| 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 |
$2$ |
$3$ |
\(\Q(\sqrt{281}) \) |
$2$ |
$[2, 0]$ |
2.1 |
\( 2 \) |
\( 2 \) |
$1.78135$ |
$(a+8)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.2 |
$1$ |
\( 1 \) |
$26.14666838$ |
$1.208088306$ |
3.768702669 |
\( -\frac{221729270561}{2} a - \frac{1747566097245}{2} \) |
\( \bigl[a + 1\) , \( a - 1\) , \( 1\) , \( -10722573175 a - 84510253275\) , \( -1749854223243365 a - 13791523843972021\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-10722573175a-84510253275\right){x}-1749854223243365a-13791523843972021$ |
| 2.1-a2 |
2.1-a |
$2$ |
$3$ |
\(\Q(\sqrt{281}) \) |
$2$ |
$[2, 0]$ |
2.1 |
\( 2 \) |
\( 2^{3} \) |
$1.78135$ |
$(a+8)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1 |
$1$ |
\( 3 \) |
$8.715556127$ |
$10.87279476$ |
3.768702669 |
\( -\frac{5689}{8} a - \frac{42005}{8} \) |
\( \bigl[a + 1\) , \( a - 1\) , \( 1\) , \( -129795215 a - 1022984525\) , \( -2499715840312 a - 19701578655459\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-129795215a-1022984525\right){x}-2499715840312a-19701578655459$ |
| 2.2-a1 |
2.2-a |
$2$ |
$3$ |
\(\Q(\sqrt{281}) \) |
$2$ |
$[2, 0]$ |
2.2 |
\( 2 \) |
\( 2 \) |
$1.78135$ |
$(-a+9)$ |
$0 \le r \le 1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.2 |
|
\( 1 \) |
$1$ |
$1.208088306$ |
3.768702669 |
\( \frac{221729270561}{2} a - 984647683903 \) |
\( \bigl[a\) , \( a + 1\) , \( a + 1\) , \( 10722573210 a - 95232826519\) , \( 1749769712990055 a - 15540627487091946\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(10722573210a-95232826519\right){x}+1749769712990055a-15540627487091946$ |
| 2.2-a2 |
2.2-a |
$2$ |
$3$ |
\(\Q(\sqrt{281}) \) |
$2$ |
$[2, 0]$ |
2.2 |
\( 2 \) |
\( 2^{3} \) |
$1.78135$ |
$(-a+9)$ |
$0 \le r \le 1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1 |
|
\( 3 \) |
$1$ |
$10.87279476$ |
3.768702669 |
\( \frac{5689}{8} a - \frac{23847}{4} \) |
\( \bigl[a\) , \( a + 1\) , \( a + 1\) , \( 129795250 a - 1152779809\) , \( 2498692855752 a - 22192208829531\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(129795250a-1152779809\right){x}+2498692855752a-22192208829531$ |
| 8.1-a1 |
8.1-a |
$1$ |
$1$ |
\(\Q(\sqrt{281}) \) |
$2$ |
$[2, 0]$ |
8.1 |
\( 2^{3} \) |
\( - 2^{9} \) |
$2.51921$ |
$(a+8), (-a+9)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 3 \) |
$0.220566705$ |
$28.26328210$ |
2.231313740 |
\( \frac{3531}{32} a + \frac{14251}{16} \) |
\( \bigl[a\) , \( -a + 1\) , \( a\) , \( -12 a + 73\) , \( -40 a + 208\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-12a+73\right){x}-40a+208$ |
| 8.1-b1 |
8.1-b |
$1$ |
$1$ |
\(\Q(\sqrt{281}) \) |
$2$ |
$[2, 0]$ |
8.1 |
\( 2^{3} \) |
\( - 2^{5} \) |
$2.51921$ |
$(a+8), (-a+9)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 3 \) |
$0.248261321$ |
$41.15306464$ |
3.656868440 |
\( \frac{1579947259}{2} a - 7016168485 \) |
\( \bigl[a\) , \( a - 1\) , \( a\) , \( 933561 a - 8291233\) , \( -1419373250 a + 12606203038\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(933561a-8291233\right){x}-1419373250a+12606203038$ |
| 8.1-c1 |
8.1-c |
$1$ |
$1$ |
\(\Q(\sqrt{281}) \) |
$2$ |
$[2, 0]$ |
8.1 |
\( 2^{3} \) |
\( 2^{9} \) |
$2.51921$ |
$(a+8), (-a+9)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 3 \) |
