| 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 |
| 10.1-a1 |
10.1-a |
$2$ |
$3$ |
\(\Q(\sqrt{11}) \) |
$2$ |
$[2, 0]$ |
10.1 |
\( 2 \cdot 5 \) |
\( - 2^{7} \cdot 5 \) |
$1.05406$ |
$(a+3), (a-4)$ |
$0$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1 |
$1$ |
\( 1 \) |
$1$ |
$43.11092390$ |
0.722135146 |
\( -\frac{378329}{80} a + \frac{707609}{80} \) |
\( \bigl[a\) , \( a + 1\) , \( a\) , \( -8 a - 32\) , \( 15 a + 47\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-8a-32\right){x}+15a+47$ |
| 10.1-a2 |
10.1-a |
$2$ |
$3$ |
\(\Q(\sqrt{11}) \) |
$2$ |
$[2, 0]$ |
10.1 |
\( 2 \cdot 5 \) |
\( - 2^{21} \cdot 5^{3} \) |
$1.05406$ |
$(a+3), (a-4)$ |
$0$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.2 |
$1$ |
\( 1 \) |
$1$ |
$4.790102655$ |
0.722135146 |
\( -\frac{4874397503}{256000} a + \frac{16590792793}{256000} \) |
\( \bigl[a\) , \( a + 1\) , \( a\) , \( 72 a + 233\) , \( 47 a + 153\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(72a+233\right){x}+47a+153$ |
| 10.1-b1 |
10.1-b |
$2$ |
$7$ |
\(\Q(\sqrt{11}) \) |
$2$ |
$[2, 0]$ |
10.1 |
\( 2 \cdot 5 \) |
\( - 2 \cdot 5 \) |
$1.05406$ |
$(a+3), (a-4)$ |
$0$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$7$ |
7B.1.3 |
$49$ |
\( 1 \) |
$1$ |
$0.241155033$ |
1.781418972 |
\( -\frac{466209435421917067326607}{10} a + \frac{1546241771017925012924657}{10} \) |
\( \bigl[1\) , \( a + 1\) , \( a + 1\) , \( -23541 a - 78106\) , \( -3623860 a - 12019033\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-23541a-78106\right){x}-3623860a-12019033$ |
| 10.1-b2 |
10.1-b |
$2$ |
$7$ |
\(\Q(\sqrt{11}) \) |
$2$ |
$[2, 0]$ |
10.1 |
\( 2 \cdot 5 \) |
\( - 2^{7} \cdot 5^{7} \) |
$1.05406$ |
$(a+3), (a-4)$ |
$0$ |
$\Z/7\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$7$ |
7B.1.1 |
$1$ |
\( 7^{2} \) |
$1$ |
$11.81659665$ |
1.781418972 |
\( -\frac{584688139}{1250000} a + \frac{1940357659}{1250000} \) |
\( \bigl[1\) , \( a + 1\) , \( a + 1\) , \( 14 a + 49\) , \( 2175 a + 7212\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(14a+49\right){x}+2175a+7212$ |
| 10.1-c1 |
10.1-c |
$2$ |
$7$ |
\(\Q(\sqrt{11}) \) |
$2$ |
$[2, 0]$ |
10.1 |
\( 2 \cdot 5 \) |
\( - 2 \cdot 5 \) |
$1.05406$ |
$(a+3), (a-4)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$7$ |
7B.6.3 |
$1$ |
\( 1 \) |
$0.411540706$ |
$8.658898230$ |
1.074432388 |
\( -\frac{466209435421917067326607}{10} a + \frac{1546241771017925012924657}{10} \) |
\( \bigl[a\) , \( -a - 1\) , \( 1\) , \( -23543 a - 78105\) , \( 3600318 a + 11940924\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-23543a-78105\right){x}+3600318a+11940924$ |
| 10.1-c2 |
10.1-c |
$2$ |
$7$ |
\(\Q(\sqrt{11}) \) |
$2$ |
$[2, 0]$ |
10.1 |
\( 2 \cdot 5 \) |
\( - 2^{7} \cdot 5^{7} \) |
$1.05406$ |
$(a+3), (a-4)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$7$ |
7B.6.1 |
$1$ |
\( 7 \) |
