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
8.1-a3
8.1-a
$4$
$21$
\(\Q(\zeta_{36})^+\)
$6$
$[6, 0]$
8.1
\( 2^{3} \)
\( 2^{126} \)
$119.27013$
$(-a^4-a^3+3a^2+2a-1)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$3, 7$
3B.1.2 , 7B.6.3
$9$
\( 2 \)
$1$
$160.8635265$
2.57985
\( -\frac{1159088625}{2097152} \)
\( \bigl[a\) , \( a^{4} - 6 a^{2} + 6\) , \( a^{5} - 5 a^{3} + 4 a\) , \( -10 a^{4} - 3 a^{2} + 5\) , \( 166 a^{4} - 246 a^{2} + 80\bigr] \)
${y}^2+a{x}{y}+\left(a^{5}-5a^{3}+4a\right){y}={x}^{3}+\left(a^{4}-6a^{2}+6\right){x}^{2}+\left(-10a^{4}-3a^{2}+5\right){x}+166a^{4}-246a^{2}+80$
8.1-b3
8.1-b
$4$
$21$
\(\Q(\zeta_{36})^+\)
$6$
$[6, 0]$
8.1
\( 2^{3} \)
\( 2^{126} \)
$119.27013$
$(-a^4-a^3+3a^2+2a-1)$
$1$
$\Z/3\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$3, 7$
3B.1.1 , 7B.1.3
$49$
\( 2 \cdot 3 \cdot 7 \)
$1.026724489$
$1.271705543$
1.59609
\( -\frac{1159088625}{2097152} \)
\( \bigl[a^{4} - 5 a^{2} + 4\) , \( -a^{4} + 6 a^{2} - 7\) , \( a^{2} - 2\) , \( -9 a^{4} - 8 a^{2} + 9\) , \( -166 a^{4} + 246 a^{2} - 81\bigr] \)
${y}^2+\left(a^{4}-5a^{2}+4\right){x}{y}+\left(a^{2}-2\right){y}={x}^{3}+\left(-a^{4}+6a^{2}-7\right){x}^{2}+\left(-9a^{4}-8a^{2}+9\right){x}-166a^{4}+246a^{2}-81$
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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.