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
12337.1-a1
12337.1-a
$4$
$6$
\(\Q(\sqrt{-3}) \)
$2$
$[0, 1]$
12337.1
\( 13^{2} \cdot 73 \)
\( 13^{6} \cdot 73^{3} \)
$1.63118$
$(-4a+1), (-9a+1)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2, 3$
2B , 3B[2]
$1$
\( 2 \)
$3.102706071$
$0.899261677$
3.221781549
\( \frac{60988685561}{389017} a - \frac{169775626841}{389017} \)
\( \bigl[a\) , \( -a\) , \( a\) , \( 141 a + 45\) , \( -389 a + 987\bigr] \)
${y}^2+a{x}{y}+a{y}={x}^{3}-a{x}^{2}+\left(141a+45\right){x}-389a+987$
12337.1-a2
12337.1-a
$4$
$6$
\(\Q(\sqrt{-3}) \)
$2$
$[0, 1]$
12337.1
\( 13^{2} \cdot 73 \)
\( 13^{6} \cdot 73^{2} \)
$1.63118$
$(-4a+1), (-9a+1)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2, 3$
2B , 3B[2]
$1$
\( 2^{3} \)
$0.517117678$
$1.348892516$
3.221781549
\( -\frac{927841113}{5329} a - \frac{395933743}{5329} \)
\( \bigl[a\) , \( -a\) , \( a\) , \( -79 a + 35\) , \( -179 a + 213\bigr] \)
${y}^2+a{x}{y}+a{y}={x}^{3}-a{x}^{2}+\left(-79a+35\right){x}-179a+213$
12337.1-a3
12337.1-a
$4$
$6$
\(\Q(\sqrt{-3}) \)
$2$
$[0, 1]$
12337.1
\( 13^{2} \cdot 73 \)
\( 13^{6} \cdot 73 \)
$1.63118$
$(-4a+1), (-9a+1)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2, 3$
2B , 3B[2]
$1$
\( 2 \)
$1.034235357$
$2.697785033$
3.221781549
\( \frac{9927}{73} a + \frac{20960}{73} \)
\( \bigl[a\) , \( -a\) , \( a\) , \( -4 a\) , \( -a + 6\bigr] \)
${y}^2+a{x}{y}+a{y}={x}^{3}-a{x}^{2}-4a{x}-a+6$
12337.1-a4
12337.1-a
$4$
$6$
\(\Q(\sqrt{-3}) \)
$2$
$[0, 1]$
12337.1
\( 13^{2} \cdot 73 \)
\( 13^{6} \cdot 73^{6} \)
$1.63118$
$(-4a+1), (-9a+1)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2, 3$
2B , 3B[2]
$1$
\( 2^{3} \)
$1.551353035$
$0.449630838$
3.221781549
\( -\frac{55816089234767}{151334226289} a + \frac{107352826006104}{151334226289} \)
\( \bigl[a\) , \( -a\) , \( a\) , \( 181 a - 30\) , \( -1160 a + 1313\bigr] \)
${y}^2+a{x}{y}+a{y}={x}^{3}-a{x}^{2}+\left(181a-30\right){x}-1160a+1313$
Download
displayed columns for
results
to
Text
Pari/GP
SageMath
Magma
Oscar
CSV
*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.