$0.058791529$ |
$8.658898230$ |
1.074432388 |
\( -\frac{584688139}{1250000} a + \frac{1940357659}{1250000} \) |
\( \bigl[a\) , \( -a - 1\) , \( 1\) , \( 12 a + 50\) , \( -2162 a - 7166\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(12a+50\right){x}-2162a-7166$ |
| 10.1-d1 |
10.1-d |
$2$ |
$3$ |
\(\Q(\sqrt{11}) \) |
$2$ |
$[2, 0]$ |
10.1 |
\( 2 \cdot 5 \) |
\( - 2^{7} \cdot 5 \) |
$1.05406$ |
$(a+3), (a-4)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 7 \) |
$0.082400613$ |
$9.456690263$ |
1.644641729 |
\( -\frac{378329}{80} a + \frac{707609}{80} \) |
\( \bigl[1\) , \( -a - 1\) , \( 0\) , \( -10 a - 31\) , \( -24 a - 79\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-10a-31\right){x}-24a-79$ |
| 10.1-d2 |
10.1-d |
$2$ |
$3$ |
\(\Q(\sqrt{11}) \) |
$2$ |
$[2, 0]$ |
10.1 |
\( 2 \cdot 5 \) |
\( - 2^{21} \cdot 5^{3} \) |
$1.05406$ |
$(a+3), (a-4)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 3 \cdot 7 \) |
$0.027466871$ |
$9.456690263$ |
1.644641729 |
\( -\frac{4874397503}{256000} a + \frac{16590792793}{256000} \) |
\( \bigl[1\) , \( -a - 1\) , \( 0\) , \( 70 a + 234\) , \( 24 a + 80\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(70a+234\right){x}+24a+80$ |
| 10.2-a1 |
10.2-a |
$2$ |
$3$ |
\(\Q(\sqrt{11}) \) |
$2$ |
$[2, 0]$ |
10.2 |
\( 2 \cdot 5 \) |
\( - 2^{7} \cdot 5 \) |
$1.05406$ |
$(a+3), (-a-4)$ |
$0$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1 |
$1$ |
\( 1 \) |
$1$ |
$43.11092390$ |
0.722135146 |
\( \frac{378329}{80} a + \frac{707609}{80} \) |
\( \bigl[a\) , \( -a + 1\) , \( a\) , \( 8 a - 32\) , \( -15 a + 47\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(8a-32\right){x}-15a+47$ |
| 10.2-a2 |
10.2-a |
$2$ |
$3$ |
\(\Q(\sqrt{11}) \) |
$2$ |
$[2, 0]$ |
10.2 |
\( 2 \cdot 5 \) |
\( - 2^{21} \cdot 5^{3} \) |
$1.05406$ |
$(a+3), (-a-4)$ |
$0$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.2 |
$1$ |
\( 1 \) |
$1$ |
$4.790102655$ |
0.722135146 |
\( \frac{4874397503}{256000} a + \frac{16590792793}{256000} \) |
\( \bigl[a\) , \( -a + 1\) , \( a\) , \( -72 a + 233\) , \( -47 a + 153\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-72a+233\right){x}-47a+153$ |
| 10.2-b1 |
10.2-b |
$2$ |
$7$ |
\(\Q(\sqrt{11}) \) |
$2$ |
$[2, 0]$ |
10.2 |
\( 2 \cdot 5 \) |
\( - 2^{7} \cdot 5^{7} \) |
$1.05406$ |
$(a+3), (-a-4)$ |
$0$ |
$\Z/7\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$7$ |
7B.1.1 |
$1$ |
\( 7^{2} \) |
$1$ |
$11.81659665$ |
1.781418972 |
\( \frac{584688139}{1250000} a + \frac{1940357659}{1250000} \) |
\( \bigl[1\) , \( -a + 1\) , \( a + 1\) , \( -15 a + 49\) , \( -2176 a + 7212\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-15a+49\right){x}-2176a+7212$ |
| 10.2-b2 |
10.2-b |
$2$ |
$7$ |
\(\Q(\sqrt{11}) \) |
$2$ |
$[2, 0]$ |
10.2 |
\( 2 \cdot 5 \) |
\( - 2 \cdot 5 \) |
$1.05406$ |
$(a+3), (-a-4)$ |
