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
261.1-a1
261.1-a
$1$
$1$
\(\Q(\sqrt{-67}) \)
$2$
$[0, 1]$
261.1
\( 3^{2} \cdot 29 \)
\( 3^{2} \cdot 29 \)
$2.93992$
$(a+3), (3)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$1$
\( 1 \)
$1$
$8.758249111$
2.139980855
\( -\frac{863}{87} a + \frac{8884}{29} \)
\( \bigl[a\) , \( a\) , \( a + 1\) , \( -4 a + 6\) , \( 12\bigr] \)
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^3+a{x}^2+\left(-4a+6\right){x}+12$
2349.1-a1
2349.1-a
$1$
$1$
\(\Q(\sqrt{-67}) \)
$2$
$[0, 1]$
2349.1
\( 3^{4} \cdot 29 \)
\( 3^{14} \cdot 29 \)
$5.09210$
$(a+3), (3)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
$1$
\( 2^{2} \)
$1.424314048$
$2.919416370$
8.128012784
\( -\frac{863}{87} a + \frac{8884}{29} \)
\( \bigl[a\) , \( -a - 1\) , \( 0\) , \( 3 a + 9\) , \( -4 a - 8\bigr] \)
${y}^2+a{x}{y}={x}^3+\left(-a-1\right){x}^2+\left(3a+9\right){x}-4a-8$
7569.1-b1
7569.1-b
$1$
$1$
\(\Q(\sqrt{-67}) \)
$2$
$[0, 1]$
7569.1
\( 3^{2} \cdot 29^{2} \)
\( 3^{2} \cdot 29^{7} \)
$6.82237$
$(a+3), (3)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
$1$
\( 2 \)
$1$
$1.626366030$
0.794768937
\( -\frac{863}{87} a + \frac{8884}{29} \)
\( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( -a + 5\) , \( -3 a - 25\bigr] \)
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^3+\left(-a+5\right){x}-3a-25$
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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.