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
20.3-a1
20.3-a
$2$
$5$
4.4.10025.1
$4$
$[4, 0]$
20.3
\( 2^{2} \cdot 5 \)
\( 2^{10} \cdot 5 \)
$13.01096$
$(a^3+2a^2-7a-9), (-2a^3-3a^2+13a+14)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$5$
5B.4.1[2]
$1$
\( 5 \)
$0.034104267$
$417.9503753$
2.847221442
\( \frac{1626299}{320} a^{3} - \frac{5889577}{320} a^{2} + \frac{155545}{64} a + \frac{225153}{8} \)
\( \bigl[a^{3} + 2 a^{2} - 6 a - 11\) , \( -a\) , \( 1\) , \( \frac{3}{2} a^{3} + \frac{5}{2} a^{2} - \frac{21}{2} a - 8\) , \( 11 a^{3} - 16 a^{2} - 94 a + 165\bigr] \)
${y}^2+\left(a^{3}+2a^{2}-6a-11\right){x}{y}+{y}={x}^{3}-a{x}^{2}+\left(\frac{3}{2}a^{3}+\frac{5}{2}a^{2}-\frac{21}{2}a-8\right){x}+11a^{3}-16a^{2}-94a+165$
20.3-a2
20.3-a
$2$
$5$
4.4.10025.1
$4$
$[4, 0]$
20.3
\( 2^{2} \cdot 5 \)
\( 2^{2} \cdot 5^{5} \)
$13.01096$
$(a^3+2a^2-7a-9), (-2a^3-3a^2+13a+14)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$5$
5B.4.1[2]
$1$
\( 1 \)
$0.170521335$
$417.9503753$
2.847221442
\( -\frac{1574721}{500} a^{3} - \frac{2118087}{500} a^{2} + \frac{424103}{20} a + \frac{843609}{50} \)
\( \bigl[\frac{1}{2} a^{3} + \frac{3}{2} a^{2} - \frac{7}{2} a - 7\) , \( a^{2} + a - 4\) , \( 1\) , \( -2 a^{3} + 19 a^{2} + 20 a - 124\) , \( -15 a^{3} + 47 a^{2} + 148 a - 416\bigr] \)
${y}^2+\left(\frac{1}{2}a^{3}+\frac{3}{2}a^{2}-\frac{7}{2}a-7\right){x}{y}+{y}={x}^{3}+\left(a^{2}+a-4\right){x}^{2}+\left(-2a^{3}+19a^{2}+20a-124\right){x}-15a^{3}+47a^{2}+148a-416$
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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.