
10.2-b2 |
10.2-b |
$4$ |
$10$ |
3.3.940.1 |
$3$ |
$[3, 0]$ |
10.2 |
\( 2 \cdot 5 \) |
\( - 2^{2} \cdot 5^{2} \) |
$4.02132$ |
$(-a-2), (-a^2+a+5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B.4.2 |
$1$ |
\( 2^{2} \) |
$0.061973775$ |
$168.0904621$ |
1.019314858 |
\( \frac{109681793539}{100} a^{2} + \frac{79391233451}{25} a + \frac{151594310171}{100} \) |
\( \bigl[a + 1\) , \( a\) , \( a^{2} - a - 5\) , \( 306 a^{2} - 182 a - 2024\) , \( 4923 a^{2} - 2965 a - 32668\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{2}-a-5\right){y}={x}^{3}+a{x}^{2}+\left(306a^{2}-182a-2024\right){x}+4923a^{2}-2965a-32668$ |
10.2-b3 |
10.2-b |
$4$ |
$10$ |
3.3.940.1 |
$3$ |
$[3, 0]$ |
10.2 |
\( 2 \cdot 5 \) |
\( 2^{20} \cdot 5^{5} \) |
$4.02132$ |
$(-a-2), (-a^2+a+5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B.4.1 |
$1$ |
\( 2 \) |
$0.619737756$ |
$33.61809242$ |
1.019314858 |
\( \frac{6982054663829}{3276800000} a^{2} - \frac{3534620649939}{819200000} a - \frac{15950242311619}{3276800000} \) |
\( \bigl[a + 1\) , \( 1\) , \( a\) , \( 365 a^{2} - 188 a - 2513\) , \( -10291 a^{2} + 6364 a + 67833\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+{x}^{2}+\left(365a^{2}-188a-2513\right){x}-10291a^{2}+6364a+67833$ |
10.2-b4 |
10.2-b |
$4$ |
$10$ |
3.3.940.1 |
$3$ |
$[3, 0]$ |
10.2 |
\( 2 \cdot 5 \) |
\( 2^{4} \cdot 5 \) |
$4.02132$ |
$(-a-2), (-a^2+a+5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B.4.2 |
$1$ |
\( 2 \) |
$0.123947551$ |
$168.0904621$ |
1.019314858 |
\( \frac{7035191109}{80} a^{2} - \frac{4032672419}{20} a - \frac{12277613459}{80} \) |
\( \bigl[a + 1\) , \( -a^{2} + 5\) , \( a^{2} - 4\) , \( -2 a^{2} + 7\) , \( a^{2} - 2 a - 7\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{2}-4\right){y}={x}^{3}+\left(-a^{2}+5\right){x}^{2}+\left(-2a^{2}+7\right){x}+a^{2}-2a-7$ |
10.3-a1 |
10.3-a |
$4$ |
$4$ |
3.3.940.1 |
$3$ |
$[3, 0]$ |
10.3 |
\( 2 \cdot 5 \) |
\( 2^{4} \cdot 5^{3} \) |
$4.02132$ |
$(-a-2), (a^2-a-7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$33.32566605$ |
1.630445064 |
\( \frac{23720555509601}{400} a^{2} + \frac{17168383605253}{100} a + \frac{32773310108297}{400} \) |
\( \bigl[a^{2} - a - 5\) , \( a - 1\) , \( a^{2} - 4\) , \( -28818 a^{2} + 66064 a + 50280\) , \( -4032774 a^{2} + 9244737 a + 7036764\bigr] \) |
${y}^2+\left(a^{2}-a-5\right){x}{y}+\left(a^{2}-4\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-28818a^{2}+66064a+50280\right){x}-4032774a^{2}+9244737a+7036764$ |
10.3-a2 |
10.3-a |
$4$ |
$4$ |
3.3.940.1 |
$3$ |
$[3, 0]$ |
10.3 |
\( 2 \cdot 5 \) |
\( 2 \cdot 5^{3} \) |
$4.02132$ |
$(-a-2), (a^2-a-7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 3 \) |
$1$ |
$66.65133211$ |
1.630445064 |
\( \frac{2403467803}{50} a^{2} - \frac{2754859882}{25} a - \frac{4193802859}{50} \) |
\( \bigl[a^{2} - a - 5\) , \( 1\) , \( 0\) , \( -4 a^{2} - 5 a + 7\) , \( -14 a^{2} - 38 a - 13\bigr] \) |
${y}^2+\left(a^{2}-a-5\right){x}{y}={x}^{3}+{x}^{2}+\left(-4a^{2}-5a+7\right){x}-14a^{2}-38a-13$ |
10.3-a3 |
