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-b2
10.1-b
$2$
$2$
\(\Q(\sqrt{209}) \)
$2$
$[2, 0]$
10.1
\( 2 \cdot 5 \)
\( 2^{2} \cdot 5 \)
$2.29727$
$(11a-85), (-4a+31)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$1$
\( 2 \)
$0.985687996$
$32.68374952$
2.228425904
\( \frac{68921}{20} a + \frac{137842}{5} \)
\( \bigl[1\) , \( -a + 1\) , \( a\) , \( -a + 17\) , \( -2 a - 8\bigr] \)
${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-a+17\right){x}-2a-8$
10.1-c2
10.1-c
$2$
$2$
\(\Q(\sqrt{209}) \)
$2$
$[2, 0]$
10.1
\( 2 \cdot 5 \)
\( 2^{2} \cdot 5 \)
$2.29727$
$(11a-85), (-4a+31)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$1$
\( 2 \)
$1$
$43.47954356$
1.503771458
\( \frac{68921}{20} a + \frac{137842}{5} \)
\( \bigl[1\) , \( 1\) , \( 1\) , \( 512138585 a - 3958020110\) , \( 13200346700953 a - 102017772594930\bigr] \)
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}+\left(512138585a-3958020110\right){x}+13200346700953a-102017772594930$
50.3-d2
50.3-d
$2$
$2$
\(\Q(\sqrt{209}) \)
$2$
$[2, 0]$
50.3
\( 2 \cdot 5^{2} \)
\( 2^{2} \cdot 5^{7} \)
$3.43522$
$(11a-85), (-4a+31)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2B
$1$
\( 2^{3} \)
$2.249613082$
$19.44464300$
12.10304509
\( \frac{68921}{20} a + \frac{137842}{5} \)
\( \bigl[1\) , \( -a - 1\) , \( 0\) , \( 199 a - 1514\) , \( 3570 a - 27613\bigr] \)
${y}^2+{x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(199a-1514\right){x}+3570a-27613$
50.3-f2
50.3-f
$2$
$2$
\(\Q(\sqrt{209}) \)
$2$
$[2, 0]$
50.3
\( 2 \cdot 5^{2} \)
\( 2^{2} \cdot 5^{7} \)
$3.43522$
$(11a-85), (-4a+31)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2B
$1$
\( 2^{3} \)
$1$
$14.61661713$
2.022105097
\( \frac{68921}{20} a + \frac{137842}{5} \)
\( \bigl[1\) , \( a + 1\) , \( 1\) , \( -3817379 a - 25684905\) , \( -10751246830 a - 72338862782\bigr] \)
${y}^2+{x}{y}+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-3817379a-25684905\right){x}-10751246830a-72338862782$
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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.