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
17.1-a1
17.1-a
$2$
$3$
\(\Q(\sqrt{21}) \)
$2$
$[2, 0]$
17.1
\( 17 \)
\( -17 \)
$0.83150$
$(-2a+3)$
0
$\Z/3\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$3$
3B.1.1
$1$
\( 1 \)
$1$
$45.16448385$
1.095077597
\( \frac{20811}{17} a - \frac{19591}{17} \)
\( \bigl[a + 1\) , \( -a\) , \( a + 1\) , \( -7\) , \( -2 a + 2\bigr] \)
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}-7{x}-2a+2$
17.1-b1
17.1-b
$2$
$3$
\(\Q(\sqrt{21}) \)
$2$
$[2, 0]$
17.1
\( 17 \)
\( -17 \)
$0.83150$
$(-2a+3)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$3$
3B.1.2
$1$
\( 1 \)
$0.092314733$
$19.62917645$
0.790848774
\( \frac{20811}{17} a - \frac{19591}{17} \)
\( \bigl[a\) , \( -a\) , \( 1\) , \( -a + 1\) , \( 0\bigr] \)
${y}^2+a{x}{y}+{y}={x}^{3}-a{x}^{2}+\left(-a+1\right){x}$
153.1-b1
153.1-b
$2$
$3$
\(\Q(\sqrt{21}) \)
$2$
$[2, 0]$
153.1
\( 3^{2} \cdot 17 \)
\( - 3^{6} \cdot 17 \)
$1.44019$
$(-a+2), (-2a+3)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
$3$
3B
$1$
\( 1 \)
$1$
$9.864496947$
2.152609712
\( \frac{20811}{17} a - \frac{19591}{17} \)
\( \bigl[1\) , \( a\) , \( a + 1\) , \( a - 2\) , \( -3\bigr] \)
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(a-2\right){x}-3$
153.1-e1
153.1-e
$2$
$3$
\(\Q(\sqrt{21}) \)
$2$
$[2, 0]$
153.1
\( 3^{2} \cdot 17 \)
\( - 3^{6} \cdot 17 \)
$1.44019$
$(-a+2), (-2a+3)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
$3$
3B
$1$
\( 1 \)
$0.162669075$
$29.95731825$
2.126807977
\( \frac{20811}{17} a - \frac{19591}{17} \)
\( \bigl[a + 1\) , \( -a - 1\) , \( a\) , \( -3 a - 6\) , \( a + 1\bigr] \)
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-3a-6\right){x}+a+1$
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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.