| 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 |
| 7.1-a4 |
7.1-a |
$4$ |
$10$ |
\(\Q(\sqrt{29}) \) |
$2$ |
$[2, 0]$ |
7.1 |
\( 7 \) |
\( - 7^{2} \) |
$0.78273$ |
$(-a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B |
$1$ |
\( 2 \) |
$1$ |
$10.14490966$ |
0.941931215 |
\( \frac{213433415640625}{49} a + \frac{467970351097797}{49} \) |
\( \bigl[1\) , \( a + 1\) , \( 1\) , \( 2 a - 28\) , \( 16 a - 33\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(2a-28\right){x}+16a-33$ |
| 49.2-d4 |
49.2-d |
$4$ |
$10$ |
\(\Q(\sqrt{29}) \) |
$2$ |
$[2, 0]$ |
49.2 |
\( 7^{2} \) |
\( - 7^{8} \) |
$1.27317$ |
$(-a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 5$ |
2B, 5B |
$1$ |
\( 2^{2} \) |
$5.989773894$ |
$0.782570221$ |
1.740863594 |
\( \frac{213433415640625}{49} a + \frac{467970351097797}{49} \) |
\( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( -24 a - 208\) , \( -260 a - 1410\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-24a-208\right){x}-260a-1410$ |
| 175.4-f4 |
175.4-f |
$4$ |
$10$ |
\(\Q(\sqrt{29}) \) |
$2$ |
$[2, 0]$ |
175.4 |
\( 5^{2} \cdot 7 \) |
\( - 5^{6} \cdot 7^{2} \) |
$1.75024$ |
$(-a+2), (-a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 5$ |
2B, 5B |
$1$ |
\( 2^{3} \) |
$0.874921159$ |
$4.536941526$ |
2.948445428 |
\( \frac{213433415640625}{49} a + \frac{467970351097797}{49} \) |
\( \bigl[a\) , \( -a\) , \( a + 1\) , \( -195 a - 446\) , \( 2527 a + 5477\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(-195a-446\right){x}+2527a+5477$ |
| 175.6-b4 |
175.6-b |
$4$ |
$10$ |
\(\Q(\sqrt{29}) \) |
$2$ |
$[2, 0]$ |
175.6 |
\( 5^{2} \cdot 7 \) |
\( - 5^{6} \cdot 7^{2} \) |
$1.75024$ |
$(-a-1), (-a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 5$ |
2B, 5B |
$1$ |
\( 2^{3} \) |
$1$ |
$4.536941526$ |
1.684977782 |
\( \frac{213433415640625}{49} a + \frac{467970351097797}{49} \) |
\( \bigl[a + 1\) , \( a - 1\) , \( a\) , \( 227 a - 735\) , \( 3219 a - 10279\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(227a-735\right){x}+3219a-10279$ |
| 343.2-c4 |
343.2-c |
$4$ |
$10$ |
\(\Q(\sqrt{29}) \) |
$2$ |
$[2, 0]$ |
343.2 |
\( 7^{3} \) |
\( - 7^{8} \) |
$2.07091$ |
$(-a), (a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 5$ |
2B, 5B |
$1$ |
\( 2^{2} \) |
$1$ |
$11.00716084$ |
2.043978456 |
\( \frac{213433415640625}{49} a + \frac{467970351097797}{49} \) |
\( \bigl[a\) , \( a + 1\) , \( a + 1\) , \( 38 a - 246\) , \( -415 a + 1624\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(38a-246\right){x}-415a+1624$ |
| 567.1-b4 |
567.1-b |
$4$ |
$10$ |
\(\Q(\sqrt{29}) \) |
$2$ |
$[2, 0]$ |
567.1 |
\( 3^{4} \cdot 7 \) |
\( - 3^{12} \cdot 7^{2} \) |
$2.34819$ |
$(-a), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 5$ |
2B, 5B |
$1$ |
\( 2^{2} \) |
$1$ |
$1.981195039$ |
0.367898682 |
\( \frac{213433415640625}{49} a + \frac{467970351097797}{49} \) |
\( \bigl[1\) , \( -1\) , \( a\) , \( 7 a - 273\) , \( -674 a + 697\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(7a-273\right){x}-674a+697$ |
*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.
