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
17.3-a6
17.3-a
$8$
$12$
\(\Q(\zeta_{9})^+\)
$3$
$[3, 0]$
17.3
\( 17 \)
\( 17 \)
$1.28960$
$(a^2-2a-3)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2, 3$
2B , 3B.1.2
$1$
\( 1 \)
$1$
$18.26148809$
0.507263558
\( \frac{5036213937953050641}{17} a^{2} - \frac{7715927403056521557}{17} a - \frac{3287155192616633274}{17} \)
\( \bigl[a^{2} + a - 2\) , \( a^{2} + a - 2\) , \( a^{2} + a - 1\) , \( -35 a^{2} + 102 a - 63\) , \( -639 a^{2} + 789 a + 777\bigr] \)
${y}^2+\left(a^{2}+a-2\right){x}{y}+\left(a^{2}+a-1\right){y}={x}^{3}+\left(a^{2}+a-2\right){x}^{2}+\left(-35a^{2}+102a-63\right){x}-639a^{2}+789a+777$
153.3-a6
153.3-a
$8$
$12$
\(\Q(\zeta_{9})^+\)
$3$
$[3, 0]$
153.3
\( 3^{2} \cdot 17 \)
\( 3^{6} \cdot 17 \)
$1.85993$
$(-a^2+1), (a^2-2a-3)$
0
$\Z/6\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2, 3$
2B , 3B.1.1
$4$
\( 2 \)
$1$
$42.26703127$
1.043630401
\( \frac{5036213937953050641}{17} a^{2} - \frac{7715927403056521557}{17} a - \frac{3287155192616633274}{17} \)
\( \bigl[a\) , \( -a^{2} + 3\) , \( a\) , \( 86 a^{2} - 14 a - 290\) , \( 819 a^{2} - 335 a - 2257\bigr] \)
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a^{2}+3\right){x}^{2}+\left(86a^{2}-14a-290\right){x}+819a^{2}-335a-2257$
289.5-b6
289.5-b
$8$
$12$
\(\Q(\zeta_{9})^+\)
$3$
$[3, 0]$
289.5
\( 17^{2} \)
\( 17^{7} \)
$2.06791$
$(a^2-2a-3)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2, 3$
2B , 3B
$1$
\( 2^{2} \)
$1.606228721$
$2.680068859$
1.434934525
\( \frac{5036213937953050641}{17} a^{2} - \frac{7715927403056521557}{17} a - \frac{3287155192616633274}{17} \)
\( \bigl[1\) , \( -a^{2} - a + 1\) , \( a^{2} + a - 1\) , \( -251 a^{2} + 600 a - 245\) , \( -5411 a^{2} + 10241 a - 127\bigr] \)
${y}^2+{x}{y}+\left(a^{2}+a-1\right){y}={x}^{3}+\left(-a^{2}-a+1\right){x}^{2}+\left(-251a^{2}+600a-245\right){x}-5411a^{2}+10241a-127$
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.