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
1587.1-a1
1587.1-a
$2$
$2$
\(\Q(\sqrt{21}) \)
$2$
$[2, 0]$
1587.1
\( 3 \cdot 23^{2} \)
\( 3^{4} \cdot 23^{2} \)
$2.58459$
$(-a+2), (23)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$2$
2B
$1$
\( 2^{2} \)
$1$
$5.788180949$
1.263084635
\( -\frac{15625}{207} \)
\( \bigl[1\) , \( 0\) , \( 1\) , \( -1\) , \( -1\bigr] \)
${y}^2+{x}{y}+{y}={x}^{3}-{x}-1$
1587.1-a2
1587.1-a
$2$
$2$
\(\Q(\sqrt{21}) \)
$2$
$[2, 0]$
1587.1
\( 3 \cdot 23^{2} \)
\( 3^{2} \cdot 23^{4} \)
$2.58459$
$(-a+2), (23)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$2$
2B
$1$
\( 2^{2} \)
$1$
$5.788180949$
1.263084635
\( \frac{413493625}{1587} \)
\( \bigl[1\) , \( 0\) , \( 1\) , \( -16\) , \( -25\bigr] \)
${y}^2+{x}{y}+{y}={x}^{3}-16{x}-25$
1587.1-b1
1587.1-b
$2$
$2$
\(\Q(\sqrt{21}) \)
$2$
$[2, 0]$
1587.1
\( 3 \cdot 23^{2} \)
\( 3^{4} \cdot 23^{2} \)
$2.58459$
$(-a+2), (23)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$2$
2B
$1$
\( 2 \)
$0.355033759$
$22.79052419$
1.765689435
\( -\frac{15625}{207} \)
\( \bigl[a\) , \( 1\) , \( a + 1\) , \( 2 a - 8\) , \( -16 a + 42\bigr] \)
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(2a-8\right){x}-16a+42$
1587.1-b2
1587.1-b
$2$
$2$
\(\Q(\sqrt{21}) \)
$2$
$[2, 0]$
1587.1
\( 3 \cdot 23^{2} \)
\( 3^{2} \cdot 23^{4} \)
$2.58459$
$(-a+2), (23)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$2$
2B
$1$
\( 2^{2} \)
$0.177516879$
$22.79052419$
1.765689435
\( \frac{413493625}{1587} \)
\( \bigl[a + 1\) , \( -a + 1\) , \( a\) , \( -79 a - 140\) , \( 516 a + 924\bigr] \)
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-79a-140\right){x}+516a+924$
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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.