| 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 |
| 126.1-a1 |
126.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
126.1 |
\( 2 \cdot 3^{2} \cdot 7 \) |
\( - 2^{2} \cdot 3^{2} \cdot 7 \) |
$1.58420$ |
$(a+3), (-a+2), (-a-2), (a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2$ |
2B |
$256$ |
\( 2 \) |
$1$ |
$0.155430454$ |
3.759820155 |
\( -\frac{9010577383592310868608127}{42} a + 567613022049721543828200 \) |
\( \bigl[a\) , \( 0\) , \( 0\) , \( 3810 a - 11423\) , \( 228018 a - 623037\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(3810a-11423\right){x}+228018a-623037$ |
| 126.1-a2 |
126.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
126.1 |
\( 2 \cdot 3^{2} \cdot 7 \) |
\( 2^{16} \cdot 3^{4} \cdot 7^{2} \) |
$1.58420$ |
$(a+3), (-a+2), (-a-2), (a)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{7} \) |
$1$ |
$2.486887276$ |
3.759820155 |
\( -\frac{7189057}{16128} \) |
\( \bigl[a\) , \( 0\) , \( 0\) , \( -3\) , \( -9\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-3{x}-9$ |
| 126.1-a3 |
126.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
126.1 |
\( 2 \cdot 3^{2} \cdot 7 \) |
\( 2^{2} \cdot 3^{32} \cdot 7^{4} \) |
$1.58420$ |
$(a+3), (-a+2), (-a-2), (a)$ |
0 |
$\Z/8\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{11} \) |
$1$ |
$0.621721819$ |
3.759820155 |
\( \frac{6359387729183}{4218578658} \) |
\( \bigl[a\) , \( 0\) , \( 0\) , \( 387\) , \( -891\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+387{x}-891$ |
| 126.1-a4 |
126.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
126.1 |
\( 2 \cdot 3^{2} \cdot 7 \) |
\( 2^{4} \cdot 3^{16} \cdot 7^{8} \) |
$1.58420$ |
$(a+3), (-a+2), (-a-2), (a)$ |
0 |
$\Z/2\Z\oplus\Z/8\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{11} \) |
$1$ |
$2.486887276$ |
3.759820155 |
\( \frac{124475734657}{63011844} \) |
\( \bigl[a\) , \( 0\) , \( 0\) , \( -103\) , \( -205\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-103{x}-205$ |
| 126.1-a5 |
126.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
126.1 |
\( 2 \cdot 3^{2} \cdot 7 \) |
\( 2^{2} \cdot 3^{8} \cdot 7^{16} \) |
$1.58420$ |
$(a+3), (-a+2), (-a-2), (a)$ |
0 |
$\Z/8\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{9} \) |
$1$ |
$2.486887276$ |
3.759820155 |
\( \frac{84448510979617}{933897762} \) |
\( \bigl[a\) , \( 0\) , \( 0\) , \( -913\) , \( 10001\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-913{x}+10001$ |
| 126.1-a6 |
126.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
126.1 |
\( 2 \cdot 3^{2} \cdot 7 \) |
\( 2^{8} \cdot 3^{8} \cdot 7^{4} \) |
$1.58420$ |
$(a+3), (-a+2), (-a-2), (a)$ |
0 |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{9} \) |
$1$ |
$2.486887276$ |
3.759820155 |
\( \frac{65597103937}{63504} \) |
\( \bigl[a\) , \( 0\) , \( 0\) , \( -83\) , \( -345\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-83{x}-345$ |
| 126.1-a7 |
126.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
126.1 |
\( 2 \cdot 3^{2} \cdot 7 \) |
\( 2^{4} \cdot 3^{4} \cdot 7^{2} \) |
$1.58420$ |
$(a+3), (-a+2), (-a-2), (a)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$16$ |
\( 2^{5} \) |
$1$ |
$0.621721819$ |
3.759820155 |
\( \frac{268498407453697}{252} \) |
\( \bigl[a\) , \( 0\) , \( 0\) , \( -1343\) , \( -19749\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-1343{x}-19749$ |
