| 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 |
| 27.2-a5 |
27.2-a |
$8$ |
$20$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
27.2 |
\( 3^{3} \) |
\( 3^{27} \) |
$0.67558$ |
$(-a), (a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 5$ |
2B, 5B |
$1$ |
\( 2^{2} \) |
$1$ |
$1.144817200$ |
0.690350747 |
\( -\frac{2927543402641}{3486784401} a + \frac{1635099303025}{3486784401} \) |
\( \bigl[1\) , \( -a - 1\) , \( a\) , \( -19 a + 15\) , \( 50 a - 96\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-19a+15\right){x}+50a-96$ |
| 27.3-a5 |
27.3-a |
$8$ |
$20$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
27.3 |
\( 3^{3} \) |
\( 3^{27} \) |
$0.67558$ |
$(-a), (a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 5$ |
2B, 5B |
$1$ |
\( 2^{2} \) |
$1$ |
$1.144817200$ |
0.690350747 |
\( -\frac{2927543402641}{3486784401} a + \frac{1635099303025}{3486784401} \) |
\( \bigl[a + 1\) , \( a + 1\) , \( a + 1\) , \( -4 a + 32\) , \( -23 a - 31\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-4a+32\right){x}-23a-31$ |
| 675.4-c5 |
675.4-c |
$8$ |
$20$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
675.4 |
\( 3^{3} \cdot 5^{2} \) |
\( 3^{27} \cdot 5^{6} \) |
$1.51064$ |
$(-a), (a-1), (-a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 5$ |
2B, 5B |
$1$ |
\( 2^{3} \) |
$1.860600554$ |
$0.511977816$ |
2.297724390 |
\( -\frac{2927543402641}{3486784401} a + \frac{1635099303025}{3486784401} \) |
\( \bigl[a\) , \( 0\) , \( a + 1\) , \( 27 a + 144\) , \( -599 a + 238\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(27a+144\right){x}-599a+238$ |
| 675.6-a5 |
675.6-a |
$8$ |
$20$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
675.6 |
\( 3^{3} \cdot 5^{2} \) |
\( 3^{27} \cdot 5^{6} \) |
$1.51064$ |
$(-a), (a-1), (a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 5$ |
2B, 5B |
$1$ |
\( 2^{4} \) |
$1$ |
$0.511977816$ |
1.234936958 |
\( -\frac{2927543402641}{3486784401} a + \frac{1635099303025}{3486784401} \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( 1\) , \( -9 a - 158\) , \( -174 a + 1125\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-9a-158\right){x}-174a+1125$ |
| 675.7-a5 |
675.7-a |
$8$ |
$20$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
675.7 |
\( 3^{3} \cdot 5^{2} \) |
\( 3^{27} \cdot 5^{6} \) |
$1.51064$ |
$(-a), (a-1), (-a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 5$ |
2B, 5B |
$1$ |
\( 2^{4} \) |
$1$ |
$0.511977816$ |
1.234936958 |
\( -\frac{2927543402641}{3486784401} a + \frac{1635099303025}{3486784401} \) |
\( \bigl[1\) , \( a + 1\) , \( 1\) , \( 99 a - 32\) , \( 162 a + 830\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(99a-32\right){x}+162a+830$ |
| 675.9-c5 |
675.9-c |
$8$ |
$20$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
675.9 |
\( 3^{3} \cdot 5^{2} \) |
\( 3^{27} \cdot 5^{6} \) |
$1.51064$ |
$(-a), (a-1), (a-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 5$ |
2B, 5B |
$1$ |
\( 2^{5} \cdot 5 \) |
$0.093030027$ |
$0.511977816$ |
2.297724390 |
\( -\frac{2927543402641}{3486784401} a + \frac{1635099303025}{3486784401} \) |
\( \bigl[a\) , \( a + 1\) , \( a + 1\) , \( -94 a - 3\) , \( 551 a - 46\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-94a-3\right){x}+551a-46$ |
| 1089.2-c5 |
1089.2-c |
$8$ |
$20$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
1089.2 |
\( 3^{2} \cdot 11^{2} \) |
\( 3^{21} \cdot 11^{6} \) |
$1.70252$ |
$(-a), (a-1), (-2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 5$ |
2B, 5B |
$1$ |
\( 2^{3} \cdot 5 \) |
$1$ |
$0.597861284$ |
3.605239194 |
