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
20.1-a1
20.1-a
$2$
$3$
\(\Q(\sqrt{29}) \)
$2$
$[2, 0]$
20.1
\( 2^{2} \cdot 5 \)
\( 2^{18} \cdot 5 \)
$1.01764$
$(-a-1), (2)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$3$
3B.1.2
$1$
\( 3^{2} \)
$1$
$0.902214666$
1.507833519
\( \frac{19984640951}{640} a - \frac{255780138153}{2560} \)
\( \bigl[a\) , \( -a + 1\) , \( 0\) , \( -142 a - 307\) , \( -1521 a - 3336\bigr] \)
${y}^2+a{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-142a-307\right){x}-1521a-3336$
100.2-c1
100.2-c
$2$
$3$
\(\Q(\sqrt{29}) \)
$2$
$[2, 0]$
100.2
\( 2^{2} \cdot 5^{2} \)
\( 2^{18} \cdot 5^{7} \)
$1.52173$
$(-a-1), (2)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
$3$
3B
$9$
\( 2 \)
$1$
$0.403482665$
1.348647298
\( \frac{19984640951}{640} a - \frac{255780138153}{2560} \)
\( \bigl[1\) , \( a + 1\) , \( 1\) , \( -76 a - 247\) , \( -881 a - 2183\bigr] \)
${y}^2+{x}{y}+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-76a-247\right){x}-881a-2183$
500.2-g1
500.2-g
$2$
$3$
\(\Q(\sqrt{29}) \)
$2$
$[2, 0]$
500.2
\( 2^{2} \cdot 5^{3} \)
\( 2^{18} \cdot 5^{7} \)
$2.27552$
$(-a-1), (-a+2), (2)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
$3$
3B
$9$
\( 1 \)
$1$
$0.403482665$
0.674323649
\( \frac{19984640951}{640} a - \frac{255780138153}{2560} \)
\( \bigl[a\) , \( 1\) , \( 0\) , \( 177 a - 601\) , \( 2337 a - 7605\bigr] \)
${y}^2+a{x}{y}={x}^{3}+{x}^{2}+\left(177a-601\right){x}+2337a-7605$
980.3-a1
980.3-a
$2$
$3$
\(\Q(\sqrt{29}) \)
$2$
$[2, 0]$
980.3
\( 2^{2} \cdot 5 \cdot 7^{2} \)
\( 2^{18} \cdot 5 \cdot 7^{6} \)
$2.69243$
$(-a-1), (a-1), (2)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
$3$
3B
$1$
\( 3^{2} \)
$1$
$2.056036315$
3.436167230
\( \frac{19984640951}{640} a - \frac{255780138153}{2560} \)
\( \bigl[a + 1\) , \( -a - 1\) , \( a\) , \( -676 a - 1504\) , \( -15909 a - 34856\bigr] \)
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-676a-1504\right){x}-15909a-34856$
980.4-i1
980.4-i
$2$
$3$
\(\Q(\sqrt{29}) \)
$2$
$[2, 0]$
980.4
\( 2^{2} \cdot 5 \cdot 7^{2} \)
\( 2^{18} \cdot 5 \cdot 7^{6} \)
$2.69243$
$(-a-1), (-a), (2)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
$3$
3B
$1$
\( 2 \cdot 3^{2} \)
$0.460794973$
$1.336861953$
4.118108629
\( \frac{19984640951}{640} a - \frac{255780138153}{2560} \)
\( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( 1353 a - 4339\) , \( 45333 a - 144721\bigr] \)
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(1353a-4339\right){x}+45333a-144721$
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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.