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
52.2-b3
52.2-b
$8$
$12$
\(\Q(\sqrt{17}) \)
$2$
$[2, 0]$
52.2
\( 2^{2} \cdot 13 \)
\( - 2^{4} \cdot 13^{12} \)
$0.98938$
$(-a+2), (-a-1), (2a+1)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2, 3$
2B , 3B.1.2
$1$
\( 2^{2} \cdot 3 \)
$1$
$1.666184411$
1.212327233
\( \frac{118223044620244625}{186384680979848} a + \frac{9884370177138500}{23298085122481} \)
\( \bigl[1\) , \( 1\) , \( a + 1\) , \( -533 a - 833\) , \( 3583 a + 5593\bigr] \)
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(-533a-833\right){x}+3583a+5593$
416.5-d3
416.5-d
$8$
$12$
\(\Q(\sqrt{17}) \)
$2$
$[2, 0]$
416.5
\( 2^{5} \cdot 13 \)
\( - 2^{16} \cdot 13^{12} \)
$1.66393$
$(-a+2), (-a-1), (2a+1)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2, 3$
2B , 3B
$1$
\( 2^{3} \cdot 3 \)
$1$
$1.870107665$
2.721406389
\( \frac{118223044620244625}{186384680979848} a + \frac{9884370177138500}{23298085122481} \)
\( \bigl[a\) , \( a - 1\) , \( 0\) , \( -3495 a - 5460\) , \( 60225 a + 94052\bigr] \)
${y}^2+a{x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-3495a-5460\right){x}+60225a+94052$
416.7-h3
416.7-h
$8$
$12$
\(\Q(\sqrt{17}) \)
$2$
$[2, 0]$
416.7
\( 2^{5} \cdot 13 \)
\( - 2^{16} \cdot 13^{12} \)
$1.66393$
$(-a+2), (-a-1), (2a+1)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2, 3$
2B , 3B
$1$
\( 2^{3} \)
$2.789159163$
$0.746540234$
2.020049667
\( \frac{118223044620244625}{186384680979848} a + \frac{9884370177138500}{23298085122481} \)
\( \bigl[a + 1\) , \( a\) , \( a + 1\) , \( -1296 a - 2033\) , \( -16967 a - 26514\bigr] \)
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(-1296a-2033\right){x}-16967a-26514$
676.5-g3
676.5-g
$8$
$12$
\(\Q(\sqrt{17}) \)
$2$
$[2, 0]$
676.5
\( 2^{2} \cdot 13^{2} \)
\( - 2^{4} \cdot 13^{18} \)
$1.87867$
$(-a+2), (-a-1), (2a+1)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2, 3$
2B , 3B
$4$
\( 2^{2} \)
$1$
$0.929576374$
0.901821548
\( \frac{118223044620244625}{186384680979848} a + \frac{9884370177138500}{23298085122481} \)
\( \bigl[1\) , \( -a + 1\) , \( a\) , \( -196 a - 747\) , \( -3157 a + 1911\bigr] \)
${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-196a-747\right){x}-3157a+1911$
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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.