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
441.1-a2
441.1-a
$6$
$8$
\(\Q(\sqrt{2}) \)
$2$
$[2, 0]$
441.1
\( 3^{2} \cdot 7^{2} \)
\( 3^{4} \cdot 7^{2} \)
$1.15823$
$(-2a+1), (2a+1), (3)$
$1$
$\Z/4\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$2$
2B
$1$
\( 2 \)
$0.975480281$
$13.02432697$
1.122971671
\( \frac{103823}{63} \)
\( \bigl[1\) , \( 0\) , \( 0\) , \( 1\) , \( 0\bigr] \)
${y}^2+{x}{y}={x}^{3}+{x}$
3087.1-h2
3087.1-h
$6$
$8$
\(\Q(\sqrt{2}) \)
$2$
$[2, 0]$
3087.1
\( 3^{2} \cdot 7^{3} \)
\( 3^{4} \cdot 7^{8} \)
$1.88394$
$(-2a+1), (2a+1), (3)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$1$
\( 2^{2} \)
$1$
$5.213351238$
1.843198006
\( \frac{103823}{63} \)
\( \bigl[a + 1\) , \( -1\) , \( 0\) , \( -4 a + 9\) , \( 0\bigr] \)
${y}^2+\left(a+1\right){x}{y}={x}^{3}-{x}^{2}+\left(-4a+9\right){x}$
3087.2-h2
3087.2-h
$6$
$8$
\(\Q(\sqrt{2}) \)
$2$
$[2, 0]$
3087.2
\( 3^{2} \cdot 7^{3} \)
\( 3^{4} \cdot 7^{8} \)
$1.88394$
$(-2a+1), (2a+1), (3)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$1$
\( 2^{2} \)
$1$
$5.213351238$
1.843198006
\( \frac{103823}{63} \)
\( \bigl[a + 1\) , \( -a - 1\) , \( 0\) , \( 4 a + 9\) , \( 0\bigr] \)
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(4a+9\right){x}$
3969.1-b2
3969.1-b
$6$
$8$
\(\Q(\sqrt{2}) \)
$2$
$[2, 0]$
3969.1
\( 3^{4} \cdot 7^{2} \)
\( 3^{16} \cdot 7^{2} \)
$2.00611$
$(-2a+1), (2a+1), (3)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2$
2B
$1$
\( 2^{2} \)
$1$
$4.869175922$
1.721513656
\( \frac{103823}{63} \)
\( \bigl[1\) , \( -1\) , \( 0\) , \( 9\) , \( 0\bigr] \)
${y}^2+{x}{y}={x}^{3}-{x}^{2}+9{x}$
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.