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-a1 441.1-a $6$
$8$
\(\Q(\sqrt{-1}) \) $2$
$[0, 1]$
441.1
\( 3^{2} \cdot 7^{2} \)
\( 3^{2} \cdot 7^{16} \)
$0.81899$
$(3), (7)$
$1$
$\Z/4\Z$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
✓
✓
$2$
2B $1$
\( 2^{3} \)
$0.746299208$
$0.862076929$
0.643367330
\( -\frac{4354703137}{17294403} \)
\( \bigl[i\) , \( 0\) , \( 0\) , \( -34\) , \( 217\bigr] \) ${y}^2+i{x}{y}={x}^{3}-34{x}+217$
3969.1-a1 3969.1-a $6$
$8$
\(\Q(\sqrt{-1}) \) $2$
$[0, 1]$
3969.1
\( 3^{4} \cdot 7^{2} \)
\( 3^{14} \cdot 7^{16} \)
$1.41853$
$(3), (7)$
0
$\Z/4\Z$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
✓
$2$
2B $4$
\( 2^{5} \)
$1$
$0.287358976$
2.298871812
\( -\frac{4354703137}{17294403} \)
\( \bigl[i\) , \( 1\) , \( 0\) , \( -306\) , \( -5859\bigr] \) ${y}^2+i{x}{y}={x}^{3}+{x}^{2}-306{x}-5859$
21609.1-a1 21609.1-a $6$
$8$
\(\Q(\sqrt{-1}) \) $2$
$[0, 1]$
21609.1
\( 3^{2} \cdot 7^{4} \)
\( 3^{2} \cdot 7^{28} \)
$2.16684$
$(3), (7)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
✓
$2$
2B $16$
\( 2^{2} \)
$1$
$0.123153847$
1.970461553
\( -\frac{4354703137}{17294403} \)
\( \bigl[i\) , \( -1\) , \( i\) , \( -1666\) , \( -72764\bigr] \) ${y}^2+i{x}{y}+i{y}={x}^{3}-{x}^{2}-1666{x}-72764$
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*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.
