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
169.2-a1
169.2-a
$2$
$3$
\(\Q(\sqrt{3}) \)
$2$
$[2, 0]$
169.2
\( 13^{2} \)
\( 13^{10} \)
$1.11609$
$(a-4)$
0
$\mathsf{trivial}$
$\textsf{potential}$
$-3$
$N(\mathrm{U}(1))$
✓
✓
$1$
\( 1 \)
$1$
$3.313232303$
0.956447781
\( 0 \)
\( \bigl[0\) , \( -a\) , \( 1\) , \( 1\) , \( 162 a + 279\bigr] \)
${y}^2+{y}={x}^{3}-a{x}^{2}+{x}+162a+279$
169.2-a2
169.2-a
$2$
$3$
\(\Q(\sqrt{3}) \)
$2$
$[2, 0]$
169.2
\( 13^{2} \)
\( 13^{10} \)
$1.11609$
$(a-4)$
0
$\mathsf{trivial}$
$\textsf{potential}$
$-3$
$N(\mathrm{U}(1))$
✓
✓
$1$
\( 1 \)
$1$
$3.313232303$
0.956447781
\( 0 \)
\( \bigl[0\) , \( a\) , \( a\) , \( 1\) , \( -162 a - 280\bigr] \)
${y}^2+a{y}={x}^{3}+a{x}^{2}+{x}-162a-280$
169.2-b1
169.2-b
$2$
$2$
\(\Q(\sqrt{3}) \)
$2$
$[2, 0]$
169.2
\( 13^{2} \)
\( 13^{3} \)
$1.11609$
$(a-4)$
$1$
$\Z/2\Z$
$\textsf{potential}$
$-4$
$N(\mathrm{U}(1))$
✓
✓
$1$
\( 2 \)
$0.328668069$
$14.48300210$
1.374122605
\( 1728 \)
\( \bigl[a + 1\) , \( a - 1\) , \( a\) , \( -22 a + 38\) , \( 19 a - 33\bigr] \)
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-22a+38\right){x}+19a-33$
169.2-b2
169.2-b
$2$
$2$
\(\Q(\sqrt{3}) \)
$2$
$[2, 0]$
169.2
\( 13^{2} \)
\( 13^{3} \)
$1.11609$
$(a-4)$
$1$
$\Z/2\Z$
$\textsf{potential}$
$-4$
$N(\mathrm{U}(1))$
✓
✓
$1$
\( 2 \)
$0.164334034$
$28.96600420$
1.374122605
\( 1728 \)
\( \bigl[a + 1\) , \( a - 1\) , \( 1\) , \( a - 1\) , \( -a + 2\bigr] \)
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(a-1\right){x}-a+2$
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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.