\( -\frac{2927543402641}{3486784401} a + \frac{1635099303025}{3486784401} \) |
\( \bigl[a\) , \( -a + 1\) , \( 1\) , \( -52 a + 109\) , \( -49 a + 614\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-52a+109\right){x}-49a+614$ |
| 2304.2-d5 |
2304.2-d |
$8$ |
$20$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
2304.2 |
\( 2^{8} \cdot 3^{2} \) |
\( 2^{24} \cdot 3^{21} \) |
$2.05331$ |
$(-a), (a-1), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 5$ |
2B, 5B |
$1$ |
\( 2^{2} \) |
$4.227056070$ |
$0.495720389$ |
2.527193171 |
\( -\frac{2927543402641}{3486784401} a + \frac{1635099303025}{3486784401} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 76 a - 160\) , \( 668 a - 116\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(76a-160\right){x}+668a-116$ |
| 2304.2-h5 |
2304.2-h |
$8$ |
$20$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
2304.2 |
\( 2^{8} \cdot 3^{2} \) |
\( 2^{24} \cdot 3^{21} \) |
$2.05331$ |
$(-a), (a-1), (2)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 5$ |
2B, 5B |
$1$ |
\( 2^{4} \cdot 5 \) |
$0.845411214$ |
$0.495720389$ |
2.527193171 |
\( -\frac{2927543402641}{3486784401} a + \frac{1635099303025}{3486784401} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 76 a - 160\) , \( -668 a + 116\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(76a-160\right){x}-668a+116$ |
| 4761.4-b5 |
4761.4-b |
$8$ |
$20$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
4761.4 |
\( 3^{2} \cdot 23^{2} \) |
\( 3^{21} \cdot 23^{6} \) |
$2.46184$ |
$(-a), (a-1), (a+4)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 5$ |
2B, 5B |
$1$ |
\( 2^{3} \cdot 5 \) |
$1$ |
$0.413459386$ |
2.493253908 |
\( -\frac{2927543402641}{3486784401} a + \frac{1635099303025}{3486784401} \) |
\( \bigl[1\) , \( 0\) , \( a\) , \( 13 a - 256\) , \( -640 a + 1883\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(13a-256\right){x}-640a+1883$ |
| 4761.6-b5 |
4761.6-b |
$8$ |
$20$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
4761.6 |
\( 3^{2} \cdot 23^{2} \) |
\( 3^{21} \cdot 23^{6} \) |
$2.46184$ |
$(-a), (a-1), (a-5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 5$ |
2B, 5B |
$1$ |
\( 2^{3} \cdot 5 \) |
$1$ |
$0.413459386$ |
2.493253908 |
\( -\frac{2927543402641}{3486784401} a + \frac{1635099303025}{3486784401} \) |
\( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( 149 a - 92\) , \( 470 a + 1394\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(149a-92\right){x}+470a+1394$ |
| 6912.2-n5 |
6912.2-n |
$8$ |
$20$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
6912.2 |
\( 2^{8} \cdot 3^{3} \) |
\( 2^{24} \cdot 3^{27} \) |
$2.70231$ |
$(-a), (a-1), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 5$ |
2B, 5B |
$1$ |
\( 2^{3} \) |
$7.432760689$ |
$0.286204300$ |
5.131211894 |
\( -\frac{2927543402641}{3486784401} a + \frac{1635099303025}{3486784401} \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( -309 a + 252\) , \( -2855 a + 5033\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(-309a+252\right){x}-2855a+5033$ |
| 6912.3-r5 |
6912.3-r |
$8$ |
$20$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
6912.3 |
\( 2^{8} \cdot 3^{3} \) |
\( 2^{24} \cdot 3^{27} \) |
$2.70231$ |
$(-a), (a-1), (2)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 5$ |
2B, 5B |
$1$ |
\( 2^{5} \cdot 5 \) |
$1.486552137$ |
$0.286204300$ |
5.131211894 |
\( -\frac{2927543402641}{3486784401} a + \frac{1635099303025}{3486784401} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -66 a + 543\) , \( 2303 a + 2883\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(-66a+543\right){x}+2303a+2883$ |
