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
$2$
$3$
5.5.65657.1
$5$
$[5, 0]$
43.1
\( 43 \)
\( -43 \)
$33.35231$
$(a^4-2a^3-4a^2+4a+2)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$3$
3B
$1$
\( 1 \)
$0.078230725$
$1874.332834$
2.86123519
\( -\frac{12952}{43} a^{4} + \frac{5048}{43} a^{3} + \frac{43307}{43} a^{2} + \frac{10999}{43} a + \frac{393}{43} \)
\( \bigl[1\) , \( -2 a^{4} + 3 a^{3} + 9 a^{2} - 10 a - 8\) , \( a^{4} - a^{3} - 4 a^{2} + 3 a + 2\) , \( -a^{4} - 2 a^{3} + 4 a^{2} + 11 a + 10\) , \( 2 a^{4} + 3 a^{3} - 9 a^{2} - 20 a - 9\bigr] \)
${y}^2+{x}{y}+\left(a^{4}-a^{3}-4a^{2}+3a+2\right){y}={x}^{3}+\left(-2a^{4}+3a^{3}+9a^{2}-10a-8\right){x}^{2}+\left(-a^{4}-2a^{3}+4a^{2}+11a+10\right){x}+2a^{4}+3a^{3}-9a^{2}-20a-9$
43.1-a2
43.1-a
$2$
$3$
5.5.65657.1
$5$
$[5, 0]$
43.1
\( 43 \)
\( - 43^{3} \)
$33.35231$
$(a^4-2a^3-4a^2+4a+2)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$3$
3B
$1$
\( 1 \)
$0.234692176$
$624.7776116$
2.86123519
\( -\frac{23968185390845}{79507} a^{4} - \frac{32340604970044}{79507} a^{3} + \frac{43993086493009}{79507} a^{2} + \frac{55492835852009}{79507} a + \frac{10232774495362}{79507} \)
\( \bigl[-2 a^{4} + 3 a^{3} + 9 a^{2} - 8 a - 6\) , \( a^{4} - 2 a^{3} - 4 a^{2} + 7 a + 2\) , \( a + 1\) , \( 5 a^{4} - 3 a^{3} - 21 a^{2} - 3 a + 6\) , \( 9 a^{4} + 2 a^{3} - 40 a^{2} - 33 a - 4\bigr] \)
${y}^2+\left(-2a^{4}+3a^{3}+9a^{2}-8a-6\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a^{4}-2a^{3}-4a^{2}+7a+2\right){x}^{2}+\left(5a^{4}-3a^{3}-21a^{2}-3a+6\right){x}+9a^{4}+2a^{3}-40a^{2}-33a-4$
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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.