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
1.1-a3
1.1-a
$4$
$15$
\(\Q(\sqrt{229}) \)
$2$
$[2, 0]$
1.1
\( 1 \)
\( 3^{12} \)
$1.35225$
$\textsf{none}$
0
$\Z/3\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$2, 3, 5$
2Cn , 3B.1.1 , 5B
$9$
\( 1 \)
$1$
$38.58216293$
2.549581091
\( 888615 a + 6445522 \)
\( \bigl[a\) , \( 0\) , \( a\) , \( -3 a\) , \( -3 a + 9\bigr] \)
${y}^2+a{x}{y}+a{y}={x}^{3}-3a{x}-3a+9$
9.2-a3
9.2-a
$4$
$15$
\(\Q(\sqrt{229}) \)
$2$
$[2, 0]$
9.2
\( 3^{2} \)
\( 3^{18} \)
$2.34216$
$(3,a)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2, 3, 5$
2Cn , 3B , 5B
$1$
\( 1 \)
$2.861929958$
$8.520409212$
3.222787782
\( 888615 a + 6445522 \)
\( \bigl[1\) , \( -1\) , \( 1\) , \( 9336 a - 75308\) , \( 1341295 a - 10819386\bigr] \)
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}+\left(9336a-75308\right){x}+1341295a-10819386$
9.3-a3
9.3-a
$4$
$15$
\(\Q(\sqrt{229}) \)
$2$
$[2, 0]$
9.3
\( 3^{2} \)
\( 3^{6} \)
$2.34216$
$(3,a+2)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2, 3, 5$
2Cn , 3B , 5B
$1$
\( 1 \)
$0.572385991$
$42.60204606$
3.222787782
\( 888615 a + 6445522 \)
\( \bigl[a + 1\) , \( a + 1\) , \( a\) , \( 7 a + 31\) , \( 9 a + 52\bigr] \)
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(7a+31\right){x}+9a+52$
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.