$0.309161687$ |
$12.78553689$ |
1.414825015 |
\( -\frac{7117687}{2} a - 28077271 \) |
\( \bigl[a\) , \( 0\) , \( a\) , \( 89825 a - 797693\) , \( 44170868 a - 392304506\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(89825a-797693\right){x}+44170868a-392304506$ |
| 8.1-d1 |
8.1-d |
$1$ |
$1$ |
\(\Q(\sqrt{281}) \) |
$2$ |
$[2, 0]$ |
8.1 |
\( 2^{3} \) |
\( - 2^{9} \) |
$2.51921$ |
$(a+8), (-a+9)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 5 \) |
$1$ |
$7.838623734$ |
2.338065440 |
\( \frac{4558651}{32} a - \frac{20213989}{16} \) |
\( \bigl[a\) , \( -a\) , \( a\) , \( 129 a - 1146\) , \( 3609 a - 32026\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}-a{x}^{2}+\left(129a-1146\right){x}+3609a-32026$ |
| 8.1-e1 |
8.1-e |
$1$ |
$1$ |
\(\Q(\sqrt{281}) \) |
$2$ |
$[2, 0]$ |
8.1 |
\( 2^{3} \) |
\( 2^{19} \) |
$2.51921$ |
$(a+8), (-a+9)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 3 \) |
$1.963905061$ |
$3.279593071$ |
2.305358867 |
\( -\frac{8847431}{2048} a - \frac{34866087}{1024} \) |
\( \bigl[a\) , \( 1\) , \( 0\) , \( -176310961228 a - 1389599655372\) , \( -118050759091841516 a - 930420281408605756\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+{x}^{2}+\left(-176310961228a-1389599655372\right){x}-118050759091841516a-930420281408605756$ |
| 8.2-a1 |
8.2-a |
$1$ |
$1$ |
\(\Q(\sqrt{281}) \) |
$2$ |
$[2, 0]$ |
8.2 |
\( 2^{3} \) |
\( - 2^{9} \) |
$2.51921$ |
$(a+8), (-a+9)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 3 \) |
$0.220566705$ |
$28.26328210$ |
2.231313740 |
\( -\frac{3531}{32} a + \frac{32033}{32} \) |
\( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( 10 a + 61\) , \( 39 a + 168\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(10a+61\right){x}+39a+168$ |
| 8.2-b1 |
8.2-b |
$1$ |
$1$ |
\(\Q(\sqrt{281}) \) |
$2$ |
$[2, 0]$ |
8.2 |
\( 2^{3} \) |
\( - 2^{5} \) |
$2.51921$ |
$(a+8), (-a+9)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 3 \) |
$0.248261321$ |
$41.15306464$ |
3.656868440 |
\( -\frac{1579947259}{2} a - \frac{12452389711}{2} \) |
\( \bigl[a + 1\) , \( a\) , \( a + 1\) , \( -933527 a - 7357637\) , \( 1411082051 a + 11121481708\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(-933527a-7357637\right){x}+1411082051a+11121481708$ |
| 8.2-c1 |
8.2-c |
$1$ |
$1$ |
\(\Q(\sqrt{281}) \) |
$2$ |
$[2, 0]$ |
8.2 |
\( 2^{3} \) |
\( 2^{9} \) |
$2.51921$ |
$(a+8), (-a+9)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 3 \) |
$0.309161687$ |
$12.78553689$ |
1.414825015 |
\( \frac{7117687}{2} a - \frac{63272229}{2} \) |
\( \bigl[a + 1\) , \( -a\) , \( a + 1\) , \( -89827 a - 707868\) , \( -44170869 a - 348133638\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(-89827a-707868\right){x}-44170869a-348133638$ |
| 8.2-d1 |
8.2-d |
$1$ |
$1$ |
\(\Q(\sqrt{281}) \) |
$2$ |
$[2, 0]$ |
8.2 |
\( 2^{3} \) |
\( - 2^{9} \) |
$2.51921$ |
$(a+8), (-a+9)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 5 \) |
$1$ |
$7.838623734$ |
2.338065440 |
\( -\frac{4558651}{32} a - \frac{35869327}{32} \) |
\( \bigl[a + 1\) , \( -1\) , \( a + 1\) , \( -131 a - 1017\) , \( -3610 a - 28417\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(-131a-1017\right){x}-3610a-28417$ |
| 8.2-e1 |
8.2-e |
$1$ |
$1$ |
\(\Q(\sqrt{281}) \) |
