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
67.1-a1
67.1-a
$1$
$1$
\(\Q(\sqrt{-51}) \)
$2$
$[0, 1]$
67.1
\( 67 \)
\( 3^{12} \cdot 67 \)
$1.82575$
$(-2a+5)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$1$
\( 1 \)
$1$
$9.070165672$
2.540154469
\( -\frac{33238}{67} a - \frac{291861}{67} \)
\( \bigl[a\) , \( -a + 1\) , \( a + 1\) , \( -a + 2\) , \( 3 a + 5\bigr] \)
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^3+\left(-a+1\right){x}^2+\left(-a+2\right){x}+3a+5$
67.1-b1
67.1-b
$1$
$1$
\(\Q(\sqrt{-51}) \)
$2$
$[0, 1]$
67.1
\( 67 \)
\( 67 \)
$1.82575$
$(-2a+5)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$1$
\( 1 \)
$1$
$9.070165672$
2.540154469
\( -\frac{33238}{67} a - \frac{291861}{67} \)
\( \bigl[a\) , \( a + 1\) , \( a\) , \( -2 a + 1\) , \( -a + 8\bigr] \)
${y}^2+a{x}{y}+a{y}={x}^3+\left(a+1\right){x}^2+\left(-2a+1\right){x}-a+8$
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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.