| 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 |
| 47432.2-a1 |
47432.2-a |
$2$ |
$2$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
47432.2 |
\( 2^{3} \cdot 7^{2} \cdot 11^{2} \) |
\( 2^{8} \cdot 7^{8} \cdot 11^{7} \) |
$3.48904$ |
$(a), (-2a+1), (-2a+3), (2a+1)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \cdot 3 \) |
$0.114635797$ |
$0.589689563$ |
4.905642647 |
\( \frac{2644802317}{12400927} a - \frac{298783506}{1771561} \) |
\( \bigl[a\) , \( 1\) , \( a\) , \( 54 a - 1\) , \( 387 a + 213\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}+\left(54a-1\right){x}+387a+213$ |
| 47432.2-a2 |
47432.2-a |
$2$ |
$2$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
47432.2 |
\( 2^{3} \cdot 7^{2} \cdot 11^{2} \) |
\( 2^{4} \cdot 7^{7} \cdot 11^{5} \) |
$3.48904$ |
$(a), (-2a+1), (-2a+3), (2a+1)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \cdot 3 \) |
$0.114635797$ |
$1.179379127$ |
4.905642647 |
\( -\frac{55773887}{9317} a + \frac{70287578}{9317} \) |
\( \bigl[a\) , \( 1\) , \( a\) , \( -16 a - 36\) , \( 44 a + 80\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}+\left(-16a-36\right){x}+44a+80$ |
| 47432.2-b1 |
47432.2-b |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
47432.2 |
\( 2^{3} \cdot 7^{2} \cdot 11^{2} \) |
\( 2^{10} \cdot 7^{7} \cdot 11^{14} \) |
$3.48904$ |
$(a), (-2a+1), (-2a+3), (2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$3.345718635$ |
$0.152083906$ |
3.077114361 |
\( \frac{7682576172708501}{21968998637047} a + \frac{3783710208788366}{21968998637047} \) |
\( \bigl[a\) , \( -1\) , \( a\) , \( 329 a - 1531\) , \( -11921 a - 22893\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(329a-1531\right){x}-11921a-22893$ |
| 47432.2-b2 |
47432.2-b |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
47432.2 |
\( 2^{3} \cdot 7^{2} \cdot 11^{2} \) |
\( 2^{10} \cdot 7^{10} \cdot 11^{11} \) |
$3.48904$ |
$(a), (-2a+1), (-2a+3), (2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$3.345718635$ |
$0.152083906$ |
3.077114361 |
\( \frac{71704185617021}{10503585169} a + \frac{49079299276110}{10503585169} \) |
\( \bigl[a\) , \( -1\) , \( a\) , \( -1001 a + 3369\) , \( 41643 a + 14291\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(-1001a+3369\right){x}+41643a+14291$ |
| 47432.2-b3 |
47432.2-b |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
47432.2 |
\( 2^{3} \cdot 7^{2} \cdot 11^{2} \) |
\( 2^{8} \cdot 7^{8} \cdot 11^{10} \) |
$3.48904$ |
$(a), (-2a+1), (-2a+3), (2a+1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{6} \) |
$1.672859317$ |
$0.304167812$ |
3.077114361 |
\( -\frac{28190263653}{12400927} a + \frac{60782002478}{12400927} \) |
\( \bigl[a\) , \( -1\) , \( a\) , \( -336 a + 639\) , \( -973 a - 4945\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(-336a+639\right){x}-973a-4945$ |
| 47432.2-b4 |
47432.2-b |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
47432.2 |
\( 2^{3} \cdot 7^{2} \cdot 11^{2} \) |
\( 2^{4} \cdot 7^{7} \cdot 11^{5} \) |
$3.48904$ |
$(a), (-2a+1), (-2a+3), (2a+1)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$3.345718635$ |
$0.608335625$ |
3.077114361 |
\( -\frac{128026038127}{9317} a + \frac{61049031418}{9317} \) |
\( \bigl[a\) , \( -1\) , \( a\) , \( -336 a + 604\) , \( -1470 a - 4952\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(-336a+604\right){x}-1470a-4952$ |
| 47432.2-c1 |
47432.2-c |
$1$ |
$1$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
47432.2 |
\( 2^{3} \cdot 7^{2} \cdot 11^{2} \) |
\( 2^{11} \cdot 7^{8} \cdot 11^{3} \) |
$3.48904$ |
$(a), (-2a+1), (-2a+3), (2a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2 \) |
$1$ |
$1.093435997$ |
1.653119841 |
\( -\frac{63014}{121} a + \frac{114562}{121} \) |
