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
175.1-a1
175.1-a
$3$
$9$
\(\Q(\sqrt{77}) \)
$2$
$[2, 0]$
175.1
\( 5^{2} \cdot 7 \)
\( 5^{18} \cdot 7^{2} \)
$2.85196$
$(a+3), (5)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$3$
3B
$1$
\( 2 \cdot 3^{2} \)
$0.040819755$
$4.862220259$
0.814258252
\( -\frac{250523582464}{13671875} \)
\( \bigl[0\) , \( a + 1\) , \( 1\) , \( 1183 a - 5772\) , \( -49618 a + 242512\bigr] \)
${y}^2+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(1183a-5772\right){x}-49618a+242512$
175.1-a2
175.1-a
$3$
$9$
\(\Q(\sqrt{77}) \)
$2$
$[2, 0]$
175.1
\( 5^{2} \cdot 7 \)
\( 5^{2} \cdot 7^{2} \)
$2.85196$
$(a+3), (5)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$3$
3B
$1$
\( 2 \)
$0.367377802$
$4.862220259$
0.814258252
\( -\frac{262144}{35} \)
\( \bigl[0\) , \( -a - 1\) , \( 1\) , \( -11 a - 40\) , \( -30 a - 116\bigr] \)
${y}^2+{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-11a-40\right){x}-30a-116$
175.1-a3
175.1-a
$3$
$9$
\(\Q(\sqrt{77}) \)
$2$
$[2, 0]$
175.1
\( 5^{2} \cdot 7 \)
\( 5^{6} \cdot 7^{6} \)
$2.85196$
$(a+3), (5)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$3$
3Cs
$1$
\( 2 \cdot 3 \)
$0.122459267$
$4.862220259$
0.814258252
\( \frac{71991296}{42875} \)
\( \bigl[0\) , \( -a - 1\) , \( 1\) , \( 79 a + 310\) , \( -20 a - 77\bigr] \)
${y}^2+{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(79a+310\right){x}-20a-77$
175.1-b1
175.1-b
$3$
$9$
\(\Q(\sqrt{77}) \)
$2$
$[2, 0]$
175.1
\( 5^{2} \cdot 7 \)
\( 5^{18} \cdot 7^{2} \)
$2.85196$
$(a+3), (5)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$3$
3B.1.2
$1$
\( 2 \cdot 3^{2} \)
$1$
$0.494084210$
1.013510185
\( -\frac{250523582464}{13671875} \)
\( \bigl[0\) , \( 1\) , \( 1\) , \( -131\) , \( -650\bigr] \)
${y}^2+{y}={x}^{3}+{x}^{2}-131{x}-650$
175.1-b2
175.1-b
$3$
$9$
\(\Q(\sqrt{77}) \)
$2$
$[2, 0]$
175.1
\( 5^{2} \cdot 7 \)
\( 5^{2} \cdot 7^{2} \)
$2.85196$
$(a+3), (5)$
0
$\Z/3\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$3$
3B.1.1
$1$
\( 2 \)
$1$
$40.02082101$
1.013510185
\( -\frac{262144}{35} \)
\( \bigl[0\) , \( 1\) , \( 1\) , \( -1\) , \( 0\bigr] \)
${y}^2+{y}={x}^{3}+{x}^{2}-{x}$
175.1-b3
175.1-b
$3$
$9$
\(\Q(\sqrt{77}) \)
$2$
$[2, 0]$
175.1
\( 5^{2} \cdot 7 \)
\( 5^{6} \cdot 7^{6} \)
$2.85196$
$(a+3), (5)$
0
$\Z/3\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$3$
3Cs.1.1
$1$
\( 2 \cdot 3^{2} \)
$1$
$4.446757890$
1.013510185
\( \frac{71991296}{42875} \)
\( \bigl[0\) , \( 1\) , \( 1\) , \( 9\) , \( 1\bigr] \)
${y}^2+{y}={x}^{3}+{x}^{2}+9{x}+1$
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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.