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
99937.1-a1
99937.1-a
$4$
$6$
\(\Q(\sqrt{-3}) \)
$2$
$[0, 1]$
99937.1
\( 37^{2} \cdot 73 \)
\( 37^{6} \cdot 73^{3} \)
$2.75189$
$(-7a+4), (-9a+1)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2, 3$
2B , 3B[2]
$1$
\( 2 \)
$5.493984262$
$0.533036440$
3.381533386
\( \frac{60988685561}{389017} a - \frac{169775626841}{389017} \)
\( \bigl[a + 1\) , \( -a\) , \( 0\) , \( -262 a - 290\) , \( -3103 a - 1420\bigr] \)
${y}^2+\left(a+1\right){x}{y}={x}^{3}-a{x}^{2}+\left(-262a-290\right){x}-3103a-1420$
99937.1-a2
99937.1-a
$4$
$6$
\(\Q(\sqrt{-3}) \)
$2$
$[0, 1]$
99937.1
\( 37^{2} \cdot 73 \)
\( 37^{6} \cdot 73^{2} \)
$2.75189$
$(-7a+4), (-9a+1)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2, 3$
2B , 3B[2]
$1$
\( 2^{3} \)
$0.915664043$
$0.799554661$
3.381533386
\( -\frac{927841113}{5329} a - \frac{395933743}{5329} \)
\( \bigl[a + 1\) , \( -a\) , \( 0\) , \( 208 a - 30\) , \( -253 a - 892\bigr] \)
${y}^2+\left(a+1\right){x}{y}={x}^{3}-a{x}^{2}+\left(208a-30\right){x}-253a-892$
99937.1-a3
99937.1-a
$4$
$6$
\(\Q(\sqrt{-3}) \)
$2$
$[0, 1]$
99937.1
\( 37^{2} \cdot 73 \)
\( 37^{6} \cdot 73 \)
$2.75189$
$(-7a+4), (-9a+1)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2, 3$
2B , 3B[2]
$1$
\( 2 \)
$1.831328087$
$1.599109322$
3.381533386
\( \frac{9927}{73} a + \frac{20960}{73} \)
\( \bigl[a + 1\) , \( -a\) , \( 0\) , \( 8 a + 5\) , \( -24 a - 8\bigr] \)
${y}^2+\left(a+1\right){x}{y}={x}^{3}-a{x}^{2}+\left(8a+5\right){x}-24a-8$
99937.1-a4
99937.1-a
$4$
$6$
\(\Q(\sqrt{-3}) \)
$2$
$[0, 1]$
99937.1
\( 37^{2} \cdot 73 \)
\( 37^{6} \cdot 73^{6} \)
$2.75189$
$(-7a+4), (-9a+1)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2, 3$
2B , 3B[2]
$1$
\( 2^{3} \)
$2.746992131$
$0.266518220$
3.381533386
\( -\frac{55816089234767}{151334226289} a + \frac{107352826006104}{151334226289} \)
\( \bigl[a + 1\) , \( -a\) , \( 0\) , \( -427 a - 90\) , \( -996 a - 5177\bigr] \)
${y}^2+\left(a+1\right){x}{y}={x}^{3}-a{x}^{2}+\left(-427a-90\right){x}-996a-5177$
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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.