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
9.3-a1
9.3-a
$2$
$3$
5.5.160801.1
$5$
$[5, 0]$
9.3
\( 3^{2} \)
\( - 3^{9} \)
$44.63825$
$(-a^4+5a^2+a-3)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$3$
3B
$1$
\( 2 \)
$0.011998716$
$10171.11186$
3.04339875
\( -10331 a^{4} - 1485 a^{3} + 14206 a^{2} + 5063 a - 1551 \)
\( \bigl[a^{2} - 1\) , \( a^{4} - 4 a^{2} + a + 1\) , \( a^{4} - a^{3} - 5 a^{2} + 4 a + 2\) , \( 6 a^{4} - 8 a^{3} - 19 a^{2} + 39 a - 7\) , \( -59 a^{4} + 74 a^{3} + 246 a^{2} - 269 a + 52\bigr] \)
${y}^2+\left(a^{2}-1\right){x}{y}+\left(a^{4}-a^{3}-5a^{2}+4a+2\right){y}={x}^{3}+\left(a^{4}-4a^{2}+a+1\right){x}^{2}+\left(6a^{4}-8a^{3}-19a^{2}+39a-7\right){x}-59a^{4}+74a^{3}+246a^{2}-269a+52$
9.3-a2
9.3-a
$2$
$3$
5.5.160801.1
$5$
$[5, 0]$
9.3
\( 3^{2} \)
\( - 3^{3} \)
$44.63825$
$(-a^4+5a^2+a-3)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$3$
3B
$1$
\( 2 \)
$0.035996150$
$3390.370622$
3.04339875
\( 461521 a^{4} + 103548 a^{3} - 2180923 a^{2} - 824570 a + 376333 \)
\( \bigl[a^{4} - 4 a^{2} + a + 1\) , \( a^{4} - a^{3} - 5 a^{2} + 3 a + 3\) , \( a^{2} - 2\) , \( 3 a^{4} + 2 a^{3} - 11 a^{2} - 3 a + 7\) , \( 5 a^{4} - 15 a^{2} + 11 a - 1\bigr] \)
${y}^2+\left(a^{4}-4a^{2}+a+1\right){x}{y}+\left(a^{2}-2\right){y}={x}^{3}+\left(a^{4}-a^{3}-5a^{2}+3a+3\right){x}^{2}+\left(3a^{4}+2a^{3}-11a^{2}-3a+7\right){x}+5a^{4}-15a^{2}+11a-1$
9.3-b1
9.3-b
$2$
$3$
5.5.160801.1
$5$
$[5, 0]$
9.3
\( 3^{2} \)
\( - 3^{3} \)
$44.63825$
$(-a^4+5a^2+a-3)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$3$
3B
$1$
\( 2 \)
$0.026884599$
$4295.471666$
2.87985121
\( -10331 a^{4} - 1485 a^{3} + 14206 a^{2} + 5063 a - 1551 \)
\( \bigl[a^{4} - a^{3} - 5 a^{2} + 5 a + 3\) , \( a^{2} + a - 1\) , \( 2 a^{4} - a^{3} - 9 a^{2} + 5 a + 2\) , \( -a^{3} + 2 a^{2} + 8 a - 4\) , \( 3 a^{4} - 2 a^{3} - 12 a^{2} + 9 a - 2\bigr] \)
${y}^2+\left(a^{4}-a^{3}-5a^{2}+5a+3\right){x}{y}+\left(2a^{4}-a^{3}-9a^{2}+5a+2\right){y}={x}^{3}+\left(a^{2}+a-1\right){x}^{2}+\left(-a^{3}+2a^{2}+8a-4\right){x}+3a^{4}-2a^{3}-12a^{2}+9a-2$
9.3-b2
9.3-b
$2$
$3$
5.5.160801.1
$5$
$[5, 0]$
9.3
\( 3^{2} \)
\( - 3^{9} \)
$44.63825$
$(-a^4+5a^2+a-3)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$3$
3B
$1$
\( 2 \)
$0.080653797$
$1431.823888$
2.87985121
\( 461521 a^{4} + 103548 a^{3} - 2180923 a^{2} - 824570 a + 376333 \)
\( \bigl[2 a^{4} - a^{3} - 9 a^{2} + 5 a + 3\) , \( a^{4} - 6 a^{2} + a + 5\) , \( a^{4} - 5 a^{2} + 3\) , \( 2 a^{4} + 5 a^{3} - 5 a^{2} - 13 a + 6\) , \( 7 a^{4} + 4 a^{3} - 26 a^{2} - 2 a + 16\bigr] \)
${y}^2+\left(2a^{4}-a^{3}-9a^{2}+5a+3\right){x}{y}+\left(a^{4}-5a^{2}+3\right){y}={x}^{3}+\left(a^{4}-6a^{2}+a+5\right){x}^{2}+\left(2a^{4}+5a^{3}-5a^{2}-13a+6\right){x}+7a^{4}+4a^{3}-26a^{2}-2a+16$
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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.