| 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 |
| 121.1-a1 |
121.1-a |
$2$ |
$11$ |
\(\Q(\sqrt{33}) \) |
$2$ |
$[2, 0]$ |
121.1 |
\( 11^{2} \) |
\( 11^{4} \) |
$1.70252$ |
$(-4a-9)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
✓ |
$11$ |
11B.1.5 |
$1$ |
\( 1 \) |
$0.467099783$ |
$30.53686771$ |
4.966005310 |
\( -24729001 \) |
\( \bigl[1\) , \( -a\) , \( a + 1\) , \( -11048 a - 26206\) , \( 1082764 a + 2568621\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(-11048a-26206\right){x}+1082764a+2568621$ |
| 121.1-a2 |
121.1-a |
$2$ |
$11$ |
\(\Q(\sqrt{33}) \) |
$2$ |
$[2, 0]$ |
121.1 |
\( 11^{2} \) |
\( 11^{8} \) |
$1.70252$ |
$(-4a-9)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
✓ |
$11$ |
11B.1.7 |
$1$ |
\( 1 \) |
$5.138097620$ |
$2.776078883$ |
4.966005310 |
\( -121 \) |
\( \bigl[1\) , \( 1\) , \( 0\) , \( -2\) , \( -7\bigr] \) |
${y}^2+{x}{y}={x}^{3}+{x}^{2}-2{x}-7$ |
| 121.1-b1 |
121.1-b |
$6$ |
$99$ |
\(\Q(\sqrt{33}) \) |
$2$ |
$[2, 0]$ |
121.1 |
\( 11^{2} \) |
\( 11^{6} \) |
$1.70252$ |
$(-4a-9)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{potential}$ |
$-99$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$11$ |
11B.1.3 |
$1$ |
\( 2 \) |
$0.269355468$ |
$7.687750184$ |
1.441876556 |
\( -6548115718144 a - 15533972619264 \) |
\( \bigl[0\) , \( -1\) , \( 1\) , \( -110 a - 227\) , \( 1012 a + 2419\bigr] \) |
${y}^2+{y}={x}^{3}-{x}^{2}+\left(-110a-227\right){x}+1012a+2419$ |
| 121.1-b2 |
121.1-b |
$6$ |
$99$ |
\(\Q(\sqrt{33}) \) |
$2$ |
$[2, 0]$ |
121.1 |
\( 11^{2} \) |
\( 11^{6} \) |
$1.70252$ |
$(-4a-9)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{potential}$ |
$-99$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$11$ |
11B.1.8 |
$1$ |
\( 2 \) |
$2.962910153$ |
$0.698886380$ |
1.441876556 |
\( -6548115718144 a - 15533972619264 \) |
\( \bigl[0\) , \( a\) , \( 1\) , \( -12371 a + 41722\) , \( 513055 a - 1730165\bigr] \) |
${y}^2+{y}={x}^{3}+a{x}^{2}+\left(-12371a+41722\right){x}+513055a-1730165$ |
| 121.1-b3 |
121.1-b |
$6$ |
$99$ |
\(\Q(\sqrt{33}) \) |
$2$ |
$[2, 0]$ |
121.1 |
\( 11^{2} \) |
\( 11^{6} \) |
$1.70252$ |
$(-4a-9)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{potential}$ |
$-11$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$3, 11$ |
3Cs, 11B.1.3 |
$1$ |
\( 2 \) |
$0.089785156$ |
$23.06325055$ |
1.441876556 |
\( -32768 \) |
\( \bigl[0\) , \( -1\) , \( 1\) , \( -7\) , \( 10\bigr] \) |
${y}^2+{y}={x}^{3}-{x}^{2}-7{x}+10$ |
| 121.1-b4 |
121.1-b |
$6$ |
$99$ |
\(\Q(\sqrt{33}) \) |
$2$ |
$[2, 0]$ |
121.1 |
\( 11^{2} \) |
\( 11^{6} \) |
$1.70252$ |
$(-4a-9)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{potential}$ |
$-11$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$3, 11$ |
3Cs, 11B.1.8 |
$1$ |
\( 2 \) |
$0.987636717$ |
$2.096659141$ |
1.441876556 |
\( -32768 \) |