| 126.1-a8 |
126.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
126.1 |
\( 2 \cdot 3^{2} \cdot 7 \) |
\( - 2^{2} \cdot 3^{2} \cdot 7 \) |
$1.58420$ |
$(a+3), (-a+2), (-a-2), (a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2$ |
2B |
$256$ |
\( 2 \) |
$1$ |
$0.155430454$ |
3.759820155 |
\( \frac{9010577383592310868608127}{42} a + 567613022049721543828200 \) |
\( \bigl[a\) , \( 0\) , \( 0\) , \( -3810 a - 11423\) , \( -228018 a - 623037\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-3810a-11423\right){x}-228018a-623037$ |
| 126.1-b1 |
126.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
126.1 |
\( 2 \cdot 3^{2} \cdot 7 \) |
\( - 2^{4} \cdot 3^{6} \cdot 7 \) |
$1.58420$ |
$(a+3), (-a+2), (-a-2), (a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$12.74821856$ |
1.204593427 |
\( -\frac{12864268}{1701} a + \frac{19360349}{972} \) |
\( \bigl[1\) , \( -a - 1\) , \( a\) , \( 24 a - 61\) , \( -87 a + 227\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(24a-61\right){x}-87a+227$ |
| 126.1-b2 |
126.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
126.1 |
\( 2 \cdot 3^{2} \cdot 7 \) |
\( - 2 \cdot 3^{24} \cdot 7 \) |
$1.58420$ |
$(a+3), (-a+2), (-a-2), (a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$3.187054640$ |
1.204593427 |
\( \frac{5671936174309}{48814981614} a + \frac{9906651325129}{6973568802} \) |
\( \bigl[1\) , \( -a - 1\) , \( a\) , \( -171 a + 454\) , \( 1361 a - 3603\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-171a+454\right){x}+1361a-3603$ |
| 126.1-b3 |
126.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
126.1 |
\( 2 \cdot 3^{2} \cdot 7 \) |
\( 2^{2} \cdot 3^{12} \cdot 7^{2} \) |
$1.58420$ |
$(a+3), (-a+2), (-a-2), (a)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$1$ |
$6.374109280$ |
1.204593427 |
\( \frac{44968234789}{826686} a + \frac{60566645036}{413343} \) |
\( \bigl[1\) , \( -a - 1\) , \( a\) , \( 54 a - 141\) , \( 239 a - 635\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(54a-141\right){x}+239a-635$ |
| 126.1-b4 |
126.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
126.1 |
\( 2 \cdot 3^{2} \cdot 7 \) |
\( 2 \cdot 3^{6} \cdot 7^{4} \) |
$1.58420$ |
$(a+3), (-a+2), (-a-2), (a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 2^{2} \) |
$1$ |
$1.593527320$ |
1.204593427 |
\( \frac{377693915174519}{23814} a + \frac{999356883108149}{23814} \) |
\( \bigl[1\) , \( -a - 1\) , \( a\) , \( 759 a - 2016\) , \( 19061 a - 50435\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(759a-2016\right){x}+19061a-50435$ |
| 126.1-c1 |
126.1-c |
$4$ |
$4$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
126.1 |
\( 2 \cdot 3^{2} \cdot 7 \) |
\( - 2 \cdot 3^{24} \cdot 7 \) |
$1.58420$ |
$(a+3), (-a+2), (-a-2), (a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$3.187054640$ |
1.204593427 |
\( -\frac{5671936174309}{48814981614} a + \frac{9906651325129}{6973568802} \) |
\( \bigl[1\) , \( a - 1\) , \( a\) , \( 170 a + 454\) , \( -1361 a - 3603\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(170a+454\right){x}-1361a-3603$ |
| 126.1-c2 |
126.1-c |
$4$ |
$4$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
126.1 |
\( 2 \cdot 3^{2} \cdot 7 \) |
\( 2^{2} \cdot 3^{12} \cdot 7^{2} \) |
