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-h2
228.1-h
$8$
$12$
\(\Q(\sqrt{57}) \)
$2$
$[2, 0]$
228.1
\( 2^{2} \cdot 3 \cdot 19 \)
\( 2^{6} \cdot 3^{12} \cdot 19^{4} \)
$2.62156$
$(a-4), (a+3), (4a+13), (10a-43)$
0
$\Z/6\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$2, 3$
2B , 3B.1.1
$1$
\( 2^{4} \cdot 3^{3} \)
$1$
$2.478846691$
3.939975182
\( \frac{3616805375}{2105352} \)
\( \bigl[1\) , \( 0\) , \( 0\) , \( 32\) , \( 8\bigr] \)
${y}^2+{x}{y}={x}^{3}+32{x}+8$
228.1-s2
228.1-s
$8$
$12$
\(\Q(\sqrt{57}) \)
$2$
$[2, 0]$
228.1
\( 2^{2} \cdot 3 \cdot 19 \)
\( 2^{6} \cdot 3^{12} \cdot 19^{4} \)
$2.62156$
$(a-4), (a+3), (4a+13), (10a-43)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$2, 3$
2B , 3B.1.2
$1$
\( 2^{3} \)
$0.709900903$
$2.380767667$
0.895441686
\( \frac{3616805375}{2105352} \)
\( \bigl[1\) , \( -a\) , \( a + 1\) , \( 386308 a + 1265132\) , \( -19979150 a - 65430062\bigr] \)
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(386308a+1265132\right){x}-19979150a-65430062$
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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.