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
405.1-c6
405.1-c
$10$
$32$
\(\Q(\zeta_{20})^+\)
$4$
$[4, 0]$
405.1
\( 3^{4} \cdot 5 \)
\( 3^{4} \cdot 5^{4} \)
$8.46419$
$(a), (3)$
0
$\Z/16\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$2$
2B
$4$
\( 2^{2} \)
$1$
$985.1451572$
1.376782212
\( \frac{56667352321}{15} \)
\( \bigl[1\) , \( 1\) , \( 1\) , \( -80\) , \( 242\bigr] \)
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-80{x}+242$
405.1-d5
405.1-d
$10$
$32$
\(\Q(\zeta_{20})^+\)
$4$
$[4, 0]$
405.1
\( 3^{4} \cdot 5 \)
\( 3^{4} \cdot 5^{4} \)
$8.46419$
$(a), (3)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$2$
2B
$16$
\( 2^{2} \)
$1$
$6.492249124$
2.322737659
\( \frac{56667352321}{15} \)
\( \bigl[a^{3} - 2 a\) , \( -a^{2} + 3\) , \( 0\) , \( -79\) , \( -322\bigr] \)
${y}^2+\left(a^{3}-2a\right){x}{y}={x}^{3}+\left(-a^{2}+3\right){x}^{2}-79{x}-322$
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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.