| 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-a1 |
7.2-a |
$4$ |
$10$ |
\(\Q(\sqrt{29}) \) |
$2$ |
$[2, 0]$ |
7.2 |
\( 7 \) |
\( - 7^{2} \) |
$0.78273$ |
$(a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B |
$1$ |
\( 2 \) |
$1$ |
$10.14490966$ |
0.941931215 |
\( -\frac{213433415640625}{49} a + \frac{97343395248346}{7} \) |
\( \bigl[1\) , \( -a - 1\) , \( 0\) , \( -27\) , \( -15 a + 10\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(-a-1\right){x}^{2}-27{x}-15a+10$ |
| 49.3-d1 |
49.3-d |
$4$ |
$10$ |
\(\Q(\sqrt{29}) \) |
$2$ |
$[2, 0]$ |
49.3 |
\( 7^{2} \) |
\( - 7^{8} \) |
$1.27317$ |
$(a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 5$ |
2B, 5B |
$1$ |
\( 2^{2} \) |
$5.989773894$ |
$0.782570221$ |
1.740863594 |
\( -\frac{213433415640625}{49} a + \frac{97343395248346}{7} \) |
\( \bigl[a\) , \( -a + 1\) , \( a\) , \( 22 a - 230\) , \( 259 a - 1669\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(22a-230\right){x}+259a-1669$ |
| 175.3-b1 |
175.3-b |
$4$ |
$10$ |
\(\Q(\sqrt{29}) \) |
$2$ |
$[2, 0]$ |
175.3 |
\( 5^{2} \cdot 7 \) |
\( - 5^{6} \cdot 7^{2} \) |
$1.75024$ |
$(-a+2), (a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 5$ |
2B, 5B |
$1$ |
\( 2^{3} \) |
$1$ |
$4.536941526$ |
1.684977782 |
\( -\frac{213433415640625}{49} a + \frac{97343395248346}{7} \) |
\( \bigl[a\) , \( a + 1\) , \( 0\) , \( -223 a - 507\) , \( -3954 a - 8640\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-223a-507\right){x}-3954a-8640$ |
| 175.5-f1 |
175.5-f |
$4$ |
$10$ |
\(\Q(\sqrt{29}) \) |
$2$ |
$[2, 0]$ |
175.5 |
\( 5^{2} \cdot 7 \) |
\( - 5^{6} \cdot 7^{2} \) |
$1.75024$ |
$(-a-1), (a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 5$ |
2B, 5B |
$1$ |
\( 2^{3} \) |
$0.874921159$ |
$4.536941526$ |
2.948445428 |
\( -\frac{213433415640625}{49} a + \frac{97343395248346}{7} \) |
\( \bigl[a + 1\) , \( -1\) , \( a\) , \( 193 a - 640\) , \( -2528 a + 8005\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}-{x}^{2}+\left(193a-640\right){x}-2528a+8005$ |
| 343.1-c1 |
343.1-c |
$4$ |
$10$ |
\(\Q(\sqrt{29}) \) |
$2$ |
$[2, 0]$ |
343.1 |
\( 7^{3} \) |
\( - 7^{8} \) |
$2.07091$ |
$(-a), (a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 5$ |
2B, 5B |
$1$ |
\( 2^{2} \) |
$1$ |
$11.00716084$ |
2.043978456 |
\( -\frac{213433415640625}{49} a + \frac{97343395248346}{7} \) |
\( \bigl[a + 1\) , \( a - 1\) , \( 0\) , \( -34 a - 205\) , \( 206 a + 1168\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-34a-205\right){x}+206a+1168$ |
| 567.2-b1 |
567.2-b |
$4$ |
$10$ |
\(\Q(\sqrt{29}) \) |
$2$ |
$[2, 0]$ |
567.2 |
\( 3^{4} \cdot 7 \) |
\( - 3^{12} \cdot 7^{2} \) |
$2.34819$ |
$(a-1), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 5$ |
2B, 5B |
$1$ |
\( 2^{2} \) |
$1$ |
$1.981195039$ |
0.367898682 |
\( -\frac{213433415640625}{49} a + \frac{97343395248346}{7} \) |
\( \bigl[1\) , \( -1\) , \( a + 1\) , \( -8 a - 266\) , \( 673 a + 23\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(-8a-266\right){x}+673a+23$ |
*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.