\( \bigl[0\) , \( -a + 1\) , \( 1\) , \( -2699 a - 6399\) , \( -130563 a - 309731\bigr] \) |
${y}^2+{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-2699a-6399\right){x}-130563a-309731$ |
| 121.1-b5 |
121.1-b |
$6$ |
$99$ |
\(\Q(\sqrt{33}) \) |
$2$ |
$[2, 0]$ |
121.1 |
\( 11^{2} \) |
\( 11^{6} \) |
$1.70252$ |
$(-4a-9)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{potential}$ |
$-99$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$11$ |
11B.1.3 |
$1$ |
\( 2 \) |
$0.269355468$ |
$7.687750184$ |
1.441876556 |
\( 6548115718144 a - 22082088337408 \) |
\( \bigl[0\) , \( -1\) , \( 1\) , \( 110 a - 337\) , \( -1012 a + 3431\bigr] \) |
${y}^2+{y}={x}^{3}-{x}^{2}+\left(110a-337\right){x}-1012a+3431$ |
| 121.1-b6 |
121.1-b |
$6$ |
$99$ |
\(\Q(\sqrt{33}) \) |
$2$ |
$[2, 0]$ |
121.1 |
\( 11^{2} \) |
\( 11^{6} \) |
$1.70252$ |
$(-4a-9)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{potential}$ |
$-99$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$11$ |
11B.1.8 |
$1$ |
\( 2 \) |
$2.962910153$ |
$0.698886380$ |
1.441876556 |
\( 6548115718144 a - 22082088337408 \) |
\( \bigl[0\) , \( -a + 1\) , \( 1\) , \( 12371 a + 29351\) , \( -513055 a - 1217110\bigr] \) |
${y}^2+{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(12371a+29351\right){x}-513055a-1217110$ |
| 121.1-c1 |
121.1-c |
$2$ |
$11$ |
\(\Q(\sqrt{33}) \) |
$2$ |
$[2, 0]$ |
121.1 |
\( 11^{2} \) |
\( 11^{10} \) |
$1.70252$ |
$(-4a-9)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$11$ |
11B.10.5 |
$1$ |
\( 1 \) |
$2.287485873$ |
$1.699138266$ |
1.353194323 |
\( -24729001 \) |
\( \bigl[1\) , \( -a - 1\) , \( 1\) , \( -2641 a - 6272\) , \( -121729 a - 288772\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-2641a-6272\right){x}-121729a-288772$ |
| 121.1-c2 |
121.1-c |
$2$ |
$11$ |
\(\Q(\sqrt{33}) \) |
$2$ |
$[2, 0]$ |
121.1 |
\( 11^{2} \) |
\( 11^{2} \) |
$1.70252$ |
$(-4a-9)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$11$ |
11B.10.4 |
$1$ |
\( 1 \) |
$0.207953261$ |
$18.69052092$ |
1.353194323 |
\( -121 \) |
\( \bigl[1\) , \( -a - 1\) , \( 1\) , \( -a - 2\) , \( 11 a + 26\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-a-2\right){x}+11a+26$ |
| 121.1-d1 |
121.1-d |
$4$ |
$22$ |
\(\Q(\sqrt{33}) \) |
$2$ |
$[2, 0]$ |
121.1 |
\( 11^{2} \) |
\( - 11^{9} \) |
$1.70252$ |
$(-4a-9)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2, 11$ |
2B, 11B.1.4 |
$1$ |
\( 2 \) |
$1$ |
$7.057677431$ |
0.614291971 |
\( -1649607317164 a + 5562936868789 \) |
\( \bigl[1\) , \( -a\) , \( a\) , \( -1643 a - 4079\) , \( 64852 a + 154652\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}-a{x}^{2}+\left(-1643a-4079\right){x}+64852a+154652$ |
| 121.1-d2 |
121.1-d |
$4$ |
$22$ |
\(\Q(\sqrt{33}) \) |
$2$ |
$[2, 0]$ |
121.1 |
\( 11^{2} \) |
\( - 11^{3} \) |
$1.70252$ |
$(-4a-9)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2, 11$ |
