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-a3
36.1-a
$8$
$20$
\(\Q(\sqrt{13}) \)
$2$
$[2, 0]$
36.1
\( 2^{2} \cdot 3^{2} \)
\( 2^{4} \cdot 3^{20} \)
$0.78920$
$(-a), (-a+1), (2)$
0
$\Z/2\Z\oplus\Z/10\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2, 5$
2Cs , 5B.1.1
$1$
\( 2^{3} \cdot 5^{2} \)
$1$
$7.710672559$
1.069277895
\( \frac{476379541}{236196} \)
\( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( 48 a - 115\) , \( -96 a + 218\bigr] \)
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(48a-115\right){x}-96a+218$
108.1-a3
108.1-a
$8$
$20$
\(\Q(\sqrt{13}) \)
$2$
$[2, 0]$
108.1
\( 2^{2} \cdot 3^{3} \)
\( 2^{4} \cdot 3^{26} \)
$1.03864$
$(-a), (-a+1), (2)$
0
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2, 5$
2Cs , 5B.4.1
$1$
\( 2^{4} \)
$1$
$4.010392437$
1.112282735
\( \frac{476379541}{236196} \)
\( \bigl[a\) , \( a\) , \( a\) , \( 82 a - 195\) , \( -239 a + 538\bigr] \)
${y}^2+a{x}{y}+a{y}={x}^{3}+a{x}^{2}+\left(82a-195\right){x}-239a+538$
108.2-a3
108.2-a
$8$
$20$
\(\Q(\sqrt{13}) \)
$2$
$[2, 0]$
108.2
\( 2^{2} \cdot 3^{3} \)
\( 2^{4} \cdot 3^{26} \)
$1.03864$
$(-a), (-a+1), (2)$
0
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2, 5$
2Cs , 5B.4.1
$1$
\( 2^{4} \)
$1$
$4.010392437$
1.112282735
\( \frac{476379541}{236196} \)
\( \bigl[a + 1\) , \( a + 1\) , \( a\) , \( -79 a - 111\) , \( 46 a + 57\bigr] \)
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-79a-111\right){x}+46a+57$
324.1-f3
324.1-f
$8$
$20$
\(\Q(\sqrt{13}) \)
$2$
$[2, 0]$
324.1
\( 2^{2} \cdot 3^{4} \)
\( 2^{4} \cdot 3^{32} \)
$1.36693$
$(-a), (-a+1), (2)$
0
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2, 5$
2Cs , 5B.4.1
$1$
\( 2^{5} \)
$1$
$2.085842366$
1.157017170
\( \frac{476379541}{236196} \)
\( \bigl[a + 1\) , \( -1\) , \( 1\) , \( 439 a - 1025\) , \( 2431 a - 5613\bigr] \)
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}-{x}^{2}+\left(439a-1025\right){x}+2431a-5613$
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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.