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
289.1-a3 289.1-a $4$
$4$
\(\Q(\sqrt{-39}) \) $2$
$[0, 1]$
289.1
\( 17^{2} \)
\( 17^{4} \)
$2.30089$
$(17)$
$2$
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
✓
✓
$2$
2B $1$
\( 2 \)
$2.401290110$
$4.247877398$
1.633368976
\( \frac{20346417}{289} \)
\( \bigl[1\) , \( -1\) , \( 1\) , \( -6\) , \( -4\bigr] \) ${y}^2+{x}{y}+{y}={x}^3-{x}^2-6{x}-4$
17.1-a3 17.1-a $4$
$4$
\(\Q(\sqrt{-663}) \) $2$
$[0, 1]$
17.1
\( 17 \)
\( 17^{16} \)
$4.67205$
$(17,a+8)$
$3$
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
✓
✓
$2$
2B $1$
\( 2 \)
$14.57706128$
$8.495754796$
4.809668949
\( \frac{20346417}{289} \)
\( \bigl[1\) , \( -1\) , \( 1\) , \( -1644\) , \( -24922\bigr] \) ${y}^2+{x}{y}+{y}={x}^3-{x}^2-1644{x}-24922$
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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.
