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
13.1-a2
13.1-a
$2$
$3$
3.3.733.1
$3$
$[3, 0]$
13.1
\( 13 \)
\( 13^{9} \)
$3.70978$
$(a+1)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$3$
3B.1.2
$1$
\( 3^{2} \)
$1$
$5.716592367$
1.900324411
\( -\frac{136393019664367616}{10604499373} a^{2} - \frac{206931227163590656}{10604499373} a + \frac{433695920698523648}{10604499373} \)
\( \bigl[0\) , \( a^{2} - 5\) , \( a^{2} - 5\) , \( -90 a^{2} - 151 a + 249\) , \( -1051 a^{2} - 1622 a + 3267\bigr] \)
${y}^2+\left(a^{2}-5\right){y}={x}^{3}+\left(a^{2}-5\right){x}^{2}+\left(-90a^{2}-151a+249\right){x}-1051a^{2}-1622a+3267$
169.2-a1
169.2-a
$2$
$3$
3.3.733.1
$3$
$[3, 0]$
169.2
\( 13^{2} \)
\( 13^{15} \)
$5.68859$
$(a+1)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
$3$
3B
$1$
\( 2^{2} \)
$1.350195084$
$8.026891763$
4.803670259
\( -\frac{136393019664367616}{10604499373} a^{2} - \frac{206931227163590656}{10604499373} a + \frac{433695920698523648}{10604499373} \)
\( \bigl[0\) , \( -a^{2} - a + 6\) , \( a^{2} - 5\) , \( 371 a^{2} + 59 a - 2510\) , \( 6607 a^{2} + 1186 a - 44859\bigr] \)
${y}^2+\left(a^{2}-5\right){y}={x}^{3}+\left(-a^{2}-a+6\right){x}^{2}+\left(371a^{2}+59a-2510\right){x}+6607a^{2}+1186a-44859$
208.3-i1
208.3-i
$2$
$3$
3.3.733.1
$3$
$[3, 0]$
208.3
\( 2^{4} \cdot 13 \)
\( 2^{12} \cdot 13^{9} \)
$5.88890$
$(a^2-6), (a+1)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
$3$
3B
$9$
\( 1 \)
$1$
$2.482426193$
0.825214531
\( -\frac{136393019664367616}{10604499373} a^{2} - \frac{206931227163590656}{10604499373} a + \frac{433695920698523648}{10604499373} \)
\( \bigl[0\) , \( -a^{2} + 4\) , \( a\) , \( 158 a^{2} + 23 a - 1080\) , \( 1898 a^{2} + 335 a - 12904\bigr] \)
${y}^2+a{y}={x}^{3}+\left(-a^{2}+4\right){x}^{2}+\left(158a^{2}+23a-1080\right){x}+1898a^{2}+335a-12904$
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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.