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
17500.2-a2 17500.2-a $2$
$3$
\(\Q(\sqrt{-7}) \) $2$
$[0, 1]$
17500.2
\( 2^{2} \cdot 5^{4} \cdot 7 \)
\( 2^{6} \cdot 5^{4} \cdot 7^{4} \)
$2.71924$
$(a), (-a+1), (-2a+1), (5)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
✓
$3$
3B $1$
\( 2 \)
$0.217698566$
$2.987220153$
1.966363334
\( \frac{397535}{392} \)
\( \bigl[1\) , \( 1\) , \( 0\) , \( 5\) , \( 5\bigr] \) ${y}^2+{x}{y}={x}^{3}+{x}^{2}+5{x}+5$
17500.2-h2 17500.2-h $2$
$3$
\(\Q(\sqrt{-7}) \) $2$
$[0, 1]$
17500.2
\( 2^{2} \cdot 5^{4} \cdot 7 \)
\( 2^{6} \cdot 5^{16} \cdot 7^{4} \)
$2.71924$
$(a), (-a+1), (-2a+1), (5)$
0
$\Z/3\Z$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
✓
$3$
3B.1.1 $1$
\( 2^{2} \cdot 3^{3} \)
$1$
$0.597444030$
5.419502837
\( \frac{397535}{392} \)
\( \bigl[1\) , \( 0\) , \( 0\) , \( 112\) , \( 392\bigr] \) ${y}^2+{x}{y}={x}^{3}+112{x}+392$
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Pari/GP
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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.