$0$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$7$ |
7B.1.3 |
$49$ |
\( 1 \) |
$1$ |
$0.241155033$ |
1.781418972 |
\( \frac{466209435421917067326607}{10} a + \frac{1546241771017925012924657}{10} \) |
\( \bigl[1\) , \( -a + 1\) , \( a + 1\) , \( 23540 a - 78106\) , \( 3623859 a - 12019033\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(23540a-78106\right){x}+3623859a-12019033$ |
| 10.2-c1 |
10.2-c |
$2$ |
$7$ |
\(\Q(\sqrt{11}) \) |
$2$ |
$[2, 0]$ |
10.2 |
\( 2 \cdot 5 \) |
\( - 2^{7} \cdot 5^{7} \) |
$1.05406$ |
$(a+3), (-a-4)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$7$ |
7B.6.1 |
$1$ |
\( 7 \) |
$0.058791529$ |
$8.658898230$ |
1.074432388 |
\( \frac{584688139}{1250000} a + \frac{1940357659}{1250000} \) |
\( \bigl[a\) , \( a - 1\) , \( 1\) , \( -13 a + 50\) , \( 2162 a - 7166\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-13a+50\right){x}+2162a-7166$ |
| 10.2-c2 |
10.2-c |
$2$ |
$7$ |
\(\Q(\sqrt{11}) \) |
$2$ |
$[2, 0]$ |
10.2 |
\( 2 \cdot 5 \) |
\( - 2 \cdot 5 \) |
$1.05406$ |
$(a+3), (-a-4)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$7$ |
7B.6.3 |
$1$ |
\( 1 \) |
$0.411540706$ |
$8.658898230$ |
1.074432388 |
\( \frac{466209435421917067326607}{10} a + \frac{1546241771017925012924657}{10} \) |
\( \bigl[a\) , \( a - 1\) , \( 1\) , \( 23542 a - 78105\) , \( -3600318 a + 11940924\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(23542a-78105\right){x}-3600318a+11940924$ |
| 10.2-d1 |
10.2-d |
$2$ |
$3$ |
\(\Q(\sqrt{11}) \) |
$2$ |
$[2, 0]$ |
10.2 |
\( 2 \cdot 5 \) |
\( - 2^{7} \cdot 5 \) |
$1.05406$ |
$(a+3), (-a-4)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 7 \) |
$0.082400613$ |
$9.456690263$ |
1.644641729 |
\( \frac{378329}{80} a + \frac{707609}{80} \) |
\( \bigl[1\) , \( a - 1\) , \( 0\) , \( 10 a - 31\) , \( 24 a - 79\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(10a-31\right){x}+24a-79$ |
| 10.2-d2 |
10.2-d |
$2$ |
$3$ |
\(\Q(\sqrt{11}) \) |
$2$ |
$[2, 0]$ |
10.2 |
\( 2 \cdot 5 \) |
\( - 2^{21} \cdot 5^{3} \) |
$1.05406$ |
$(a+3), (-a-4)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 3 \cdot 7 \) |
$0.027466871$ |
$9.456690263$ |
1.644641729 |
\( \frac{4874397503}{256000} a + \frac{16590792793}{256000} \) |
\( \bigl[1\) , \( a - 1\) , \( 0\) , \( -70 a + 234\) , \( -24 a + 80\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-70a+234\right){x}-24a+80$ |
| 11.1-a1 |
11.1-a |
$3$ |
$25$ |
\(\Q(\sqrt{11}) \) |
$2$ |
$[2, 0]$ |
11.1 |
\( 11 \) |
\( 11^{2} \) |
$1.07948$ |
$(a)$ |
$0$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$5$ |
5B.4.2 |
$1$ |
\( 2 \) |
$1$ |
$8.512583687$ |
2.566640553 |
\( -\frac{52893159101157376}{11} \) |
\( \bigl[0\) , \( 1\) , \( a\) , \( -7820\) , \( 263577\bigr] \) |
${y}^2+a{y}={x}^{3}+{x}^{2}-7820{x}+263577$ |
| 11.1-a2 |
11.1-a |
$3$ |
$25$ |
\(\Q(\sqrt{11}) \) |
$2$ |
$[2, 0]$ |
11.1 |
\( 11 \) |
