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
43.1-a1
43.1-a
$2$
$3$
4.4.1957.1
$4$
$[4, 0]$
43.1
\( 43 \)
\( - 43^{3} \)
$6.32583$
$(-a^2-a+3)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$3$
3B
$1$
\( 3 \)
$0.006791259$
$669.3900782$
1.233148718
\( \frac{1592683107521}{79507} a^{3} + \frac{629635995686}{79507} a^{2} - \frac{6120072768045}{79507} a - \frac{4012649003175}{79507} \)
\( \bigl[a^{2} - 1\) , \( 2 a^{3} - a^{2} - 8 a\) , \( 0\) , \( -3 a^{3} + 3 a^{2} + 10 a - 7\) , \( -a^{3} - 2 a^{2} + 4 a + 9\bigr] \)
${y}^2+\left(a^{2}-1\right){x}{y}={x}^{3}+\left(2a^{3}-a^{2}-8a\right){x}^{2}+\left(-3a^{3}+3a^{2}+10a-7\right){x}-a^{3}-2a^{2}+4a+9$
43.1-a2
43.1-a
$2$
$3$
4.4.1957.1
$4$
$[4, 0]$
43.1
\( 43 \)
\( -43 \)
$6.32583$
$(-a^2-a+3)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$3$
3B
$1$
\( 1 \)
$0.020373779$
$669.3900782$
1.233148718
\( \frac{655988}{43} a^{3} - \frac{455074}{43} a^{2} - \frac{2306280}{43} a + \frac{943113}{43} \)
\( \bigl[1\) , \( -a - 1\) , \( a^{2} - a - 1\) , \( a\) , \( -a^{2} + a + 1\bigr] \)
${y}^2+{x}{y}+\left(a^{2}-a-1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+a{x}-a^{2}+a+1$
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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.