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
28.1-b5
28.1-b
$6$
$18$
\(\Q(\sqrt{161}) \)
$2$
$[2, 0]$
28.1
\( 2^{2} \cdot 7 \)
\( 2^{2} \cdot 7^{4} \)
$2.60820$
$(a+6), (-a+7), (-32a+219)$
$1$
$\Z/6\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$2, 3$
2B , 3B.1.1
$1$
\( 2^{2} \)
$3.781729651$
$35.33144352$
2.340056850
\( \frac{128787625}{98} \)
\( \bigl[1\) , \( 0\) , \( 1\) , \( -11\) , \( 12\bigr] \)
${y}^2+{x}{y}+{y}={x}^{3}-11{x}+12$
28.1-e5
28.1-e
$6$
$18$
\(\Q(\sqrt{161}) \)
$2$
$[2, 0]$
28.1
\( 2^{2} \cdot 7 \)
\( 2^{2} \cdot 7^{4} \)
$2.60820$
$(a+6), (-a+7), (-32a+219)$
$2$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$2, 3$
2B , 3B
$1$
\( 2 \)
$2.790171969$
$7.027708105$
3.090734813
\( \frac{128787625}{98} \)
\( \bigl[1\) , \( -a + 1\) , \( a\) , \( 459852999 a - 3147366710\) , \( 13512395687294 a - 92482738061398\bigr] \)
${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(459852999a-3147366710\right){x}+13512395687294a-92482738061398$
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.