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
4.1-a1
4.1-a
$1$
$1$
\(\Q(\sqrt{53}) \)
$2$
$[2, 0]$
4.1
\( 2^{2} \)
\( 2^{34} \)
$0.92001$
$(2)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$1$
\( 1 \)
$1$
$8.120880803$
1.115488766
\( -\frac{25153757}{131072} \)
\( \bigl[a\) , \( a\) , \( 1\) , \( -40 a - 124\) , \( 801 a + 2515\bigr] \)
${y}^2+a{x}{y}+{y}={x}^{3}+a{x}^{2}+\left(-40a-124\right){x}+801a+2515$
4.1-b1
4.1-b
$2$
$5$
\(\Q(\sqrt{53}) \)
$2$
$[2, 0]$
4.1
\( 2^{2} \)
\( 2^{20} \)
$0.92001$
$(2)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$5$
5B.1.2
$4$
\( 2 \)
$1$
$0.853190410$
0.937557727
\( -\frac{9814089221}{1024} \)
\( \bigl[a + 1\) , \( -a + 1\) , \( 1\) , \( 311 a - 1287\) , \( 6283 a - 26012\bigr] \)
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(311a-1287\right){x}+6283a-26012$
4.1-b2
4.1-b
$2$
$5$
\(\Q(\sqrt{53}) \)
$2$
$[2, 0]$
4.1
\( 2^{2} \)
\( 2^{4} \)
$0.92001$
$(2)$
0
$\Z/5\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$5$
5B.1.1
$4$
\( 2 \)
$1$
$21.32976027$
0.937557727
\( \frac{6859}{4} \)
\( \bigl[a\) , \( 1\) , \( 1\) , \( 3 a + 15\) , \( 5 a + 17\bigr] \)
${y}^2+a{x}{y}+{y}={x}^{3}+{x}^{2}+\left(3a+15\right){x}+5a+17$
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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.