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
11.1-a1
11.1-a
$3$
$25$
\(\Q(\sqrt{33}) \)
$2$
$[2, 0]$
11.1
\( 11 \)
\( 11^{2} \)
$0.93485$
$(-4a-9)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$5$
5B.4.2
$1$
\( 2 \)
$1$
$8.512583687$
2.963701228
\( -\frac{52893159101157376}{11} \)
\( \bigl[0\) , \( -a + 1\) , \( 1\) , \( -2877883 a - 6827148\) , \( 4506151140 a + 10689858189\bigr] \)
${y}^2+{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-2877883a-6827148\right){x}+4506151140a+10689858189$
11.1-a2
11.1-a
$3$
$25$
\(\Q(\sqrt{33}) \)
$2$
$[2, 0]$
11.1
\( 11 \)
\( 11^{10} \)
$0.93485$
$(-4a-9)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$5$
5Cs.4.1
$1$
\( 2 \)
$1$
$8.512583687$
2.963701228
\( -\frac{122023936}{161051} \)
\( \bigl[0\) , \( a\) , \( 1\) , \( 3803 a - 12821\) , \( -394830 a + 1331479\bigr] \)
${y}^2+{y}={x}^{3}+a{x}^{2}+\left(3803a-12821\right){x}-394830a+1331479$
11.1-a3
11.1-a
$3$
$25$
\(\Q(\sqrt{33}) \)
$2$
$[2, 0]$
11.1
\( 11 \)
\( 11^{2} \)
$0.93485$
$(-4a-9)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$5$
5B.4.1
$1$
\( 2 \)
$1$
$8.512583687$
2.963701228
\( -\frac{4096}{11} \)
\( \bigl[0\) , \( -a + 1\) , \( 1\) , \( -123 a - 288\) , \( -2880 a - 6831\bigr] \)
${y}^2+{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-123a-288\right){x}-2880a-6831$
11.1-b1
11.1-b
$3$
$25$
\(\Q(\sqrt{33}) \)
$2$
$[2, 0]$
11.1
\( 11 \)
\( 11^{2} \)
$0.93485$
$(-4a-9)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$5$
5B.1.2
$1$
\( 2 \)
$7.655751664$
$0.064435690$
0.343492567
\( -\frac{52893159101157376}{11} \)
\( \bigl[0\) , \( -1\) , \( 1\) , \( -7820\) , \( -263580\bigr] \)
${y}^2+{y}={x}^{3}-{x}^{2}-7820{x}-263580$
11.1-b2
11.1-b
$3$
$25$
\(\Q(\sqrt{33}) \)
$2$
$[2, 0]$
11.1
\( 11 \)
\( 11^{10} \)
$0.93485$
$(-4a-9)$
$1$
$\Z/5\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$5$
5Cs.1.1
$1$
\( 2 \cdot 5 \)
$1.531150332$
$1.610892258$
0.343492567
\( -\frac{122023936}{161051} \)
\( \bigl[0\) , \( -1\) , \( 1\) , \( -10\) , \( -20\bigr] \)
${y}^2+{y}={x}^{3}-{x}^{2}-10{x}-20$
11.1-b3
11.1-b
$3$
$25$
\(\Q(\sqrt{33}) \)
$2$
$[2, 0]$
11.1
\( 11 \)
\( 11^{2} \)
$0.93485$
$(-4a-9)$
$1$
$\Z/5\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$5$
5B.1.1
$1$
\( 2 \)
$0.306230066$
$40.27230645$
0.343492567
\( -\frac{4096}{11} \)
\( \bigl[0\) , \( -1\) , \( 1\) , \( 0\) , \( 0\bigr] \)
${y}^2+{y}={x}^{3}-{x}^{2}$
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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.