2B, 11B.1.6 |
$1$ |
\( 2 \) |
$1$ |
$7.057677431$ |
0.614291971 |
\( -357236 a + 1203885 \) |
\( \bigl[1\) , \( -a\) , \( a\) , \( -3 a - 4\) , \( -5 a - 13\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}-a{x}^{2}+\left(-3a-4\right){x}-5a-13$ |
| 121.1-d3 |
121.1-d |
$4$ |
$22$ |
\(\Q(\sqrt{33}) \) |
$2$ |
$[2, 0]$ |
121.1 |
\( 11^{2} \) |
\( - 11^{3} \) |
$1.70252$ |
$(-4a-9)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2, 11$ |
2B, 11B.1.6 |
$1$ |
\( 2 \) |
$1$ |
$7.057677431$ |
0.614291971 |
\( 357236 a + 846649 \) |
\( \bigl[1\) , \( a - 1\) , \( a + 1\) , \( 2 a - 7\) , \( 4 a - 18\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(2a-7\right){x}+4a-18$ |
| 121.1-d4 |
121.1-d |
$4$ |
$22$ |
\(\Q(\sqrt{33}) \) |
$2$ |
$[2, 0]$ |
121.1 |
\( 11^{2} \) |
\( - 11^{9} \) |
$1.70252$ |
$(-4a-9)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2, 11$ |
2B, 11B.1.4 |
$1$ |
\( 2 \) |
$1$ |
$7.057677431$ |
0.614291971 |
\( 1649607317164 a + 3913329551625 \) |
\( \bigl[1\) , \( a - 1\) , \( a + 1\) , \( 1642 a - 5722\) , \( -64853 a + 219504\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(1642a-5722\right){x}-64853a+219504$ |
| 121.1-e1 |
121.1-e |
$3$ |
$25$ |
\(\Q(\sqrt{33}) \) |
$2$ |
$[2, 0]$ |
121.1 |
\( 11^{2} \) |
\( 11^{8} \) |
$1.70252$ |
$(-4a-9)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$5$ |
5B.4.2 |
$1$ |
\( 2 \) |
$19.53044489$ |
$0.223304562$ |
3.036775978 |
\( -\frac{52893159101157376}{11} \) |
\( \bigl[0\) , \( a - 1\) , \( 1\) , \( 688189 a - 2322636\) , \( 526275039 a - 1774717815\bigr] \) |
${y}^2+{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(688189a-2322636\right){x}+526275039a-1774717815$ |
| 121.1-e2 |
121.1-e |
$3$ |
$25$ |
\(\Q(\sqrt{33}) \) |
$2$ |
$[2, 0]$ |
121.1 |
\( 11^{2} \) |
\( 11^{16} \) |
$1.70252$ |
$(-4a-9)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$5$ |
5Cs.4.1 |
$1$ |
\( 2 \) |
$3.906088979$ |
$1.116522814$ |
3.036775978 |
\( -\frac{122023936}{161051} \) |
\( \bigl[0\) , \( a - 1\) , \( 1\) , \( 909 a - 3066\) , \( 44829 a - 151175\bigr] \) |
${y}^2+{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(909a-3066\right){x}+44829a-151175$ |
| 121.1-e3 |
121.1-e |
$3$ |
$25$ |
\(\Q(\sqrt{33}) \) |
$2$ |
$[2, 0]$ |
121.1 |
\( 11^{2} \) |
\( 11^{8} \) |
$1.70252$ |
$(-4a-9)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$5$ |
5B.4.1 |
$1$ |
\( 2 \) |
$0.781217795$ |
$5.582614074$ |
3.036775978 |
\( -\frac{4096}{11} \) |
\( \bigl[0\) , \( a - 1\) , \( 1\) , \( 29 a - 96\) , \( -381 a + 1285\bigr] \) |
${y}^2+{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(29a-96\right){x}-381a+1285$ |
| 121.1-f1 |
121.1-f |
$4$ |
$22$ |
\(\Q(\sqrt{33}) \) |
$2$ |
$[2, 0]$ |
121.1 |
\( 11^{2} \) |
\( - 11^{3} \) |
$1.70252$ |
$(-4a-9)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2, 11$ |
2B, 11B.10.4 |