\( 11^{10} \) |
$1.07948$ |
$(a)$ |
$0$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$5$ |
5Cs.4.1 |
$1$ |
\( 2 \) |
$1$ |
$8.512583687$ |
2.566640553 |
\( -\frac{122023936}{161051} \) |
\( \bigl[0\) , \( 1\) , \( a\) , \( -10\) , \( 17\bigr] \) |
${y}^2+a{y}={x}^{3}+{x}^{2}-10{x}+17$ |
| 11.1-a3 |
11.1-a |
$3$ |
$25$ |
\(\Q(\sqrt{11}) \) |
$2$ |
$[2, 0]$ |
11.1 |
\( 11 \) |
\( 11^{2} \) |
$1.07948$ |
$(a)$ |
$0$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$5$ |
5B.4.1 |
$1$ |
\( 2 \) |
$1$ |
$8.512583687$ |
2.566640553 |
\( -\frac{4096}{11} \) |
\( \bigl[0\) , \( 1\) , \( a\) , \( 0\) , \( -3\bigr] \) |
${y}^2+a{y}={x}^{3}+{x}^{2}-3$ |
| 11.1-b1 |
11.1-b |
$3$ |
$25$ |
\(\Q(\sqrt{11}) \) |
$2$ |
$[2, 0]$ |
11.1 |
\( 11 \) |
\( 11^{2} \) |
$1.07948$ |
$(a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$5$ |
5B.1.2 |
$1$ |
\( 2 \) |
$22.07430201$ |
$0.064435690$ |
0.857723124 |
\( -\frac{52893159101157376}{11} \) |
\( \bigl[0\) , \( -1\) , \( 1\) , \( -7820\) , \( -263580\bigr] \) |
${y}^2+{y}={x}^{3}-{x}^{2}-7820{x}-263580$ |
| 11.1-b2 |
11.1-b |
$3$ |
$25$ |
\(\Q(\sqrt{11}) \) |
$2$ |
$[2, 0]$ |
11.1 |
\( 11 \) |
\( 11^{10} \) |
$1.07948$ |
$(a)$ |
$1$ |
$\Z/5\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$5$ |
5Cs.1.1 |
$1$ |
\( 2 \cdot 5 \) |
$4.414860402$ |
$1.610892258$ |
0.857723124 |
\( -\frac{122023936}{161051} \) |
\( \bigl[0\) , \( -1\) , \( 1\) , \( -10\) , \( -20\bigr] \) |
${y}^2+{y}={x}^{3}-{x}^{2}-10{x}-20$ |
| 11.1-b3 |
11.1-b |
$3$ |
$25$ |
\(\Q(\sqrt{11}) \) |
$2$ |
$[2, 0]$ |
11.1 |
\( 11 \) |
\( 11^{2} \) |
$1.07948$ |
$(a)$ |
$1$ |
$\Z/5\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$5$ |
5B.1.1 |
$1$ |
\( 2 \) |
$0.882972080$ |
$40.27230645$ |
0.857723124 |
\( -\frac{4096}{11} \) |
\( \bigl[0\) , \( -1\) , \( 1\) , \( 0\) , \( 0\bigr] \) |
${y}^2+{y}={x}^{3}-{x}^{2}$ |
| 16.1-a1 |
16.1-a |
$1$ |
$1$ |
\(\Q(\sqrt{11}) \) |
$2$ |
$[2, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{4} \) |
$1.18548$ |
$(a+3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 1 \) |
$0.235813649$ |
$21.93426914$ |
1.559537297 |
\( 1024 \) |
\( \bigl[0\) , \( a\) , \( a + 1\) , \( 4\) , \( -3\bigr] \) |
${y}^2+\left(a+1\right){y}={x}^{3}+a{x}^{2}+4{x}-3$ |
| 16.1-b1 |
16.1-b |
$2$ |
$11$ |
\(\Q(\sqrt{11}) \) |
$2$ |
$[2, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{12} \) |
$1.18548$ |
$(a+3)$ |
$0$ |
$\mathsf{trivial}$ |
$\textsf{potential}$ |
$-11$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 1 \) |
$1$ |
$11.53162527$ |
1.738457921 |
\( -32768 \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( 1\) , \( a\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+{x}+a$ |
| 16.1-b2 |
16.1-b |
$2$ |
$11$ |
\(\Q(\sqrt{11}) \) |
$2$ |
$[2, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{12} \) |
$1.18548$ |
$(a+3)$ |
$0$ |
