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-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
\( -\frac{23968185390845}{79507} a^{4} - \frac{32340604970044}{79507} a^{3} + \frac{43993086493009}{79507} a^{2} + \frac{55492835852009}{79507} a + \frac{10232774495362}{79507} \)
\( \bigl[-2 a^{4} + 3 a^{3} + 9 a^{2} - 8 a - 6\) , \( a^{4} - 2 a^{3} - 4 a^{2} + 7 a + 2\) , \( a + 1\) , \( 5 a^{4} - 3 a^{3} - 21 a^{2} - 3 a + 6\) , \( 9 a^{4} + 2 a^{3} - 40 a^{2} - 33 a - 4\bigr] \)
${y}^2+\left(-2a^{4}+3a^{3}+9a^{2}-8a-6\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a^{4}-2a^{3}-4a^{2}+7a+2\right){x}^{2}+\left(5a^{4}-3a^{3}-21a^{2}-3a+6\right){x}+9a^{4}+2a^{3}-40a^{2}-33a-4$
387.1-h2
387.1-h
$2$
$3$
5.5.65657.1
$5$
$[5, 0]$
387.1
\( 3^{2} \cdot 43 \)
\( - 3^{6} \cdot 43^{3} \)
$41.54800$
$(-a^4+a^3+4a^2-2a-2), (a^4-2a^3-4a^2+4a+2)$
$0 \le r \le 1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
$3$
3B.1.2
\( 3 \)
$1$
$20.73764449$
3.21180093
\( -\frac{23968185390845}{79507} a^{4} - \frac{32340604970044}{79507} a^{3} + \frac{43993086493009}{79507} a^{2} + \frac{55492835852009}{79507} a + \frac{10232774495362}{79507} \)
\( \bigl[a^{3} - 4 a - 1\) , \( -a^{4} + 5 a^{2} - 2\) , \( a^{2} - 2\) , \( 8 a^{4} + a^{3} - 35 a^{2} - 29 a - 4\) , \( 60 a^{4} + 21 a^{3} - 268 a^{2} - 246 a - 44\bigr] \)
${y}^2+\left(a^{3}-4a-1\right){x}{y}+\left(a^{2}-2\right){y}={x}^{3}+\left(-a^{4}+5a^{2}-2\right){x}^{2}+\left(8a^{4}+a^{3}-35a^{2}-29a-4\right){x}+60a^{4}+21a^{3}-268a^{2}-246a-44$
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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.