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-a2
20.2-a
$2$
$3$
\(\Q(\sqrt{29}) \)
$2$
$[2, 0]$
20.2
\( 2^{2} \cdot 5 \)
\( 2^{6} \cdot 5^{3} \)
$1.01764$
$(-a+2), (2)$
0
$\Z/3\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$3$
3B.1.1
$1$
\( 3^{2} \)
$1$
$8.119932001$
1.507833519
\( -\frac{124021}{1000} a + \frac{296769}{1000} \)
\( \bigl[1\) , \( a\) , \( a\) , \( -2 a - 2\) , \( -13 a - 30\bigr] \)
${y}^2+{x}{y}+a{y}={x}^{3}+a{x}^{2}+\left(-2a-2\right){x}-13a-30$
100.3-c2
100.3-c
$2$
$3$
\(\Q(\sqrt{29}) \)
$2$
$[2, 0]$
100.3
\( 2^{2} \cdot 5^{2} \)
\( 2^{6} \cdot 5^{9} \)
$1.52173$
$(-a+2), (2)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
$3$
3B
$1$
\( 2 \)
$1$
$3.631343985$
1.348647298
\( -\frac{124021}{1000} a + \frac{296769}{1000} \)
\( \bigl[1\) , \( -a - 1\) , \( 0\) , \( -2 a + 11\) , \( 4 a - 15\bigr] \)
${y}^2+{x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-2a+11\right){x}+4a-15$
500.1-g2
500.1-g
$2$
$3$
\(\Q(\sqrt{29}) \)
$2$
$[2, 0]$
500.1
\( 2^{2} \cdot 5^{3} \)
\( 2^{6} \cdot 5^{9} \)
$2.27552$
$(-a-1), (-a+2), (2)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
$3$
3B
$1$
\( 1 \)
$1$
$3.631343985$
0.674323649
\( -\frac{124021}{1000} a + \frac{296769}{1000} \)
\( \bigl[a + 1\) , \( -a + 1\) , \( 0\) , \( -2 a + 1\) , \( -7 a - 13\bigr] \)
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-2a+1\right){x}-7a-13$
980.5-i2
980.5-i
$2$
$3$
\(\Q(\sqrt{29}) \)
$2$
$[2, 0]$
980.5
\( 2^{2} \cdot 5 \cdot 7^{2} \)
\( 2^{6} \cdot 5^{3} \cdot 7^{6} \)
$2.69243$
$(-a+2), (a-1), (2)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
$3$
3B
$1$
\( 2 \cdot 3^{2} \)
$0.153598324$
$4.010585859$
4.118108629
\( -\frac{124021}{1000} a + \frac{296769}{1000} \)
\( \bigl[a\) , \( -1\) , \( a\) , \( -10 a - 24\) , \( -119 a - 262\bigr] \)
${y}^2+a{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(-10a-24\right){x}-119a-262$
980.6-a2
980.6-a
$2$
$3$
\(\Q(\sqrt{29}) \)
$2$
$[2, 0]$
980.6
\( 2^{2} \cdot 5 \cdot 7^{2} \)
\( 2^{6} \cdot 5^{3} \cdot 7^{6} \)
$2.69243$
$(-a+2), (-a), (2)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
$3$
3B
$1$
\( 3 \)
$1$
$6.168108947$
3.436167230
\( -\frac{124021}{1000} a + \frac{296769}{1000} \)
\( \bigl[a\) , \( -1\) , \( a + 1\) , \( -21 a + 61\) , \( 113 a - 365\bigr] \)
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(-21a+61\right){x}+113a-365$
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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.