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
$2$
$3$
\(\Q(\sqrt{77}) \)
$2$
$[2, 0]$
176.1
\( 2^{4} \cdot 11 \)
\( 2^{16} \cdot 11^{6} \)
$2.85603$
$(a-6), (2)$
$2$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$3$
3B
$1$
\( 2 \cdot 3 \)
$0.224246258$
$9.327341860$
5.720697453
\( -\frac{199794688}{1331} \)
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -695 a - 2700\) , \( 22426 a + 87181\bigr] \)
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(-695a-2700\right){x}+22426a+87181$
176.1-a2
176.1-a
$2$
$3$
\(\Q(\sqrt{77}) \)
$2$
$[2, 0]$
176.1
\( 2^{4} \cdot 11 \)
\( 2^{16} \cdot 11^{2} \)
$2.85603$
$(a-6), (2)$
$2$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$3$
3B
$1$
\( 2 \cdot 3 \)
$0.224246258$
$9.327341860$
5.720697453
\( \frac{8192}{11} \)
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 25 a + 100\) , \( 106 a + 413\bigr] \)
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(25a+100\right){x}+106a+413$
176.1-b1
176.1-b
$2$
$3$
\(\Q(\sqrt{77}) \)
$2$
$[2, 0]$
176.1
\( 2^{4} \cdot 11 \)
\( 2^{16} \cdot 11^{6} \)
$2.85603$
$(a-6), (2)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$3$
3B.1.2
$4$
\( 2 \cdot 3 \)
$1$
$0.647455648$
1.770826053
\( -\frac{199794688}{1331} \)
\( \bigl[0\) , \( 1\) , \( 0\) , \( -77\) , \( -289\bigr] \)
${y}^2={x}^{3}+{x}^{2}-77{x}-289$
176.1-b2
176.1-b
$2$
$3$
\(\Q(\sqrt{77}) \)
$2$
$[2, 0]$
176.1
\( 2^{4} \cdot 11 \)
\( 2^{16} \cdot 11^{2} \)
$2.85603$
$(a-6), (2)$
0
$\Z/3\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$3$
3B.1.1
$4$
\( 2 \cdot 3 \)
$1$
$5.827100832$
1.770826053
\( \frac{8192}{11} \)
\( \bigl[0\) , \( 1\) , \( 0\) , \( 3\) , \( -1\bigr] \)
${y}^2={x}^{3}+{x}^{2}+3{x}-1$
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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.