$2$ |
$[2, 0]$ |
8.2 |
\( 2^{3} \) |
\( 2^{19} \) |
$2.51921$ |
$(a+8), (-a+9)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 3 \) |
$1.963905061$ |
$3.279593071$ |
2.305358867 |
\( \frac{8847431}{2048} a - \frac{78579605}{2048} \) |
\( \bigl[a + 1\) , \( -a + 1\) , \( 0\) , \( 176310961228 a - 1565910616600\) , \( 118050759091841516 a - 1048471040500447272\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(176310961228a-1565910616600\right){x}+118050759091841516a-1048471040500447272$ |
| 10.1-a1 |
10.1-a |
$2$ |
$3$ |
\(\Q(\sqrt{281}) \) |
$2$ |
$[2, 0]$ |
10.1 |
\( 2 \cdot 5 \) |
\( 2^{15} \cdot 5^{6} \) |
$2.66374$ |
$(a+8), (76a-675)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.2 |
$4$ |
\( 2 \) |
$1$ |
$2.951504640$ |
1.408576042 |
\( -\frac{261108983809}{512000000} a - \frac{1173450089661}{512000000} \) |
\( \bigl[a + 1\) , \( 0\) , \( 1\) , \( -154530561 a + 1372467591\) , \( -51351733447 a + 456081823416\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(-154530561a+1372467591\right){x}-51351733447a+456081823416$ |
| 10.1-a2 |
10.1-a |
$2$ |
$3$ |
\(\Q(\sqrt{281}) \) |
$2$ |
$[2, 0]$ |
10.1 |
\( 2 \cdot 5 \) |
\( 2^{5} \cdot 5^{2} \) |
$2.66374$ |
$(a+8), (76a-675)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1 |
$4$ |
\( 2 \) |
$1$ |
$26.56354176$ |
1.408576042 |
\( \frac{660871}{800} a - \frac{4544341}{800} \) |
\( \bigl[a + 1\) , \( 0\) , \( 1\) , \( 26278784 a - 233395544\) , \( -226734468978 a + 2013748378232\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(26278784a-233395544\right){x}-226734468978a+2013748378232$ |
| 10.1-b1 |
10.1-b |
$2$ |
$2$ |
\(\Q(\sqrt{281}) \) |
$2$ |
$[2, 0]$ |
10.1 |
\( 2 \cdot 5 \) |
\( - 2^{7} \cdot 5^{2} \) |
$2.66374$ |
$(a+8), (76a-675)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$9$ |
\( 2 \) |
$1$ |
$8.738892550$ |
2.345933804 |
\( -\frac{308802729387}{3200} a + \frac{2742636922177}{3200} \) |
\( \bigl[1\) , \( -a\) , \( a + 1\) , \( -7741537904 a - 61015142364\) , \( 1819621258097761 a + 14341394634313752\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(-7741537904a-61015142364\right){x}+1819621258097761a+14341394634313752$ |
| 10.1-b2 |
10.1-b |
$2$ |
$2$ |
\(\Q(\sqrt{281}) \) |
$2$ |
$[2, 0]$ |
10.1 |
\( 2 \cdot 5 \) |
\( - 2^{14} \cdot 5 \) |
$2.66374$ |
$(a+8), (76a-675)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$9$ |
\( 2 \) |
$1$ |
$8.738892550$ |
2.345933804 |
\( \frac{11904923487}{81920} a + \frac{90594706723}{81920} \) |
\( \bigl[1\) , \( -a - 1\) , \( a\) , \( -1803235 a - 14212225\) , \( 3820368896 a + 30110341775\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-1803235a-14212225\right){x}+3820368896a+30110341775$ |
| 10.1-c1 |
10.1-c |
$4$ |
$4$ |
\(\Q(\sqrt{281}) \) |
$2$ |
$[2, 0]$ |
10.1 |
\( 2 \cdot 5 \) |
\( - 2 \cdot 5^{4} \) |
$2.66374$ |
$(a+8), (76a-675)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$21.02671032$ |
0.627174187 |
\( -\frac{24057}{1250} a + \frac{2081997}{1250} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( 218821757 a - 1943471410\) , \( -1130714585274 a + 10042472465670\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}+\left(218821757a-1943471410\right){x}-1130714585274a+10042472465670$ |
| 10.1-c2 |