$\mathsf{trivial}$ |
$\textsf{potential}$ |
$-11$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 1 \) |
$1$ |
$11.53162527$ |
1.738457921 |
\( -32768 \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( 1\) , \( -a\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+{x}-a$ |
| 16.1-c1 |
16.1-c |
$1$ |
$1$ |
\(\Q(\sqrt{11}) \) |
$2$ |
$[2, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{4} \) |
$1.18548$ |
$(a+3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 1 \) |
$0.235813649$ |
$21.93426914$ |
1.559537297 |
\( 1024 \) |
\( \bigl[0\) , \( -a\) , \( a + 1\) , \( 4\) , \( -a - 3\bigr] \) |
${y}^2+\left(a+1\right){y}={x}^{3}-a{x}^{2}+4{x}-a-3$ |
| 20.1-a1 |
20.1-a |
$2$ |
$2$ |
\(\Q(\sqrt{11}) \) |
$2$ |
$[2, 0]$ |
20.1 |
\( 2^{2} \cdot 5 \) |
\( 2^{8} \cdot 5^{2} \) |
$1.25349$ |
$(a+3), (a-4)$ |
$0$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$7.019918163$ |
1.587438723 |
\( -\frac{12288}{25} a - \frac{28672}{25} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -12 a + 46\) , \( 82 a - 269\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(-12a+46\right){x}+82a-269$ |
| 20.1-a2 |
20.1-a |
$2$ |
$2$ |
\(\Q(\sqrt{11}) \) |
$2$ |
$[2, 0]$ |
20.1 |
\( 2^{2} \cdot 5 \) |
\( 2^{4} \cdot 5 \) |
$1.25349$ |
$(a+3), (a-4)$ |
$0$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 3 \) |
$1$ |
$14.03983632$ |
1.587438723 |
\( \frac{9052192}{5} a + \frac{30047888}{5} \) |
\( \bigl[a + 1\) , \( -1\) , \( a + 1\) , \( -3 a - 13\) , \( -8 a - 28\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(-3a-13\right){x}-8a-28$ |
| 20.1-b1 |
20.1-b |
$2$ |
$2$ |
\(\Q(\sqrt{11}) \) |
$2$ |
$[2, 0]$ |
20.1 |
\( 2^{2} \cdot 5 \) |
\( 2^{8} \cdot 5^{2} \) |
$1.25349$ |
$(a+3), (a-4)$ |
$0$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$24.21146987$ |
1.825008208 |
\( -\frac{12288}{25} a - \frac{28672}{25} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -12 a + 46\) , \( -82 a + 269\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(-12a+46\right){x}-82a+269$ |
| 20.1-b2 |
20.1-b |
$2$ |
$2$ |
\(\Q(\sqrt{11}) \) |
$2$ |
$[2, 0]$ |
20.1 |
\( 2^{2} \cdot 5 \) |
\( 2^{4} \cdot 5 \) |
$1.25349$ |
$(a+3), (a-4)$ |
$0$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$48.42293974$ |
1.825008208 |
\( \frac{9052192}{5} a + \frac{30047888}{5} \) |
\( \bigl[a + 1\) , \( -a + 1\) , \( a + 1\) , \( -5 a - 9\) , \( a + 8\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-5a-9\right){x}+a+8$ |
| 20.2-a1 |
20.2-a |
$2$ |
$2$ |
\(\Q(\sqrt{11}) \) |
$2$ |
$[2, 0]$ |
20.2 |
\( 2^{2} \cdot 5 \) |
\( 2^{8} \cdot 5^{2} \) |
$1.25349$ |
$(a+3), (-a-4)$ |
$0$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$7.019918163$ |
1.587438723 |
\( \frac{12288}{25} a - \frac{28672}{25} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 12 a + 46\) , \( -82 a - 269\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(12a+46\right){x}-82a-269$ |
