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
171.1-f1
171.1-f
$6$
$8$
\(\Q(\sqrt{19}) \)
$2$
$[2, 0]$
171.1
\( 3^{2} \cdot 19 \)
\( - 3^{10} \cdot 19 \)
$2.81705$
$(-a-4), (-a+4), (a)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2$
2B
$1$
\( 2^{2} \)
$5.203787826$
$0.565538563$
0.675157357
\( -\frac{80836867580206264835}{124659} a + \frac{18545249299658286056}{6561} \)
\( \bigl[a\) , \( 1\) , \( a\) , \( 175 a - 860\) , \( 3178 a - 14456\bigr] \)
${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}+\left(175a-860\right){x}+3178a-14456$
171.1-i1
171.1-i
$6$
$8$
\(\Q(\sqrt{19}) \)
$2$
$[2, 0]$
171.1
\( 3^{2} \cdot 19 \)
\( - 3^{10} \cdot 19 \)
$2.81705$
$(-a-4), (-a+4), (a)$
0
$\Z/4\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2$
2B
$1$
\( 2^{4} \)
$1$
$9.423048177$
1.080897756
\( -\frac{80836867580206264835}{124659} a + \frac{18545249299658286056}{6561} \)
\( \bigl[1\) , \( 0\) , \( 1\) , \( 175 a - 862\) , \( -2828 a + 12735\bigr] \)
${y}^2+{x}{y}+{y}={x}^{3}+\left(175a-862\right){x}-2828a+12735$
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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.