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
841.1-CMa1
841.1-CMa
$1$
$1$
\(\Q(\sqrt{-1}) \)
$2$
$[0, 1]$
841.1
\( 29^{2} \)
\( 29^{9} \)
$0.96243$
$(-2a+5)$
0
$\Z/2\Z$
$\textsf{yes}$
$-4$
$\mathrm{U}(1)$
✓
✓
$29$
29Cs.7.1
$1$
\( 2 \)
$1$
$1.100312223$
0.550156111
\( 1728 \)
\( \bigl[i + 1\) , \( i\) , \( i\) , \( -36 i + 16\) , \( 8 i + 18\bigr] \)
${y}^2+\left(i+1\right){x}{y}+i{y}={x}^{3}+i{x}^{2}+\left(-36i+16\right){x}+8i+18$
841.1-a1
841.1-a
$2$
$29$
\(\Q(\sqrt{-1}) \)
$2$
$[0, 1]$
841.1
\( 29^{2} \)
\( 29^{10} \)
$0.96243$
$(-2a+5)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$29$
29B.7.2
$1$
\( 1 \)
$1.530163672$
$0.275151377$
0.842053285
\( -278824619 a - 321016092 \)
\( \bigl[1\) , \( i\) , \( 1\) , \( 2080 i - 3751\) , \( 73352 i - 79386\bigr] \)
${y}^2+{x}{y}+{y}={x}^{3}+i{x}^{2}+\left(2080i-3751\right){x}+73352i-79386$
841.1-a2
841.1-a
$2$
$29$
\(\Q(\sqrt{-1}) \)
$2$
$[0, 1]$
841.1
\( 29^{2} \)
\( 29^{2} \)
$0.96243$
$(-2a+5)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$29$
29B.7.1
$1$
\( 1 \)
$0.052764264$
$7.979389957$
0.842053285
\( -59 a - 12 \)
\( \bigl[1\) , \( i\) , \( 1\) , \( -1\) , \( 0\bigr] \)
${y}^2+{x}{y}+{y}={x}^{3}+i{x}^{2}-{x}$
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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.