$1$ |
\( 2 \) |
$1$ |
$4.922210220$ |
0.428423408 |
\( -1649607317164 a + 5562936868789 \) |
\( \bigl[1\) , \( 0\) , \( a + 1\) , \( -7001 a - 16608\) , \( -541087 a - 1283611\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-7001a-16608\right){x}-541087a-1283611$ |
| 121.1-f2 |
121.1-f |
$4$ |
$22$ |
\(\Q(\sqrt{33}) \) |
$2$ |
$[2, 0]$ |
121.1 |
\( 11^{2} \) |
\( - 11^{9} \) |
$1.70252$ |
$(-4a-9)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2, 11$ |
2B, 11B.10.5 |
$1$ |
\( 2 \) |
$1$ |
$4.922210220$ |
0.428423408 |
\( -357236 a + 1203885 \) |
\( \bigl[1\) , \( -a - 1\) , \( 0\) , \( 32 a - 106\) , \( 184 a - 613\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(32a-106\right){x}+184a-613$ |
| 121.1-f3 |
121.1-f |
$4$ |
$22$ |
\(\Q(\sqrt{33}) \) |
$2$ |
$[2, 0]$ |
121.1 |
\( 11^{2} \) |
\( - 11^{9} \) |
$1.70252$ |
$(-4a-9)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2, 11$ |
2B, 11B.10.5 |
$1$ |
\( 2 \) |
$1$ |
$4.922210220$ |
0.428423408 |
\( 357236 a + 846649 \) |
\( \bigl[1\) , \( 0\) , \( a + 1\) , \( 1380 a - 4656\) , \( 83690 a - 282231\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(1380a-4656\right){x}+83690a-282231$ |
| 121.1-f4 |
121.1-f |
$4$ |
$22$ |
\(\Q(\sqrt{33}) \) |
$2$ |
$[2, 0]$ |
121.1 |
\( 11^{2} \) |
\( - 11^{3} \) |
$1.70252$ |
$(-4a-9)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2, 11$ |
2B, 11B.10.4 |
$1$ |
\( 2 \) |
$1$ |
$4.922210220$ |
0.428423408 |
\( 1649607317164 a + 3913329551625 \) |
\( \bigl[1\) , \( a + 1\) , \( 0\) , \( -130 a - 327\) , \( -1652 a - 3880\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-130a-327\right){x}-1652a-3880$ |
| 121.1-g1 |
121.1-g |
$3$ |
$25$ |
\(\Q(\sqrt{33}) \) |
$2$ |
$[2, 0]$ |
121.1 |
\( 11^{2} \) |
\( 11^{8} \) |
$1.70252$ |
$(-4a-9)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$5$ |
5B.4.2 |
$1$ |
\( 2 \) |
$19.53044489$ |
$0.223304562$ |
3.036775978 |
\( -\frac{52893159101157376}{11} \) |
\( \bigl[0\) , \( -a\) , \( 1\) , \( -688189 a - 1634447\) , \( -526275039 a - 1248442776\bigr] \) |
${y}^2+{y}={x}^{3}-a{x}^{2}+\left(-688189a-1634447\right){x}-526275039a-1248442776$ |
| 121.1-g2 |
121.1-g |
$3$ |
$25$ |
\(\Q(\sqrt{33}) \) |
$2$ |
$[2, 0]$ |
121.1 |
\( 11^{2} \) |
\( 11^{16} \) |
$1.70252$ |
$(-4a-9)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$5$ |
5Cs.4.1 |
$1$ |
\( 2 \) |
$3.906088979$ |
$1.116522814$ |
3.036775978 |
\( -\frac{122023936}{161051} \) |
\( \bigl[0\) , \( -a\) , \( 1\) , \( -909 a - 2157\) , \( -44829 a - 106346\bigr] \) |
${y}^2+{y}={x}^{3}-a{x}^{2}+\left(-909a-2157\right){x}-44829a-106346$ |
| 121.1-g3 |
121.1-g |
$3$ |
$25$ |
\(\Q(\sqrt{33}) \) |
$2$ |
$[2, 0]$ |
121.1 |
\( 11^{2} \) |
\( 11^{8} \) |
$1.70252$ |
$(-4a-9)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$5$ |
5B.4.1 |
$1$ |
\( 2 \) |
$0.781217795$ |
$5.582614074$ |
