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-a5
17.1-a
$8$
$12$
\(\Q(\zeta_{9})^+\)
$3$
$[3, 0]$
17.1
\( 17 \)
\( 17^{3} \)
$1.28960$
$(2a^2-a-3)$
0
$\Z/6\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2, 3$
2B , 3B.1.1
$1$
\( 3 \)
$1$
$54.78446428$
0.507263558
\( \frac{11224223245743811083}{4913} a^{2} + \frac{21094639493182324371}{4913} a + \frac{5972284442955277116}{4913} \)
\( \bigl[1\) , \( a^{2} - 2\) , \( a^{2} + a - 2\) , \( 1029 a^{2} - 331 a - 3016\) , \( 20866 a^{2} - 7345 a - 59899\bigr] \)
${y}^2+{x}{y}+\left(a^{2}+a-2\right){y}={x}^{3}+\left(a^{2}-2\right){x}^{2}+\left(1029a^{2}-331a-3016\right){x}+20866a^{2}-7345a-59899$
153.1-a5
153.1-a
$8$
$12$
\(\Q(\zeta_{9})^+\)
$3$
$[3, 0]$
153.1
\( 3^{2} \cdot 17 \)
\( 3^{6} \cdot 17^{3} \)
$1.85993$
$(-a^2+1), (2a^2-a-3)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2, 3$
2B , 3B.1.2
$4$
\( 2 \)
$1$
$4.696336808$
1.043630401
\( \frac{11224223245743811083}{4913} a^{2} + \frac{21094639493182324371}{4913} a + \frac{5972284442955277116}{4913} \)
\( \bigl[a^{2} + a - 1\) , \( -a^{2} - a + 1\) , \( 1\) , \( -59 a^{2} - 107 a - 139\) , \( -922 a^{2} - 1006 a + 149\bigr] \)
${y}^2+\left(a^{2}+a-1\right){x}{y}+{y}={x}^{3}+\left(-a^{2}-a+1\right){x}^{2}+\left(-59a^{2}-107a-139\right){x}-922a^{2}-1006a+149$
289.4-b1
289.4-b
$8$
$12$
\(\Q(\zeta_{9})^+\)
$3$
$[3, 0]$
289.4
\( 17^{2} \)
\( 17^{9} \)
$2.06791$
$(2a^2-a-3)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2, 3$
2B , 3B
$1$
\( 2^{2} \)
$4.818686163$
$0.893356286$
1.434934525
\( \frac{11224223245743811083}{4913} a^{2} + \frac{21094639493182324371}{4913} a + \frac{5972284442955277116}{4913} \)
\( \bigl[a^{2} + a - 1\) , \( a + 1\) , \( a\) , \( 5883 a^{2} - 1755 a - 17479\) , \( 298686 a^{2} - 100328 a - 866470\bigr] \)
${y}^2+\left(a^{2}+a-1\right){x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(5883a^{2}-1755a-17479\right){x}+298686a^{2}-100328a-866470$
Download
displayed columns for
results
to
Text
Pari/GP
SageMath
Magma
Oscar
CSV
*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.