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
38416.1-a1
38416.1-a
$2$
$3$
\(\Q(\sqrt{-11}) \)
$2$
$[0, 1]$
38416.1
\( 2^{4} \cdot 7^{4} \)
\( 2^{8} \cdot 7^{4} \)
$4.14919$
$(2), (7)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$2, 3$
2Cn , 3B
$1$
\( 3 \)
$0.086035450$
$4.520767792$
1.407260647
\( 1792 \)
\( \bigl[0\) , \( -1\) , \( 0\) , \( -2\) , \( 1\bigr] \)
${y}^2={x}^{3}-{x}^{2}-2{x}+1$
38416.1-a2
38416.1-a
$2$
$3$
\(\Q(\sqrt{-11}) \)
$2$
$[0, 1]$
38416.1
\( 2^{4} \cdot 7^{4} \)
\( 2^{8} \cdot 7^{4} \)
$4.14919$
$(2), (7)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$2, 3$
2Cn , 3B
$1$
\( 3 \)
$0.258106352$
$1.506922597$
1.407260647
\( 406749952 \)
\( \bigl[0\) , \( -1\) , \( 0\) , \( -142\) , \( 701\bigr] \)
${y}^2={x}^{3}-{x}^{2}-142{x}+701$
38416.1-b1
38416.1-b
$2$
$3$
\(\Q(\sqrt{-11}) \)
$2$
$[0, 1]$
38416.1
\( 2^{4} \cdot 7^{4} \)
\( 2^{8} \cdot 7^{16} \)
$4.14919$
$(2), (7)$
$1$
$\Z/3\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$2, 3$
2Cn , 3B.1.1
$1$
\( 3^{2} \)
$15.00012778$
$0.645823970$
11.68349474
\( 1792 \)
\( \bigl[0\) , \( 1\) , \( 0\) , \( -114\) , \( -127\bigr] \)
${y}^2={x}^{3}+{x}^{2}-114{x}-127$
38416.1-b2
38416.1-b
$2$
$3$
\(\Q(\sqrt{-11}) \)
$2$
$[0, 1]$
38416.1
\( 2^{4} \cdot 7^{4} \)
\( 2^{8} \cdot 7^{16} \)
$4.14919$
$(2), (7)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$2, 3$
2Cn , 3B.1.2
$1$
\( 3^{2} \)
$5.000042593$
$0.215274656$
11.68349474
\( 406749952 \)
\( \bigl[0\) , \( 1\) , \( 0\) , \( -6974\) , \( -226507\bigr] \)
${y}^2={x}^{3}+{x}^{2}-6974{x}-226507$
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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.