3.036775978 |
\( -\frac{4096}{11} \) |
\( \bigl[0\) , \( -a\) , \( 1\) , \( -29 a - 67\) , \( 381 a + 904\bigr] \) |
${y}^2+{y}={x}^{3}-a{x}^{2}+\left(-29a-67\right){x}+381a+904$ |
| 121.1-h1 |
121.1-h |
$4$ |
$22$ |
\(\Q(\sqrt{33}) \) |
$2$ |
$[2, 0]$ |
121.1 |
\( 11^{2} \) |
\( - 11^{9} \) |
$1.70252$ |
$(-4a-9)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2, 11$ |
2B, 11B.1.7 |
$121$ |
\( 2 \) |
$1$ |
$0.312079919$ |
3.286731521 |
\( -1649607317164 a + 5562936868789 \) |
\( \bigl[1\) , \( 1\) , \( 0\) , \( 68013 a - 229363\) , \( 16391683 a - 55277372\bigr] \) |
${y}^2+{x}{y}={x}^{3}+{x}^{2}+\left(68013a-229363\right){x}+16391683a-55277372$ |
| 121.1-h2 |
121.1-h |
$4$ |
$22$ |
\(\Q(\sqrt{33}) \) |
$2$ |
$[2, 0]$ |
121.1 |
\( 11^{2} \) |
\( - 11^{3} \) |
$1.70252$ |
$(-4a-9)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2, 11$ |
2B, 11B.1.5 |
$1$ |
\( 2 \) |
$1$ |
$37.76167025$ |
3.286731521 |
\( -357236 a + 1203885 \) |
\( \bigl[1\) , \( 1\) , \( 0\) , \( 133 a - 448\) , \( -1359 a + 4583\bigr] \) |
${y}^2+{x}{y}={x}^{3}+{x}^{2}+\left(133a-448\right){x}-1359a+4583$ |
| 121.1-h3 |
121.1-h |
$4$ |
$22$ |
\(\Q(\sqrt{33}) \) |
$2$ |
$[2, 0]$ |
121.1 |
\( 11^{2} \) |
\( - 11^{3} \) |
$1.70252$ |
$(-4a-9)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2, 11$ |
2B, 11B.1.5 |
$1$ |
\( 2 \) |
$1$ |
$37.76167025$ |
3.286731521 |
\( 357236 a + 846649 \) |
\( \bigl[1\) , \( 1\) , \( 0\) , \( -133 a - 315\) , \( 1359 a + 3224\bigr] \) |
${y}^2+{x}{y}={x}^{3}+{x}^{2}+\left(-133a-315\right){x}+1359a+3224$ |
| 121.1-h4 |
121.1-h |
$4$ |
$22$ |
\(\Q(\sqrt{33}) \) |
$2$ |
$[2, 0]$ |
121.1 |
\( 11^{2} \) |
\( - 11^{9} \) |
$1.70252$ |
$(-4a-9)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2, 11$ |
2B, 11B.1.7 |
$121$ |
\( 2 \) |
$1$ |
$0.312079919$ |
3.286731521 |
\( 1649607317164 a + 3913329551625 \) |
\( \bigl[1\) , \( 1\) , \( 0\) , \( -68013 a - 161350\) , \( -16391683 a - 38885689\bigr] \) |
${y}^2+{x}{y}={x}^{3}+{x}^{2}+\left(-68013a-161350\right){x}-16391683a-38885689$ |
| 121.1-i1 |
121.1-i |
$4$ |
$22$ |
\(\Q(\sqrt{33}) \) |
$2$ |
$[2, 0]$ |
121.1 |
\( 11^{2} \) |
\( - 11^{3} \) |
$1.70252$ |
$(-4a-9)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2, 11$ |
2B, 11B.10.4 |
$1$ |
\( 2 \) |
$1$ |
$4.922210220$ |
0.428423408 |
\( -1649607317164 a + 5562936868789 \) |
\( \bigl[1\) , \( -a - 1\) , \( 1\) , \( 132 a - 459\) , \( 1521 a - 5074\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(132a-459\right){x}+1521a-5074$ |
| 121.1-i2 |
121.1-i |
$4$ |
$22$ |
\(\Q(\sqrt{33}) \) |
$2$ |
$[2, 0]$ |
121.1 |
\( 11^{2} \) |
\( - 11^{9} \) |
$1.70252$ |
$(-4a-9)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2, 11$ |
2B, 11B.10.5 |
$1$ |
\( 2 \) |
$1$ |
$4.922210220$ |
0.428423408 |
\( -357236 a + 1203885 \) |
