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
10.4-b2
10.4-b
$2$
$2$
\(\Q(\sqrt{209}) \)
$2$
$[2, 0]$
10.4
\( 2 \cdot 5 \)
\( - 2 \cdot 5^{2} \)
$2.29727$
$(11a+74), (-4a-27)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$1$
\( 2 \)
$1.971375992$
$16.34187476$
2.228425904
\( \frac{56211}{50} a + \frac{378211}{50} \)
\( \bigl[1\) , \( -a + 1\) , \( a\) , \( -12491186 a - 84045873\) , \( -61050477246 a - 410773016901\bigr] \)
${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-12491186a-84045873\right){x}-61050477246a-410773016901$
10.4-c2
10.4-c
$2$
$2$
\(\Q(\sqrt{209}) \)
$2$
$[2, 0]$
10.4
\( 2 \cdot 5 \)
\( - 2 \cdot 5^{2} \)
$2.29727$
$(11a+74), (-4a-27)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$1$
\( 2 \)
$1$
$43.47954356$
1.503771458
\( \frac{56211}{50} a + \frac{378211}{50} \)
\( \bigl[1\) , \( 1\) , \( 1\) , \( 0\) , \( -3 a + 23\bigr] \)
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-3a+23$
50.6-d2
50.6-d
$2$
$2$
\(\Q(\sqrt{209}) \)
$2$
$[2, 0]$
50.6
\( 2 \cdot 5^{2} \)
\( - 2 \cdot 5^{8} \)
$3.43522$
$(11a+74), (-4a-27)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2B
$1$
\( 2^{2} \)
$4.499226165$
$19.44464300$
12.10304509
\( \frac{56211}{50} a + \frac{378211}{50} \)
\( \bigl[1\) , \( a + 1\) , \( 1\) , \( 93108 a - 719551\) , \( -1558031245928 a + 12041113839211\bigr] \)
${y}^2+{x}{y}+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(93108a-719551\right){x}-1558031245928a+12041113839211$
50.6-f2
50.6-f
$2$
$2$
\(\Q(\sqrt{209}) \)
$2$
$[2, 0]$
50.6
\( 2 \cdot 5^{2} \)
\( - 2 \cdot 5^{8} \)
$3.43522$
$(11a+74), (-4a-27)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2B
$4$
\( 2^{2} \)
$1$
$7.308308569$
2.022105097
\( \frac{56211}{50} a + \frac{378211}{50} \)
\( \bigl[1\) , \( a - 1\) , \( 0\) , \( -5 a - 15\) , \( -24 a - 177\bigr] \)
${y}^2+{x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-5a-15\right){x}-24a-177$
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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.