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
181.3-a1
181.3-a
$2$
$5$
\(\Q(\zeta_{7})^+\)
$3$
$[3, 0]$
181.3
\( 181 \)
\( - 181^{5} \)
$1.48770$
$(a^2-5a-2)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$5$
5B.1.2
$1$
\( 5 \)
$1$
$1.167848697$
0.834177641
\( \frac{44023832204770836564641}{194264244901} a^{2} - \frac{24431384735829497330761}{194264244901} a - \frac{98920654043308873836255}{194264244901} \)
\( \bigl[a^{2} - 1\) , \( a^{2} - 2\) , \( a^{2} + a - 1\) , \( 274 a^{2} - 170 a - 634\) , \( 2618 a^{2} - 1512 a - 5956\bigr] \)
${y}^2+\left(a^{2}-1\right){x}{y}+\left(a^{2}+a-1\right){y}={x}^{3}+\left(a^{2}-2\right){x}^{2}+\left(274a^{2}-170a-634\right){x}+2618a^{2}-1512a-5956$
181.3-a2
181.3-a
$2$
$5$
\(\Q(\zeta_{7})^+\)
$3$
$[3, 0]$
181.3
\( 181 \)
\( -181 \)
$1.48770$
$(a^2-5a-2)$
0
$\Z/5\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$5$
5B.1.1
$1$
\( 1 \)
$1$
$145.9810872$
0.834177641
\( -\frac{876412025}{181} a^{2} + \frac{1969280916}{181} a - \frac{702828304}{181} \)
\( \bigl[a^{2} - 1\) , \( a^{2} - 2\) , \( a^{2} + a - 1\) , \( -a^{2} + 1\) , \( -a - 1\bigr] \)
${y}^2+\left(a^{2}-1\right){x}{y}+\left(a^{2}+a-1\right){y}={x}^{3}+\left(a^{2}-2\right){x}^{2}+\left(-a^{2}+1\right){x}-a-1$
181.3-b1
181.3-b
$2$
$3$
\(\Q(\zeta_{7})^+\)
$3$
$[3, 0]$
181.3
\( 181 \)
\( - 181^{3} \)
$1.48770$
$(a^2-5a-2)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$3$
3B.1.2
$1$
\( 3 \)
$1$
$1.896361674$
0.812726431
\( -\frac{35619208763908905877}{5929741} a^{2} + \frac{80035625147780316014}{5929741} a - \frac{28564382984194822905}{5929741} \)
\( \bigl[a^{2} - 2\) , \( -a^{2} - a + 1\) , \( a^{2} + a - 1\) , \( -205 a^{2} + 174 a - 37\) , \( -1656 a^{2} + 1874 a - 506\bigr] \)
${y}^2+\left(a^{2}-2\right){x}{y}+\left(a^{2}+a-1\right){y}={x}^{3}+\left(-a^{2}-a+1\right){x}^{2}+\left(-205a^{2}+174a-37\right){x}-1656a^{2}+1874a-506$
181.3-b2
181.3-b
$2$
$3$
\(\Q(\zeta_{7})^+\)
$3$
$[3, 0]$
181.3
\( 181 \)
\( -181 \)
$1.48770$
$(a^2-5a-2)$
0
$\Z/3\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$3$
3B.1.1
$1$
\( 1 \)
$1$
$51.20176520$
0.812726431
\( \frac{294686878478}{181} a^{2} - \frac{163537056709}{181} a - \frac{662158683937}{181} \)
\( \bigl[a^{2} - 2\) , \( -a^{2} - a + 1\) , \( a^{2} + a - 1\) , \( 4 a - 2\) , \( -8 a^{2} - a + 2\bigr] \)
${y}^2+\left(a^{2}-2\right){x}{y}+\left(a^{2}+a-1\right){y}={x}^{3}+\left(-a^{2}-a+1\right){x}^{2}+\left(4a-2\right){x}-8a^{2}-a+2$
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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.