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-a1
10.4-a
$1$
$1$
\(\Q(\sqrt{209}) \)
$2$
$[2, 0]$
10.4
\( 2 \cdot 5 \)
\( 2^{2} \cdot 5^{16} \)
$2.29727$
$(11a+74), (-4a-27)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$1$
\( 2^{5} \)
$1$
$3.072924513$
6.801876264
\( -\frac{20383137018133}{610351562500} a - \frac{179472364456183}{610351562500} \)
\( \bigl[a + 1\) , \( -1\) , \( 1\) , \( -19297590 a - 129842196\) , \( 251996522818 a + 1695537473231\bigr] \)
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}-{x}^{2}+\left(-19297590a-129842196\right){x}+251996522818a+1695537473231$
10.4-d1
10.4-d
$1$
$1$
\(\Q(\sqrt{209}) \)
$2$
$[2, 0]$
10.4
\( 2 \cdot 5 \)
\( 2^{2} \cdot 5^{16} \)
$2.29727$
$(11a+74), (-4a-27)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$1$
\( 2^{5} \)
$0.109314649$
$2.711568399$
1.312217311
\( -\frac{20383137018133}{610351562500} a - \frac{179472364456183}{610351562500} \)
\( \bigl[a + 1\) , \( -a\) , \( 1\) , \( 264 a - 2002\) , \( -31126 a + 240608\bigr] \)
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}-a{x}^{2}+\left(264a-2002\right){x}-31126a+240608$
50.6-b1
50.6-b
$1$
$1$
\(\Q(\sqrt{209}) \)
$2$
$[2, 0]$
50.6
\( 2 \cdot 5^{2} \)
\( 2^{2} \cdot 5^{22} \)
$3.43522$
$(11a+74), (-4a-27)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
$1$
\( 2^{3} \)
$2.966204112$
$1.374253620$
4.511435598
\( -\frac{20383137018133}{610351562500} a - \frac{179472364456183}{610351562500} \)
\( \bigl[a + 1\) , \( -a - 1\) , \( 1\) , \( -8 a - 15\) , \( 61 a + 75\bigr] \)
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-8a-15\right){x}+61a+75$
50.6-e1
50.6-e
$1$
$1$
\(\Q(\sqrt{209}) \)
$2$
$[2, 0]$
50.6
\( 2 \cdot 5^{2} \)
\( 2^{2} \cdot 5^{22} \)
$3.43522$
$(11a+74), (-4a-27)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
$4$
\( 2^{3} \)
$1$
$1.212650253$
2.684184703
\( -\frac{20383137018133}{610351562500} a - \frac{179472364456183}{610351562500} \)
\( \bigl[a + 1\) , \( a + 1\) , \( a\) , \( 17230672287 a - 133165805710\) , \( -16851530563242249 a + 130235640913374884\bigr] \)
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(17230672287a-133165805710\right){x}-16851530563242249a+130235640913374884$
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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.