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
225.2-a2
225.2-a
$8$
$16$
\(\Q(\sqrt{-2}) \)
$2$
$[0, 1]$
225.2
\( 3^{2} \cdot 5^{2} \)
\( 3^{2} \cdot 5^{2} \)
$0.97888$
$(-a-1), (a-1), (5)$
0
$\Z/4\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$2$
2B
$1$
\( 1 \)
$1$
$8.942806850$
0.395219960
\( -\frac{1}{15} \)
\( \bigl[1\) , \( 1\) , \( 1\) , \( 0\) , \( 0\bigr] \)
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}$
2025.3-a2
2025.3-a
$8$
$16$
\(\Q(\sqrt{-2}) \)
$2$
$[0, 1]$
2025.3
\( 3^{4} \cdot 5^{2} \)
\( 3^{14} \cdot 5^{2} \)
$1.69547$
$(-a-1), (a-1), (5)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2$
2B
$1$
\( 2^{2} \)
$1$
$2.980935616$
2.107839788
\( -\frac{1}{15} \)
\( \bigl[1\) , \( -1\) , \( 0\) , \( 0\) , \( -5\bigr] \)
${y}^2+{x}{y}={x}^{3}-{x}^{2}-5$
3600.2-f2
3600.2-f
$8$
$16$
\(\Q(\sqrt{-2}) \)
$2$
$[0, 1]$
3600.2
\( 2^{4} \cdot 3^{2} \cdot 5^{2} \)
\( 2^{12} \cdot 3^{2} \cdot 5^{2} \)
$1.95776$
$(a), (-a-1), (a-1), (5)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2$
2B
$1$
\( 2^{2} \)
$1$
$4.471403425$
3.161759683
\( -\frac{1}{15} \)
\( \bigl[a\) , \( 0\) , \( a\) , \( 1\) , \( 2\bigr] \)
${y}^2+a{x}{y}+a{y}={x}^{3}+{x}+2$
5625.2-b2
5625.2-b
$8$
$16$
\(\Q(\sqrt{-2}) \)
$2$
$[0, 1]$
5625.2
\( 3^{2} \cdot 5^{4} \)
\( 3^{2} \cdot 5^{14} \)
$2.18884$
$(-a-1), (a-1), (5)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2$
2B
$1$
\( 2^{2} \)
$2.148891872$
$1.788561370$
5.435423749
\( -\frac{1}{15} \)
\( \bigl[1\) , \( 0\) , \( 1\) , \( -1\) , \( 23\bigr] \)
${y}^2+{x}{y}+{y}={x}^{3}-{x}+23$
32400.3-c2
32400.3-c
$8$
$16$
\(\Q(\sqrt{-2}) \)
$2$
$[0, 1]$
32400.3
\( 2^{4} \cdot 3^{4} \cdot 5^{2} \)
\( 2^{12} \cdot 3^{14} \cdot 5^{2} \)
$3.39094$
$(a), (-a-1), (a-1), (5)$
$2$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2$
2B
$1$
\( 2^{6} \)
$0.107645511$
$1.490467808$
7.260783784
\( -\frac{1}{15} \)
\( \bigl[a\) , \( -1\) , \( 0\) , \( 0\) , \( -40\bigr] \)
${y}^2+a{x}{y}={x}^{3}-{x}^{2}-40$
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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.