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
$2$
$5$
\(\Q(\sqrt{29}) \)
$2$
$[2, 0]$
13.1
\( 13 \)
\( -13 \)
$0.91374$
$(a+4)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$5$
5B
$1$
\( 1 \)
$0.145011373$
$18.79911555$
1.012442762
\( \frac{6367743011}{13} a - \frac{20195061566}{13} \)
\( \bigl[1\) , \( -a - 1\) , \( 1\) , \( -75 a - 165\) , \( -492 a - 1079\bigr] \)
${y}^2+{x}{y}+{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-75a-165\right){x}-492a-1079$
169.3-c2
169.3-c
$2$
$5$
\(\Q(\sqrt{29}) \)
$2$
$[2, 0]$
169.3
\( 13^{2} \)
\( - 13^{7} \)
$1.73504$
$(a+4)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
$5$
5B
$1$
\( 2 \)
$1$
$1.941399411$
0.721017640
\( \frac{6367743011}{13} a - \frac{20195061566}{13} \)
\( \bigl[a\) , \( a - 1\) , \( 1\) , \( 326 a - 1064\) , \( 5157 a - 16446\bigr] \)
${y}^2+a{x}{y}+{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(326a-1064\right){x}+5157a-16446$
325.5-a2
325.5-a
$2$
$5$
\(\Q(\sqrt{29}) \)
$2$
$[2, 0]$
325.5
\( 5^{2} \cdot 13 \)
\( - 5^{6} \cdot 13 \)
$2.04319$
$(-a-1), (a+4)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
$5$
5B
$1$
\( 2 \)
$1$
$8.407220057$
3.122363143
\( \frac{6367743011}{13} a - \frac{20195061566}{13} \)
\( \bigl[a + 1\) , \( -1\) , \( a + 1\) , \( -45 a - 128\) , \( -380 a - 768\bigr] \)
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(-45a-128\right){x}-380a-768$
325.6-b2
325.6-b
$2$
$5$
\(\Q(\sqrt{29}) \)
$2$
$[2, 0]$
325.6
\( 5^{2} \cdot 13 \)
\( - 5^{6} \cdot 13 \)
$2.04319$
$(-a+2), (a+4)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
$5$
5B
$1$
\( 1 \)
$1.060549784$
$8.407220057$
3.311421559
\( \frac{6367743011}{13} a - \frac{20195061566}{13} \)
\( \bigl[1\) , \( 0\) , \( 1\) , \( 62 a - 220\) , \( -481 a + 1495\bigr] \)
${y}^2+{x}{y}+{y}={x}^{3}+\left(62a-220\right){x}-481a+1495$
637.3-a2
637.3-a
$2$
$5$
\(\Q(\sqrt{29}) \)
$2$
$[2, 0]$
637.3
\( 7^{2} \cdot 13 \)
\( - 7^{6} \cdot 13 \)
$2.41753$
$(-a), (a+4)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
$5$
5B
$1$
\( 1 \)
$1$
$18.26555270$
3.391827987
\( \frac{6367743011}{13} a - \frac{20195061566}{13} \)
\( \bigl[a\) , \( -a + 1\) , \( a\) , \( 484 a - 1556\) , \( -8879 a + 28349\bigr] \)
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(484a-1556\right){x}-8879a+28349$
637.5-a2
637.5-a
$2$
$5$
\(\Q(\sqrt{29}) \)
$2$
$[2, 0]$
637.5
\( 7^{2} \cdot 13 \)
\( - 7^{6} \cdot 13 \)
$2.41753$
$(a-1), (a+4)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
$5$
5B
$1$
\( 1 \)
$7.739686524$
$1.029184243$
2.958335987
\( \frac{6367743011}{13} a - \frac{20195061566}{13} \)
\( \bigl[a\) , \( -a + 1\) , \( a + 1\) , \( -366 a - 805\) , \( -6275 a - 13775\bigr] \)
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-366a-805\right){x}-6275a-13775$
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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.