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
400.2-a1
400.2-a
$2$
$3$
\(\Q(\sqrt{21}) \)
$2$
$[2, 0]$
400.2
\( 2^{4} \cdot 5^{2} \)
\( 2^{16} \cdot 5^{8} \)
$1.83132$
$(-a), (2)$
$1$
$\mathsf{trivial}$
$\textsf{potential}$
$-3$
$N(\mathrm{U}(1))$
✓
✓
$7$
7Ns.2.1
$1$
\( 1 \)
$1.743375040$
$3.812279058$
2.900653519
\( 0 \)
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( a + 2\) , \( -8 a + 3\bigr] \)
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(a+2\right){x}-8a+3$
400.2-a2
400.2-a
$2$
$3$
\(\Q(\sqrt{21}) \)
$2$
$[2, 0]$
400.2
\( 2^{4} \cdot 5^{2} \)
\( 2^{16} \cdot 5^{8} \)
$1.83132$
$(-a), (2)$
$1$
$\mathsf{trivial}$
$\textsf{potential}$
$-3$
$N(\mathrm{U}(1))$
✓
✓
$7$
7Ns.2.1
$1$
\( 3 \)
$0.581125013$
$3.812279058$
2.900653519
\( 0 \)
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( a + 2\) , \( 416 a - 1163\bigr] \)
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(a+2\right){x}+416a-1163$
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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.