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 |
134199.7-a1 |
134199.7-a |
$4$ |
$4$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
134199.7 |
\( 3^{2} \cdot 13 \cdot 31 \cdot 37 \) |
\( 3^{7} \cdot 13^{2} \cdot 31 \cdot 37 \) |
$2.96235$ |
$(-2a+1), (4a-3), (6a-5), (-7a+4)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1.181400004$ |
$1.743707208$ |
2.378701242 |
\( \frac{3074077600}{581529} a - \frac{339172305263}{581529} \) |
\( \bigl[1\) , \( a\) , \( a + 1\) , \( -55 a + 26\) , \( 91 a - 120\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(-55a+26\right){x}+91a-120$ |
134199.7-a2 |
134199.7-a |
$4$ |
$4$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
134199.7 |
\( 3^{2} \cdot 13 \cdot 31 \cdot 37 \) |
\( 3^{10} \cdot 13^{8} \cdot 31 \cdot 37 \) |
$2.96235$ |
$(-2a+1), (4a-3), (6a-5), (-7a+4)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1.181400004$ |
$0.435926802$ |
2.378701242 |
\( \frac{38041716070089006}{935643136987} a - \frac{750025198610512667}{8420788232883} \) |
\( \bigl[1\) , \( a\) , \( a + 1\) , \( -385 a + 626\) , \( 3265 a + 2700\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(-385a+626\right){x}+3265a+2700$ |
134199.7-a3 |
134199.7-a |
$4$ |
$4$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
134199.7 |
\( 3^{2} \cdot 13 \cdot 31 \cdot 37 \) |
\( 3^{8} \cdot 13^{4} \cdot 31^{2} \cdot 37^{2} \) |
$2.96235$ |
$(-2a+1), (4a-3), (6a-5), (-7a+4)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$0.590700002$ |
$0.871853604$ |
2.378701242 |
\( -\frac{21975427845360}{37575108649} a + \frac{112219616857967}{112725325947} \) |
\( \bigl[1\) , \( a\) , \( a + 1\) , \( -55 a + 41\) , \( 166 a - 96\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(-55a+41\right){x}+166a-96$ |
134199.7-a4 |
134199.7-a |
$4$ |
$4$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
134199.7 |
\( 3^{2} \cdot 13 \cdot 31 \cdot 37 \) |
\( 3^{7} \cdot 13^{2} \cdot 31^{4} \cdot 37^{4} \) |
$2.96235$ |
$(-2a+1), (4a-3), (6a-5), (-7a+4)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$0.295350001$ |
$0.435926802$ |
2.378701242 |
\( \frac{1669618709134603634}{877529309726667} a + \frac{1751461029196170083}{877529309726667} \) |
\( \bigl[1\) , \( a\) , \( a + 1\) , \( 275 a - 304\) , \( 1627 a - 1416\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(275a-304\right){x}+1627a-1416$ |
*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.