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
2116.1-a1
2116.1-a
$2$
$2$
\(\Q(\sqrt{21}) \)
$2$
$[2, 0]$
2116.1
\( 2^{2} \cdot 23^{2} \)
\( 2^{20} \cdot 23^{2} \)
$2.77733$
$(2), (23)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$2$
2B
$4$
\( 2 \cdot 5 \)
$1$
$1.747176977$
3.812652738
\( -\frac{116930169}{23552} \)
\( \bigl[1\) , \( -1\) , \( 0\) , \( -10\) , \( -12\bigr] \)
${y}^2+{x}{y}={x}^{3}-{x}^{2}-10{x}-12$
2116.1-a2
2116.1-a
$2$
$2$
\(\Q(\sqrt{21}) \)
$2$
$[2, 0]$
2116.1
\( 2^{2} \cdot 23^{2} \)
\( 2^{10} \cdot 23^{4} \)
$2.77733$
$(2), (23)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$2$
2B
$4$
\( 2 \cdot 5 \)
$1$
$1.747176977$
3.812652738
\( \frac{545138290809}{16928} \)
\( \bigl[1\) , \( -1\) , \( 0\) , \( -170\) , \( -812\bigr] \)
${y}^2+{x}{y}={x}^{3}-{x}^{2}-170{x}-812$
2116.1-b1
2116.1-b
$2$
$2$
\(\Q(\sqrt{21}) \)
$2$
$[2, 0]$
2116.1
\( 2^{2} \cdot 23^{2} \)
\( 2^{20} \cdot 23^{2} \)
$2.77733$
$(2), (23)$
$2$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$2$
2B
$1$
\( 2 \cdot 5 \)
$0.129626505$
$13.22648541$
3.741352470
\( -\frac{116930169}{23552} \)
\( \bigl[a\) , \( -a + 1\) , \( 0\) , \( 50 a - 140\) , \( -288 a + 804\bigr] \)
${y}^2+a{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(50a-140\right){x}-288a+804$
2116.1-b2
2116.1-b
$2$
$2$
\(\Q(\sqrt{21}) \)
$2$
$[2, 0]$
2116.1
\( 2^{2} \cdot 23^{2} \)
\( 2^{10} \cdot 23^{4} \)
$2.77733$
$(2), (23)$
$2$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$2$
2B
$1$
\( 2 \cdot 5 \)
$0.129626505$
$13.22648541$
3.741352470
\( \frac{545138290809}{16928} \)
\( \bigl[a\) , \( -a + 1\) , \( 0\) , \( 850 a - 2380\) , \( -19488 a + 54404\bigr] \)
${y}^2+a{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(850a-2380\right){x}-19488a+54404$
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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.