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
32.1-a1
32.1-a
$4$
$4$
\(\Q(\sqrt{74}) \)
$2$
$[2, 0]$
32.1
\( 2^{5} \)
\( 2^{12} \)
$3.65655$
$(2,a)$
0
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{potential}$
$-4$
$N(\mathrm{U}(1))$
✓
✓
✓
$2$
2Cs
$1$
\( 2^{2} \)
$1$
$27.50074327$
0.399612058
\( 1728 \)
\( \bigl[0\) , \( 0\) , \( 0\) , \( -1\) , \( 0\bigr] \)
${y}^2={x}^{3}-{x}$
32.1-a2
32.1-a
$4$
$4$
\(\Q(\sqrt{74}) \)
$2$
$[2, 0]$
32.1
\( 2^{5} \)
\( 2^{24} \)
$3.65655$
$(2,a)$
0
$\Z/4\Z$
$\textsf{potential}$
$-4$
$N(\mathrm{U}(1))$
✓
✓
✓
$4$
\( 2 \)
$1$
$13.75037163$
0.399612058
\( 1728 \)
\( \bigl[0\) , \( 0\) , \( 0\) , \( 4\) , \( 0\bigr] \)
${y}^2={x}^{3}+4{x}$
32.1-a3
32.1-a
$4$
$4$
\(\Q(\sqrt{74}) \)
$2$
$[2, 0]$
32.1
\( 2^{5} \)
\( 2^{18} \)
$3.65655$
$(2,a)$
0
$\Z/2\Z$
$\textsf{potential}$
$-16$
$N(\mathrm{U}(1))$
✓
✓
✓
$1$
\( 2 \)
$1$
$13.75037163$
0.399612058
\( 287496 \)
\( \bigl[0\) , \( 0\) , \( 0\) , \( -11\) , \( -14\bigr] \)
${y}^2={x}^{3}-11{x}-14$
32.1-a4
32.1-a
$4$
$4$
\(\Q(\sqrt{74}) \)
$2$
$[2, 0]$
32.1
\( 2^{5} \)
\( 2^{18} \)
$3.65655$
$(2,a)$
0
$\Z/4\Z$
$\textsf{potential}$
$-16$
$N(\mathrm{U}(1))$
✓
✓
✓
$1$
\( 2 \)
$1$
$55.00148654$
0.399612058
\( 287496 \)
\( \bigl[0\) , \( 0\) , \( 0\) , \( -11\) , \( 14\bigr] \)
${y}^2={x}^{3}-11{x}+14$
32.1-b1
32.1-b
$4$
$4$
\(\Q(\sqrt{74}) \)
$2$
$[2, 0]$
32.1
\( 2^{5} \)
\( 2^{12} \)
$3.65655$
$(2,a)$
$1$
$\Z/2\Z$
$\textsf{potential}$
$-4$
$N(\mathrm{U}(1))$
✓
✓
✓
$1$
\( 2 \)
$6.782710350$
$13.75037163$
5.420905692
\( 1728 \)
\( \bigl[0\) , \( 0\) , \( 0\) , \( 1\) , \( 0\bigr] \)
${y}^2={x}^{3}+{x}$
32.1-b2
32.1-b
$4$
$4$
\(\Q(\sqrt{74}) \)
$2$
$[2, 0]$
32.1
\( 2^{5} \)
\( 2^{24} \)
$3.65655$
$(2,a)$
$1$
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{potential}$
$-4$
$N(\mathrm{U}(1))$
✓
✓
✓
$2$
2Cs
$1$
\( 2 \)
$13.56542070$
$27.50074327$
5.420905692
\( 1728 \)
\( \bigl[0\) , \( 0\) , \( 0\) , \( -4\) , \( 0\bigr] \)
${y}^2={x}^{3}-4{x}$
32.1-b3
32.1-b
$4$
$4$
\(\Q(\sqrt{74}) \)
$2$
$[2, 0]$
32.1
\( 2^{5} \)
\( 2^{6} \)
$3.65655$
$(2,a)$
$1$
$\Z/2\Z$
$\textsf{potential}$
$-16$
$N(\mathrm{U}(1))$
✓
✓
✓
$1$
\( 2 \)
$6.782710350$
$13.75037163$
5.420905692
\( 287496 \)
\( \bigl[a\) , \( 1\) , \( 0\) , \( 124\) , \( 255\bigr] \)
${y}^2+a{x}{y}={x}^{3}+{x}^{2}+124{x}+255$
32.1-b4
32.1-b
$4$
$4$
\(\Q(\sqrt{74}) \)
$2$
$[2, 0]$
32.1
\( 2^{5} \)
\( 2^{6} \)
$3.65655$
$(2,a)$
$1$
$\Z/4\Z$
$\textsf{potential}$
$-16$
$N(\mathrm{U}(1))$
✓
✓
✓
$1$
\( 2 \)
$6.782710350$
$55.00148654$
5.420905692
\( 287496 \)
\( \bigl[a\) , \( 1\) , \( a\) , \( 87\) , \( 240\bigr] \)
${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}+87{x}+240$
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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.