10.3-a |
$4$ |
$4$ |
3.3.940.1 |
$3$ |
$[3, 0]$ |
10.3 |
\( 2 \cdot 5 \) |
\( - 2 \cdot 5^{12} \) |
$4.02132$ |
$(-a-2), (a^2-a-7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$16.66283302$ |
1.630445064 |
\( -\frac{8249041263949}{6250} a^{2} + \frac{12429350495779}{15625} a + \frac{273734017379507}{31250} \) |
\( \bigl[1\) , \( a^{2} - a - 4\) , \( a^{2} - a - 5\) , \( 43 a^{2} - 100 a - 72\) , \( 2869 a^{2} - 6576 a - 5010\bigr] \) |
${y}^2+{x}{y}+\left(a^{2}-a-5\right){y}={x}^{3}+\left(a^{2}-a-4\right){x}^{2}+\left(43a^{2}-100a-72\right){x}+2869a^{2}-6576a-5010$ |
10.3-a4 |
10.3-a |
$4$ |
$4$ |
3.3.940.1 |
$3$ |
$[3, 0]$ |
10.3 |
\( 2 \cdot 5 \) |
\( 2^{2} \cdot 5^{6} \) |
$4.02132$ |
$(-a-2), (a^2-a-7)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$66.65133211$ |
1.630445064 |
\( \frac{22283521}{500} a^{2} + \frac{845721}{5} a + \frac{87411109}{500} \) |
\( \bigl[1\) , \( a^{2} - a - 4\) , \( a^{2} - a - 5\) , \( -77 a^{2} + 175 a + 138\) , \( 636 a^{2} - 1457 a - 1114\bigr] \) |
${y}^2+{x}{y}+\left(a^{2}-a-5\right){y}={x}^{3}+\left(a^{2}-a-4\right){x}^{2}+\left(-77a^{2}+175a+138\right){x}+636a^{2}-1457a-1114$ |
10.3-b1 |
10.3-b |
$2$ |
$2$ |
3.3.940.1 |
$3$ |
$[3, 0]$ |
10.3 |
\( 2 \cdot 5 \) |
\( 2^{7} \cdot 5^{6} \) |
$4.02132$ |
$(-a-2), (a^2-a-7)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.343736707$ |
$88.77942622$ |
1.493019839 |
\( -\frac{193827}{16000} a^{2} + \frac{5771573}{4000} a + \frac{5261121}{3200} \) |
\( \bigl[a^{2} - a - 5\) , \( a^{2} - a - 4\) , \( 1\) , \( -651 a^{2} + 391 a + 4325\) , \( -17579 a^{2} + 10594 a + 116670\bigr] \) |
${y}^2+\left(a^{2}-a-5\right){x}{y}+{y}={x}^{3}+\left(a^{2}-a-4\right){x}^{2}+\left(-651a^{2}+391a+4325\right){x}-17579a^{2}+10594a+116670$ |
10.3-b2 |
10.3-b |
$2$ |
$2$ |
3.3.940.1 |
$3$ |
$[3, 0]$ |
10.3 |
\( 2 \cdot 5 \) |
\( 2^{14} \cdot 5^{3} \) |
$4.02132$ |
$(-a-2), (a^2-a-7)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.171868353$ |
$177.5588524$ |
1.493019839 |
\( \frac{267566946241}{409600} a^{2} - \frac{153109164807}{102400} a - \frac{464857186103}{409600} \) |
\( \bigl[1\) , \( a^{2} - a - 6\) , \( 1\) , \( -14 a^{2} - 37 a - 11\) , \( 72 a^{2} + 207 a + 96\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(a^{2}-a-6\right){x}^{2}+\left(-14a^{2}-37a-11\right){x}+72a^{2}+207a+96$ |
10.4-a1 |
10.4-a |
$2$ |
$5$ |
3.3.940.1 |
$3$ |
$[3, 0]$ |
10.4 |
\( 2 \cdot 5 \) |
\( - 2^{5} \cdot 5^{5} \) |
$4.02132$ |
$(a+1), (-a^2+a+5)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.4.1 |
$1$ |
\( 5 \) |
$1$ |
$30.40009460$ |
4.957708782 |
\( -\frac{61275099}{25000} a^{2} - \frac{180652339}{25000} a - \frac{23030009}{6250} \) |
\( \bigl[a^{2} - 4\) , \( 1\) , \( 1\) , \( 627 a^{2} - 1437 a - 1086\) , \( -4844453 a^{2} + 11105433 a + 8453065\bigr] \) |
${y}^2+\left(a^{2}-4\right){x}{y}+{y}={x}^{3}+{x}^{2}+\left(627a^{2}-1437a-1086\right){x}-4844453a^{2}+11105433a+8453065$ |
10.4-a2 |
10.4-a |
$2$ |
$5$ |
3.3.940.1 |
$3$ |
$[3, 0]$ |
10.4 |
\( 2 \cdot 5 \) |