| 8649.4-c5 |
8649.4-c |
$8$ |
$20$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
8649.4 |
\( 3^{2} \cdot 31^{2} \) |
\( 3^{21} \cdot 31^{6} \) |
$2.85809$ |
$(-a), (a-1), (-3a+4)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 5$ |
2B, 5B |
$1$ |
\( 2^{4} \cdot 5 \) |
$0.622335744$ |
$0.356136040$ |
5.346066004 |
\( -\frac{2927543402641}{3486784401} a + \frac{1635099303025}{3486784401} \) |
\( \bigl[1\) , \( a\) , \( 1\) , \( 28 a + 319\) , \( 1860 a - 124\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+a{x}^{2}+\left(28a+319\right){x}+1860a-124$ |
| 8649.6-c5 |
8649.6-c |
$8$ |
$20$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
8649.6 |
\( 3^{2} \cdot 31^{2} \) |
\( 3^{21} \cdot 31^{6} \) |
$2.85809$ |
$(-a), (a-1), (3a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 5$ |
2B, 5B |
$1$ |
\( 2^{2} \) |
$12.44671488$ |
$0.356136040$ |
5.346066004 |
\( -\frac{2927543402641}{3486784401} a + \frac{1635099303025}{3486784401} \) |
\( \bigl[a + 1\) , \( -a + 1\) , \( 0\) , \( -201 a + 48\) , \( -1812 a + 1134\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-201a+48\right){x}-1812a+1134$ |
| 9801.3-l5 |
9801.3-l |
$8$ |
$20$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
9801.3 |
\( 3^{4} \cdot 11^{2} \) |
\( 3^{33} \cdot 11^{6} \) |
$2.94885$ |
$(-a), (a-1), (-2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 5$ |
2B, 5B |
$1$ |
\( 2^{5} \) |
$1$ |
$0.199287094$ |
0.961397118 |
\( -\frac{2927543402641}{3486784401} a + \frac{1635099303025}{3486784401} \) |
\( \bigl[a\) , \( -a\) , \( a\) , \( -464 a + 987\) , \( 802 a - 17976\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}-a{x}^{2}+\left(-464a+987\right){x}+802a-17976$ |
| 16875.13-bc6 |
16875.13-bc |
$8$ |
$20$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
16875.13 |
\( 3^{3} \cdot 5^{4} \) |
\( 3^{27} \cdot 5^{12} \) |
$3.37789$ |
$(-a), (a-1), (-a-1), (a-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 5$ |
2B, 5B |
$1$ |
\( 2^{7} \cdot 5 \) |
$0.155996685$ |
$0.228963440$ |
6.892315432 |
\( -\frac{2927543402641}{3486784401} a + \frac{1635099303025}{3486784401} \) |
\( \bigl[a + 1\) , \( -a\) , \( 1\) , \( -103 a + 849\) , \( -4897 a - 5573\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}-a{x}^{2}+\left(-103a+849\right){x}-4897a-5573$ |
| 16875.8-ba6 |
16875.8-ba |
$8$ |
$20$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
16875.8 |
\( 3^{3} \cdot 5^{4} \) |
\( 3^{27} \cdot 5^{12} \) |
$3.37789$ |
$(-a), (a-1), (-a-1), (a-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 5$ |
2B, 5B |
$1$ |
\( 2^{5} \) |
$3.119933717$ |
$0.228963440$ |
6.892315432 |
\( -\frac{2927543402641}{3486784401} a + \frac{1635099303025}{3486784401} \) |
\( \bigl[1\) , \( a - 1\) , \( a + 1\) , \( -484 a + 394\) , \( 5630 a - 8841\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-484a+394\right){x}+5630a-8841$ |
| 19881.4-a6 |
19881.4-a |
$8$ |
$20$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
19881.4 |
\( 3^{2} \cdot 47^{2} \) |
\( 3^{21} \cdot 47^{6} \) |
$3.51920$ |
$(-a), (a-1), (-2a+7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 5$ |
2B, 5B |
$1$ |
\( 2^{3} \) |
$1$ |
$0.289233001$ |
0.348828124 |
\( -\frac{2927543402641}{3486784401} a + \frac{1635099303025}{3486784401} \) |
\( \bigl[a\) , \( -a - 1\) , \( a + 1\) , \( 300 a - 29\) , \( -323 a + 5852\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(300a-29\right){x}-323a+5852$ |
| 19881.6-b6 |
19881.6-b |
$8$ |
$20$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
19881.6 |
\( 3^{2} \cdot 47^{2} \) |
