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-a8
17.1-a
$8$
$12$
\(\Q(\zeta_{9})^+\)
$3$
$[3, 0]$
17.1
\( 17 \)
\( - 17^{12} \)
$1.28960$
$(2a^2-a-3)$
0
$\Z/6\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2, 3$
2B , 3B.1.1
$1$
\( 2^{2} \cdot 3 \)
$1$
$13.69611607$
0.507263558
\( \frac{4075073731548124101}{582622237229761} a^{2} - \frac{3433122709460467011}{582622237229761} a - \frac{810676269288190764}{582622237229761} \)
\( \bigl[1\) , \( a^{2} - 2\) , \( a^{2} + a - 2\) , \( -311 a^{2} + 119 a + 874\) , \( 1414 a^{2} - 463 a - 4127\bigr] \)
${y}^2+{x}{y}+\left(a^{2}+a-2\right){y}={x}^{3}+\left(a^{2}-2\right){x}^{2}+\left(-311a^{2}+119a+874\right){x}+1414a^{2}-463a-4127$
153.1-a8
153.1-a
$8$
$12$
\(\Q(\zeta_{9})^+\)
$3$
$[3, 0]$
153.1
\( 3^{2} \cdot 17 \)
\( - 3^{6} \cdot 17^{12} \)
$1.85993$
$(-a^2+1), (2a^2-a-3)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2, 3$
2B , 3B.1.2
$1$
\( 2^{2} \)
$1$
$9.392673617$
1.043630401
\( \frac{4075073731548124101}{582622237229761} a^{2} - \frac{3433122709460467011}{582622237229761} a - \frac{810676269288190764}{582622237229761} \)
\( \bigl[a^{2} + a - 1\) , \( -a^{2} - a + 1\) , \( 1\) , \( -29 a^{2} + 13 a + 41\) , \( 2 a^{2} - 58 a + 23\bigr] \)
${y}^2+\left(a^{2}+a-1\right){x}{y}+{y}={x}^{3}+\left(-a^{2}-a+1\right){x}^{2}+\left(-29a^{2}+13a+41\right){x}+2a^{2}-58a+23$
289.4-b4
289.4-b
$8$
$12$
\(\Q(\zeta_{9})^+\)
$3$
$[3, 0]$
289.4
\( 17^{2} \)
\( - 17^{18} \)
$2.06791$
$(2a^2-a-3)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2, 3$
2B , 3B
$1$
\( 2^{2} \)
$1.204671540$
$3.573425146$
1.434934525
\( \frac{4075073731548124101}{582622237229761} a^{2} - \frac{3433122709460467011}{582622237229761} a - \frac{810676269288190764}{582622237229761} \)
\( \bigl[a^{2} + a - 1\) , \( a + 1\) , \( a\) , \( -1847 a^{2} + 765 a + 5101\) , \( 18050 a^{2} - 7176 a - 50254\bigr] \)
${y}^2+\left(a^{2}+a-1\right){x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-1847a^{2}+765a+5101\right){x}+18050a^{2}-7176a-50254$
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.