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
8450.1-b2 8450.1-b $4$
$4$
\(\Q(\sqrt{-2}) \) $2$
$[0, 1]$
8450.1
\( 2 \cdot 5^{2} \cdot 13^{2} \)
\( 2^{16} \cdot 5^{2} \cdot 13^{2} \)
$2.42325$
$(a), (5), (13)$
0
$\Z/4\Z$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
✓
✓
$2$
2B $1$
\( 2^{4} \)
$1$
$2.703967938$
1.911994065
\( \frac{33076161}{16640} \)
\( \bigl[1\) , \( -1\) , \( 1\) , \( -7\) , \( -1\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}-7{x}-1$
650.2-a2 650.2-a $4$
$4$
\(\Q(\sqrt{-26}) \) $2$
$[0, 1]$
650.2
\( 2 \cdot 5^{2} \cdot 13 \)
\( 2^{28} \cdot 5^{2} \cdot 13^{2} \)
$4.60133$
$(2,a), (5,a+2), (5,a+3), (13,a)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
✓
✓
$2$
2B $1$
\( 2^{2} \)
$2.324883658$
$2.703967938$
2.465733209
\( \frac{33076161}{16640} \)
\( \bigl[a\) , \( -1\) , \( a\) , \( 5\) , \( 77\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^3-{x}^2+5{x}+77$
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.