| 20.2-a2 |
20.2-a |
$2$ |
$2$ |
\(\Q(\sqrt{11}) \) |
$2$ |
$[2, 0]$ |
20.2 |
\( 2^{2} \cdot 5 \) |
\( 2^{4} \cdot 5 \) |
$1.25349$ |
$(a+3), (-a-4)$ |
$0$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 3 \) |
$1$ |
$14.03983632$ |
1.587438723 |
\( -\frac{9052192}{5} a + \frac{30047888}{5} \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( a - 13\) , \( 7 a - 28\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(a-13\right){x}+7a-28$ |
| 20.2-b1 |
20.2-b |
$2$ |
$2$ |
\(\Q(\sqrt{11}) \) |
$2$ |
$[2, 0]$ |
20.2 |
\( 2^{2} \cdot 5 \) |
\( 2^{8} \cdot 5^{2} \) |
$1.25349$ |
$(a+3), (-a-4)$ |
$0$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$24.21146987$ |
1.825008208 |
\( \frac{12288}{25} a - \frac{28672}{25} \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( 12 a + 46\) , \( 82 a + 269\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(12a+46\right){x}+82a+269$ |
| 20.2-b2 |
20.2-b |
$2$ |
$2$ |
\(\Q(\sqrt{11}) \) |
$2$ |
$[2, 0]$ |
20.2 |
\( 2^{2} \cdot 5 \) |
\( 2^{4} \cdot 5 \) |
$1.25349$ |
$(a+3), (-a-4)$ |
$0$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$48.42293974$ |
1.825008208 |
\( -\frac{9052192}{5} a + \frac{30047888}{5} \) |
\( \bigl[a + 1\) , \( 1\) , \( a + 1\) , \( 3 a - 9\) , \( -2 a + 8\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(3a-9\right){x}-2a+8$ |
| 25.1-a1 |
25.1-a |
$4$ |
$6$ |
\(\Q(\sqrt{11}) \) |
$2$ |
$[2, 0]$ |
25.1 |
\( 5^{2} \) |
\( 5^{3} \) |
$1.32541$ |
$(a-4), (-a-4)$ |
$0$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$1$ |
$20.40849255$ |
1.538348007 |
\( -\frac{1889792}{25} a + \frac{6312128}{25} \) |
\( \bigl[a + 1\) , \( 0\) , \( a\) , \( -2 a - 10\) , \( -4 a - 16\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(-2a-10\right){x}-4a-16$ |
| 25.1-a2 |
25.1-a |
$4$ |
$6$ |
\(\Q(\sqrt{11}) \) |
$2$ |
$[2, 0]$ |
25.1 |
\( 5^{2} \) |
\( 5^{9} \) |
$1.32541$ |
$(a-4), (-a-4)$ |
$0$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$1$ |
$20.40849255$ |
1.538348007 |
\( -\frac{161632821248}{15625} a + \frac{536216861888}{15625} \) |
\( \bigl[a + 1\) , \( -a\) , \( a\) , \( 126 a - 425\) , \( -1231 a + 4080\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}-a{x}^{2}+\left(126a-425\right){x}-1231a+4080$ |
| 25.1-a3 |
25.1-a |
$4$ |
$6$ |
\(\Q(\sqrt{11}) \) |
$2$ |
$[2, 0]$ |
25.1 |
\( 5^{2} \) |
\( 5^{3} \) |
$1.32541$ |
$(a-4), (-a-4)$ |
$0$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$1$ |
$20.40849255$ |
1.538348007 |
\( \frac{1889792}{25} a + \frac{6312128}{25} \) |
\( \bigl[a + 1\) , \( -a\) , \( a\) , \( a - 10\) , \( 4 a - 16\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}-a{x}^{2}+\left(a-10\right){x}+4a-16$ |
| 25.1-a4 |
25.1-a |
$4$ |
$6$ |
\(\Q(\sqrt{11}) \) |
$2$ |
$[2, 0]$ |
25.1 |
\( 5^{2} \) |
\( 5^{9} \) |