10.1-c |
$4$ |
$4$ |
\(\Q(\sqrt{281}) \) |
$2$ |
$[2, 0]$ |
10.1 |
\( 2 \cdot 5 \) |
\( 2^{2} \cdot 5^{2} \) |
$2.66374$ |
$(a+8), (76a-675)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$1$ |
$42.05342064$ |
0.627174187 |
\( -\frac{3680721}{100} a + \frac{32889591}{100} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -11583724658 a - 91297442210\) , \( -714852485748825 a - 5634129386992050\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}+\left(-11583724658a-91297442210\right){x}-714852485748825a-5634129386992050$ |
| 10.1-c3 |
10.1-c |
$4$ |
$4$ |
\(\Q(\sqrt{281}) \) |
$2$ |
$[2, 0]$ |
10.1 |
\( 2 \cdot 5 \) |
\( 2 \cdot 5 \) |
$2.66374$ |
$(a+8), (76a-675)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$42.05342064$ |
0.627174187 |
\( -\frac{228020060151}{10} a + \frac{2025167265351}{10} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -100994859853 a - 795993745810\) , \( 50077230611295710 a + 394685060527877970\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}+\left(-100994859853a-795993745810\right){x}+50077230611295710a+394685060527877970$ |
| 10.1-c4 |
10.1-c |
$4$ |
$4$ |
\(\Q(\sqrt{281}) \) |
$2$ |
$[2, 0]$ |
10.1 |
\( 2 \cdot 5 \) |
\( - 2^{4} \cdot 5 \) |
$2.66374$ |
$(a+8), (76a-675)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$21.02671032$ |
0.627174187 |
\( \frac{5137263}{80} a + \frac{40468707}{80} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -1850543 a - 14585105\) , \( -3963454072 a - 31238071499\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}+\left(-1850543a-14585105\right){x}-3963454072a-31238071499$ |
| 10.4-a1 |
10.4-a |
$2$ |
$3$ |
\(\Q(\sqrt{281}) \) |
$2$ |
$[2, 0]$ |
10.4 |
\( 2 \cdot 5 \) |
\( 2^{5} \cdot 5^{2} \) |
$2.66374$ |
$(-a+9), (-76a-599)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1 |
$4$ |
\( 2 \) |
$1$ |
$26.56354176$ |
1.408576042 |
\( -\frac{660871}{800} a - \frac{388347}{80} \) |
\( \bigl[a\) , \( -a + 1\) , \( 1\) , \( -26278785 a - 207116759\) , \( 226734468978 a + 1787013909254\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-26278785a-207116759\right){x}+226734468978a+1787013909254$ |
| 10.4-a2 |
10.4-a |
$2$ |
$3$ |
\(\Q(\sqrt{281}) \) |
$2$ |
$[2, 0]$ |
10.4 |
\( 2 \cdot 5 \) |
\( 2^{15} \cdot 5^{6} \) |
$2.66374$ |
$(-a+9), (-76a-599)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.2 |
$4$ |
\( 2 \) |
$1$ |
$2.951504640$ |
1.408576042 |
\( \frac{261108983809}{512000000} a - \frac{143455907347}{51200000} \) |
\( \bigl[a\) , \( -a + 1\) , \( 1\) , \( 154530560 a + 1217937031\) , \( 51351733447 a + 404730089969\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(154530560a+1217937031\right){x}+51351733447a+404730089969$ |
| 10.4-b1 |
10.4-b |
$2$ |
$2$ |
\(\Q(\sqrt{281}) \) |
$2$ |
$[2, 0]$ |
10.4 |
\( 2 \cdot 5 \) |
\( - 2^{14} \cdot 5 \) |
$2.66374$ |
$(-a+9), (-76a-599)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$9$ |
\( 2 \) |
$1$ |
$8.738892550$ |
2.345933804 |
\( -\frac{11904923487}{81920} a + \frac{10249963021}{8192} \) |
\( \bigl[1\) , \( a + 1\) , \( a\) , \( 1803236 a - 16015460\) , \( -3818565661 a + 33914695211\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(1803236a-16015460\right){x}-3818565661a+33914695211$ |
| 10.4-b2 |
10.4-b |
$2$ |
