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
20.2-b1
20.2-b
$1$
$1$
\(\Q(\sqrt{29}) \)
$2$
$[2, 0]$
20.2
\( 2^{2} \cdot 5 \)
\( 2^{2} \cdot 5^{7} \)
$1.01764$
$(-a+2), (2)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$1$
\( 1 \)
$1$
$5.994874057$
1.113220165
\( \frac{119629571}{156250} a - \frac{118018719}{156250} \)
\( \bigl[a + 1\) , \( -1\) , \( 1\) , \( a + 1\) , \( a + 1\bigr] \)
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}-{x}^{2}+\left(a+1\right){x}+a+1$
100.3-a1
100.3-a
$1$
$1$
\(\Q(\sqrt{29}) \)
$2$
$[2, 0]$
100.3
\( 2^{2} \cdot 5^{2} \)
\( 2^{2} \cdot 5^{13} \)
$1.52173$
$(-a+2), (2)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
$1$
\( 2^{2} \)
$0.556354545$
$2.680989181$
2.215836389
\( \frac{119629571}{156250} a - \frac{118018719}{156250} \)
\( \bigl[1\) , \( a - 1\) , \( a\) , \( 17 a + 40\) , \( 24 a + 51\bigr] \)
${y}^2+{x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(17a+40\right){x}+24a+51$
500.1-k1
500.1-k
$1$
$1$
\(\Q(\sqrt{29}) \)
$2$
$[2, 0]$
500.1
\( 2^{2} \cdot 5^{3} \)
\( 2^{2} \cdot 5^{13} \)
$2.27552$
$(-a-1), (-a+2), (2)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
$1$
\( 7 \)
$1$
$2.680989181$
3.484930349
\( \frac{119629571}{156250} a - \frac{118018719}{156250} \)
\( \bigl[a\) , \( a\) , \( a + 1\) , \( 15 a - 42\) , \( 56 a - 173\bigr] \)
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(15a-42\right){x}+56a-173$
980.5-d1
980.5-d
$1$
$1$
\(\Q(\sqrt{29}) \)
$2$
$[2, 0]$
980.5
\( 2^{2} \cdot 5 \cdot 7^{2} \)
\( 2^{2} \cdot 5^{7} \cdot 7^{6} \)
$2.69243$
$(-a+2), (a-1), (2)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
$1$
\( 2 \)
$0.481711107$
$5.802134982$
2.076038870
\( \frac{119629571}{156250} a - \frac{118018719}{156250} \)
\( \bigl[1\) , \( a + 1\) , \( 0\) , \( 7 a - 4\) , \( -5 a + 39\bigr] \)
${y}^2+{x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(7a-4\right){x}-5a+39$
980.6-j1
980.6-j
$1$
$1$
\(\Q(\sqrt{29}) \)
$2$
$[2, 0]$
980.6
\( 2^{2} \cdot 5 \cdot 7^{2} \)
\( 2^{2} \cdot 5^{7} \cdot 7^{6} \)
$2.69243$
$(-a+2), (-a), (2)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
$1$
\( 7 \)
$1$
$2.177387149$
2.830314501
\( \frac{119629571}{156250} a - \frac{118018719}{156250} \)
\( \bigl[a\) , \( a - 1\) , \( a\) , \( 7 a + 5\) , \( 8 a + 8\bigr] \)
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(7a+5\right){x}+8a+8$
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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.