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-h6
228.1-h
$8$
$12$
\(\Q(\sqrt{57}) \)
$2$
$[2, 0]$
228.1
\( 2^{2} \cdot 3 \cdot 19 \)
\( 2^{15} \cdot 3^{3} \cdot 19 \)
$2.62156$
$(a-4), (a+3), (4a+13), (10a-43)$
0
$\Z/6\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2, 3$
2B , 3B.1.1
$1$
\( 2^{2} \cdot 3^{3} \)
$1$
$9.915386767$
3.939975182
\( \frac{13676826625}{700416} a + \frac{201556775125}{700416} \)
\( \bigl[1\) , \( a + 1\) , \( a + 1\) , \( -2126 a - 6960\) , \( 99563 a + 326059\bigr] \)
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-2126a-6960\right){x}+99563a+326059$
228.1-s6
228.1-s
$8$
$12$
\(\Q(\sqrt{57}) \)
$2$
$[2, 0]$
228.1
\( 2^{2} \cdot 3 \cdot 19 \)
\( 2^{15} \cdot 3^{3} \cdot 19 \)
$2.62156$
$(a-4), (a+3), (4a+13), (10a-43)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2, 3$
2B , 3B.1.2
$1$
\( 2 \)
$0.709900903$
$9.523070670$
0.895441686
\( \frac{13676826625}{700416} a + \frac{201556775125}{700416} \)
\( \bigl[1\) , \( 1\) , \( 0\) , \( 365 a - 1560\) , \( -7195 a + 30758\bigr] \)
${y}^2+{x}{y}={x}^{3}+{x}^{2}+\left(365a-1560\right){x}-7195a+30758$
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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.