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
28609.1-a1
28609.1-a
$2$
$3$
\(\Q(\sqrt{-3}) \)
$2$
$[0, 1]$
28609.1
\( 7 \cdot 61 \cdot 67 \)
\( 7 \cdot 61^{3} \cdot 67^{3} \)
$2.01291$
$(-3a+1), (-9a+5), (9a-7)$
0
$\Z/3\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$3$
3B.1.1[2]
$1$
\( 3^{2} \)
$1$
$1.412916590$
1.631495548
\( \frac{561449070899200}{477872405521} a - \frac{1238034549116928}{477872405521} \)
\( \bigl[0\) , \( -a\) , \( a\) , \( -18 a + 27\) , \( -42 a - 36\bigr] \)
${y}^2+a{y}={x}^{3}-a{x}^{2}+\left(-18a+27\right){x}-42a-36$
28609.1-a2
28609.1-a
$2$
$3$
\(\Q(\sqrt{-3}) \)
$2$
$[0, 1]$
28609.1
\( 7 \cdot 61 \cdot 67 \)
\( 7^{3} \cdot 61 \cdot 67 \)
$2.01291$
$(-3a+1), (-9a+5), (9a-7)$
0
$\Z/3\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$3$
3B.1.1[2]
$1$
\( 3 \)
$1$
$4.238749772$
1.631495548
\( -\frac{445575168}{1401841} a + \frac{1840836608}{1401841} \)
\( \bigl[0\) , \( -a\) , \( a\) , \( 2 a - 3\) , \( a + 1\bigr] \)
${y}^2+a{y}={x}^{3}-a{x}^{2}+\left(2a-3\right){x}+a+1$
28609.1-b1
28609.1-b
$1$
$1$
\(\Q(\sqrt{-3}) \)
$2$
$[0, 1]$
28609.1
\( 7 \cdot 61 \cdot 67 \)
\( 7^{5} \cdot 61 \cdot 67^{2} \)
$2.01291$
$(-3a+1), (-9a+5), (9a-7)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$1$
\( 2 \)
$0.236667719$
$1.586601582$
1.734348100
\( \frac{593270166124082}{4602244003} a - \frac{925840943805369}{4602244003} \)
\( \bigl[a\) , \( a - 1\) , \( 0\) , \( -21 a - 34\) , \( -94 a - 44\bigr] \)
${y}^2+a{x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-21a-34\right){x}-94a-44$
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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.