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-h5
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
\( -\frac{13676826625}{700416} a + \frac{107616800875}{350208} \)
\( \bigl[1\) , \( -a - 1\) , \( a + 1\) , \( 2127 a - 9087\) , \( -101691 a + 434709\bigr] \)
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(2127a-9087\right){x}-101691a+434709$
228.1-s5
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
\( -\frac{13676826625}{700416} a + \frac{107616800875}{350208} \)
\( \bigl[1\) , \( 1\) , \( 0\) , \( -365 a - 1195\) , \( 7195 a + 23563\bigr] \)
${y}^2+{x}{y}={x}^{3}+{x}^{2}+\left(-365a-1195\right){x}+7195a+23563$
Download
displayed columns for
results
to
Text
Pari/GP
SageMath
Magma
Oscar
CSV
*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.