$2$ |
\(\Q(\sqrt{281}) \) |
$2$ |
$[2, 0]$ |
10.4 |
\( 2 \cdot 5 \) |
\( - 2^{7} \cdot 5^{2} \) |
$2.66374$ |
$(-a+9), (-76a-599)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$9$ |
\( 2 \) |
$1$ |
$8.738892550$ |
2.345933804 |
\( \frac{308802729387}{3200} a + \frac{243383419279}{320} \) |
\( \bigl[1\) , \( a - 1\) , \( a\) , \( 7741537903 a - 68756680267\) , \( -1819621258097762 a + 16161015892411514\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(7741537903a-68756680267\right){x}-1819621258097762a+16161015892411514$ |
| 10.4-c1 |
10.4-c |
$4$ |
$4$ |
\(\Q(\sqrt{281}) \) |
$2$ |
$[2, 0]$ |
10.4 |
\( 2 \cdot 5 \) |
\( - 2^{4} \cdot 5 \) |
$2.66374$ |
$(-a+9), (-76a-599)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$21.02671032$ |
0.627174187 |
\( -\frac{5137263}{80} a + \frac{4560597}{8} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( 1850543 a - 16435648\) , \( 3963454072 a - 35201525571\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}+\left(1850543a-16435648\right){x}+3963454072a-35201525571$ |
| 10.4-c2 |
10.4-c |
$4$ |
$4$ |
\(\Q(\sqrt{281}) \) |
$2$ |
$[2, 0]$ |
10.4 |
\( 2 \cdot 5 \) |
\( - 2 \cdot 5^{4} \) |
$2.66374$ |
$(-a+9), (-76a-599)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$21.02671032$ |
0.627174187 |
\( \frac{24057}{1250} a + \frac{205794}{125} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -218821757 a - 1724649653\) , \( 1130714585274 a + 8911757880396\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}+\left(-218821757a-1724649653\right){x}+1130714585274a+8911757880396$ |
| 10.4-c3 |
10.4-c |
$4$ |
$4$ |
\(\Q(\sqrt{281}) \) |
$2$ |
$[2, 0]$ |
10.4 |
\( 2 \cdot 5 \) |
\( 2^{2} \cdot 5^{2} \) |
$2.66374$ |
$(-a+9), (-76a-599)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$1$ |
$42.05342064$ |
0.627174187 |
\( \frac{3680721}{100} a + \frac{2920887}{10} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( 11583724658 a - 102881166868\) , \( 714852485748825 a - 6348981872740875\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}+\left(11583724658a-102881166868\right){x}+714852485748825a-6348981872740875$ |
| 10.4-c4 |
10.4-c |
$4$ |
$4$ |
\(\Q(\sqrt{281}) \) |
$2$ |
$[2, 0]$ |
10.4 |
\( 2 \cdot 5 \) |
\( 2 \cdot 5 \) |
$2.66374$ |
$(-a+9), (-76a-599)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$42.05342064$ |
0.627174187 |
\( \frac{228020060151}{10} a + 179714720520 \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( 100994859853 a - 896988605663\) , \( -50077230611295710 a + 444762291139173680\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}+\left(100994859853a-896988605663\right){x}-50077230611295710a+444762291139173680$ |
| 14.1-a1 |
14.1-a |
$2$ |
$2$ |
\(\Q(\sqrt{281}) \) |
$2$ |
$[2, 0]$ |
14.1 |
\( 2 \cdot 7 \) |
\( - 2^{2} \cdot 7 \) |
$2.89750$ |
$(a+8), (-8a-63)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$47.99431742$ |
1.431550469 |
\( -\frac{16951}{28} a + \frac{148705}{28} \) |
\( \bigl[1\) , \( 1\) , \( a\) , \( 10952341163 a - 97273517120\) , \( -1644217316045472 a + 14603160991297568\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+{x}^{2}+\left(10952341163a-97273517120\right){x}-1644217316045472a+14603160991297568$ |
| 14.1-a2 |
14.1-a |
$2$ |
$2$ |