\( \bigl[0\) , \( -a + 1\) , \( a\) , \( 16 a + 16\) , \( -66 a + 63\bigr] \) |
${y}^2+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(16a+16\right){x}-66a+63$ |
| 47432.2-d1 |
47432.2-d |
$1$ |
$1$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
47432.2 |
\( 2^{3} \cdot 7^{2} \cdot 11^{2} \) |
\( 2^{8} \cdot 7^{6} \cdot 11^{2} \) |
$3.48904$ |
$(a), (-2a+1), (-2a+3), (2a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2^{3} \) |
$0.173511834$ |
$1.972089999$ |
4.138631791 |
\( -\frac{93184}{11} a + \frac{91136}{11} \) |
\( \bigl[0\) , \( a\) , \( a\) , \( -9 a - 10\) , \( 13 a + 13\bigr] \) |
${y}^2+a{y}={x}^{3}+a{x}^{2}+\left(-9a-10\right){x}+13a+13$ |
| 47432.2-e1 |
47432.2-e |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
47432.2 |
\( 2^{3} \cdot 7^{2} \cdot 11^{2} \) |
\( 2^{10} \cdot 7^{7} \cdot 11^{2} \) |
$3.48904$ |
$(a), (-2a+1), (-2a+3), (2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$1.066286788$ |
1.612074097 |
\( \frac{38575149}{77} a - \frac{59957858}{77} \) |
\( \bigl[a\) , \( -a + 1\) , \( a\) , \( -92 a - 13\) , \( 464 a - 335\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-92a-13\right){x}+464a-335$ |
| 47432.2-e2 |
47432.2-e |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
47432.2 |
\( 2^{3} \cdot 7^{2} \cdot 11^{2} \) |
\( 2^{4} \cdot 7^{7} \cdot 11^{5} \) |
$3.48904$ |
$(a), (-2a+1), (-2a+3), (2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$1.066286788$ |
1.612074097 |
\( -\frac{18158053}{102487} a - \frac{4183990914}{102487} \) |
\( \bigl[a\) , \( -a\) , \( 0\) , \( 56 a - 63\) , \( -224 a + 112\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-a{x}^{2}+\left(56a-63\right){x}-224a+112$ |
| 47432.2-e3 |
47432.2-e |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
47432.2 |
\( 2^{3} \cdot 7^{2} \cdot 11^{2} \) |
\( 2^{8} \cdot 7^{8} \cdot 11^{4} \) |
$3.48904$ |
$(a), (-2a+1), (-2a+3), (2a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$1$ |
$1.066286788$ |
1.612074097 |
\( -\frac{3477}{7} a + \frac{411230}{847} \) |
\( \bigl[a\) , \( 0\) , \( a\) , \( -8 a + 34\) , \( 28 a + 79\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-8a+34\right){x}+28a+79$ |
| 47432.2-e4 |
47432.2-e |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
47432.2 |
\( 2^{3} \cdot 7^{2} \cdot 11^{2} \) |
\( 2^{10} \cdot 7^{10} \cdot 11^{5} \) |
$3.48904$ |
$(a), (-2a+1), (-2a+3), (2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$0.533143394$ |
1.612074097 |
\( \frac{1947114319}{717409} a + \frac{952108826}{717409} \) |
\( \bigl[a\) , \( 0\) , \( a\) , \( -43 a - 176\) , \( 434 a + 667\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-43a-176\right){x}+434a+667$ |
| 47432.2-f1 |
47432.2-f |
$2$ |
$2$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
47432.2 |
\( 2^{3} \cdot 7^{2} \cdot 11^{2} \) |
\( 2^{8} \cdot 7^{3} \cdot 11^{5} \) |
$3.48904$ |
$(a), (-2a+1), (-2a+3), (2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$0.895554797$ |
$1.157104187$ |
6.266652210 |
\( \frac{1828928779}{1331} a - \frac{2081130034}{1331} \) |
\( \bigl[a\) , \( 0\) , \( a\) , \( -48 a + 138\) , \( -296 a - 249\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-48a+138\right){x}-296a-249$ |
| 47432.2-f2 |
47432.2-f |
$2$ |
$2$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
47432.2 |
\( 2^{3} \cdot 7^{2} \cdot 11^{2} \) |
\( 2^{10} \cdot 7^{3} \cdot 11^{7} \) |
$3.48904$ |
$(a), (-2a+1), (-2a+3), (2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1.791109595$ |
$1.157104187$ |
6.266652210 |
\( \frac{1441308793}{1771561} a + \frac{2057331390}{1771561} \) |
\( \bigl[a\) , \( -a + 1\) , \( a\) , \( -24 a - 5\) , \( -36 a + 41\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-24a-5\right){x}-36a+41$ |
*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.
