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
17.2-a1
17.2-a
$2$
$3$
\(\Q(\sqrt{21}) \)
$2$
$[2, 0]$
17.2
\( 17 \)
\( -17 \)
$0.83150$
$(2a+1)$
0
$\Z/3\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$3$
3B.1.1
$1$
\( 1 \)
$1$
$45.16448385$
1.095077597
\( -\frac{20811}{17} a + \frac{1220}{17} \)
\( \bigl[a\) , \( 0\) , \( a\) , \( -2 a - 5\) , \( a + 1\bigr] \)
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-2a-5\right){x}+a+1$
17.2-a2
17.2-a
$2$
$3$
\(\Q(\sqrt{21}) \)
$2$
$[2, 0]$
17.2
\( 17 \)
\( - 17^{3} \)
$0.83150$
$(2a+1)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$3$
3B.1.2
$1$
\( 1 \)
$1$
$5.018275983$
1.095077597
\( -\frac{2723256379739}{4913} a + \frac{7601399159655}{4913} \)
\( \bigl[a\) , \( 0\) , \( a\) , \( 13 a + 20\) , \( -11 a - 22\bigr] \)
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(13a+20\right){x}-11a-22$
17.2-b1
17.2-b
$2$
$3$
\(\Q(\sqrt{21}) \)
$2$
$[2, 0]$
17.2
\( 17 \)
\( -17 \)
$0.83150$
$(2a+1)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$3$
3B.1.2
$1$
\( 1 \)
$0.092314733$
$19.62917645$
0.790848774
\( -\frac{20811}{17} a + \frac{1220}{17} \)
\( \bigl[a + 1\) , \( -1\) , \( 1\) , \( 0\) , \( 0\bigr] \)
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}-{x}^{2}$
17.2-b2
17.2-b
$2$
$3$
\(\Q(\sqrt{21}) \)
$2$
$[2, 0]$
17.2
\( 17 \)
\( - 17^{3} \)
$0.83150$
$(2a+1)$
$1$
$\Z/3\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$3$
3B.1.1
$1$
\( 3 \)
$0.276944199$
$19.62917645$
0.790848774
\( -\frac{2723256379739}{4913} a + \frac{7601399159655}{4913} \)
\( \bigl[a + 1\) , \( -1\) , \( 1\) , \( 10 a - 25\) , \( -26 a + 76\bigr] \)
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}-{x}^{2}+\left(10a-25\right){x}-26a+76$
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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.