\(\Q(\sqrt{281}) \) |
$2$ |
$[2, 0]$ |
14.1 |
\( 2 \cdot 7 \) |
\( 2 \cdot 7^{2} \) |
$2.89750$ |
$(a+8), (-8a-63)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$47.99431742$ |
1.431550469 |
\( -\frac{506069041}{98} a + \frac{4518388905}{98} \) |
\( \bigl[1\) , \( 1\) , \( a\) , \( 170833106718 a - 1517258902280\) , \( -111270016236236200 a + 988247687665829246\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+{x}^{2}+\left(170833106718a-1517258902280\right){x}-111270016236236200a+988247687665829246$ |
| 14.2-a1 |
14.2-a |
$1$ |
$1$ |
\(\Q(\sqrt{281}) \) |
$2$ |
$[2, 0]$ |
14.2 |
\( 2 \cdot 7 \) |
\( - 2^{19} \cdot 7^{5} \) |
$2.89750$ |
$(a+8), (-8a+71)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 19 \) |
$0.448046864$ |
$4.653343937$ |
4.726275482 |
\( -\frac{5470476676442199}{8811708416} a + \frac{6940765886964435}{1258815488} \) |
\( \bigl[a + 1\) , \( 1\) , \( 1\) , \( 353944 a - 3143353\) , \( -330283279 a + 2933420569\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+{x}^{2}+\left(353944a-3143353\right){x}-330283279a+2933420569$ |
| 14.3-a1 |
14.3-a |
$1$ |
$1$ |
\(\Q(\sqrt{281}) \) |
$2$ |
$[2, 0]$ |
14.3 |
\( 2 \cdot 7 \) |
\( - 2^{19} \cdot 7^{5} \) |
$2.89750$ |
$(-a+9), (-8a-63)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 19 \) |
$0.448046864$ |
$4.653343937$ |
4.726275482 |
\( \frac{5470476676442199}{8811708416} a + \frac{21557442266154423}{4405854208} \) |
\( \bigl[a\) , \( -a - 1\) , \( a + 1\) , \( -353944 a - 2789479\) , \( 330637222 a + 2605926699\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-353944a-2789479\right){x}+330637222a+2605926699$ |
| 14.4-a1 |
14.4-a |
$2$ |
$2$ |
\(\Q(\sqrt{281}) \) |
$2$ |
$[2, 0]$ |
14.4 |
\( 2 \cdot 7 \) |
\( - 2^{2} \cdot 7 \) |
$2.89750$ |
$(-a+9), (-8a+71)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$47.99431742$ |
1.431550469 |
\( \frac{16951}{28} a + \frac{9411}{2} \) |
\( \bigl[1\) , \( 1\) , \( a + 1\) , \( -10952341164 a - 86321175957\) , \( 1644217316045471 a + 12958943675252096\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(-10952341164a-86321175957\right){x}+1644217316045471a+12958943675252096$ |
| 14.4-a2 |
14.4-a |
$2$ |
$2$ |
\(\Q(\sqrt{281}) \) |
$2$ |
$[2, 0]$ |
14.4 |
\( 2 \cdot 7 \) |
\( 2 \cdot 7^{2} \) |
$2.89750$ |
$(-a+9), (-8a+71)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$47.99431742$ |
1.431550469 |
\( \frac{506069041}{98} a + \frac{286594276}{7} \) |
\( \bigl[1\) , \( 1\) , \( a + 1\) , \( -170833106719 a - 1346425795562\) , \( 111270016236236199 a + 876977671429593046\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(-170833106719a-1346425795562\right){x}+111270016236236199a+876977671429593046$ |
| 16.2-a1 |
16.2-a |
$1$ |
$1$ |
\(\Q(\sqrt{281}) \) |
$2$ |
$[2, 0]$ |
16.2 |
\( 2^{4} \) |
\( - 2^{7} \) |
$2.99586$ |
$(a+8), (-a+9)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$21.12801157$ |
7.562349007 |
\( -\frac{1689803}{8} a + \frac{14063137}{8} \) |
\( \bigl[a + 1\) , \( a - 1\) , \( a + 1\) , \( -127386 a - 1004017\) , \( 70815594 a + 558135027\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-127386a-1004017\right){x}+70815594a+558135027$ |
| 16.2-b1 |
16.2-b |
$1$ |
$1$ |
\(\Q(\sqrt{281}) \) |
$2$ |
$[2, 0]$ |
16.2 |