\( 3^{21} \cdot 47^{6} \) |
$3.51920$ |
$(-a), (a-1), (2a+5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 5$ |
2B, 5B |
$1$ |
\( 2^{3} \) |
$1$ |
$0.289233001$ |
0.348828124 |
\( -\frac{2927543402641}{3486784401} a + \frac{1635099303025}{3486784401} \) |
\( \bigl[a\) , \( -a - 1\) , \( a\) , \( -65 a - 465\) , \( -283 a + 5970\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-65a-465\right){x}-283a+5970$ |
| 20736.3-bi6 |
20736.3-bi |
$8$ |
$20$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
20736.3 |
\( 2^{8} \cdot 3^{4} \) |
\( 2^{24} \cdot 3^{33} \) |
$3.55645$ |
$(-a), (a-1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 5$ |
2B, 5B |
$4$ |
\( 2^{5} \) |
$1$ |
$0.165240129$ |
3.188593517 |
\( -\frac{2927543402641}{3486784401} a + \frac{1635099303025}{3486784401} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 675 a - 1434\) , \( -17956 a + 6602\bigr] \) |
${y}^2={x}^{3}+\left(675a-1434\right){x}-17956a+6602$ |
| 20736.3-bl6 |
20736.3-bl |
$8$ |
$20$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
20736.3 |
\( 2^{8} \cdot 3^{4} \) |
\( 2^{24} \cdot 3^{33} \) |
$3.55645$ |
$(-a), (a-1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 5$ |
2B, 5B |
$4$ |
\( 2^{5} \) |
$1$ |
$0.165240129$ |
3.188593517 |
\( -\frac{2927543402641}{3486784401} a + \frac{1635099303025}{3486784401} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 675 a - 1434\) , \( 17956 a - 6602\bigr] \) |
${y}^2={x}^{3}+\left(675a-1434\right){x}+17956a-6602$ |
| 27225.4-f6 |
27225.4-f |
$8$ |
$20$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
27225.4 |
\( 3^{2} \cdot 5^{2} \cdot 11^{2} \) |
\( 3^{21} \cdot 5^{6} \cdot 11^{6} \) |
$3.80695$ |
$(-a), (a-1), (-a-1), (-2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 5$ |
2B, 5B |
$1$ |
\( 2^{4} \cdot 5 \) |
$0.568845360$ |
$0.267371694$ |
3.668624767 |
\( -\frac{2927543402641}{3486784401} a + \frac{1635099303025}{3486784401} \) |
\( \bigl[a + 1\) , \( a\) , \( a + 1\) , \( 276 a + 243\) , \( 3044 a - 7244\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(276a+243\right){x}+3044a-7244$ |
| 27225.6-c6 |
27225.6-c |
$8$ |
$20$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
27225.6 |
\( 3^{2} \cdot 5^{2} \cdot 11^{2} \) |
\( 3^{21} \cdot 5^{6} \cdot 11^{6} \) |
$3.80695$ |
$(-a), (a-1), (a-2), (-2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 5$ |
2B, 5B |
$1$ |
\( 2^{4} \) |
$2.844226804$ |
$0.267371694$ |
3.668624767 |
\( -\frac{2927543402641}{3486784401} a + \frac{1635099303025}{3486784401} \) |
\( \bigl[1\) , \( -a + 1\) , \( 0\) , \( -226 a - 355\) , \( -2143 a - 5243\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-226a-355\right){x}-2143a-5243$ |
| 31329.4-b6 |
31329.4-b |
$8$ |
$20$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
31329.4 |
\( 3^{2} \cdot 59^{2} \) |
\( 3^{21} \cdot 59^{6} \) |
$3.94295$ |
$(-a), (a-1), (a+7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 5$ |
2B, 5B |
$1$ |
\( 2^{3} \cdot 5 \) |
$1$ |
$0.258149190$ |
1.556698190 |
\( -\frac{2927543402641}{3486784401} a + \frac{1635099303025}{3486784401} \) |
\( \bigl[a + 1\) , \( 0\) , \( 1\) , \( 136 a - 670\) , \( -4125 a + 6242\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(136a-670\right){x}-4125a+6242$ |
| 31329.6-b6 |
31329.6-b |
$8$ |
$20$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
31329.6 |
\( 3^{2} \cdot 59^{2} \) |
\( 3^{21} \cdot 59^{6} \) |
$3.94295$ |
$(-a), (a-1), (a-8)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 5$ |
2B, 5B |
$1$ |
\( 2^{3} \cdot 5 \) |
$1$ |
$0.258149190$ |
1.556698190 |
