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
722.1-a1
722.1-a
$2$
$5$
\(\Q(\sqrt{2}) \)
$2$
$[2, 0]$
722.1
\( 2 \cdot 19^{2} \)
\( 2^{2} \cdot 19^{10} \)
$1.31014$
$(a), (19)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$5$
5B.1.2
$1$
\( 2 \cdot 5 \)
$1$
$0.671163407$
2.372920982
\( -\frac{37966934881}{4952198} \)
\( \bigl[1\) , \( 1\) , \( 1\) , \( -70\) , \( -279\bigr] \)
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-70{x}-279$
722.1-a2
722.1-a
$2$
$5$
\(\Q(\sqrt{2}) \)
$2$
$[2, 0]$
722.1
\( 2 \cdot 19^{2} \)
\( 2^{10} \cdot 19^{2} \)
$1.31014$
$(a), (19)$
0
$\Z/5\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$5$
5B.1.1
$1$
\( 2 \cdot 5 \)
$1$
$16.77908518$
2.372920982
\( -\frac{1}{608} \)
\( \bigl[1\) , \( 1\) , \( 1\) , \( 0\) , \( 1\bigr] \)
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}+1$
722.1-b1
722.1-b
$3$
$9$
\(\Q(\sqrt{2}) \)
$2$
$[2, 0]$
722.1
\( 2 \cdot 19^{2} \)
\( 2^{6} \cdot 19^{2} \)
$1.31014$
$(a), (19)$
$1$
$\Z/3\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$3$
3B.1.1
$1$
\( 2 \)
$0.278258698$
$32.17041206$
1.406623475
\( -\frac{413493625}{152} \)
\( \bigl[1\) , \( 0\) , \( 1\) , \( -16\) , \( 22\bigr] \)
${y}^2+{x}{y}+{y}={x}^{3}-16{x}+22$
722.1-b2
722.1-b
$3$
$9$
\(\Q(\sqrt{2}) \)
$2$
$[2, 0]$
722.1
\( 2 \cdot 19^{2} \)
\( 2^{54} \cdot 19^{2} \)
$1.31014$
$(a), (19)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$3$
3B.1.2
$1$
\( 2 \)
$2.504328284$
$0.397165580$
1.406623475
\( -\frac{69173457625}{2550136832} \)
\( \bigl[1\) , \( 0\) , \( 1\) , \( -86\) , \( -2456\bigr] \)
${y}^2+{x}{y}+{y}={x}^{3}-86{x}-2456$
722.1-b3
722.1-b
$3$
$9$
\(\Q(\sqrt{2}) \)
$2$
$[2, 0]$
722.1
\( 2 \cdot 19^{2} \)
\( 2^{18} \cdot 19^{6} \)
$1.31014$
$(a), (19)$
$1$
$\Z/3\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$3$
3Cs.1.1
$1$
\( 2 \cdot 3 \)
$0.834776094$
$3.574490228$
1.406623475
\( \frac{94196375}{3511808} \)
\( \bigl[1\) , \( 0\) , \( 1\) , \( 9\) , \( 90\bigr] \)
${y}^2+{x}{y}+{y}={x}^{3}+9{x}+90$
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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.