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
$8$
$20$
\(\Q(\sqrt{13}) \)
$2$
$[2, 0]$
36.1
\( 2^{2} \cdot 3^{2} \)
\( 2^{40} \cdot 3^{2} \)
$0.78920$
$(-a), (-a+1), (2)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2, 5$
2B , 5B.1.2
$25$
\( 2 \)
$1$
$0.308426902$
1.069277895
\( -\frac{4395631034341}{3145728} \)
\( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( 1023 a - 2390\) , \( 24243 a - 55924\bigr] \)
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(1023a-2390\right){x}+24243a-55924$
108.1-a1
108.1-a
$8$
$20$
\(\Q(\sqrt{13}) \)
$2$
$[2, 0]$
108.1
\( 2^{2} \cdot 3^{3} \)
\( 2^{40} \cdot 3^{8} \)
$1.03864$
$(-a), (-a+1), (2)$
0
$\Z/4\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2, 5$
2B , 5B.4.2
$1$
\( 2^{4} \cdot 5 \)
$1$
$0.802078487$
1.112282735
\( -\frac{4395631034341}{3145728} \)
\( \bigl[a\) , \( a\) , \( a\) , \( 1707 a - 4095\) , \( 53306 a - 122129\bigr] \)
${y}^2+a{x}{y}+a{y}={x}^{3}+a{x}^{2}+\left(1707a-4095\right){x}+53306a-122129$
108.2-a1
108.2-a
$8$
$20$
\(\Q(\sqrt{13}) \)
$2$
$[2, 0]$
108.2
\( 2^{2} \cdot 3^{3} \)
\( 2^{40} \cdot 3^{8} \)
$1.03864$
$(-a), (-a+1), (2)$
0
$\Z/4\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2, 5$
2B , 5B.4.2
$1$
\( 2^{4} \cdot 5 \)
$1$
$0.802078487$
1.112282735
\( -\frac{4395631034341}{3145728} \)
\( \bigl[a + 1\) , \( a + 1\) , \( a\) , \( -1704 a - 2386\) , \( -57399 a - 73940\bigr] \)
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-1704a-2386\right){x}-57399a-73940$
324.1-f1
324.1-f
$8$
$20$
\(\Q(\sqrt{13}) \)
$2$
$[2, 0]$
324.1
\( 2^{2} \cdot 3^{4} \)
\( 2^{40} \cdot 3^{14} \)
$1.36693$
$(-a), (-a+1), (2)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2, 5$
2B , 5B.4.2
$1$
\( 2^{3} \)
$1$
$2.085842366$
1.157017170
\( -\frac{4395631034341}{3145728} \)
\( \bigl[a + 1\) , \( -1\) , \( 1\) , \( 9214 a - 21500\) , \( -657647 a + 1516071\bigr] \)
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}-{x}^{2}+\left(9214a-21500\right){x}-657647a+1516071$
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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.