\( -\frac{2927543402641}{3486784401} a + \frac{1635099303025}{3486784401} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( 365 a - 397\) , \( 3543 a + 3449\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(365a-397\right){x}+3543a+3449$ |
| 36864.2-t6 |
36864.2-t |
$8$ |
$20$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
36864.2 |
\( 2^{12} \cdot 3^{2} \) |
\( 2^{36} \cdot 3^{21} \) |
$4.10663$ |
$(-a), (a-1), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 5$ |
2B, 5B |
$1$ |
\( 2^{2} \) |
$27.99058310$ |
$0.247860194$ |
8.367242985 |
\( -\frac{2927543402641}{3486784401} a + \frac{1635099303025}{3486784401} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 301 a - 638\) , \( -5308 a + 2469\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(301a-638\right){x}-5308a+2469$ |
| 36864.2-bg6 |
36864.2-bg |
$8$ |
$20$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
36864.2 |
\( 2^{12} \cdot 3^{2} \) |
\( 2^{36} \cdot 3^{21} \) |
$4.10663$ |
$(-a), (a-1), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 5$ |
2B, 5B |
$1$ |
\( 2^{4} \cdot 5 \) |
$1.399529155$ |
$0.247860194$ |
8.367242985 |
\( -\frac{2927543402641}{3486784401} a + \frac{1635099303025}{3486784401} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 301 a - 638\) , \( 5308 a - 2469\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(301a-638\right){x}+5308a-2469$ |
| 36963.4-a6 |
36963.4-a |
$8$ |
$20$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
36963.4 |
\( 3^{3} \cdot 37^{2} \) |
\( 3^{27} \cdot 37^{6} \) |
$4.10938$ |
$(-a), (a-1), (-3a-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 5$ |
2B, 5B |
$1$ |
\( 2^{3} \) |
$8.679764015$ |
$0.188206788$ |
3.940368569 |
\( -\frac{2927543402641}{3486784401} a + \frac{1635099303025}{3486784401} \) |
\( \bigl[a + 1\) , \( a - 1\) , \( 0\) , \( 370 a + 852\) , \( -10947 a + 11484\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(370a+852\right){x}-10947a+11484$ |
| 36963.6-a6 |
36963.6-a |
$8$ |
$20$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
36963.6 |
\( 3^{3} \cdot 37^{2} \) |
\( 3^{27} \cdot 37^{6} \) |
$4.10938$ |
$(-a), (a-1), (3a-5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 5$ |
2B, 5B |
$1$ |
\( 2^{3} \) |
$18.41816575$ |
$0.188206788$ |
8.361328871 |
\( -\frac{2927543402641}{3486784401} a + \frac{1635099303025}{3486784401} \) |
\( \bigl[a\) , \( 0\) , \( a\) , \( 112 a - 1248\) , \( -7880 a + 19759\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(112a-1248\right){x}-7880a+19759$ |
| 36963.7-a6 |
36963.7-a |
$8$ |
$20$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
36963.7 |
\( 3^{3} \cdot 37^{2} \) |
\( 3^{27} \cdot 37^{6} \) |
$4.10938$ |
$(-a), (a-1), (-3a-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 5$ |
2B, 5B |
$1$ |
\( 2^{5} \cdot 5 \) |
$0.920908287$ |
$0.188206788$ |
8.361328871 |
\( -\frac{2927543402641}{3486784401} a + \frac{1635099303025}{3486784401} \) |
\( \bigl[a\) , \( a + 1\) , \( a\) , \( 722 a - 523\) , \( 6310 a + 13409\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(722a-523\right){x}+6310a+13409$ |
| 36963.9-a6 |
36963.9-a |
$8$ |
$20$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
36963.9 |
\( 3^{3} \cdot 37^{2} \) |
\( 3^{27} \cdot 37^{6} \) |
$4.10938$ |
$(-a), (a-1), (3a-5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 5$ |
2B, 5B |
$1$ |
\( 2^{5} \cdot 5 \) |
$0.433988200$ |
$0.188206788$ |
3.940368569 |
\( -\frac{2927543402641}{3486784401} a + \frac{1635099303025}{3486784401} \) |
