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
10.1-b1
10.1-b
$2$
$2$
\(\Q(\sqrt{209}) \)
$2$
$[2, 0]$
10.1
\( 2 \cdot 5 \)
\( - 2 \cdot 5^{2} \)
$2.29727$
$(11a-85), (-4a+31)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$1$
\( 2 \)
$1.971375992$
$16.34187476$
2.228425904
\( -\frac{56211}{50} a + \frac{217211}{25} \)
\( \bigl[1\) , \( a\) , \( a + 1\) , \( 12491185 a - 96537059\) , \( 61050477245 a - 471823494147\bigr] \)
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(12491185a-96537059\right){x}+61050477245a-471823494147$
10.1-c1
10.1-c
$2$
$2$
\(\Q(\sqrt{209}) \)
$2$
$[2, 0]$
10.1
\( 2 \cdot 5 \)
\( - 2 \cdot 5^{2} \)
$2.29727$
$(11a-85), (-4a+31)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$1$
\( 2 \)
$1$
$43.47954356$
1.503771458
\( -\frac{56211}{50} a + \frac{217211}{25} \)
\( \bigl[1\) , \( 1\) , \( 1\) , \( 0\) , \( 3 a + 20\bigr] \)
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}+3a+20$
50.3-d1
50.3-d
$2$
$2$
\(\Q(\sqrt{209}) \)
$2$
$[2, 0]$
50.3
\( 2 \cdot 5^{2} \)
\( - 2 \cdot 5^{8} \)
$3.43522$
$(11a-85), (-4a+31)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2B
$1$
\( 2^{2} \)
$4.499226165$
$19.44464300$
12.10304509
\( -\frac{56211}{50} a + \frac{217211}{25} \)
\( \bigl[1\) , \( -a - 1\) , \( 0\) , \( -93106 a - 626444\) , \( 1558031339035 a + 10483083219727\bigr] \)
${y}^2+{x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-93106a-626444\right){x}+1558031339035a+10483083219727$
50.3-f1
50.3-f
$2$
$2$
\(\Q(\sqrt{209}) \)
$2$
$[2, 0]$
50.3
\( 2 \cdot 5^{2} \)
\( - 2 \cdot 5^{8} \)
$3.43522$
$(11a-85), (-4a+31)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2B
$4$
\( 2^{2} \)
$1$
$7.308308569$
2.022105097
\( -\frac{56211}{50} a + \frac{217211}{25} \)
\( \bigl[1\) , \( -a\) , \( 0\) , \( 5 a - 20\) , \( 24 a - 201\bigr] \)
${y}^2+{x}{y}={x}^{3}-a{x}^{2}+\left(5a-20\right){x}+24a-201$
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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.