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
\( -\frac{12952}{43} a^{4} + \frac{5048}{43} a^{3} + \frac{43307}{43} a^{2} + \frac{10999}{43} a + \frac{393}{43} \)
\( \bigl[1\) , \( -2 a^{4} + 3 a^{3} + 9 a^{2} - 10 a - 8\) , \( a^{4} - a^{3} - 4 a^{2} + 3 a + 2\) , \( -a^{4} - 2 a^{3} + 4 a^{2} + 11 a + 10\) , \( 2 a^{4} + 3 a^{3} - 9 a^{2} - 20 a - 9\bigr] \)
${y}^2+{x}{y}+\left(a^{4}-a^{3}-4a^{2}+3a+2\right){y}={x}^{3}+\left(-2a^{4}+3a^{3}+9a^{2}-10a-8\right){x}^{2}+\left(-a^{4}-2a^{3}+4a^{2}+11a+10\right){x}+2a^{4}+3a^{3}-9a^{2}-20a-9$
387.1-h1
387.1-h
$2$
$3$
5.5.65657.1
$5$
$[5, 0]$
387.1
\( 3^{2} \cdot 43 \)
\( - 3^{6} \cdot 43 \)
$41.54800$
$(-a^4+a^3+4a^2-2a-2), (a^4-2a^3-4a^2+4a+2)$
$0 \le r \le 1$
$\Z/3\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$3$
3B.1.1
\( 1 \)
$1$
$1679.749203$
3.21180093
\( -\frac{12952}{43} a^{4} + \frac{5048}{43} a^{3} + \frac{43307}{43} a^{2} + \frac{10999}{43} a + \frac{393}{43} \)
\( \bigl[a^{4} - a^{3} - 4 a^{2} + 3 a + 3\) , \( -a^{4} + a^{3} + 4 a^{2} - 3 a - 2\) , \( -a^{4} + 2 a^{3} + 4 a^{2} - 5 a - 3\) , \( -a^{4} + 2 a^{3} + a^{2} - 3 a + 1\) , \( a^{4} - 3 a^{3} + 3 a\bigr] \)
${y}^2+\left(a^{4}-a^{3}-4a^{2}+3a+3\right){x}{y}+\left(-a^{4}+2a^{3}+4a^{2}-5a-3\right){y}={x}^{3}+\left(-a^{4}+a^{3}+4a^{2}-3a-2\right){x}^{2}+\left(-a^{4}+2a^{3}+a^{2}-3a+1\right){x}+a^{4}-3a^{3}+3a$
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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.