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
4225.1-a1
4225.1-a
$2$
$2$
\(\Q(\sqrt{3}) \)
$2$
$[2, 0]$
4225.1
\( 5^{2} \cdot 13^{2} \)
\( 5^{4} \cdot 13^{4} \)
$2.49566$
$(a+4), (a-4), (5)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$2$
2B
$1$
\( 2^{3} \)
$0.819087883$
$6.464450893$
6.114085539
\( \frac{6967871}{4225} \)
\( \bigl[a\) , \( -1\) , \( 0\) , \( 4\) , \( -1\bigr] \)
${y}^2+a{x}{y}={x}^{3}-{x}^{2}+4{x}-1$
4225.1-a2
4225.1-a
$2$
$2$
\(\Q(\sqrt{3}) \)
$2$
$[2, 0]$
4225.1
\( 5^{2} \cdot 13^{2} \)
\( 5^{2} \cdot 13^{2} \)
$2.49566$
$(a+4), (a-4), (5)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$2$
2B
$1$
\( 1 \)
$1.638175766$
$25.85780357$
6.114085539
\( \frac{117649}{65} \)
\( \bigl[a\) , \( -1\) , \( 0\) , \( -1\) , \( 0\bigr] \)
${y}^2+a{x}{y}={x}^{3}-{x}^{2}-{x}$
4225.1-b1
4225.1-b
$2$
$2$
\(\Q(\sqrt{3}) \)
$2$
$[2, 0]$
4225.1
\( 5^{2} \cdot 13^{2} \)
\( 5^{4} \cdot 13^{4} \)
$2.49566$
$(a+4), (a-4), (5)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$2$
2B
$1$
\( 2^{3} \)
$0.187757049$
$7.243777871$
1.570473975
\( \frac{6967871}{4225} \)
\( \bigl[1\) , \( 0\) , \( 0\) , \( 4\) , \( 1\bigr] \)
${y}^2+{x}{y}={x}^{3}+4{x}+1$
4225.1-b2
4225.1-b
$2$
$2$
\(\Q(\sqrt{3}) \)
$2$
$[2, 0]$
4225.1
\( 5^{2} \cdot 13^{2} \)
\( 5^{2} \cdot 13^{2} \)
$2.49566$
$(a+4), (a-4), (5)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$2$
2B
$1$
\( 1 \)
$0.375514098$
$28.97511148$
1.570473975
\( \frac{117649}{65} \)
\( \bigl[1\) , \( 0\) , \( 0\) , \( -1\) , \( 0\bigr] \)
${y}^2+{x}{y}={x}^{3}-{x}$
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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.