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-h8
228.1-h
$8$
$12$
\(\Q(\sqrt{57}) \)
$2$
$[2, 0]$
228.1
\( 2^{2} \cdot 3 \cdot 19 \)
\( 2^{5} \cdot 3 \cdot 19^{3} \)
$2.62156$
$(a-4), (a+3), (4a+13), (10a-43)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2, 3$
2B , 3B.1.2
$9$
\( 2^{2} \cdot 3 \)
$1$
$1.101709640$
3.939975182
\( \frac{25477549476528524375}{17328} a + \frac{41718432722015743375}{8664} \)
\( \bigl[1\) , \( -a - 1\) , \( a + 1\) , \( 10157 a - 43417\) , \( 1002709 a - 4286507\bigr] \)
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(10157a-43417\right){x}+1002709a-4286507$
228.1-s8
228.1-s
$8$
$12$
\(\Q(\sqrt{57}) \)
$2$
$[2, 0]$
228.1
\( 2^{2} \cdot 3 \cdot 19 \)
\( 2^{5} \cdot 3 \cdot 19^{3} \)
$2.62156$
$(a-4), (a+3), (4a+13), (10a-43)$
$1$
$\Z/6\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2, 3$
2B , 3B.1.1
$1$
\( 2 \cdot 3 \)
$2.129702711$
$9.523070670$
0.895441686
\( \frac{25477549476528524375}{17328} a + \frac{41718432722015743375}{8664} \)
\( \bigl[1\) , \( 1\) , \( 0\) , \( -29535 a - 96725\) , \( 5355845 a + 17539949\bigr] \)
${y}^2+{x}{y}={x}^{3}+{x}^{2}+\left(-29535a-96725\right){x}+5355845a+17539949$
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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.