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
147.1-a3
147.1-a
$8$
$16$
\(\Q(\sqrt{3}) \)
$2$
$[2, 0]$
147.1
\( 3 \cdot 7^{2} \)
\( 3^{4} \cdot 7^{2} \)
$1.07785$
$(a), (7)$
0
$\Z/4\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$2$
2B
$1$
\( 2^{2} \)
$1$
$13.02432697$
0.939949835
\( \frac{103823}{63} \)
\( \bigl[a\) , \( -a + 1\) , \( 0\) , \( -56 a + 97\) , \( 0\bigr] \)
${y}^2+a{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-56a+97\right){x}$
147.1-b3
147.1-b
$8$
$16$
\(\Q(\sqrt{3}) \)
$2$
$[2, 0]$
147.1
\( 3 \cdot 7^{2} \)
\( 3^{4} \cdot 7^{2} \)
$1.07785$
$(a), (7)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$2$
2B
$1$
\( 2 \)
$0.373149604$
$14.60752776$
1.573508462
\( \frac{103823}{63} \)
\( \bigl[1\) , \( a + 1\) , \( 1\) , \( -54 a + 96\) , \( -55 a + 96\bigr] \)
${y}^2+{x}{y}+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-54a+96\right){x}-55a+96$
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.