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
36.1-a1
36.1-a
$1$
$1$
\(\Q(\sqrt{53}) \)
$2$
$[2, 0]$
36.1
\( 2^{2} \cdot 3^{2} \)
\( 2^{2} \cdot 3^{4} \)
$1.59350$
$(2), (3)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$1$
\( 2 \)
$1$
$7.106415608$
1.952282511
\( \frac{20833}{18} a - \frac{43171}{9} \)
\( \bigl[a + 1\) , \( a - 1\) , \( a + 1\) , \( 3 a + 6\) , \( 4 a + 11\bigr] \)
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(3a+6\right){x}+4a+11$
36.1-b1
36.1-b
$1$
$1$
\(\Q(\sqrt{53}) \)
$2$
$[2, 0]$
36.1
\( 2^{2} \cdot 3^{2} \)
\( 2^{2} \cdot 3^{18} \)
$1.59350$
$(2), (3)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$1$
\( 1 \)
$1$
$13.36566751$
1.835915627
\( -\frac{6362477477}{39366} \)
\( \bigl[a\) , \( 1\) , \( 1\) , \( -270 a - 843\) , \( 4165 a + 13079\bigr] \)
${y}^2+a{x}{y}+{y}={x}^{3}+{x}^{2}+\left(-270a-843\right){x}+4165a+13079$
36.1-c1
36.1-c
$1$
$1$
\(\Q(\sqrt{53}) \)
$2$
$[2, 0]$
36.1
\( 2^{2} \cdot 3^{2} \)
\( 2^{22} \cdot 3^{2} \)
$1.59350$
$(2), (3)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$1$
\( 1 \)
$1$
$13.90397201$
1.909857437
\( -\frac{1953125}{6144} \)
\( \bigl[a\) , \( a\) , \( 0\) , \( -15 a - 47\) , \( 157 a + 493\bigr] \)
${y}^2+a{x}{y}={x}^{3}+a{x}^{2}+\left(-15a-47\right){x}+157a+493$
36.1-d1
36.1-d
$1$
$1$
\(\Q(\sqrt{53}) \)
$2$
$[2, 0]$
36.1
\( 2^{2} \cdot 3^{2} \)
\( 2^{2} \cdot 3^{4} \)
$1.59350$
$(2), (3)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$1$
\( 2 \)
$1$
$7.106415608$
1.952282511
\( -\frac{20833}{18} a - \frac{65509}{18} \)
\( \bigl[a\) , \( a + 1\) , \( 1\) , \( 3 a + 11\) , \( 2 a + 6\bigr] \)
${y}^2+a{x}{y}+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(3a+11\right){x}+2a+6$
36.1-e1
36.1-e
$2$
$5$
\(\Q(\sqrt{53}) \)
$2$
$[2, 0]$
36.1
\( 2^{2} \cdot 3^{2} \)
\( 2^{2} \cdot 3^{4} \)
$1.59350$
$(2), (3)$
0
$\Z/5\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$5$
5B.1.1
$1$
\( 2 \)
$1$
$48.14860131$
0.529097522
\( -\frac{3307949}{18} \)
\( \bigl[a\) , \( 1\) , \( 0\) , \( -21 a - 62\) , \( 68 a + 215\bigr] \)
${y}^2+a{x}{y}={x}^{3}+{x}^{2}+\left(-21a-62\right){x}+68a+215$
36.1-e2
36.1-e
$2$
$5$
\(\Q(\sqrt{53}) \)
$2$
$[2, 0]$
36.1
\( 2^{2} \cdot 3^{2} \)
\( 2^{10} \cdot 3^{20} \)
$1.59350$
$(2), (3)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$5$
5B.1.2
$1$
\( 2 \)
$1$
$1.925944052$
0.529097522
\( \frac{1160935651}{1889568} \)
\( \bigl[a\) , \( 1\) , \( 0\) , \( 154 a + 488\) , \( -2384 a - 7484\bigr] \)
${y}^2+a{x}{y}={x}^{3}+{x}^{2}+\left(154a+488\right){x}-2384a-7484$
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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.