| 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 |
| 7.2-a3 |
7.2-a |
$4$ |
$10$ |
\(\Q(\sqrt{29}) \) |
$2$ |
$[2, 0]$ |
7.2 |
\( 7 \) |
\( - 7^{5} \) |
$0.78273$ |
$(a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B |
$1$ |
\( 1 \) |
$1$ |
$20.28981932$ |
0.941931215 |
\( \frac{173650213}{16807} a + \frac{58516320}{2401} \) |
\( \bigl[a\) , \( -1\) , \( 0\) , \( -a + 3\) , \( 0\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-{x}^{2}+\left(-a+3\right){x}$ |
| 49.3-d3 |
49.3-d |
$4$ |
$10$ |
\(\Q(\sqrt{29}) \) |
$2$ |
$[2, 0]$ |
49.3 |
\( 7^{2} \) |
\( - 7^{11} \) |
$1.27317$ |
$(a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 5$ |
2B, 5B |
$1$ |
\( 2^{2} \) |
$0.598977389$ |
$7.825702212$ |
1.740863594 |
\( \frac{173650213}{16807} a + \frac{58516320}{2401} \) |
\( \bigl[a + 1\) , \( -1\) , \( 0\) , \( -10 a + 31\) , \( 0\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}-{x}^{2}+\left(-10a+31\right){x}$ |
| 175.3-b3 |
175.3-b |
$4$ |
$10$ |
\(\Q(\sqrt{29}) \) |
$2$ |
$[2, 0]$ |
175.3 |
\( 5^{2} \cdot 7 \) |
\( - 5^{6} \cdot 7^{5} \) |
$1.75024$ |
$(-a+2), (a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 5$ |
2B, 5B |
$1$ |
\( 2^{2} \) |
$1$ |
$9.073883053$ |
1.684977782 |
\( \frac{173650213}{16807} a + \frac{58516320}{2401} \) |
\( \bigl[a + 1\) , \( a - 1\) , \( a + 1\) , \( -7 a - 10\) , \( 3 a + 2\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-7a-10\right){x}+3a+2$ |
| 175.5-f3 |
175.5-f |
$4$ |
$10$ |
\(\Q(\sqrt{29}) \) |
$2$ |
$[2, 0]$ |
175.5 |
\( 5^{2} \cdot 7 \) |
\( - 5^{6} \cdot 7^{5} \) |
$1.75024$ |
$(-a-1), (a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 5$ |
2B, 5B |
$1$ |
\( 2 \cdot 5 \) |
$0.349968463$ |
$9.073883053$ |
2.948445428 |
\( \frac{173650213}{16807} a + \frac{58516320}{2401} \) |
\( \bigl[1\) , \( 1\) , \( 0\) , \( -37 a + 118\) , \( 0\bigr] \) |
${y}^2+{x}{y}={x}^{3}+{x}^{2}+\left(-37a+118\right){x}$ |
| 343.1-c3 |
343.1-c |
$4$ |
$10$ |
\(\Q(\sqrt{29}) \) |
$2$ |
$[2, 0]$ |
343.1 |
\( 7^{3} \) |
\( - 7^{11} \) |
$2.07091$ |
$(-a), (a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 5$ |
2B, 5B |
$1$ |
\( 2 \cdot 5 \) |
$1$ |
$4.402864339$ |
2.043978456 |
\( \frac{173650213}{16807} a + \frac{58516320}{2401} \) |
\( \bigl[1\) , \( -a + 1\) , \( 1\) , \( -7 a + 13\) , \( -6 a + 13\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-7a+13\right){x}-6a+13$ |
| 567.2-b3 |
567.2-b |
$4$ |
$10$ |
\(\Q(\sqrt{29}) \) |
$2$ |
$[2, 0]$ |
567.2 |
\( 3^{4} \cdot 7 \) |
\( - 3^{12} \cdot 7^{5} \) |
$2.34819$ |
$(a-1), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 5$ |
2B, 5B |
$1$ |
\( 2 \) |
$1$ |
$3.962390079$ |
0.367898682 |
\( \frac{173650213}{16807} a + \frac{58516320}{2401} \) |
\( \bigl[a\) , \( -a - 1\) , \( a\) , \( -11 a + 22\) , \( -10 a + 24\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-11a+22\right){x}-10a+24$ |
*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.
