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
181.2-a1
181.2-a
$2$
$5$
\(\Q(\zeta_{7})^+\)
$3$
$[3, 0]$
181.2
\( 181 \)
\( -181 \)
$1.48770$
$(-5a^2+4a+5)$
0
$\Z/5\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$5$
5B.1.1
$1$
\( 1 \)
$1$
$145.9810872$
0.834177641
\( \frac{1969280916}{181} a^{2} - \frac{1092868891}{181} a - \frac{4424933270}{181} \)
\( \bigl[a + 1\) , \( a\) , \( a\) , \( a^{2} - 1\) , \( 0\bigr] \)
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+a{x}^{2}+\left(a^{2}-1\right){x}$
181.2-a2
181.2-a
$2$
$5$
\(\Q(\zeta_{7})^+\)
$3$
$[3, 0]$
181.2
\( 181 \)
\( - 181^{5} \)
$1.48770$
$(-5a^2+4a+5)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$5$
5B.1.2
$1$
\( 5 \)
$1$
$1.167848697$
0.834177641
\( -\frac{24431384735829497330761}{194264244901} a^{2} - \frac{19592447468941339233880}{194264244901} a + \frac{13558395102062296623788}{194264244901} \)
\( \bigl[a + 1\) , \( a\) , \( a\) , \( -169 a^{2} - 105 a + 84\) , \( -1786 a^{2} - 1362 a + 962\bigr] \)
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+a{x}^{2}+\left(-169a^{2}-105a+84\right){x}-1786a^{2}-1362a+962$
181.2-b1
181.2-b
$2$
$3$
\(\Q(\zeta_{7})^+\)
$3$
$[3, 0]$
181.2
\( 181 \)
\( - 181^{3} \)
$1.48770$
$(-5a^2+4a+5)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$3$
3B.1.2
$1$
\( 3 \)
$1$
$1.896361674$
0.812726431
\( \frac{80035625147780316014}{5929741} a^{2} - \frac{44416416383871410137}{5929741} a - \frac{179838425659792950673}{5929741} \)
\( \bigl[a^{2} - 2\) , \( 1\) , \( a\) , \( -175 a^{2} + 406 a - 167\) , \( -2210 a^{2} + 5007 a - 1845\bigr] \)
${y}^2+\left(a^{2}-2\right){x}{y}+a{y}={x}^{3}+{x}^{2}+\left(-175a^{2}+406a-167\right){x}-2210a^{2}+5007a-1845$
181.2-b2
181.2-b
$2$
$3$
\(\Q(\zeta_{7})^+\)
$3$
$[3, 0]$
181.2
\( 181 \)
\( -181 \)
$1.48770$
$(-5a^2+4a+5)$
0
$\Z/3\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$3$
3B.1.1
$1$
\( 1 \)
$1$
$51.20176520$
0.812726431
\( -\frac{163537056709}{181} a^{2} - \frac{131149821769}{181} a + \frac{90752129728}{181} \)
\( \bigl[a^{2} - 2\) , \( 1\) , \( a\) , \( -4 a + 3\) , \( -11 a^{2} + 25 a - 9\bigr] \)
${y}^2+\left(a^{2}-2\right){x}{y}+a{y}={x}^{3}+{x}^{2}+\left(-4a+3\right){x}-11a^{2}+25a-9$
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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.