$1.58420$ |
$(a+3), (-a+2), (-a-2), (a)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$1$ |
$6.374109280$ |
1.204593427 |
\( -\frac{44968234789}{826686} a + \frac{60566645036}{413343} \) |
\( \bigl[1\) , \( a - 1\) , \( a\) , \( -55 a - 141\) , \( -239 a - 635\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-55a-141\right){x}-239a-635$ |
| 126.1-c3 |
126.1-c |
$4$ |
$4$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
126.1 |
\( 2 \cdot 3^{2} \cdot 7 \) |
\( - 2^{4} \cdot 3^{6} \cdot 7 \) |
$1.58420$ |
$(a+3), (-a+2), (-a-2), (a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$12.74821856$ |
1.204593427 |
\( \frac{12864268}{1701} a + \frac{19360349}{972} \) |
\( \bigl[1\) , \( a - 1\) , \( a\) , \( -25 a - 61\) , \( 87 a + 227\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-25a-61\right){x}+87a+227$ |
| 126.1-c4 |
126.1-c |
$4$ |
$4$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
126.1 |
\( 2 \cdot 3^{2} \cdot 7 \) |
\( 2 \cdot 3^{6} \cdot 7^{4} \) |
$1.58420$ |
$(a+3), (-a+2), (-a-2), (a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 2^{2} \) |
$1$ |
$1.593527320$ |
1.204593427 |
\( -\frac{377693915174519}{23814} a + \frac{999356883108149}{23814} \) |
\( \bigl[1\) , \( a - 1\) , \( a\) , \( -760 a - 2016\) , \( -19061 a - 50435\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-760a-2016\right){x}-19061a-50435$ |
| 126.1-d1 |
126.1-d |
$4$ |
$4$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
126.1 |
\( 2 \cdot 3^{2} \cdot 7 \) |
\( - 2 \cdot 3^{24} \cdot 7 \) |
$1.58420$ |
$(a+3), (-a+2), (-a-2), (a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \cdot 5 \) |
$0.130533259$ |
$3.789977720$ |
1.869858836 |
\( -\frac{5671936174309}{48814981614} a + \frac{9906651325129}{6973568802} \) |
\( \bigl[a\) , \( -a - 1\) , \( 1\) , \( 170 a + 454\) , \( 1361 a + 3601\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(170a+454\right){x}+1361a+3601$ |
| 126.1-d2 |
126.1-d |
$4$ |
$4$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
126.1 |
\( 2 \cdot 3^{2} \cdot 7 \) |
\( 2^{2} \cdot 3^{12} \cdot 7^{2} \) |
$1.58420$ |
$(a+3), (-a+2), (-a-2), (a)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \cdot 5 \) |
$0.065266629$ |
$15.15991088$ |
1.869858836 |
\( -\frac{44968234789}{826686} a + \frac{60566645036}{413343} \) |
\( \bigl[a\) , \( -a - 1\) , \( 1\) , \( -55 a - 141\) , \( 239 a + 633\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-55a-141\right){x}+239a+633$ |
| 126.1-d3 |
126.1-d |
$4$ |
$4$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
126.1 |
\( 2 \cdot 3^{2} \cdot 7 \) |
\( - 2^{4} \cdot 3^{6} \cdot 7 \) |
$1.58420$ |
$(a+3), (-a+2), (-a-2), (a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \cdot 5 \) |
$0.130533259$ |
$15.15991088$ |
1.869858836 |
\( \frac{12864268}{1701} a + \frac{19360349}{972} \) |
\( \bigl[a\) , \( -a - 1\) , \( 1\) , \( -25 a - 61\) , \( -87 a - 229\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-25a-61\right){x}-87a-229$ |
| 126.1-d4 |
126.1-d |
$4$ |
$4$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
126.1 |
\( 2 \cdot 3^{2} \cdot 7 \) |
\( 2 \cdot 3^{6} \cdot 7^{4} \) |
$1.58420$ |
$(a+3), (-a+2), (-a-2), (a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \cdot 5 \) |
$0.130533259$ |
