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
400.2-a1
400.2-a
$4$
$6$
\(\Q(\sqrt{-11}) \)
$2$
$[0, 1]$
400.2
\( 2^{4} \cdot 5^{2} \)
\( 2^{16} \cdot 5^{12} \)
$1.32541$
$(-a-1), (a-2), (2)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2, 3$
2B , 3B.1.2
$1$
\( 2^{2} \cdot 3 \)
$0.242753107$
$1.070515942$
0.940248913
\( -\frac{20720464}{15625} \)
\( \bigl[0\) , \( 1\) , \( 0\) , \( -36\) , \( -140\bigr] \)
${y}^2={x}^{3}+{x}^{2}-36{x}-140$
400.2-a2
400.2-a
$4$
$6$
\(\Q(\sqrt{-11}) \)
$2$
$[0, 1]$
400.2
\( 2^{4} \cdot 5^{2} \)
\( 2^{16} \cdot 5^{4} \)
$1.32541$
$(-a-1), (a-2), (2)$
$1$
$\Z/6\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2, 3$
2B , 3B.1.1
$1$
\( 2^{2} \cdot 3 \)
$0.728259321$
$3.211547828$
0.940248913
\( \frac{21296}{25} \)
\( \bigl[0\) , \( 1\) , \( 0\) , \( 4\) , \( 4\bigr] \)
${y}^2={x}^{3}+{x}^{2}+4{x}+4$
400.2-a3
400.2-a
$4$
$6$
\(\Q(\sqrt{-11}) \)
$2$
$[0, 1]$
400.2
\( 2^{4} \cdot 5^{2} \)
\( 2^{8} \cdot 5^{2} \)
$1.32541$
$(-a-1), (a-2), (2)$
$1$
$\Z/6\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2, 3$
2B , 3B.1.1
$1$
\( 3 \)
$1.456518643$
$6.423095656$
0.940248913
\( \frac{16384}{5} \)
\( \bigl[0\) , \( 1\) , \( 0\) , \( -1\) , \( 0\bigr] \)
${y}^2={x}^{3}+{x}^{2}-{x}$
400.2-a4
400.2-a
$4$
$6$
\(\Q(\sqrt{-11}) \)
$2$
$[0, 1]$
400.2
\( 2^{4} \cdot 5^{2} \)
\( 2^{8} \cdot 5^{6} \)
$1.32541$
$(-a-1), (a-2), (2)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2, 3$
2B , 3B.1.2
$1$
\( 3 \)
$0.485506214$
$2.141031885$
0.940248913
\( \frac{488095744}{125} \)
\( \bigl[0\) , \( 1\) , \( 0\) , \( -41\) , \( -116\bigr] \)
${y}^2={x}^{3}+{x}^{2}-41{x}-116$
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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.