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
392.1-a4 392.1-a $4$
$4$
\(\Q(\sqrt{-2}) \) $2$
$[0, 1]$
392.1
\( 2^{3} \cdot 7^{2} \)
\( 2^{10} \cdot 7^{2} \)
$1.12462$
$(a), (7)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
✓
$2$
2B $1$
\( 2 \)
$1.069108576$
$2.008147859$
1.518107418
\( \frac{1443468546}{7} \)
\( \bigl[a\) , \( -1\) , \( a\) , \( -73\) , \( -211\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}-{x}^{2}-73{x}-211$
784.1-b4 784.1-b $4$
$4$
\(\Q(\sqrt{-2}) \) $2$
$[0, 1]$
784.1
\( 2^{4} \cdot 7^{2} \)
\( 2^{10} \cdot 7^{2} \)
$1.33740$
$(a), (7)$
$1$
$\Z/4\Z$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
✓
$2$
2B $1$
\( 2^{2} \)
$2.786954333$
$2.008147859$
1.978702696
\( \frac{1443468546}{7} \)
\( \bigl[a\) , \( -1\) , \( 0\) , \( -74\) , \( 286\bigr] \) ${y}^2+a{x}{y}={x}^{3}-{x}^{2}-74{x}+286$
19208.1-d4 19208.1-d $4$
$4$
\(\Q(\sqrt{-2}) \) $2$
$[0, 1]$
19208.1
\( 2^{3} \cdot 7^{4} \)
\( 2^{10} \cdot 7^{14} \)
$2.97546$
$(a), (7)$
$2$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
✓
$2$
2B $1$
\( 2^{3} \)
$3.657265035$
$0.286878265$
5.935114063
\( \frac{1443468546}{7} \)
\( \bigl[a\) , \( -1\) , \( a\) , \( -3661\) , \( 87153\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}-{x}^{2}-3661{x}+87153$
31752.3-i4 31752.3-i $4$
$4$
\(\Q(\sqrt{-2}) \) $2$
$[0, 1]$
31752.3
\( 2^{3} \cdot 3^{4} \cdot 7^{2} \)
\( 2^{10} \cdot 3^{12} \cdot 7^{2} \)
$3.37385$
$(a), (-a-1), (a-1), (7)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
✓
$2$
2B $4$
\( 2^{3} \)
$1$
$0.669382619$
3.786599916
\( \frac{1443468546}{7} \)
\( \bigl[a\) , \( -1\) , \( a\) , \( -671\) , \( 7053\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}-{x}^{2}-671{x}+7053$
38416.1-f4 38416.1-f $4$
$4$
\(\Q(\sqrt{-2}) \) $2$
$[0, 1]$
38416.1
\( 2^{4} \cdot 7^{4} \)
\( 2^{10} \cdot 7^{14} \)
$3.53844$
$(a), (7)$
0
$\Z/4\Z$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
✓
$2$
2B $16$
\( 2^{4} \)
$1$
$0.286878265$
3.245657071
\( \frac{1443468546}{7} \)
\( \bigl[a\) , \( -1\) , \( 0\) , \( -3662\) , \( -83490\bigr] \) ${y}^2+a{x}{y}={x}^{3}-{x}^{2}-3662{x}-83490$
Download
displayed columns for
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.