$15.15991088$ |
1.869858836 |
\( -\frac{377693915174519}{23814} a + \frac{999356883108149}{23814} \) |
\( \bigl[a\) , \( -a - 1\) , \( 1\) , \( -760 a - 2016\) , \( 19061 a + 50433\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-760a-2016\right){x}+19061a+50433$ |
| 126.1-e1 |
126.1-e |
$4$ |
$4$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
126.1 |
\( 2 \cdot 3^{2} \cdot 7 \) |
\( - 2^{4} \cdot 3^{6} \cdot 7 \) |
$1.58420$ |
$(a+3), (-a+2), (-a-2), (a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \cdot 5 \) |
$0.130533259$ |
$15.15991088$ |
1.869858836 |
\( -\frac{12864268}{1701} a + \frac{19360349}{972} \) |
\( \bigl[a\) , \( a - 1\) , \( 1\) , \( 24 a - 61\) , \( 87 a - 229\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(24a-61\right){x}+87a-229$ |
| 126.1-e2 |
126.1-e |
$4$ |
$4$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
126.1 |
\( 2 \cdot 3^{2} \cdot 7 \) |
\( - 2 \cdot 3^{24} \cdot 7 \) |
$1.58420$ |
$(a+3), (-a+2), (-a-2), (a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \cdot 5 \) |
$0.130533259$ |
$3.789977720$ |
1.869858836 |
\( \frac{5671936174309}{48814981614} a + \frac{9906651325129}{6973568802} \) |
\( \bigl[a\) , \( a - 1\) , \( 1\) , \( -171 a + 454\) , \( -1361 a + 3601\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-171a+454\right){x}-1361a+3601$ |
| 126.1-e3 |
126.1-e |
$4$ |
$4$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
126.1 |
\( 2 \cdot 3^{2} \cdot 7 \) |
\( 2^{2} \cdot 3^{12} \cdot 7^{2} \) |
$1.58420$ |
$(a+3), (-a+2), (-a-2), (a)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \cdot 5 \) |
$0.065266629$ |
$15.15991088$ |
1.869858836 |
\( \frac{44968234789}{826686} a + \frac{60566645036}{413343} \) |
\( \bigl[a\) , \( a - 1\) , \( 1\) , \( 54 a - 141\) , \( -239 a + 633\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(54a-141\right){x}-239a+633$ |
| 126.1-e4 |
126.1-e |
$4$ |
$4$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
126.1 |
\( 2 \cdot 3^{2} \cdot 7 \) |
\( 2 \cdot 3^{6} \cdot 7^{4} \) |
$1.58420$ |
$(a+3), (-a+2), (-a-2), (a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \cdot 5 \) |
$0.130533259$ |
$15.15991088$ |
1.869858836 |
\( \frac{377693915174519}{23814} a + \frac{999356883108149}{23814} \) |
\( \bigl[a\) , \( a - 1\) , \( 1\) , \( 759 a - 2016\) , \( -19061 a + 50433\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(759a-2016\right){x}-19061a+50433$ |
| 126.1-f1 |
126.1-f |
$8$ |
$16$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
126.1 |
\( 2 \cdot 3^{2} \cdot 7 \) |
\( - 2^{2} \cdot 3^{2} \cdot 7 \) |
$1.58420$ |
$(a+3), (-a+2), (-a-2), (a)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2$ |
2B |
$4$ |
\( 2 \) |
$2.310811814$ |
$6.039367514$ |
2.637406196 |
\( -\frac{9010577383592310868608127}{42} a + 567613022049721543828200 \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( 3810 a - 11424\) , \( -224208 a + 611613\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}+\left(3810a-11424\right){x}-224208a+611613$ |
| 126.1-f2 |
126.1-f |
$8$ |
$16$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
126.1 |
\( 2 \cdot 3^{2} \cdot 7 \) |
\( 2^{16} \cdot 3^{4} \cdot 7^{2} \) |
$1.58420$ |
$(a+3), (-a+2), (-a-2), (a)$ |
$1$ |
$\Z/8\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{7} \) |
