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
44.1-a5
44.1-a
$8$
$12$
4.4.5225.1
$4$
$[4, 0]$
44.1
\( 2^{2} \cdot 11 \)
\( - 2^{6} \cdot 11^{12} \)
$10.36605$
$(a), (a^3-3a^2-3a+8)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2, 3$
2B , 3B
$1$
\( 2^{2} \cdot 3 \)
$0.716310362$
$21.95470761$
2.610760241
\( -\frac{28953410747113802400653552025}{25107427013768} a^{3} + \frac{83473005206164029082786776435}{25107427013768} a^{2} + \frac{74446688779846789784297290345}{25107427013768} a - \frac{169137353721569990304141626235}{25107427013768} \)
\( \bigl[1\) , \( -a^{2} + a + 3\) , \( a + 1\) , \( -\frac{129}{2} a^{3} - 148 a^{2} + 87 a + \frac{477}{2}\) , \( 3377 a^{3} + 7086 a^{2} - 4943 a - 11909\bigr] \)
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a^{2}+a+3\right){x}^{2}+\left(-\frac{129}{2}a^{3}-148a^{2}+87a+\frac{477}{2}\right){x}+3377a^{3}+7086a^{2}-4943a-11909$
44.1-b1
44.1-b
$8$
$12$
4.4.5225.1
$4$
$[4, 0]$
44.1
\( 2^{2} \cdot 11 \)
\( - 2^{6} \cdot 11^{12} \)
$10.36605$
$(a), (a^3-3a^2-3a+8)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2, 3$
2B , 3B.1.2
$1$
\( 2 \cdot 3 \)
$4.554116642$
$6.756452446$
2.554059304
\( -\frac{28953410747113802400653552025}{25107427013768} a^{3} + \frac{83473005206164029082786776435}{25107427013768} a^{2} + \frac{74446688779846789784297290345}{25107427013768} a - \frac{169137353721569990304141626235}{25107427013768} \)
\( \bigl[-\frac{1}{2} a^{3} + 2 a^{2} + a - \frac{11}{2}\) , \( -\frac{1}{2} a^{3} + 2 a^{2} + 2 a - \frac{13}{2}\) , \( 0\) , \( \frac{155}{2} a^{3} - 261 a^{2} - 186 a + \frac{991}{2}\) , \( 849 a^{3} - 3036 a^{2} - 2272 a + 6014\bigr] \)
${y}^2+\left(-\frac{1}{2}a^{3}+2a^{2}+a-\frac{11}{2}\right){x}{y}={x}^{3}+\left(-\frac{1}{2}a^{3}+2a^{2}+2a-\frac{13}{2}\right){x}^{2}+\left(\frac{155}{2}a^{3}-261a^{2}-186a+\frac{991}{2}\right){x}+849a^{3}-3036a^{2}-2272a+6014$
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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.