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
32.1-a1
32.1-a
$1$
$1$
5.5.65657.1
$5$
$[5, 0]$
32.1
\( 2^{5} \)
\( - 2^{10} \)
$32.38128$
$(2)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$1$
\( 2 \)
$1$
$126.7141884$
0.989041978
\( 26869605 a^{4} - 40011890 a^{3} - \frac{497646017}{4} a^{2} + \frac{294534937}{2} a + \frac{162685211}{4} \)
\( \bigl[-a^{4} + a^{3} + 5 a^{2} - 3 a - 3\) , \( -a^{4} + a^{3} + 5 a^{2} - 3 a - 3\) , \( -2 a^{4} + 3 a^{3} + 9 a^{2} - 8 a - 7\) , \( -3 a^{4} + 4 a^{3} + 8 a^{2} - 5 a - 7\) , \( -a^{4} - 2 a^{3} + 7 a^{2} + a - 6\bigr] \)
${y}^2+\left(-a^{4}+a^{3}+5a^{2}-3a-3\right){x}{y}+\left(-2a^{4}+3a^{3}+9a^{2}-8a-7\right){y}={x}^{3}+\left(-a^{4}+a^{3}+5a^{2}-3a-3\right){x}^{2}+\left(-3a^{4}+4a^{3}+8a^{2}-5a-7\right){x}-a^{4}-2a^{3}+7a^{2}+a-6$
288.1-b1
288.1-b
$1$
$1$
5.5.65657.1
$5$
$[5, 0]$
288.1
\( 2^{5} \cdot 3^{2} \)
\( - 2^{10} \cdot 3^{6} \)
$40.33837$
$(-a^4+a^3+4a^2-2a-2), (2)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
$1$
\( 2^{2} \)
$1$
$124.6989166$
1.94662436
\( 26869605 a^{4} - 40011890 a^{3} - \frac{497646017}{4} a^{2} + \frac{294534937}{2} a + \frac{162685211}{4} \)
\( \bigl[a^{2} - 2\) , \( 2 a^{4} - 2 a^{3} - 9 a^{2} + 5 a + 6\) , \( a^{3} - 3 a - 1\) , \( -4 a^{3} - 7 a^{2} + 10 a + 10\) , \( 3 a^{4} + 2 a^{3} - 10 a^{2} - 2 a + 4\bigr] \)
${y}^2+\left(a^{2}-2\right){x}{y}+\left(a^{3}-3a-1\right){y}={x}^{3}+\left(2a^{4}-2a^{3}-9a^{2}+5a+6\right){x}^{2}+\left(-4a^{3}-7a^{2}+10a+10\right){x}+3a^{4}+2a^{3}-10a^{2}-2a+4$
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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.