$1.32541$ |
$(a-4), (-a-4)$ |
$0$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$1$ |
$20.40849255$ |
1.538348007 |
\( \frac{161632821248}{15625} a + \frac{536216861888}{15625} \) |
\( \bigl[a + 1\) , \( 0\) , \( a\) , \( -127 a - 425\) , \( 1231 a + 4080\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(-127a-425\right){x}+1231a+4080$ |
| 25.1-b1 |
25.1-b |
$4$ |
$6$ |
\(\Q(\sqrt{11}) \) |
$2$ |
$[2, 0]$ |
25.1 |
\( 5^{2} \) |
\( 5^{3} \) |
$1.32541$ |
$(a-4), (-a-4)$ |
$0$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2 \) |
$1$ |
$44.54190593$ |
0.373052498 |
\( -\frac{1889792}{25} a + \frac{6312128}{25} \) |
\( \bigl[a + 1\) , \( -a\) , \( 1\) , \( -4 a - 5\) , \( -a\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}-a{x}^{2}+\left(-4a-5\right){x}-a$ |
| 25.1-b2 |
25.1-b |
$4$ |
$6$ |
\(\Q(\sqrt{11}) \) |
$2$ |
$[2, 0]$ |
25.1 |
\( 5^{2} \) |
\( 5^{9} \) |
$1.32541$ |
$(a-4), (-a-4)$ |
$0$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2 \) |
$1$ |
$4.949100658$ |
0.373052498 |
\( -\frac{161632821248}{15625} a + \frac{536216861888}{15625} \) |
\( \bigl[a + 1\) , \( 0\) , \( 1\) , \( 128 a - 420\) , \( 1486 a - 4926\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(128a-420\right){x}+1486a-4926$ |
| 25.1-b3 |
25.1-b |
$4$ |
$6$ |
\(\Q(\sqrt{11}) \) |
$2$ |
$[2, 0]$ |
25.1 |
\( 5^{2} \) |
\( 5^{3} \) |
$1.32541$ |
$(a-4), (-a-4)$ |
$0$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2 \) |
$1$ |
$44.54190593$ |
0.373052498 |
\( \frac{1889792}{25} a + \frac{6312128}{25} \) |
\( \bigl[a + 1\) , \( 0\) , \( 1\) , \( 3 a - 5\) , \( a\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(3a-5\right){x}+a$ |
| 25.1-b4 |
25.1-b |
$4$ |
$6$ |
\(\Q(\sqrt{11}) \) |
$2$ |
$[2, 0]$ |
25.1 |
\( 5^{2} \) |
\( 5^{9} \) |
$1.32541$ |
$(a-4), (-a-4)$ |
$0$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2 \) |
$1$ |
$4.949100658$ |
0.373052498 |
\( \frac{161632821248}{15625} a + \frac{536216861888}{15625} \) |
\( \bigl[a + 1\) , \( -a\) , \( 1\) , \( -129 a - 420\) , \( -1486 a - 4926\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}-a{x}^{2}+\left(-129a-420\right){x}-1486a-4926$ |
| 25.2-a1 |
25.2-a |
$2$ |
$11$ |
\(\Q(\sqrt{11}) \) |
$2$ |
$[2, 0]$ |
25.2 |
\( 5^{2} \) |
\( 5^{6} \) |
$1.32541$ |
$(a-4)$ |
$0$ |
$\mathsf{trivial}$ |
$\textsf{potential}$ |
$-11$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 1 \) |
$1$ |
$10.31419920$ |
1.554924035 |
\( -32768 \) |
\( \bigl[0\) , \( -a - 1\) , \( 1\) , \( 6 a - 14\) , \( -9 a + 27\bigr] \) |
${y}^2+{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(6a-14\right){x}-9a+27$ |
| 25.2-a2 |
25.2-a |
$2$ |
$11$ |
\(\Q(\sqrt{11}) \) |
$2$ |
$[2, 0]$ |
25.2 |
\( 5^{2} \) |
\( 5^{6} \) |
$1.32541$ |
$(a-4)$ |
$0$ |
$\mathsf{trivial}$ |
$\textsf{potential}$ |
$-11$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 1 \) |
