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
228.1-h3
228.1-h
$8$
$12$
\(\Q(\sqrt{57}) \)
$2$
$[2, 0]$
228.1
\( 2^{2} \cdot 3 \cdot 19 \)
\( 2^{12} \cdot 3^{6} \cdot 19^{2} \)
$2.62156$
$(a-4), (a+3), (4a+13), (10a-43)$
0
$\Z/2\Z\oplus\Z/6\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$2, 3$
2Cs , 3B.1.1
$1$
\( 2^{4} \cdot 3^{3} \)
$1$
$9.915386767$
3.939975182
\( \frac{57066625}{32832} \)
\( \bigl[1\) , \( 0\) , \( 0\) , \( -8\) , \( 0\bigr] \)
${y}^2+{x}{y}={x}^{3}-8{x}$
228.1-s3
228.1-s
$8$
$12$
\(\Q(\sqrt{57}) \)
$2$
$[2, 0]$
228.1
\( 2^{2} \cdot 3 \cdot 19 \)
\( 2^{12} \cdot 3^{6} \cdot 19^{2} \)
$2.62156$
$(a-4), (a+3), (4a+13), (10a-43)$
$1$
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$2, 3$
2Cs , 3B.1.2
$1$
\( 2^{4} \)
$0.354950451$
$9.523070670$
0.895441686
\( \frac{57066625}{32832} \)
\( \bigl[1\) , \( -a\) , \( a + 1\) , \( -96892 a - 317308\) , \( -2306310 a - 7552974\bigr] \)
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(-96892a-317308\right){x}-2306310a-7552974$
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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.