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-a3
225.2-a
$8$
$16$
\(\Q(\sqrt{-2}) \)
$2$
$[0, 1]$
225.2
\( 3^{2} \cdot 5^{2} \)
\( 3^{4} \cdot 5^{16} \)
$0.97888$
$(-a-1), (a-1), (5)$
0
$\Z/8\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$2$
2B
$1$
\( 2^{5} \)
$1$
$1.117850856$
0.395219960
\( \frac{4733169839}{3515625} \)
\( \bigl[1\) , \( 1\) , \( 1\) , \( 35\) , \( -28\bigr] \)
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}+35{x}-28$
2025.3-a3
2025.3-a
$8$
$16$
\(\Q(\sqrt{-2}) \)
$2$
$[0, 1]$
2025.3
\( 3^{4} \cdot 5^{2} \)
\( 3^{16} \cdot 5^{16} \)
$1.69547$
$(-a-1), (a-1), (5)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2$
2B
$1$
\( 2^{5} \)
$1$
$0.372616952$
2.107839788
\( \frac{4733169839}{3515625} \)
\( \bigl[1\) , \( -1\) , \( 0\) , \( 315\) , \( 1066\bigr] \)
${y}^2+{x}{y}={x}^{3}-{x}^{2}+315{x}+1066$
3600.2-f3
3600.2-f
$8$
$16$
\(\Q(\sqrt{-2}) \)
$2$
$[0, 1]$
3600.2
\( 2^{4} \cdot 3^{2} \cdot 5^{2} \)
\( 2^{12} \cdot 3^{4} \cdot 5^{16} \)
$1.95776$
$(a), (-a-1), (a-1), (5)$
0
$\Z/4\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2$
2B
$1$
\( 2^{7} \)
$1$
$0.558925428$
3.161759683
\( \frac{4733169839}{3515625} \)
\( \bigl[a\) , \( 0\) , \( a\) , \( 141\) , \( -362\bigr] \)
${y}^2+a{x}{y}+a{y}={x}^{3}+141{x}-362$
5625.2-b3
5625.2-b
$8$
$16$
\(\Q(\sqrt{-2}) \)
$2$
$[0, 1]$
5625.2
\( 3^{2} \cdot 5^{4} \)
\( 3^{4} \cdot 5^{28} \)
$2.18884$
$(-a-1), (a-1), (5)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2$
2B
$1$
\( 2^{4} \)
$4.297783744$
$0.223570171$
5.435423749
\( \frac{4733169839}{3515625} \)
\( \bigl[1\) , \( 0\) , \( 1\) , \( 874\) , \( -5227\bigr] \)
${y}^2+{x}{y}+{y}={x}^{3}+874{x}-5227$
32400.3-c3
32400.3-c
$8$
$16$
\(\Q(\sqrt{-2}) \)
$2$
$[0, 1]$
32400.3
\( 2^{4} \cdot 3^{4} \cdot 5^{2} \)
\( 2^{12} \cdot 3^{16} \cdot 5^{16} \)
$3.39094$
$(a), (-a-1), (a-1), (5)$
$2$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2$
2B
$1$
\( 2^{7} \)
$0.430582047$
$0.186308476$
7.260783784
\( \frac{4733169839}{3515625} \)
\( \bigl[a\) , \( -1\) , \( 0\) , \( 1260\) , \( 8528\bigr] \)
${y}^2+a{x}{y}={x}^{3}-{x}^{2}+1260{x}+8528$
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Pari/GP
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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.