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-c4
52.2-c
$4$
$14$
\(\Q(\sqrt{17}) \)
$2$
$[2, 0]$
52.2
\( 2^{2} \cdot 13 \)
\( 2^{3} \cdot 13^{7} \)
$0.98938$
$(-a+2), (-a-1), (2a+1)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2, 7$
2B , 7B.1.3
$49$
\( 2 \)
$1$
$0.373004709$
2.216439792
\( \frac{189319137825824778059}{250994068} a + \frac{150462674108446482047}{125497034} \)
\( \bigl[1\) , \( a + 1\) , \( a + 1\) , \( 776 a - 4448\) , \( 27437 a - 120469\bigr] \)
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(776a-4448\right){x}+27437a-120469$
416.5-a4
416.5-a
$4$
$14$
\(\Q(\sqrt{17}) \)
$2$
$[2, 0]$
416.5
\( 2^{5} \cdot 13 \)
\( 2^{15} \cdot 13^{7} \)
$1.66393$
$(-a+2), (-a-1), (2a+1)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2, 7$
2B , 7B.6.3
$1$
\( 2^{2} \cdot 7 \)
$1$
$0.705621057$
1.197967709
\( \frac{189319137825824778059}{250994068} a + \frac{150462674108446482047}{125497034} \)
\( \bigl[a\) , \( -a\) , \( 0\) , \( -573 a - 14695\) , \( -339566 a + 83858\bigr] \)
${y}^2+a{x}{y}={x}^{3}-a{x}^{2}+\left(-573a-14695\right){x}-339566a+83858$
416.7-a4
416.7-a
$4$
$14$
\(\Q(\sqrt{17}) \)
$2$
$[2, 0]$
416.7
\( 2^{5} \cdot 13 \)
\( 2^{15} \cdot 13^{7} \)
$1.66393$
$(-a+2), (-a-1), (2a+1)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2, 7$
2B , 7B.6.3
$1$
\( 2^{2} \cdot 7 \)
$1$
$0.854044318$
1.449953208
\( \frac{189319137825824778059}{250994068} a + \frac{150462674108446482047}{125497034} \)
\( \bigl[a + 1\) , \( a - 1\) , \( 0\) , \( 7552 a - 25344\) , \( 701846 a - 1628106\bigr] \)
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(7552a-25344\right){x}+701846a-1628106$
676.5-k4
676.5-k
$4$
$14$
\(\Q(\sqrt{17}) \)
$2$
$[2, 0]$
676.5
\( 2^{2} \cdot 13^{2} \)
\( 2^{3} \cdot 13^{13} \)
$1.87867$
$(-a+2), (-a-1), (2a+1)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2, 7$
2B , 7B.6.3
$1$
\( 2^{3} \)
$1.783787644$
$1.792362879$
3.101734516
\( \frac{189319137825824778059}{250994068} a + \frac{150462674108446482047}{125497034} \)
\( \bigl[1\) , \( a - 1\) , \( 0\) , \( 407966 a - 1046425\) , \( -204219854 a + 523139251\bigr] \)
${y}^2+{x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(407966a-1046425\right){x}-204219854a+523139251$
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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.