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
176.1-a1
176.1-a
$2$
$3$
\(\Q(\sqrt{33}) \)
$2$
$[2, 0]$
176.1
\( 2^{4} \cdot 11 \)
\( 2^{16} \cdot 11^{6} \)
$1.86971$
$(-a-2), (-a+3), (-4a-9)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$3$
3B.1.2
$9$
\( 2 \)
$1$
$0.647455648$
2.028736108
\( -\frac{199794688}{1331} \)
\( \bigl[0\) , \( 1\) , \( 0\) , \( -77\) , \( -289\bigr] \)
${y}^2={x}^{3}+{x}^{2}-77{x}-289$
176.1-a2
176.1-a
$2$
$3$
\(\Q(\sqrt{33}) \)
$2$
$[2, 0]$
176.1
\( 2^{4} \cdot 11 \)
\( 2^{16} \cdot 11^{2} \)
$1.86971$
$(-a-2), (-a+3), (-4a-9)$
0
$\Z/3\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$3$
3B.1.1
$1$
\( 2 \cdot 3^{2} \)
$1$
$5.827100832$
2.028736108
\( \frac{8192}{11} \)
\( \bigl[0\) , \( 1\) , \( 0\) , \( 3\) , \( -1\bigr] \)
${y}^2={x}^{3}+{x}^{2}+3{x}-1$
176.1-b1
176.1-b
$2$
$3$
\(\Q(\sqrt{33}) \)
$2$
$[2, 0]$
176.1
\( 2^{4} \cdot 11 \)
\( 2^{16} \cdot 11^{6} \)
$1.86971$
$(-a-2), (-a+3), (-4a-9)$
$1$
$\Z/3\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$3$
3B.1.1
$1$
\( 2 \cdot 3^{3} \)
$0.172006545$
$9.327341860$
3.351406788
\( -\frac{199794688}{1331} \)
\( \bigl[0\) , \( -a\) , \( 0\) , \( 28459 a - 95968\) , \( -4431843 a + 14945420\bigr] \)
${y}^2={x}^{3}-a{x}^{2}+\left(28459a-95968\right){x}-4431843a+14945420$
176.1-b2
176.1-b
$2$
$3$
\(\Q(\sqrt{33}) \)
$2$
$[2, 0]$
176.1
\( 2^{4} \cdot 11 \)
\( 2^{16} \cdot 11^{2} \)
$1.86971$
$(-a-2), (-a+3), (-4a-9)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$3$
3B.1.2
$1$
\( 2 \)
$0.516019637$
$9.327341860$
3.351406788
\( \frac{8192}{11} \)
\( \bigl[0\) , \( -a\) , \( 0\) , \( -981 a + 3312\) , \( -33363 a + 112508\bigr] \)
${y}^2={x}^{3}-a{x}^{2}+\left(-981a+3312\right){x}-33363a+112508$
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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.