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
82369.3-a1
82369.3-a
$1$
$1$
\(\Q(\sqrt{-1}) \)
$2$
$[0, 1]$
82369.3
\( 7^{2} \cdot 41^{2} \)
\( 7^{2} \cdot 41^{2} \)
$3.02768$
$(4a+5), (7)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
$1$
\( 1 \)
$0.359858130$
$5.348047378$
3.849076661
\( -\frac{729}{7} a + 1728 \)
\( \bigl[i\) , \( 1\) , \( i + 1\) , \( i\) , \( 0\bigr] \)
${y}^2+i{x}{y}+\left(i+1\right){y}={x}^{3}+{x}^{2}+i{x}$
82369.3-b1
82369.3-b
$2$
$2$
\(\Q(\sqrt{-1}) \)
$2$
$[0, 1]$
82369.3
\( 7^{2} \cdot 41^{2} \)
\( 7^{4} \cdot 41^{10} \)
$3.02768$
$(4a+5), (7)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2B
$1$
\( 2^{3} \)
$1.181608371$
$0.332330083$
1.570736033
\( -\frac{18657297}{138462289} a + \frac{73533528}{19780327} \)
\( \bigl[i\) , \( 1\) , \( 0\) , \( 57 i - 8\) , \( 1917 i - 3083\bigr] \)
${y}^2+i{x}{y}={x}^{3}+{x}^{2}+\left(57i-8\right){x}+1917i-3083$
82369.3-b2
82369.3-b
$2$
$2$
\(\Q(\sqrt{-1}) \)
$2$
$[0, 1]$
82369.3
\( 7^{2} \cdot 41^{2} \)
\( 7^{2} \cdot 41^{8} \)
$3.02768$
$(4a+5), (7)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2B
$1$
\( 2 \)
$2.363216742$
$0.664660166$
1.570736033
\( -\frac{379593216}{11767} a + \frac{726554313}{11767} \)
\( \bigl[1\) , \( -1\) , \( 0\) , \( 102 i - 208\) , \( -880 i + 1089\bigr] \)
${y}^2+{x}{y}={x}^{3}-{x}^{2}+\left(102i-208\right){x}-880i+1089$
82369.3-c1
82369.3-c
$1$
$1$
\(\Q(\sqrt{-1}) \)
$2$
$[0, 1]$
82369.3
\( 7^{2} \cdot 41^{2} \)
\( 7^{2} \cdot 41^{8} \)
$3.02768$
$(4a+5), (7)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
$1$
\( 3 \)
$1.327023761$
$0.835224677$
6.650177964
\( -\frac{729}{7} a + 1728 \)
\( \bigl[i\) , \( 1\) , \( 0\) , \( -14 i - 66\) , \( 19 i - 64\bigr] \)
${y}^2+i{x}{y}={x}^{3}+{x}^{2}+\left(-14i-66\right){x}+19i-64$
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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.