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-a1
20.2-a
$2$
$3$
\(\Q(\sqrt{29}) \)
$2$
$[2, 0]$
20.2
\( 2^{2} \cdot 5 \)
\( 2^{18} \cdot 5 \)
$1.01764$
$(-a+2), (2)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$3$
3B.1.2
$1$
\( 3^{2} \)
$1$
$0.902214666$
1.507833519
\( -\frac{19984640951}{640} a - \frac{175841574349}{2560} \)
\( \bigl[a + 1\) , \( 0\) , \( 0\) , \( 142 a - 449\) , \( 1521 a - 4857\bigr] \)
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(142a-449\right){x}+1521a-4857$
100.3-c1
100.3-c
$2$
$3$
\(\Q(\sqrt{29}) \)
$2$
$[2, 0]$
100.3
\( 2^{2} \cdot 5^{2} \)
\( 2^{18} \cdot 5^{7} \)
$1.52173$
$(-a+2), (2)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
$3$
3B
$9$
\( 2 \)
$1$
$0.403482665$
1.348647298
\( -\frac{19984640951}{640} a - \frac{175841574349}{2560} \)
\( \bigl[1\) , \( -a - 1\) , \( 0\) , \( 78 a - 324\) , \( 804 a - 2740\bigr] \)
${y}^2+{x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(78a-324\right){x}+804a-2740$
500.1-g1
500.1-g
$2$
$3$
\(\Q(\sqrt{29}) \)
$2$
$[2, 0]$
500.1
\( 2^{2} \cdot 5^{3} \)
\( 2^{18} \cdot 5^{7} \)
$2.27552$
$(-a-1), (-a+2), (2)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
$3$
3B
$9$
\( 1 \)
$1$
$0.403482665$
0.674323649
\( -\frac{19984640951}{640} a - \frac{175841574349}{2560} \)
\( \bigl[a + 1\) , \( -a + 1\) , \( 0\) , \( -177 a - 424\) , \( -2337 a - 5268\bigr] \)
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-177a-424\right){x}-2337a-5268$
980.5-i1
980.5-i
$2$
$3$
\(\Q(\sqrt{29}) \)
$2$
$[2, 0]$
980.5
\( 2^{2} \cdot 5 \cdot 7^{2} \)
\( 2^{18} \cdot 5 \cdot 7^{6} \)
$2.69243$
$(-a+2), (a-1), (2)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
$3$
3B
$1$
\( 2 \cdot 3^{2} \)
$0.460794973$
$1.336861953$
4.118108629
\( -\frac{19984640951}{640} a - \frac{175841574349}{2560} \)
\( \bigl[a\) , \( -1\) , \( a\) , \( -1355 a - 2984\) , \( -45334 a - 99387\bigr] \)
${y}^2+a{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(-1355a-2984\right){x}-45334a-99387$
980.6-a1
980.6-a
$2$
$3$
\(\Q(\sqrt{29}) \)
$2$
$[2, 0]$
980.6
\( 2^{2} \cdot 5 \cdot 7^{2} \)
\( 2^{18} \cdot 5 \cdot 7^{6} \)
$2.69243$
$(-a+2), (-a), (2)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
$3$
3B
$1$
\( 3^{2} \)
$1$
$2.056036315$
3.436167230
\( -\frac{19984640951}{640} a - \frac{175841574349}{2560} \)
\( \bigl[a\) , \( -1\) , \( a + 1\) , \( 674 a - 2179\) , \( 15908 a - 50765\bigr] \)
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(674a-2179\right){x}+15908a-50765$
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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.