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
50.6-a1
50.6-a
$4$
$14$
\(\Q(\sqrt{-31}) \)
$2$
$[0, 1]$
50.6
\( 2 \cdot 5^{2} \)
\( 2^{26} \cdot 5^{13} \)
$1.32301$
$(2,a+1), (5,a+3)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2, 7$
2B , 7B
$1$
\( 2^{2} \cdot 7 \)
$1$
$0.619695306$
1.558207877
\( \frac{780929100411181}{1280000000} a - \frac{336050998176533}{160000000} \)
\( \bigl[a\) , \( a + 1\) , \( 0\) , \( 605 a + 472\) , \( 1753 a + 27576\bigr] \)
${y}^2+a{x}{y}={x}^3+\left(a+1\right){x}^2+\left(605a+472\right){x}+1753a+27576$
50.6-a2
50.6-a
$4$
$14$
\(\Q(\sqrt{-31}) \)
$2$
$[0, 1]$
50.6
\( 2 \cdot 5^{2} \)
\( 2^{14} \cdot 5^{7} \)
$1.32301$
$(2,a+1), (5,a+3)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2, 7$
2B , 7B
$1$
\( 2^{2} \)
$1$
$4.337867144$
1.558207877
\( -\frac{2911}{20} a - \frac{47529}{5} \)
\( \bigl[a\) , \( a + 1\) , \( 0\) , \( -5 a - 8\) , \( -11 a + 24\bigr] \)
${y}^2+a{x}{y}={x}^3+\left(a+1\right){x}^2+\left(-5a-8\right){x}-11a+24$
50.6-a3
50.6-a
$4$
$14$
\(\Q(\sqrt{-31}) \)
$2$
$[0, 1]$
50.6
\( 2 \cdot 5^{2} \)
\( 2^{13} \cdot 5^{8} \)
$1.32301$
$(2,a+1), (5,a+3)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2, 7$
2B , 7B
$1$
\( 2^{2} \)
$1$
$4.337867144$
1.558207877
\( \frac{19951}{50} a - \frac{33947}{25} \)
\( \bigl[a + 1\) , \( 0\) , \( 0\) , \( -a + 9\) , \( 8 a - 8\bigr] \)
${y}^2+\left(a+1\right){x}{y}={x}^3+\left(-a+9\right){x}+8a-8$
50.6-a4
50.6-a
$4$
$14$
\(\Q(\sqrt{-31}) \)
$2$
$[0, 1]$
50.6
\( 2 \cdot 5^{2} \)
\( 2^{19} \cdot 5^{20} \)
$1.32301$
$(2,a+1), (5,a+3)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2, 7$
2B , 7B
$1$
\( 2^{2} \cdot 7 \)
$1$
$0.619695306$
1.558207877
\( -\frac{379001974281391}{781250000000} a + \frac{34453608603063}{97656250000} \)
\( \bigl[a + 1\) , \( 0\) , \( 0\) , \( 144 a - 256\) , \( -1415 a - 2097\bigr] \)
${y}^2+\left(a+1\right){x}{y}={x}^3+\left(144a-256\right){x}-1415a-2097$
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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.