| 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 |
| 29241.1-a1 |
29241.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
29241.1 |
\( 3^{4} \cdot 19^{2} \) |
\( 3^{14} \cdot 19^{8} \) |
$2.33704$ |
$(3), (19)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$4$ |
\( 2^{4} \) |
$1$ |
$0.544114833$ |
2.176459332 |
\( \frac{67419143}{390963} \) |
\( \bigl[i\) , \( 1\) , \( i\) , \( 77\) , \( 790\bigr] \) |
${y}^2+i{x}{y}+i{y}={x}^{3}+{x}^{2}+77{x}+790$ |
| 29241.1-a2 |
29241.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
29241.1 |
\( 3^{4} \cdot 19^{2} \) |
\( 3^{14} \cdot 19^{2} \) |
$2.33704$ |
$(3), (19)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$4$ |
\( 2^{2} \) |
$1$ |
$2.176459332$ |
2.176459332 |
\( \frac{389017}{57} \) |
\( \bigl[i\) , \( 1\) , \( i\) , \( -13\) , \( -20\bigr] \) |
${y}^2+i{x}{y}+i{y}={x}^{3}+{x}^{2}-13{x}-20$ |
| 29241.1-a3 |
29241.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
29241.1 |
\( 3^{4} \cdot 19^{2} \) |
\( 3^{16} \cdot 19^{4} \) |
$2.33704$ |
$(3), (19)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$4$ |
\( 2^{3} \) |
$1$ |
$1.088229666$ |
2.176459332 |
\( \frac{30664297}{3249} \) |
\( \bigl[i\) , \( 1\) , \( i\) , \( -58\) , \( 142\bigr] \) |
${y}^2+i{x}{y}+i{y}={x}^{3}+{x}^{2}-58{x}+142$ |
| 29241.1-a4 |
29241.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
29241.1 |
\( 3^{4} \cdot 19^{2} \) |
\( 3^{20} \cdot 19^{2} \) |
$2.33704$ |
$(3), (19)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$4$ |
\( 2^{2} \) |
$1$ |
$0.544114833$ |
2.176459332 |
\( \frac{115714886617}{1539} \) |
\( \bigl[i\) , \( 1\) , \( i\) , \( -913\) , \( 10402\bigr] \) |
${y}^2+i{x}{y}+i{y}={x}^{3}+{x}^{2}-913{x}+10402$ |
| 29241.1-b1 |
29241.1-b |
$3$ |
$9$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
29241.1 |
\( 3^{4} \cdot 19^{2} \) |
\( 3^{12} \cdot 19^{2} \) |
$2.33704$ |
$(3), (19)$ |
$2$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$3$ |
3B.1.1 |
$1$ |
\( 2^{2} \) |
$5.606459454$ |
$0.311769669$ |
3.107420464 |
\( -\frac{50357871050752}{19} \) |
\( \bigl[0\) , \( 0\) , \( i\) , \( -6924\) , \( -221760\bigr] \) |
${y}^2+i{y}={x}^{3}-6924{x}-221760$ |
| 29241.1-b2 |
29241.1-b |
$3$ |
$9$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
29241.1 |
\( 3^{4} \cdot 19^{2} \) |
\( 3^{12} \cdot 19^{6} \) |
$2.33704$ |
$(3), (19)$ |
$2$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$3$ |
3Cs.1.1 |
$1$ |
\( 2^{2} \cdot 3 \) |
$0.622939939$ |
$0.935309008$ |
3.107420464 |
\( -\frac{89915392}{6859} \) |
\( \bigl[0\) , \( 0\) , \( i\) , \( -84\) , \( -315\bigr] \) |
${y}^2+i{y}={x}^{3}-84{x}-315$ |
| 29241.1-b3 |
29241.1-b |
$3$ |
$9$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
29241.1 |
\( 3^{4} \cdot 19^{2} \) |
\( 3^{12} \cdot 19^{2} \) |
$2.33704$ |
$(3), (19)$ |
$2$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$3$ |
3B.1.2 |
$1$ |
\( 2^{2} \) |
$0.069215548$ |
$2.805927025$ |
3.107420464 |
\( \frac{32768}{19} \) |
\( \bigl[0\) , \( 0\) , \( i\) , \( 6\) , \( 0\bigr] \) |
${y}^2+i{y}={x}^{3}+6{x}$ |
| 29241.1-c1 |
29241.1-c |
$2$ |
$5$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
29241.1 |
\( 3^{4} \cdot 19^{2} \) |
\( 3^{16} \cdot 19^{10} \) |
$2.33704$ |
$(3), (19)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$5$ |
5B.4.2 |
$1$ |
\( 2^{2} \cdot 5 \) |
$1$ |
$0.090588610$ |
1.811772200 |
\( -\frac{9358714467168256}{22284891} \) |
\( \bigl[0\) , \( 0\) , \( 1\) , \( -39513\) , \( 3023145\bigr] \) |
${y}^2+{y}={x}^{3}-39513{x}+3023145$ |
| 29241.1-c2 |
29241.1-c |
$2$ |
$5$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
29241.1 |
\( 3^{4} \cdot 19^{2} \) |
\( 3^{32} \cdot 19^{2} \) |
$2.33704$ |
$(3), (19)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$5$ |
5B.4.1 |
$1$ |
\( 2^{2} \) |
$1$ |
$0.452943050$ |
1.811772200 |
\( \frac{841232384}{1121931} \) |
\( \bigl[0\) , \( 0\) , \( i\) , \( 177\) , \( -1035\bigr] \) |
${y}^2+i{y}={x}^{3}+177{x}-1035$ |
| 29241.1-d1 |
29241.1-d |
$1$ |
$1$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
29241.1 |
\( 3^{4} \cdot 19^{2} \) |
\( 3^{16} \cdot 19^{2} \) |
$2.33704$ |
$(3), (19)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
|
|
$1$ |
\( 2^{2} \) |
$1$ |
$1.776214705$ |
7.104858821 |
\( -\frac{1404928}{171} \) |
\( \bigl[0\) , \( 0\) , \( i\) , \( -21\) , \( 41\bigr] \) |
${y}^2+i{y}={x}^{3}-21{x}+41$ |
*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.
