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
57.1-d1
57.1-d
$6$
$8$
\(\Q(\sqrt{57}) \)
$2$
$[2, 0]$
57.1
\( 3 \cdot 19 \)
\( 3^{2} \cdot 19^{8} \)
$1.85372$
$(4a+13), (10a-43)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$2$
2B
$1$
\( 2^{2} \)
$1$
$2.262154252$
0.299629650
\( \frac{67419143}{390963} \)
\( \bigl[1\) , \( -a\) , \( a\) , \( 102428 a + 335449\) , \( -104265070 a - 341459474\bigr] \)
${y}^2+{x}{y}+a{y}={x}^{3}-a{x}^{2}+\left(102428a+335449\right){x}-104265070a-341459474$
57.1-g1
57.1-g
$6$
$8$
\(\Q(\sqrt{57}) \)
$2$
$[2, 0]$
57.1
\( 3 \cdot 19 \)
\( 3^{2} \cdot 19^{8} \)
$1.85372$
$(4a+13), (10a-43)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$2$
2B
$1$
\( 2^{2} \)
$3.892773922$
$4.711524088$
4.858622600
\( \frac{67419143}{390963} \)
\( \bigl[1\) , \( 0\) , \( 1\) , \( 8\) , \( 29\bigr] \)
${y}^2+{x}{y}+{y}={x}^{3}+8{x}+29$
171.1-e1
171.1-e
$6$
$8$
\(\Q(\sqrt{57}) \)
$2$
$[2, 0]$
171.1
\( 3^{2} \cdot 19 \)
\( 3^{8} \cdot 19^{8} \)
$2.43964$
$(4a+13), (10a-43)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$1$
\( 2^{4} \)
$1$
$1.884869071$
0.998628029
\( \frac{67419143}{390963} \)
\( \bigl[1\) , \( a\) , \( 0\) , \( 1018 a + 3337\) , \( 104632 a + 342660\bigr] \)
${y}^2+{x}{y}={x}^{3}+a{x}^{2}+\left(1018a+3337\right){x}+104632a+342660$
171.1-h1
171.1-h
$6$
$8$
\(\Q(\sqrt{57}) \)
$2$
$[2, 0]$
171.1
\( 3^{2} \cdot 19 \)
\( 3^{8} \cdot 19^{8} \)
$2.43964$
$(4a+13), (10a-43)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$1$
\( 2^{4} \)
$1$
$1.884869071$
0.998628029
\( \frac{67419143}{390963} \)
\( \bigl[1\) , \( -a + 1\) , \( 0\) , \( -1018 a + 4355\) , \( -104632 a + 447292\bigr] \)
${y}^2+{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-1018a+4355\right){x}-104632a+447292$
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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.