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
32.2-a1
32.2-a
$4$
$10$
\(\Q(\sqrt{-31}) \)
$2$
$[0, 1]$
32.2
\( 2^{5} \)
\( 2^{19} \)
$1.18333$
$(2,a), (2,a+1)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2, 5$
2B , 5B
$1$
\( 2^{2} \)
$1$
$3.684514436$
1.323516656
\( \frac{514073}{32} a - 48120 \)
\( \bigl[a\) , \( -a + 1\) , \( a\) , \( -2 a + 8\) , \( 4\bigr] \)
${y}^2+a{x}{y}+a{y}={x}^3+\left(-a+1\right){x}^2+\left(-2a+8\right){x}+4$
32.2-a2
32.2-a
$4$
$10$
\(\Q(\sqrt{-31}) \)
$2$
$[0, 1]$
32.2
\( 2^{5} \)
\( 2^{31} \)
$1.18333$
$(2,a), (2,a+1)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2, 5$
2B , 5B
$1$
\( 2^{2} \)
$1$
$3.684514436$
1.323516656
\( -\frac{514073}{32} a - \frac{1025767}{32} \)
\( \bigl[a\) , \( 0\) , \( a\) , \( 2 a + 32\) , \( -20 a + 16\bigr] \)
${y}^2+a{x}{y}+a{y}={x}^3+\left(2a+32\right){x}-20a+16$
32.2-a3
32.2-a
$4$
$10$
\(\Q(\sqrt{-31}) \)
$2$
$[0, 1]$
32.2
\( 2^{5} \)
\( 2^{35} \)
$1.18333$
$(2,a), (2,a+1)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2, 5$
2B , 5B
$1$
\( 2^{2} \)
$1$
$3.684514436$
1.323516656
\( \frac{85169}{1024} a + \frac{12167}{128} \)
\( \bigl[0\) , \( -1\) , \( 0\) , \( 8\) , \( -4 a + 16\bigr] \)
${y}^2={x}^3-{x}^2+8{x}-4a+16$
32.2-a4
32.2-a
$4$
$10$
\(\Q(\sqrt{-31}) \)
$2$
$[0, 1]$
32.2
\( 2^{5} \)
\( 2^{35} \)
$1.18333$
$(2,a), (2,a+1)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2, 5$
2B , 5B
$1$
\( 2^{2} \)
$1$
$3.684514436$
1.323516656
\( -\frac{85169}{1024} a + \frac{182505}{1024} \)
\( \bigl[0\) , \( 1\) , \( 0\) , \( 8\) , \( -4 a - 12\bigr] \)
${y}^2={x}^3+{x}^2+8{x}-4a-12$
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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.