\( \bigl[1\) , \( -a\) , \( 1\) , \( -619 a - 328\) , \( 10942 a + 3767\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-a{x}^{2}+\left(-619a-328\right){x}+10942a+3767$ |
| 40401.4-a6 |
40401.4-a |
$8$ |
$20$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
40401.4 |
\( 3^{2} \cdot 67^{2} \) |
\( 3^{21} \cdot 67^{6} \) |
$4.20178$ |
$(-a), (a-1), (-3a-5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 5$ |
2B, 5B |
$1$ |
\( 2^{4} \cdot 5 \) |
$1.165624530$ |
$0.242247538$ |
6.811012775 |
\( -\frac{2927543402641}{3486784401} a + \frac{1635099303025}{3486784401} \) |
\( \bigl[a + 1\) , \( a\) , \( 1\) , \( -215 a - 532\) , \( -2139 a - 7696\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+a{x}^{2}+\left(-215a-532\right){x}-2139a-7696$ |
| 40401.6-a6 |
40401.6-a |
$8$ |
$20$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
40401.6 |
\( 3^{2} \cdot 67^{2} \) |
\( 3^{21} \cdot 67^{6} \) |
$4.20178$ |
$(-a), (a-1), (3a-8)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 5$ |
2B, 5B |
$1$ |
\( 2^{2} \) |
$23.31249060$ |
$0.242247538$ |
6.811012775 |
\( -\frac{2927543402641}{3486784401} a + \frac{1635099303025}{3486784401} \) |
\( \bigl[1\) , \( -a + 1\) , \( a + 1\) , \( 378 a + 179\) , \( 2553 a - 9295\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(378a+179\right){x}+2553a-9295$ |
| 42849.7-c6 |
42849.7-c |
$8$ |
$20$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
42849.7 |
\( 3^{4} \cdot 23^{2} \) |
\( 3^{33} \cdot 23^{6} \) |
$4.26403$ |
$(-a), (a-1), (a+4)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 5$ |
2B, 5B |
$1$ |
\( 2^{5} \) |
$1$ |
$0.137819795$ |
0.664867708 |
\( -\frac{2927543402641}{3486784401} a + \frac{1635099303025}{3486784401} \) |
\( \bigl[1\) , \( -1\) , \( a\) , \( 121 a - 2304\) , \( 17273 a - 50820\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(121a-2304\right){x}+17273a-50820$ |
| 42849.9-d6 |
42849.9-d |
$8$ |
$20$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
42849.9 |
\( 3^{4} \cdot 23^{2} \) |
\( 3^{33} \cdot 23^{6} \) |
$4.26403$ |
$(-a), (a-1), (a-5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 5$ |
2B, 5B |
$1$ |
\( 2^{5} \) |
$1$ |
$0.137819795$ |
0.664867708 |
\( -\frac{2927543402641}{3486784401} a + \frac{1635099303025}{3486784401} \) |
\( \bigl[a + 1\) , \( -1\) , \( 1\) , \( 1354 a - 833\) , \( -13544 a - 40856\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}-{x}^{2}+\left(1354a-833\right){x}-13544a-40856$ |
| 45369.4-a6 |
45369.4-a |
$8$ |
$20$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
45369.4 |
\( 3^{2} \cdot 71^{2} \) |
\( 3^{21} \cdot 71^{6} \) |
$4.32538$ |
$(-a), (a-1), (-5a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 5$ |
2B, 5B |
$1$ |
\( 2^{3} \) |
$1$ |
$0.235324746$ |
0.283812322 |
\( -\frac{2927543402641}{3486784401} a + \frac{1635099303025}{3486784401} \) |
\( \bigl[a + 1\) , \( 1\) , \( 1\) , \( -426 a + 525\) , \( 3560 a - 9834\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+{x}^{2}+\left(-426a+525\right){x}+3560a-9834$ |
| 45369.6-a6 |
45369.6-a |
$8$ |
$20$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
45369.6 |
\( 3^{2} \cdot 71^{2} \) |
\( 3^{21} \cdot 71^{6} \) |
$4.32538$ |
$(-a), (a-1), (5a-4)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 5$ |
2B, 5B |
$1$ |
\( 2^{3} \) |
$1$ |
$0.235324746$ |
0.283812322 |
\( -\frac{2927543402641}{3486784401} a + \frac{1635099303025}{3486784401} \) |
\( \bigl[1\) , \( 1\) , \( a\) , \( -198 a + 799\) , \( -2836 a - 7569\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+{x}^{2}+\left(-198a+799\right){x}-2836a-7569$ |
*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.
