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
2116.2-a1
2116.2-a
$1$
$1$
\(\Q(\sqrt{-11}) \)
$2$
$[0, 1]$
2116.2
\( 2^{2} \cdot 23^{2} \)
\( 2^{2} \cdot 23^{4} \)
$2.01008$
$(a+4), (a-5), (2)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$1$
\( 3 \)
$0.177538112$
$4.382249009$
2.814968585
\( -\frac{118305}{24334} a - \frac{1089229}{24334} \)
\( \bigl[a + 1\) , \( a\) , \( a\) , \( -a - 1\) , \( -a + 3\bigr] \)
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+a{x}^{2}+\left(-a-1\right){x}-a+3$
2116.2-b1
2116.2-b
$2$
$2$
\(\Q(\sqrt{-11}) \)
$2$
$[0, 1]$
2116.2
\( 2^{2} \cdot 23^{2} \)
\( 2^{20} \cdot 23^{2} \)
$2.01008$
$(a+4), (a-5), (2)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$2$
2B
$1$
\( 2 \cdot 5 \)
$1$
$2.403591625$
3.623550713
\( -\frac{116930169}{23552} \)
\( \bigl[1\) , \( -1\) , \( 0\) , \( -10\) , \( -12\bigr] \)
${y}^2+{x}{y}={x}^{3}-{x}^{2}-10{x}-12$
2116.2-b2
2116.2-b
$2$
$2$
\(\Q(\sqrt{-11}) \)
$2$
$[0, 1]$
2116.2
\( 2^{2} \cdot 23^{2} \)
\( 2^{10} \cdot 23^{4} \)
$2.01008$
$(a+4), (a-5), (2)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$2$
2B
$1$
\( 2^{2} \cdot 5 \)
$1$
$1.201795812$
3.623550713
\( \frac{545138290809}{16928} \)
\( \bigl[1\) , \( -1\) , \( 0\) , \( -170\) , \( -812\bigr] \)
${y}^2+{x}{y}={x}^{3}-{x}^{2}-170{x}-812$
2116.2-c1
2116.2-c
$1$
$1$
\(\Q(\sqrt{-11}) \)
$2$
$[0, 1]$
2116.2
\( 2^{2} \cdot 23^{2} \)
\( 2^{8} \cdot 23^{5} \)
$2.01008$
$(a+4), (a-5), (2)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$1$
\( 2^{2} \)
$1$
$1.997993567$
4.819341814
\( -\frac{1408304799}{194672} a - \frac{3814256493}{194672} \)
\( \bigl[1\) , \( -1\) , \( a + 1\) , \( -4 a - 19\) , \( -9 a - 26\bigr] \)
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(-4a-19\right){x}-9a-26$
2116.2-d1
2116.2-d
$1$
$1$
\(\Q(\sqrt{-11}) \)
$2$
$[0, 1]$
2116.2
\( 2^{2} \cdot 23^{2} \)
\( 2^{2} \cdot 23^{4} \)
$2.01008$
$(a+4), (a-5), (2)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$1$
\( 3 \)
$0.177538112$
$4.382249009$
2.814968585
\( \frac{118305}{24334} a - \frac{603767}{12167} \)
\( \bigl[a\) , \( a - 1\) , \( a\) , \( -a + 1\) , \( 2\bigr] \)
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-a+1\right){x}+2$
2116.2-e1
2116.2-e
$1$
$1$
\(\Q(\sqrt{-11}) \)
$2$
$[0, 1]$
2116.2
\( 2^{2} \cdot 23^{2} \)
\( 2^{8} \cdot 23^{5} \)
$2.01008$
$(a+4), (a-5), (2)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$1$
\( 2^{2} \)
$1$
$1.997993567$
4.819341814
\( \frac{1408304799}{194672} a - \frac{1305640323}{48668} \)
\( \bigl[1\) , \( -1\) , \( a\) , \( 3 a - 22\) , \( 8 a - 34\bigr] \)
${y}^2+{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(3a-22\right){x}+8a-34$
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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.