\( - 2 \cdot 5 \) |
$4.02132$ |
$(a+1), (-a^2+a+5)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.4.2 |
$1$ |
\( 1 \) |
$1$ |
$152.0004730$ |
4.957708782 |
\( -\frac{7961}{10} a^{2} + \frac{21879}{10} a + \frac{2378}{5} \) |
\( \bigl[a\) , \( -a^{2} + 2 a + 4\) , \( a^{2} - a - 5\) , \( -213 a^{2} + 489 a + 373\) , \( 4232 a^{2} - 9700 a - 7387\bigr] \) |
${y}^2+a{x}{y}+\left(a^{2}-a-5\right){y}={x}^{3}+\left(-a^{2}+2a+4\right){x}^{2}+\left(-213a^{2}+489a+373\right){x}+4232a^{2}-9700a-7387$ |
16.1-a1 |
16.1-a |
$1$ |
$1$ |
3.3.940.1 |
$3$ |
$[3, 0]$ |
16.1 |
\( 2^{4} \) |
\( - 2^{12} \) |
$4.34900$ |
$(-a-2), (a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
|
|
$1$ |
\( 3 \) |
$0.065519200$ |
$142.6219394$ |
2.743048637 |
\( 176 a^{2} + 192 a - 464 \) |
\( \bigl[0\) , \( a^{2} - 4\) , \( a^{2} - a - 4\) , \( a + 5\) , \( 2 a^{2} - 2 a - 6\bigr] \) |
${y}^2+\left(a^{2}-a-4\right){y}={x}^{3}+\left(a^{2}-4\right){x}^{2}+\left(a+5\right){x}+2a^{2}-2a-6$ |
16.3-a1 |
16.3-a |
$1$ |
$1$ |
3.3.940.1 |
$3$ |
$[3, 0]$ |
16.3 |
\( 2^{4} \) |
\( - 2^{10} \) |
$4.34900$ |
$(-a-2), (a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2^{2} \) |
$0.020911567$ |
$250.9796113$ |
2.054198191 |
\( -\frac{357289}{64} a^{2} + \frac{160863}{16} a + \frac{560143}{64} \) |
\( \bigl[a^{2} - 5\) , \( a^{2} - 2 a - 6\) , \( a + 1\) , \( -a^{2} - a + 1\) , \( 0\bigr] \) |
${y}^2+\left(a^{2}-5\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a^{2}-2a-6\right){x}^{2}+\left(-a^{2}-a+1\right){x}$ |
16.3-b1 |
16.3-b |
$4$ |
$4$ |
3.3.940.1 |
$3$ |
$[3, 0]$ |
16.3 |
\( 2^{4} \) |
\( - 2^{23} \) |
$4.34900$ |
$(-a-2), (a+1)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$104.4171066$ |
2.554282874 |
\( -\frac{14358055}{4096} a^{2} + \frac{1931345}{1024} a + \frac{102398881}{4096} \) |
\( \bigl[a + 1\) , \( a^{2} - 2 a - 5\) , \( a^{2} - 5\) , \( -116019 a^{2} + 265977 a + 202392\) , \( 21568154 a^{2} - 49442942 a - 37633959\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{2}-5\right){y}={x}^{3}+\left(a^{2}-2a-5\right){x}^{2}+\left(-116019a^{2}+265977a+202392\right){x}+21568154a^{2}-49442942a-37633959$ |
16.3-b2 |
16.3-b |
$4$ |
$4$ |
3.3.940.1 |
$3$ |
$[3, 0]$ |
16.3 |
\( 2^{4} \) |
\( 2^{11} \) |
$4.34900$ |
$(-a-2), (a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$52.20855334$ |
2.554282874 |
\( \frac{15529}{8} a^{2} + \frac{12161}{2} a + \frac{29905}{8} \) |
\( \bigl[a + 1\) , \( -a\) , \( a^{2} - a - 4\) , \( -4 a^{2} + a + 28\) , \( 8 a^{2} - 4 a - 56\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{2}-a-4\right){y}={x}^{3}-a{x}^{2}+\left(-4a^{2}+a+28\right){x}+8a^{2}-4a-56$ |
16.3-b3 |
16.3-b |
$4$ |
$4$ |
3.3.940.1 |
$3$ |
$[3, 0]$ |
16.3 |
\( 2^{4} \) |
\( 2^{16} \) |
$4.34900$ |
$(-a-2), (a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$104.4171066$ |
2.554282874 |
\( \frac{392825}{64} a^{2} - \frac{228975}{16} a - \frac{469183}{64} \) |
