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
1.1-a1
1.1-a
$6$
$99$
\(\Q(\sqrt{33}) \)
$2$
$[2, 0]$
1.1
\( 1 \)
\( 1 \)
$0.51333$
$\textsf{none}$
0
$\mathsf{trivial}$
$\textsf{potential}$
$-99$
$N(\mathrm{U}(1))$
✓
✓
✓
$3$
3B.1.2
$1$
\( 1 \)
$1$
$2.562583394$
0.446088510
\( -6548115718144 a - 15533972619264 \)
\( \bigl[0\) , \( -a\) , \( 1\) , \( -435 a - 1030\) , \( -7890 a - 18717\bigr] \)
${y}^2+{y}={x}^{3}-a{x}^{2}+\left(-435a-1030\right){x}-7890a-18717$
1.1-a2
1.1-a
$6$
$99$
\(\Q(\sqrt{33}) \)
$2$
$[2, 0]$
1.1
\( 1 \)
\( 1 \)
$0.51333$
$\textsf{none}$
0
$\Z/3\Z$
$\textsf{potential}$
$-99$
$N(\mathrm{U}(1))$
✓
✓
✓
$3$
3B.1.1
$1$
\( 1 \)
$1$
$23.06325055$
0.446088510
\( -6548115718144 a - 15533972619264 \)
\( \bigl[0\) , \( a - 1\) , \( 1\) , \( -25 a + 85\) , \( 72 a - 243\bigr] \)
${y}^2+{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-25a+85\right){x}+72a-243$
1.1-a3
1.1-a
$6$
$99$
\(\Q(\sqrt{33}) \)
$2$
$[2, 0]$
1.1
\( 1 \)
\( 1 \)
$0.51333$
$\textsf{none}$
0
$\Z/3\Z$
$\textsf{potential}$
$-11$
$N(\mathrm{U}(1))$
✓
✓
✓
$3$
3Cs.1.1
$1$
\( 1 \)
$1$
$23.06325055$
0.446088510
\( -32768 \)
\( \bigl[0\) , \( a - 1\) , \( 1\) , \( 5 a - 15\) , \( 6 a - 20\bigr] \)
${y}^2+{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(5a-15\right){x}+6a-20$
1.1-a4
1.1-a
$6$
$99$
\(\Q(\sqrt{33}) \)
$2$
$[2, 0]$
1.1
\( 1 \)
\( 1 \)
$0.51333$
$\textsf{none}$
0
$\Z/3\Z$
$\textsf{potential}$
$-11$
$N(\mathrm{U}(1))$
✓
✓
✓
$3$
3Cs.1.1
$1$
\( 1 \)
$1$
$23.06325055$
0.446088510
\( -32768 \)
\( \bigl[0\) , \( -a\) , \( 1\) , \( -5 a - 10\) , \( -6 a - 14\bigr] \)
${y}^2+{y}={x}^{3}-a{x}^{2}+\left(-5a-10\right){x}-6a-14$
1.1-a5
1.1-a
$6$
$99$
\(\Q(\sqrt{33}) \)
$2$
$[2, 0]$
1.1
\( 1 \)
\( 1 \)
$0.51333$
$\textsf{none}$
0
$\mathsf{trivial}$
$\textsf{potential}$
$-99$
$N(\mathrm{U}(1))$
✓
✓
✓
$3$
3B.1.2
$1$
\( 1 \)
$1$
$2.562583394$
0.446088510
\( 6548115718144 a - 22082088337408 \)
\( \bigl[0\) , \( a - 1\) , \( 1\) , \( 435 a - 1465\) , \( 7890 a - 26607\bigr] \)
${y}^2+{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(435a-1465\right){x}+7890a-26607$
1.1-a6
1.1-a
$6$
$99$
\(\Q(\sqrt{33}) \)
$2$
$[2, 0]$
1.1
\( 1 \)
\( 1 \)
$0.51333$
$\textsf{none}$
0
$\Z/3\Z$
$\textsf{potential}$
$-99$
$N(\mathrm{U}(1))$
✓
✓
✓
$3$
3B.1.1
$1$
\( 1 \)
$1$
$23.06325055$
0.446088510
\( 6548115718144 a - 22082088337408 \)
\( \bigl[0\) , \( -a\) , \( 1\) , \( 25 a + 60\) , \( -72 a - 171\bigr] \)
${y}^2+{y}={x}^{3}-a{x}^{2}+\left(25a+60\right){x}-72a-171$
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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.