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
867.1-a1
867.1-a
$2$
$3$
\(\Q(\sqrt{3}) \)
$2$
$[2, 0]$
867.1
\( 3 \cdot 17^{2} \)
\( 3^{2} \cdot 17^{6} \)
$1.67971$
$(a), (17)$
$1$
$\Z/3\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$3$
3B.1.1
$1$
\( 2 \cdot 3 \)
$0.338669215$
$15.25179482$
1.988130049
\( -\frac{23100424192}{14739} \)
\( \bigl[0\) , \( -1\) , \( a\) , \( -59\) , \( 195\bigr] \)
${y}^2+a{y}={x}^{3}-{x}^{2}-59{x}+195$
867.1-a2
867.1-a
$2$
$3$
\(\Q(\sqrt{3}) \)
$2$
$[2, 0]$
867.1
\( 3 \cdot 17^{2} \)
\( 3^{6} \cdot 17^{2} \)
$1.67971$
$(a), (17)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$3$
3B.1.2
$1$
\( 2 \)
$0.112889738$
$15.25179482$
1.988130049
\( \frac{32768}{459} \)
\( \bigl[0\) , \( -1\) , \( a\) , \( 1\) , \( 0\bigr] \)
${y}^2+a{y}={x}^{3}-{x}^{2}+{x}$
867.1-b1
867.1-b
$2$
$3$
\(\Q(\sqrt{3}) \)
$2$
$[2, 0]$
867.1
\( 3 \cdot 17^{2} \)
\( 3^{2} \cdot 17^{6} \)
$1.67971$
$(a), (17)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$3$
3B.1.2
$1$
\( 2 \cdot 3 \)
$1$
$0.739701511$
1.281200599
\( -\frac{23100424192}{14739} \)
\( \bigl[0\) , \( 1\) , \( 1\) , \( -59\) , \( -196\bigr] \)
${y}^2+{y}={x}^{3}+{x}^{2}-59{x}-196$
867.1-b2
867.1-b
$2$
$3$
\(\Q(\sqrt{3}) \)
$2$
$[2, 0]$
867.1
\( 3 \cdot 17^{2} \)
\( 3^{6} \cdot 17^{2} \)
$1.67971$
$(a), (17)$
0
$\Z/3\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$3$
3B.1.1
$1$
\( 2 \cdot 3 \)
$1$
$6.657313600$
1.281200599
\( \frac{32768}{459} \)
\( \bigl[0\) , \( 1\) , \( 1\) , \( 1\) , \( -1\bigr] \)
${y}^2+{y}={x}^{3}+{x}^{2}+{x}-1$
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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.