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
$1$
$1$
6.6.1683101.1
$6$
$[6, 0]$
43.1
\( 43 \)
\( 43^{6} \)
$158.60469$
$(a^5-3a^4-2a^3+8a^2+a-3)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$1$
\( 2 \)
$1$
$1431.168640$
2.20631
\( \frac{1545053960593002}{6321363049} a^{5} - \frac{5385447961550674}{6321363049} a^{4} - \frac{3504729616418335}{6321363049} a^{3} + \frac{21722107126780968}{6321363049} a^{2} - \frac{58735384383778}{6321363049} a - \frac{21448949004140755}{6321363049} \)
\( \bigl[a^{3} - 3 a - 2\) , \( a^{4} - a^{3} - 6 a^{2} + 3 a + 8\) , \( 1\) , \( 6 a^{5} - 13 a^{4} - 21 a^{3} + 44 a^{2} + 18 a - 31\) , \( 12 a^{5} - 28 a^{4} - 54 a^{3} + 131 a^{2} + 61 a - 153\bigr] \)
${y}^2+\left(a^{3}-3a-2\right){x}{y}+{y}={x}^{3}+\left(a^{4}-a^{3}-6a^{2}+3a+8\right){x}^{2}+\left(6a^{5}-13a^{4}-21a^{3}+44a^{2}+18a-31\right){x}+12a^{5}-28a^{4}-54a^{3}+131a^{2}+61a-153$
43.1-b1
43.1-b
$1$
$1$
6.6.1683101.1
$6$
$[6, 0]$
43.1
\( 43 \)
\( 43^{4} \)
$158.60469$
$(a^5-3a^4-2a^3+8a^2+a-3)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$1$
\( 2^{2} \)
$0.025703319$
$7960.994389$
3.78541
\( -\frac{6862418975964}{3418801} a^{5} + \frac{30848750157018}{3418801} a^{4} - \frac{18712098139415}{3418801} a^{3} - \frac{61009164594246}{3418801} a^{2} + \frac{42761979884482}{3418801} a + \frac{32262339489542}{3418801} \)
\( \bigl[a^{5} - 2 a^{4} - 4 a^{3} + 5 a^{2} + 6 a + 1\) , \( a^{5} - 2 a^{4} - 4 a^{3} + 4 a^{2} + 7 a + 3\) , \( a^{5} - 2 a^{4} - 3 a^{3} + 5 a^{2} + 2 a - 1\) , \( -4 a^{5} + 22 a^{4} - 11 a^{3} - 98 a^{2} + 64 a + 138\) , \( -42 a^{5} + 155 a^{4} + 69 a^{3} - 639 a^{2} + 90 a + 692\bigr] \)
${y}^2+\left(a^{5}-2a^{4}-4a^{3}+5a^{2}+6a+1\right){x}{y}+\left(a^{5}-2a^{4}-3a^{3}+5a^{2}+2a-1\right){y}={x}^{3}+\left(a^{5}-2a^{4}-4a^{3}+4a^{2}+7a+3\right){x}^{2}+\left(-4a^{5}+22a^{4}-11a^{3}-98a^{2}+64a+138\right){x}-42a^{5}+155a^{4}+69a^{3}-639a^{2}+90a+692$
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Pari/GP
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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.