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-a1
52.2-a
$4$
$6$
\(\Q(\sqrt{17}) \)
$2$
$[2, 0]$
52.2
\( 2^{2} \cdot 13 \)
\( 2^{7} \cdot 13^{6} \)
$0.98938$
$(-a+2), (-a-1), (2a+1)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2, 3$
2B , 3B.1.2
$1$
\( 2^{2} \cdot 3 \)
$1$
$1.732900761$
1.260870508
\( \frac{6735205351063}{308915776} a - \frac{17258074890723}{308915776} \)
\( \bigl[1\) , \( 0\) , \( a + 1\) , \( -32 a - 50\) , \( -1378 a - 2152\bigr] \)
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-32a-50\right){x}-1378a-2152$
416.5-h1
416.5-h
$4$
$6$
\(\Q(\sqrt{17}) \)
$2$
$[2, 0]$
416.5
\( 2^{5} \cdot 13 \)
\( 2^{19} \cdot 13^{6} \)
$1.66393$
$(-a+2), (-a-1), (2a+1)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2, 3$
2B , 3B
$1$
\( 2^{3} \)
$0.623726544$
$3.148201778$
1.904988320
\( \frac{6735205351063}{308915776} a - \frac{17258074890723}{308915776} \)
\( \bigl[a\) , \( -1\) , \( 0\) , \( -207 a - 324\) , \( -23149 a - 36148\bigr] \)
${y}^2+a{x}{y}={x}^{3}-{x}^{2}+\left(-207a-324\right){x}-23149a-36148$
416.7-b1
416.7-b
$4$
$6$
\(\Q(\sqrt{17}) \)
$2$
$[2, 0]$
416.7
\( 2^{5} \cdot 13 \)
\( 2^{19} \cdot 13^{6} \)
$1.66393$
$(-a+2), (-a-1), (2a+1)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2, 3$
2B , 3B
$1$
\( 2^{3} \cdot 3 \)
$1$
$1.632579223$
2.375751734
\( \frac{6735205351063}{308915776} a - \frac{17258074890723}{308915776} \)
\( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( -78 a - 124\) , \( 5244 a + 8187\bigr] \)
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-78a-124\right){x}+5244a+8187$
676.5-a1
676.5-a
$4$
$6$
\(\Q(\sqrt{17}) \)
$2$
$[2, 0]$
676.5
\( 2^{2} \cdot 13^{2} \)
\( 2^{7} \cdot 13^{12} \)
$1.87867$
$(-a+2), (-a-1), (2a+1)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2, 3$
2B , 3B
$1$
\( 2^{3} \cdot 3 \)
$1$
$3.290420844$
4.788265656
\( \frac{6735205351063}{308915776} a - \frac{17258074890723}{308915776} \)
\( \bigl[1\) , \( a\) , \( a\) , \( 6 a - 88\) , \( 469 a + 1156\bigr] \)
${y}^2+{x}{y}+a{y}={x}^{3}+a{x}^{2}+\left(6a-88\right){x}+469a+1156$
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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.