\( 2^{4} \) |
\( - 2^{5} \) |
$2.99586$ |
$(a+8), (-a+9)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2 \) |
$1.220567052$ |
$23.95923738$ |
6.978168698 |
\( -\frac{283}{2} a + \frac{5393}{2} \) |
\( \bigl[a + 1\) , \( 0\) , \( 0\) , \( 73693967 a + 580821060\) , \( -445468355683 a - 3510971009712\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(73693967a+580821060\right){x}-445468355683a-3510971009712$ |
| 16.3-a1 |
16.3-a |
$1$ |
$1$ |
\(\Q(\sqrt{281}) \) |
$2$ |
$[2, 0]$ |
16.3 |
\( 2^{4} \) |
\( - 2^{7} \) |
$2.99586$ |
$(a+8), (-a+9)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$21.12801157$ |
7.562349007 |
\( \frac{1689803}{8} a + \frac{6186667}{4} \) |
\( \bigl[a\) , \( a + 1\) , \( 0\) , \( 127421 a - 1131401\) , \( -71819611 a + 637868797\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(127421a-1131401\right){x}-71819611a+637868797$ |
| 16.3-b1 |
16.3-b |
$1$ |
$1$ |
\(\Q(\sqrt{281}) \) |
$2$ |
$[2, 0]$ |
16.3 |
\( 2^{4} \) |
\( - 2^{5} \) |
$2.99586$ |
$(a+8), (-a+9)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2 \) |
$1.220567052$ |
$23.95923738$ |
6.978168698 |
\( \frac{283}{2} a + 2555 \) |
\( \bigl[a\) , \( -a + 1\) , \( 0\) , \( -73693967 a + 654515027\) , \( 445468355683 a - 3956439365395\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-73693967a+654515027\right){x}+445468355683a-3956439365395$ |
| 16.4-a1 |
16.4-a |
$2$ |
$3$ |
\(\Q(\sqrt{281}) \) |
$2$ |
$[2, 0]$ |
16.4 |
\( 2^{4} \) |
\( 2^{13} \) |
$2.99586$ |
$(a+8)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B |
$1$ |
\( 2 \) |
$2.495711571$ |
$2.479697577$ |
1.476726069 |
\( -\frac{221729270561}{2} a - \frac{1747566097245}{2} \) |
\( \bigl[0\) , \( -a\) , \( a\) , \( -192 a - 1495\) , \( -3641 a - 28699\bigr] \) |
${y}^2+a{y}={x}^{3}-a{x}^{2}+\left(-192a-1495\right){x}-3641a-28699$ |
| 16.4-a2 |
16.4-a |
$2$ |
$3$ |
\(\Q(\sqrt{281}) \) |
$2$ |
$[2, 0]$ |
16.4 |
\( 2^{4} \) |
\( 2^{15} \) |
$2.99586$ |
$(a+8)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B |
$1$ |
\( 2 \) |
$0.831903857$ |
$7.439092733$ |
1.476726069 |
\( -\frac{5689}{8} a - \frac{42005}{8} \) |
\( \bigl[0\) , \( -a\) , \( a\) , \( -2 a + 5\) , \( -2 a - 13\bigr] \) |
${y}^2+a{y}={x}^{3}-a{x}^{2}+\left(-2a+5\right){x}-2a-13$ |
| 16.5-a1 |
16.5-a |
$2$ |
$3$ |
\(\Q(\sqrt{281}) \) |
$2$ |
$[2, 0]$ |
16.5 |
\( 2^{4} \) |
\( 2^{13} \) |
$2.99586$ |
$(-a+9)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B |
$1$ |
\( 2 \) |
$2.495711571$ |
$2.479697577$ |
1.476726069 |
\( \frac{221729270561}{2} a - 984647683903 \) |
\( \bigl[0\) , \( a - 1\) , \( a + 1\) , \( 192 a - 1687\) , \( 3640 a - 32340\bigr] \) |
${y}^2+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(192a-1687\right){x}+3640a-32340$ |
| 16.5-a2 |
16.5-a |
$2$ |
$3$ |
\(\Q(\sqrt{281}) \) |
$2$ |
$[2, 0]$ |
16.5 |
\( 2^{4} \) |
\( 2^{15} \) |
$2.99586$ |
$(-a+9)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B |
$1$ |
\( 2 \) |
$0.831903857$ |
$7.439092733$ |
1.476726069 |
\( \frac{5689}{8} a - \frac{23847}{4} \) |
\( \bigl[0\) , \( a - 1\) , \( a + 1\) , \( 2 a + 3\) , \( a - 15\bigr] \) |
${y}^2+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(2a+3\right){x}+a-15$ |
*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.
