| 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 |
| 29.4-a1 |
29.4-a |
$2$ |
$3$ |
\(\Q(\sqrt{5}, \sqrt{7})\) |
$4$ |
$[4, 0]$ |
29.4 |
\( 29 \) |
\( 29 \) |
$19.05752$ |
$(a-1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 1 \) |
$0.183254829$ |
$501.7034145$ |
2.626844961 |
\( \frac{5568759973}{667} a^{3} + \frac{154187636}{667} a^{2} - \frac{83217892687}{667} a - \frac{2746289531}{23} \) |
\( \bigl[-\frac{4}{23} a^{3} + \frac{6}{23} a^{2} + \frac{63}{23} a - \frac{21}{23}\) , \( -\frac{1}{23} a^{3} - \frac{10}{23} a^{2} + \frac{33}{23} a + \frac{104}{23}\) , \( -\frac{1}{23} a^{3} + \frac{13}{23} a^{2} - \frac{13}{23} a - \frac{103}{23}\) , \( -\frac{9}{23} a^{3} + \frac{25}{23} a^{2} + \frac{228}{23} a + \frac{292}{23}\) , \( -\frac{83}{23} a^{3} - \frac{186}{23} a^{2} + \frac{554}{23} a + \frac{743}{23}\bigr] \) |
${y}^2+\left(-\frac{4}{23}a^{3}+\frac{6}{23}a^{2}+\frac{63}{23}a-\frac{21}{23}\right){x}{y}+\left(-\frac{1}{23}a^{3}+\frac{13}{23}a^{2}-\frac{13}{23}a-\frac{103}{23}\right){y}={x}^{3}+\left(-\frac{1}{23}a^{3}-\frac{10}{23}a^{2}+\frac{33}{23}a+\frac{104}{23}\right){x}^{2}+\left(-\frac{9}{23}a^{3}+\frac{25}{23}a^{2}+\frac{228}{23}a+\frac{292}{23}\right){x}-\frac{83}{23}a^{3}-\frac{186}{23}a^{2}+\frac{554}{23}a+\frac{743}{23}$ |
| 29.4-a2 |
29.4-a |
$2$ |
$3$ |
\(\Q(\sqrt{5}, \sqrt{7})\) |
$4$ |
$[4, 0]$ |
29.4 |
\( 29 \) |
\( 29^{3} \) |
$19.05752$ |
$(a-1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 3 \) |
$0.061084943$ |
$501.7034145$ |
2.626844961 |
\( -\frac{12031685}{560947} a^{3} + \frac{56963125}{560947} a^{2} - \frac{2991900}{560947} a - \frac{7798921}{19343} \) |
\( \bigl[-\frac{1}{23} a^{3} + \frac{13}{23} a^{2} - \frac{13}{23} a - \frac{103}{23}\) , \( \frac{4}{23} a^{3} - \frac{6}{23} a^{2} - \frac{63}{23} a + \frac{44}{23}\) , \( -\frac{1}{23} a^{3} + \frac{13}{23} a^{2} - \frac{13}{23} a - \frac{80}{23}\) , \( -\frac{42}{23} a^{3} + \frac{247}{23} a^{2} - \frac{201}{23} a - \frac{370}{23}\) , \( -\frac{250}{23} a^{3} + \frac{1295}{23} a^{2} - \frac{398}{23} a - \frac{2474}{23}\bigr] \) |
${y}^2+\left(-\frac{1}{23}a^{3}+\frac{13}{23}a^{2}-\frac{13}{23}a-\frac{103}{23}\right){x}{y}+\left(-\frac{1}{23}a^{3}+\frac{13}{23}a^{2}-\frac{13}{23}a-\frac{80}{23}\right){y}={x}^{3}+\left(\frac{4}{23}a^{3}-\frac{6}{23}a^{2}-\frac{63}{23}a+\frac{44}{23}\right){x}^{2}+\left(-\frac{42}{23}a^{3}+\frac{247}{23}a^{2}-\frac{201}{23}a-\frac{370}{23}\right){x}-\frac{250}{23}a^{3}+\frac{1295}{23}a^{2}-\frac{398}{23}a-\frac{2474}{23}$ |