\( \bigl[a + 1\) , \( -a^{2} + a + 6\) , \( a^{2} - a - 4\) , \( -411 a^{2} + 952 a + 692\) , \( -9369 a^{2} + 21517 a + 16236\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{2}-a-4\right){y}={x}^{3}+\left(-a^{2}+a+6\right){x}^{2}+\left(-411a^{2}+952a+692\right){x}-9369a^{2}+21517a+16236$ |
16.3-b4 |
16.3-b |
$4$ |
$4$ |
3.3.940.1 |
$3$ |
$[3, 0]$ |
16.3 |
\( 2^{4} \) |
\( 2^{14} \) |
$4.34900$ |
$(-a-2), (a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$4$ |
\( 3 \) |
$1$ |
$26.10427667$ |
2.554282874 |
\( \frac{2955149311}{8} a^{2} - \frac{1695875071}{2} a - \frac{5103413233}{8} \) |
\( \bigl[a + 1\) , \( -a^{2} + a + 6\) , \( a^{2} - a - 4\) , \( -6541 a^{2} + 15162 a + 10932\) , \( -612967 a^{2} + 1407035 a + 1064156\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{2}-a-4\right){y}={x}^{3}+\left(-a^{2}+a+6\right){x}^{2}+\left(-6541a^{2}+15162a+10932\right){x}-612967a^{2}+1407035a+1064156$ |
16.4-a1 |
16.4-a |
$1$ |
$1$ |
3.3.940.1 |
$3$ |
$[3, 0]$ |
16.4 |
\( 2^{4} \) |
\( - 2^{5} \) |
$4.34900$ |
$(-a-2), (a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2 \) |
$1$ |
$28.03962680$ |
1.829103572 |
\( -\frac{55372771}{2} a^{2} + \frac{126939965}{2} a + 48304494 \) |
\( \bigl[a^{2} - 4\) , \( 0\) , \( a\) , \( 3 a^{2} - 2 a - 19\) , \( -3 a^{2} + 2 a + 19\bigr] \) |
${y}^2+\left(a^{2}-4\right){x}{y}+a{y}={x}^{3}+\left(3a^{2}-2a-19\right){x}-3a^{2}+2a+19$ |
16.4-b1 |
16.4-b |
$1$ |
$1$ |
3.3.940.1 |
$3$ |
$[3, 0]$ |
16.4 |
\( 2^{4} \) |
\( - 2^{7} \) |
$4.34900$ |
$(-a-2), (a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2 \cdot 3 \) |
$0.020684313$ |
$275.8143528$ |
3.349396386 |
\( -\frac{665}{4} a^{2} - \frac{1931}{4} a - 233 \) |
\( \bigl[a\) , \( a^{2} - a - 4\) , \( 0\) , \( -3 a + 1\) , \( a^{2} - 1\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(a^{2}-a-4\right){x}^{2}+\left(-3a+1\right){x}+a^{2}-1$ |
16.4-c1 |
16.4-c |
$1$ |
$1$ |
3.3.940.1 |
$3$ |
$[3, 0]$ |
16.4 |
\( 2^{4} \) |
\( - 2^{11} \) |
$4.34900$ |
$(-a-2), (a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2 \) |
$0.028098905$ |
$297.5924836$ |
1.636434724 |
\( \frac{46477839}{16} a^{2} - \frac{28086419}{16} a - \frac{77159361}{4} \) |
\( \bigl[a^{2} - 4\) , \( a + 1\) , \( a\) , \( -a^{2} - 3 a\) , \( a + 1\bigr] \) |
${y}^2+\left(a^{2}-4\right){x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-a^{2}-3a\right){x}+a+1$ |
16.4-d1 |
16.4-d |
$4$ |
$4$ |
3.3.940.1 |
$3$ |
$[3, 0]$ |
16.4 |
\( 2^{4} \) |
\( 2^{14} \) |
$4.34900$ |
$(-a-2), (a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$4$ |
\( 1 \) |
$1$ |
$27.71711614$ |
0.904032648 |
\( -\frac{1869285816463}{4} a^{2} + \frac{1148471734001}{4} a + 3114012934081 \) |
\( \bigl[a^{2} - 4\) , \( -a - 1\) , \( a^{2} - 4\) , \( 9453243 a^{2} - 5697518 a - 62738784\) , \( 27206223747 a^{2} - 16397325199 a - 180560817484\bigr] \) |
${y}^2+\left(a^{2}-4\right){x}{y}+\left(a^{2}-4\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(9453243a^{2}-5697518a-62738784\right){x}+27206223747a^{2}-16397325199a-180560817484$ |
*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.