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
109.1-a1
109.1-a
$2$
$11$
4.4.725.1
$4$
$[4, 0]$
109.1
\( 109 \)
\( 109^{11} \)
$4.32500$
$(-a^3+a^2+5a)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$11$
11B.1.2
$121$
\( 1 \)
$1$
$0.188236531$
0.845902442
\( \frac{16235216636009362328759362787732}{25804264053054077850709} a^{3} - \frac{4260010497864756660724731056719}{25804264053054077850709} a^{2} - \frac{51855684642834574989082645270777}{25804264053054077850709} a - \frac{22019771839812368650729782793234}{25804264053054077850709} \)
\( \bigl[a^{3} - 3 a\) , \( -a^{3} + 2 a^{2} + a - 3\) , \( a^{2} - a\) , \( 540 a^{3} - 71 a^{2} - 1805 a - 989\) , \( 10516 a^{3} - 2406 a^{2} - 33972 a - 15480\bigr] \)
${y}^2+\left(a^{3}-3a\right){x}{y}+\left(a^{2}-a\right){y}={x}^{3}+\left(-a^{3}+2a^{2}+a-3\right){x}^{2}+\left(540a^{3}-71a^{2}-1805a-989\right){x}+10516a^{3}-2406a^{2}-33972a-15480$
109.1-a2
109.1-a
$2$
$11$
4.4.725.1
$4$
$[4, 0]$
109.1
\( 109 \)
\( 109 \)
$4.32500$
$(-a^3+a^2+5a)$
0
$\Z/11\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$11$
11B.1.1
$1$
\( 1 \)
$1$
$2755.971058$
0.845902442
\( \frac{3718291}{109} a^{3} - \frac{9007348}{109} a^{2} + \frac{1282551}{109} a + \frac{2463928}{109} \)
\( \bigl[a^{3} - 3 a\) , \( -a^{3} + 2 a^{2} + a - 3\) , \( a^{2} - a\) , \( -a^{2} + 1\) , \( -a^{2} + a + 1\bigr] \)
${y}^2+\left(a^{3}-3a\right){x}{y}+\left(a^{2}-a\right){y}={x}^{3}+\left(-a^{3}+2a^{2}+a-3\right){x}^{2}+\left(-a^{2}+1\right){x}-a^{2}+a+1$
109.1-b1
109.1-b
$1$
$1$
4.4.725.1
$4$
$[4, 0]$
109.1
\( 109 \)
\( 109 \)
$4.32500$
$(-a^3+a^2+5a)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$1$
\( 1 \)
$1$
$22.90788173$
0.850777369
\( -\frac{5067738978911}{109} a^{3} + \frac{7485983125541}{109} a^{2} + \frac{11630034812778}{109} a - \frac{10618018451270}{109} \)
\( \bigl[a^{3} - a^{2} - 2 a + 2\) , \( -a^{2} + 2 a + 1\) , \( a^{2} - a - 1\) , \( 4 a^{3} - 15 a - 8\) , \( -8 a^{3} + 2 a^{2} + 25 a + 8\bigr] \)
${y}^2+\left(a^{3}-a^{2}-2a+2\right){x}{y}+\left(a^{2}-a-1\right){y}={x}^{3}+\left(-a^{2}+2a+1\right){x}^{2}+\left(4a^{3}-15a-8\right){x}-8a^{3}+2a^{2}+25a+8$
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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.