\( \bigl[1\) , \( 0\) , \( a\) , \( -1381 a - 3275\) , \( -83691 a - 198540\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(-1381a-3275\right){x}-83691a-198540$ |
| 121.1-i3 |
121.1-i |
$4$ |
$22$ |
\(\Q(\sqrt{33}) \) |
$2$ |
$[2, 0]$ |
121.1 |
\( 11^{2} \) |
\( - 11^{9} \) |
$1.70252$ |
$(-4a-9)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2, 11$ |
2B, 11B.10.5 |
$1$ |
\( 2 \) |
$1$ |
$4.922210220$ |
0.428423408 |
\( 357236 a + 846649 \) |
\( \bigl[1\) , \( a + 1\) , \( 1\) , \( -30 a - 75\) , \( -215 a - 504\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-30a-75\right){x}-215a-504$ |
| 121.1-i4 |
121.1-i |
$4$ |
$22$ |
\(\Q(\sqrt{33}) \) |
$2$ |
$[2, 0]$ |
121.1 |
\( 11^{2} \) |
\( - 11^{3} \) |
$1.70252$ |
$(-4a-9)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2, 11$ |
2B, 11B.10.4 |
$1$ |
\( 2 \) |
$1$ |
$4.922210220$ |
0.428423408 |
\( 1649607317164 a + 3913329551625 \) |
\( \bigl[1\) , \( 0\) , \( a\) , \( 7000 a - 23608\) , \( 541086 a - 1824697\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(7000a-23608\right){x}+541086a-1824697$ |
| 121.1-j1 |
121.1-j |
$2$ |
$11$ |
\(\Q(\sqrt{33}) \) |
$2$ |
$[2, 0]$ |
121.1 |
\( 11^{2} \) |
\( 11^{4} \) |
$1.70252$ |
$(-4a-9)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
✓ |
$11$ |
11B.1.6 |
$1$ |
\( 3 \) |
$1.460386125$ |
$1.039981560$ |
1.586308376 |
\( -24729001 \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -30\) , \( -76\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-30{x}-76$ |
| 121.1-j2 |
121.1-j |
$2$ |
$11$ |
\(\Q(\sqrt{33}) \) |
$2$ |
$[2, 0]$ |
121.1 |
\( 11^{2} \) |
\( 11^{8} \) |
$1.70252$ |
$(-4a-9)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
✓ |
$11$ |
11B.1.4 |
$1$ |
\( 3 \) |
$0.132762375$ |
$11.43979716$ |
1.586308376 |
\( -121 \) |
\( \bigl[1\) , \( a - 1\) , \( a + 1\) , \( 927 a - 3126\) , \( -102858 a + 346862\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(927a-3126\right){x}-102858a+346862$ |
| 121.1-k1 |
121.1-k |
$2$ |
$11$ |
\(\Q(\sqrt{33}) \) |
$2$ |
$[2, 0]$ |
121.1 |
\( 11^{2} \) |
\( 11^{10} \) |
$1.70252$ |
$(-4a-9)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$11$ |
11B.10.5 |
$1$ |
\( 1 \) |
$2.287485873$ |
$1.699138266$ |
1.353194323 |
\( -24729001 \) |
\( \bigl[1\) , \( a + 1\) , \( 0\) , \( 2643 a - 8913\) , \( 124371 a - 419414\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(2643a-8913\right){x}+124371a-419414$ |
| 121.1-k2 |
121.1-k |
$2$ |
$11$ |
\(\Q(\sqrt{33}) \) |
$2$ |
$[2, 0]$ |
121.1 |
\( 11^{2} \) |
\( 11^{2} \) |
$1.70252$ |
$(-4a-9)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$11$ |
11B.10.4 |
$1$ |
\( 1 \) |
$0.207953261$ |
$18.69052092$ |
1.353194323 |
\( -121 \) |
\( \bigl[1\) , \( a + 1\) , \( 0\) , \( 3 a - 3\) , \( -9 a + 34\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(3a-3\right){x}-9a+34$ |
*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.