| 29.4-b1 |
29.4-b |
$2$ |
$3$ |
\(\Q(\sqrt{5}, \sqrt{7})\) |
$4$ |
$[4, 0]$ |
29.4 |
\( 29 \) |
\( 29 \) |
$19.05752$ |
$(a-1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 1 \) |
$0.527378321$ |
$217.9490740$ |
3.284046195 |
\( \frac{5568759973}{667} a^{3} + \frac{154187636}{667} a^{2} - \frac{83217892687}{667} a - \frac{2746289531}{23} \) |
\( \bigl[\frac{1}{23} a^{3} + \frac{10}{23} a^{2} - \frac{33}{23} a - \frac{58}{23}\) , \( -\frac{1}{23} a^{3} + \frac{13}{23} a^{2} - \frac{13}{23} a - \frac{126}{23}\) , \( \frac{1}{23} a^{3} + \frac{10}{23} a^{2} - \frac{33}{23} a - \frac{58}{23}\) , \( \frac{14}{23} a^{3} + \frac{48}{23} a^{2} - \frac{209}{23} a - \frac{122}{23}\) , \( \frac{70}{23} a^{3} + \frac{240}{23} a^{2} - \frac{470}{23} a - \frac{725}{23}\bigr] \) |
${y}^2+\left(\frac{1}{23}a^{3}+\frac{10}{23}a^{2}-\frac{33}{23}a-\frac{58}{23}\right){x}{y}+\left(\frac{1}{23}a^{3}+\frac{10}{23}a^{2}-\frac{33}{23}a-\frac{58}{23}\right){y}={x}^{3}+\left(-\frac{1}{23}a^{3}+\frac{13}{23}a^{2}-\frac{13}{23}a-\frac{126}{23}\right){x}^{2}+\left(\frac{14}{23}a^{3}+\frac{48}{23}a^{2}-\frac{209}{23}a-\frac{122}{23}\right){x}+\frac{70}{23}a^{3}+\frac{240}{23}a^{2}-\frac{470}{23}a-\frac{725}{23}$ |
| 29.4-b2 |
29.4-b |
$2$ |
$3$ |
\(\Q(\sqrt{5}, \sqrt{7})\) |
$4$ |
$[4, 0]$ |
29.4 |
\( 29 \) |
\( 29^{3} \) |
$19.05752$ |
$(a-1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 3 \) |
$0.175792773$ |
$217.9490740$ |
3.284046195 |
\( -\frac{12031685}{560947} a^{3} + \frac{56963125}{560947} a^{2} - \frac{2991900}{560947} a - \frac{7798921}{19343} \) |
\( \bigl[-\frac{3}{23} a^{3} + \frac{16}{23} a^{2} + \frac{30}{23} a - \frac{102}{23}\) , \( -a\) , \( 1\) , \( -\frac{43}{23} a^{3} + \frac{237}{23} a^{2} - \frac{191}{23} a - \frac{197}{23}\) , \( \frac{24}{23} a^{3} - \frac{105}{23} a^{2} - \frac{79}{23} a + \frac{379}{23}\bigr] \) |
${y}^2+\left(-\frac{3}{23}a^{3}+\frac{16}{23}a^{2}+\frac{30}{23}a-\frac{102}{23}\right){x}{y}+{y}={x}^{3}-a{x}^{2}+\left(-\frac{43}{23}a^{3}+\frac{237}{23}a^{2}-\frac{191}{23}a-\frac{197}{23}\right){x}+\frac{24}{23}a^{3}-\frac{105}{23}a^{2}-\frac{79}{23}a+\frac{379}{23}$ |
*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.
