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
$2$
$3$
4.4.16317.1
$4$
$[4, 0]$
17.1
\( 17 \)
\( - 17^{3} \)
$16.26540$
$(a^3-2a^2-3a+2)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$3$
3B
$1$
\( 1 \)
$1$
$413.6401340$
3.238191387
\( -\frac{52354566}{4913} a^{3} + \frac{40253922}{4913} a^{2} + \frac{264541626}{4913} a + \frac{53538489}{4913} \)
\( \bigl[a^{2} - a - 3\) , \( -a^{3} + a^{2} + 4 a - 1\) , \( a^{3} - a^{2} - 3 a + 2\) , \( -2 a^{2} + a + 8\) , \( -a^{3} + 3 a\bigr] \)
${y}^2+\left(a^{2}-a-3\right){x}{y}+\left(a^{3}-a^{2}-3a+2\right){y}={x}^{3}+\left(-a^{3}+a^{2}+4a-1\right){x}^{2}+\left(-2a^{2}+a+8\right){x}-a^{3}+3a$
17.1-a2
17.1-a
$2$
$3$
4.4.16317.1
$4$
$[4, 0]$
17.1
\( 17 \)
\( -17 \)
$16.26540$
$(a^3-2a^2-3a+2)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$3$
3B
$1$
\( 1 \)
$1$
$413.6401340$
3.238191387
\( -\frac{35927415}{17} a^{3} - \frac{26434188}{17} a^{2} + \frac{70640748}{17} a + \frac{12827025}{17} \)
\( \bigl[a\) , \( -a - 1\) , \( a^{3} - 4 a - 1\) , \( 9 a^{3} - 8 a^{2} - 47 a - 8\) , \( -37 a^{3} + 29 a^{2} + 181 a + 31\bigr] \)
${y}^2+a{x}{y}+\left(a^{3}-4a-1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(9a^{3}-8a^{2}-47a-8\right){x}-37a^{3}+29a^{2}+181a+31$
17.1-b1
17.1-b
$2$
$3$
4.4.16317.1
$4$
$[4, 0]$
17.1
\( 17 \)
\( -17 \)
$16.26540$
$(a^3-2a^2-3a+2)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$3$
3B
$1$
\( 1 \)
$0.129667076$
$533.0003637$
2.164198337
\( -\frac{35927415}{17} a^{3} - \frac{26434188}{17} a^{2} + \frac{70640748}{17} a + \frac{12827025}{17} \)
\( \bigl[a^{2} - a - 3\) , \( a^{3} - 2 a^{2} - 3 a + 3\) , \( a^{3} - a^{2} - 3 a + 2\) , \( a^{3} - 2 a^{2} - 6 a + 5\) , \( -3 a^{3} + 5 a^{2} + 10 a - 15\bigr] \)
${y}^2+\left(a^{2}-a-3\right){x}{y}+\left(a^{3}-a^{2}-3a+2\right){y}={x}^{3}+\left(a^{3}-2a^{2}-3a+3\right){x}^{2}+\left(a^{3}-2a^{2}-6a+5\right){x}-3a^{3}+5a^{2}+10a-15$
17.1-b2
17.1-b
$2$
$3$
4.4.16317.1
$4$
$[4, 0]$
17.1
\( 17 \)
\( - 17^{3} \)
$16.26540$
$(a^3-2a^2-3a+2)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$3$
3B
$1$
\( 3 \)
$0.043222358$
$533.0003637$
2.164198337
\( -\frac{52354566}{4913} a^{3} + \frac{40253922}{4913} a^{2} + \frac{264541626}{4913} a + \frac{53538489}{4913} \)
\( \bigl[a^{2} - a - 2\) , \( a^{3} - a^{2} - 4 a + 2\) , \( a^{2} - 2\) , \( 2 a^{3} - 6 a^{2} + 2 a + 3\) , \( 6 a^{3} - 22 a^{2} + 14 a + 4\bigr] \)
${y}^2+\left(a^{2}-a-2\right){x}{y}+\left(a^{2}-2\right){y}={x}^{3}+\left(a^{3}-a^{2}-4a+2\right){x}^{2}+\left(2a^{3}-6a^{2}+2a+3\right){x}+6a^{3}-22a^{2}+14a+4$
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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.