$1$ |
$10.31419920$ |
1.554924035 |
\( -32768 \) |
\( \bigl[0\) , \( a + 1\) , \( a\) , \( 6 a - 14\) , \( 9 a - 30\bigr] \) |
${y}^2+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(6a-14\right){x}+9a-30$ |
| 25.2-b1 |
25.2-b |
$2$ |
$2$ |
\(\Q(\sqrt{11}) \) |
$2$ |
$[2, 0]$ |
25.2 |
\( 5^{2} \) |
\( 5^{9} \) |
$1.32541$ |
$(a-4)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2 \) |
$1.282876014$ |
$8.224640586$ |
1.590652365 |
\( 1728 \) |
\( \bigl[a + 1\) , \( a\) , \( a\) , \( 2 a + 9\) , \( 4 a + 7\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+a{x}^{2}+\left(2a+9\right){x}+4a+7$ |
| 25.2-b2 |
25.2-b |
$2$ |
$2$ |
\(\Q(\sqrt{11}) \) |
$2$ |
$[2, 0]$ |
25.2 |
\( 5^{2} \) |
\( 5^{9} \) |
$1.32541$ |
$(a-4)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2 \) |
$0.641438007$ |
$16.44928117$ |
1.590652365 |
\( 1728 \) |
\( \bigl[a + 1\) , \( a\) , \( 1\) , \( -93 a - 306\) , \( -251 a - 833\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+a{x}^{2}+\left(-93a-306\right){x}-251a-833$ |
| 25.3-a1 |
25.3-a |
$2$ |
$11$ |
\(\Q(\sqrt{11}) \) |
$2$ |
$[2, 0]$ |
25.3 |
\( 5^{2} \) |
\( 5^{6} \) |
$1.32541$ |
$(-a-4)$ |
$0$ |
$\mathsf{trivial}$ |
$\textsf{potential}$ |
$-11$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 1 \) |
$1$ |
$10.31419920$ |
1.554924035 |
\( -32768 \) |
\( \bigl[0\) , \( a - 1\) , \( 1\) , \( -6 a - 14\) , \( 9 a + 27\bigr] \) |
${y}^2+{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-6a-14\right){x}+9a+27$ |
| 25.3-a2 |
25.3-a |
$2$ |
$11$ |
\(\Q(\sqrt{11}) \) |
$2$ |
$[2, 0]$ |
25.3 |
\( 5^{2} \) |
\( 5^{6} \) |
$1.32541$ |
$(-a-4)$ |
$0$ |
$\mathsf{trivial}$ |
$\textsf{potential}$ |
$-11$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 1 \) |
$1$ |
$10.31419920$ |
1.554924035 |
\( -32768 \) |
\( \bigl[0\) , \( -a + 1\) , \( a\) , \( -6 a - 14\) , \( -9 a - 30\bigr] \) |
${y}^2+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-6a-14\right){x}-9a-30$ |
| 25.3-b1 |
25.3-b |
$2$ |
$2$ |
\(\Q(\sqrt{11}) \) |
$2$ |
$[2, 0]$ |
25.3 |
\( 5^{2} \) |
\( 5^{9} \) |
$1.32541$ |
$(-a-4)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2 \) |
$0.641438007$ |
$16.44928117$ |
1.590652365 |
\( 1728 \) |
\( \bigl[a + 1\) , \( a\) , \( a\) , \( 98 a - 311\) , \( -60 a + 215\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+a{x}^{2}+\left(98a-311\right){x}-60a+215$ |
| 25.3-b2 |
25.3-b |
$2$ |
$2$ |
\(\Q(\sqrt{11}) \) |
$2$ |
$[2, 0]$ |
25.3 |
\( 5^{2} \) |
\( 5^{9} \) |
$1.32541$ |
$(-a-4)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2 \) |
$1.282876014$ |
$8.224640586$ |
1.590652365 |
\( 1728 \) |
\( \bigl[a + 1\) , \( a\) , \( 1\) , \( 3 a + 14\) , \( 5 a + 15\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+a{x}^{2}+\left(3a+14\right){x}+5a+15$ |
*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.