$0.288851476$ |
$12.07873502$ |
2.637406196 |
\( -\frac{7189057}{16128} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -4\) , \( 5\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-4{x}+5$ |
| 126.1-f3 |
126.1-f |
$8$ |
$16$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
126.1 |
\( 2 \cdot 3^{2} \cdot 7 \) |
\( 2^{2} \cdot 3^{32} \cdot 7^{4} \) |
$1.58420$ |
$(a+3), (-a+2), (-a-2), (a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$2.310811814$ |
$0.754920939$ |
2.637406196 |
\( \frac{6359387729183}{4218578658} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( 386\) , \( 1277\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}+386{x}+1277$ |
| 126.1-f4 |
126.1-f |
$8$ |
$16$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
126.1 |
\( 2 \cdot 3^{2} \cdot 7 \) |
\( 2^{4} \cdot 3^{16} \cdot 7^{8} \) |
$1.58420$ |
$(a+3), (-a+2), (-a-2), (a)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$1.155405907$ |
$3.019683757$ |
2.637406196 |
\( \frac{124475734657}{63011844} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -104\) , \( 101\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-104{x}+101$ |
| 126.1-f5 |
126.1-f |
$8$ |
$16$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
126.1 |
\( 2 \cdot 3^{2} \cdot 7 \) |
\( 2^{2} \cdot 3^{8} \cdot 7^{16} \) |
$1.58420$ |
$(a+3), (-a+2), (-a-2), (a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$2.310811814$ |
$0.754920939$ |
2.637406196 |
\( \frac{84448510979617}{933897762} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -914\) , \( -10915\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-914{x}-10915$ |
| 126.1-f6 |
126.1-f |
$8$ |
$16$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
126.1 |
\( 2 \cdot 3^{2} \cdot 7 \) |
\( 2^{8} \cdot 3^{8} \cdot 7^{4} \) |
$1.58420$ |
$(a+3), (-a+2), (-a-2), (a)$ |
$1$ |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{6} \) |
$0.577702953$ |
$12.07873502$ |
2.637406196 |
\( \frac{65597103937}{63504} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -84\) , \( 261\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-84{x}+261$ |
| 126.1-f7 |
126.1-f |
$8$ |
$16$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
126.1 |
\( 2 \cdot 3^{2} \cdot 7 \) |
\( 2^{4} \cdot 3^{4} \cdot 7^{2} \) |
$1.58420$ |
$(a+3), (-a+2), (-a-2), (a)$ |
$1$ |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$1.155405907$ |
$12.07873502$ |
2.637406196 |
\( \frac{268498407453697}{252} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -1344\) , \( 18405\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-1344{x}+18405$ |
| 126.1-f8 |
126.1-f |
$8$ |
$16$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
126.1 |
\( 2 \cdot 3^{2} \cdot 7 \) |
\( - 2^{2} \cdot 3^{2} \cdot 7 \) |
$1.58420$ |
$(a+3), (-a+2), (-a-2), (a)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2$ |
2B |
$4$ |
\( 2 \) |
$2.310811814$ |
$6.039367514$ |
2.637406196 |
\( \frac{9010577383592310868608127}{42} a + 567613022049721543828200 \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -3810 a - 11424\) , \( 224208 a + 611613\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}+\left(-3810a-11424\right){x}+224208a+611613$ |
*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.
