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-a3
175.1-a
$3$
$9$
\(\Q(\sqrt{21}) \)
$2$
$[2, 0]$
175.1
\( 5^{2} \cdot 7 \)
\( 5^{6} \cdot 7^{6} \)
$1.48939$
$(-a), (-a+1), (a+3)$
$1$
$\Z/3\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$3$
3Cs.1.1
$1$
\( 2 \cdot 3 \)
$1.352388612$
$4.446757890$
1.749742251
\( \frac{71991296}{42875} \)
\( \bigl[0\) , \( 1\) , \( 1\) , \( 9\) , \( 1\bigr] \)
${y}^2+{y}={x}^{3}+{x}^{2}+9{x}+1$
175.1-b3
175.1-b
$3$
$9$
\(\Q(\sqrt{21}) \)
$2$
$[2, 0]$
175.1
\( 5^{2} \cdot 7 \)
\( 5^{6} \cdot 7^{6} \)
$1.48939$
$(-a), (-a+1), (a+3)$
$1$
$\Z/3\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$3$
3Cs.1.1
$1$
\( 2 \cdot 3^{3} \)
$0.122459267$
$4.862220259$
1.559185847
\( \frac{71991296}{42875} \)
\( \bigl[0\) , \( a\) , \( 1\) , \( -43 a + 123\) , \( -14 a + 40\bigr] \)
${y}^2+{y}={x}^{3}+a{x}^{2}+\left(-43a+123\right){x}-14a+40$
1575.1-i3
1575.1-i
$3$
$9$
\(\Q(\sqrt{21}) \)
$2$
$[2, 0]$
1575.1
\( 3^{2} \cdot 5^{2} \cdot 7 \)
\( 3^{6} \cdot 5^{6} \cdot 7^{6} \)
$2.57969$
$(-a+2), (-a), (-a+1), (a+3)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$3$
3Cs
$1$
\( 2 \cdot 3 \)
$1$
$2.684592849$
3.514957126
\( \frac{71991296}{42875} \)
\( \bigl[0\) , \( -a - 1\) , \( 1\) , \( -25 a + 80\) , \( 11 a - 39\bigr] \)
${y}^2+{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-25a+80\right){x}+11a-39$
1575.1-n3
1575.1-n
$3$
$9$
\(\Q(\sqrt{21}) \)
$2$
$[2, 0]$
1575.1
\( 3^{2} \cdot 5^{2} \cdot 7 \)
\( 3^{6} \cdot 5^{6} \cdot 7^{6} \)
$2.57969$
$(-a+2), (-a), (-a+1), (a+3)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$3$
3Cs
$1$
\( 2 \cdot 3 \)
$1$
$2.684592849$
3.514957126
\( \frac{71991296}{42875} \)
\( \bigl[0\) , \( a + 1\) , \( 1\) , \( 27 a + 54\) , \( 15 a + 26\bigr] \)
${y}^2+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(27a+54\right){x}+15a+26$
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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.