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
13.2-a1
13.2-a
$2$
$5$
\(\Q(\sqrt{29}) \)
$2$
$[2, 0]$
13.2
\( 13 \)
\( -13 \)
$0.91374$
$(a-5)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$5$
5B
$1$
\( 1 \)
$0.145011373$
$18.79911555$
1.012442762
\( -\frac{6367743011}{13} a - \frac{13827318555}{13} \)
\( \bigl[1\) , \( a + 1\) , \( 0\) , \( 77 a - 240\) , \( 568 a - 1811\bigr] \)
${y}^2+{x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(77a-240\right){x}+568a-1811$
169.2-c1
169.2-c
$2$
$5$
\(\Q(\sqrt{29}) \)
$2$
$[2, 0]$
169.2
\( 13^{2} \)
\( - 13^{7} \)
$1.73504$
$(a-5)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
$5$
5B
$1$
\( 2 \)
$1$
$1.941399411$
0.721017640
\( -\frac{6367743011}{13} a - \frac{13827318555}{13} \)
\( \bigl[a + 1\) , \( a\) , \( 0\) , \( -322 a - 734\) , \( -6221 a - 13562\bigr] \)
${y}^2+\left(a+1\right){x}{y}={x}^{3}+a{x}^{2}+\left(-322a-734\right){x}-6221a-13562$
325.3-b1
325.3-b
$2$
$5$
\(\Q(\sqrt{29}) \)
$2$
$[2, 0]$
325.3
\( 5^{2} \cdot 13 \)
\( - 5^{6} \cdot 13 \)
$2.04319$
$(-a-1), (a-5)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
$5$
5B
$1$
\( 1 \)
$1.060549784$
$8.407220057$
3.311421559
\( -\frac{6367743011}{13} a - \frac{13827318555}{13} \)
\( \bigl[1\) , \( 0\) , \( 1\) , \( -62 a - 158\) , \( 481 a + 1014\bigr] \)
${y}^2+{x}{y}+{y}={x}^{3}+\left(-62a-158\right){x}+481a+1014$
325.4-a1
325.4-a
$2$
$5$
\(\Q(\sqrt{29}) \)
$2$
$[2, 0]$
325.4
\( 5^{2} \cdot 13 \)
\( - 5^{6} \cdot 13 \)
$2.04319$
$(-a+2), (a-5)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
$5$
5B
$1$
\( 2 \)
$1$
$8.407220057$
3.122363143
\( -\frac{6367743011}{13} a - \frac{13827318555}{13} \)
\( \bigl[a\) , \( -a\) , \( a\) , \( 43 a - 171\) , \( 379 a - 1147\bigr] \)
${y}^2+a{x}{y}+a{y}={x}^{3}-a{x}^{2}+\left(43a-171\right){x}+379a-1147$
637.4-a1
637.4-a
$2$
$5$
\(\Q(\sqrt{29}) \)
$2$
$[2, 0]$
637.4
\( 7^{2} \cdot 13 \)
\( - 7^{6} \cdot 13 \)
$2.41753$
$(-a), (a-5)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
$5$
5B
$1$
\( 1 \)
$7.739686524$
$1.029184243$
2.958335987
\( -\frac{6367743011}{13} a - \frac{13827318555}{13} \)
\( \bigl[a + 1\) , \( 0\) , \( a\) , \( 364 a - 1170\) , \( 6274 a - 20049\bigr] \)
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(364a-1170\right){x}+6274a-20049$
637.6-a1
637.6-a
$2$
$5$
\(\Q(\sqrt{29}) \)
$2$
$[2, 0]$
637.6
\( 7^{2} \cdot 13 \)
\( - 7^{6} \cdot 13 \)
$2.41753$
$(a-1), (a-5)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
$5$
5B
$1$
\( 1 \)
$1$
$18.26555270$
3.391827987
\( -\frac{6367743011}{13} a - \frac{13827318555}{13} \)
\( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( -486 a - 1072\) , \( 8878 a + 19470\bigr] \)
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-486a-1072\right){x}+8878a+19470$
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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.