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
228.2-a1
228.2-a
$4$
$10$
\(\Q(\sqrt{-3}) \)
$2$
$[0, 1]$
228.2
\( 2^{2} \cdot 3 \cdot 19 \)
\( 2^{10} \cdot 3^{2} \cdot 19^{10} \)
$0.60143$
$(-2a+1), (-5a+2), (2)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2, 5$
2B , 5B.1.2
$1$
\( 2^{2} \)
$1$
$0.548223191$
0.633033614
\( \frac{612993539767699445}{588582360748896} a - \frac{160110064682580223}{196194120249632} \)
\( \bigl[1\) , \( -a - 1\) , \( 1\) , \( -140 a + 35\) , \( -615 a + 881\bigr] \)
${y}^2+{x}{y}+{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-140a+35\right){x}-615a+881$
228.2-a2
228.2-a
$4$
$10$
\(\Q(\sqrt{-3}) \)
$2$
$[0, 1]$
228.2
\( 2^{2} \cdot 3 \cdot 19 \)
\( 2^{4} \cdot 3^{5} \cdot 19 \)
$0.60143$
$(-2a+1), (-5a+2), (2)$
0
$\Z/10\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2, 5$
2B , 5B.1.1
$1$
\( 2 \cdot 5 \)
$1$
$5.482231917$
0.633033614
\( -\frac{212831}{2052} a + \frac{418543}{2052} \)
\( \bigl[1\) , \( -a - 1\) , \( 1\) , \( 0\) , \( a - 1\bigr] \)
${y}^2+{x}{y}+{y}={x}^{3}+\left(-a-1\right){x}^{2}+a-1$
228.2-a3
228.2-a
$4$
$10$
\(\Q(\sqrt{-3}) \)
$2$
$[0, 1]$
228.2
\( 2^{2} \cdot 3 \cdot 19 \)
\( 2^{20} \cdot 3 \cdot 19^{5} \)
$0.60143$
$(-2a+1), (-5a+2), (2)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2, 5$
2B , 5B.1.2
$1$
\( 2 \)
$1$
$1.096446383$
0.633033614
\( -\frac{38854777864121}{7606576128} a + \frac{1338875320873}{475411008} \)
\( \bigl[1\) , \( -a - 1\) , \( 1\) , \( 20 a + 35\) , \( -167 a + 113\bigr] \)
${y}^2+{x}{y}+{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(20a+35\right){x}-167a+113$
228.2-a4
228.2-a
$4$
$10$
\(\Q(\sqrt{-3}) \)
$2$
$[0, 1]$
228.2
\( 2^{2} \cdot 3 \cdot 19 \)
\( 2^{2} \cdot 3^{10} \cdot 19^{2} \)
$0.60143$
$(-2a+1), (-5a+2), (2)$
0
$\Z/10\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2, 5$
2B , 5B.1.1
$1$
\( 2^{2} \cdot 5 \)
$1$
$2.741115958$
0.633033614
\( \frac{537398275}{175446} a + \frac{667275508}{87723} \)
\( \bigl[1\) , \( -a - 1\) , \( 1\) , \( 10 a - 10\) , \( 9 a - 1\bigr] \)
${y}^2+{x}{y}+{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(10a-10\right){x}+9a-1$
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*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.