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
9.1-a1
9.1-a
$2$
$3$
5.5.81509.1
$5$
$[5, 0]$
9.1
\( 3^{2} \)
\( - 3^{2} \)
$31.78086$
$(a^2-a-1)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$3$
3B
$1$
\( 1 \)
$0.005353504$
$18888.18572$
1.77090657
\( -53060 a^{4} + \frac{432928}{3} a^{3} + 15463 a^{2} - \frac{565285}{3} a + \frac{188426}{3} \)
\( \bigl[a^{3} - a^{2} - 3 a + 2\) , \( -a^{4} + 5 a^{2} + a - 4\) , \( a^{4} - a^{3} - 4 a^{2} + 2 a + 3\) , \( -a^{4} + 2 a^{3} + a^{2} - 2 a + 2\) , \( -2 a^{3} + 4 a^{2} + 3 a - 5\bigr] \)
${y}^2+\left(a^{3}-a^{2}-3a+2\right){x}{y}+\left(a^{4}-a^{3}-4a^{2}+2a+3\right){y}={x}^{3}+\left(-a^{4}+5a^{2}+a-4\right){x}^{2}+\left(-a^{4}+2a^{3}+a^{2}-2a+2\right){x}-2a^{3}+4a^{2}+3a-5$
9.1-a2
9.1-a
$2$
$3$
5.5.81509.1
$5$
$[5, 0]$
9.1
\( 3^{2} \)
\( - 3^{6} \)
$31.78086$
$(a^2-a-1)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$3$
3B
$1$
\( 1 \)
$0.016060513$
$6296.061908$
1.77090657
\( \frac{286946845}{27} a^{4} + \frac{61919467}{27} a^{3} - \frac{1359497734}{27} a^{2} - \frac{791995172}{27} a + \frac{472024472}{27} \)
\( \bigl[a^{3} - 3 a\) , \( -a^{2} + 1\) , \( a^{4} - 4 a^{2} + 1\) , \( a^{4} - 6 a^{2} - 5 a + 3\) , \( -a^{4} - a^{3} + 4 a^{2} + 4 a - 2\bigr] \)
${y}^2+\left(a^{3}-3a\right){x}{y}+\left(a^{4}-4a^{2}+1\right){y}={x}^{3}+\left(-a^{2}+1\right){x}^{2}+\left(a^{4}-6a^{2}-5a+3\right){x}-a^{4}-a^{3}+4a^{2}+4a-2$
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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.