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
43681.1-a1
43681.1-a
$2$
$3$
\(\Q(\sqrt{-1}) \)
$2$
$[0, 1]$
43681.1
\( 11^{2} \cdot 19^{2} \)
\( 11^{6} \cdot 19^{4} \)
$2.58370$
$(11), (19)$
$1$
$\Z/3\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$3$
3B.1.1
$1$
\( 2 \cdot 3 \)
$0.665117363$
$1.457660782$
1.292687329
\( -\frac{2258403328}{480491} \)
\( \bigl[0\) , \( -1\) , \( i\) , \( -27\) , \( -55\bigr] \)
${y}^2+i{y}={x}^{3}-{x}^{2}-27{x}-55$
43681.1-a2
43681.1-a
$2$
$3$
\(\Q(\sqrt{-1}) \)
$2$
$[0, 1]$
43681.1
\( 11^{2} \cdot 19^{2} \)
\( 11^{2} \cdot 19^{12} \)
$2.58370$
$(11), (19)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$3$
3B.1.2
$1$
\( 2 \cdot 3 \)
$0.221705787$
$0.485886927$
1.292687329
\( \frac{790939860992}{517504691} \)
\( \bigl[0\) , \( -1\) , \( i\) , \( 193\) , \( 308\bigr] \)
${y}^2+i{y}={x}^{3}-{x}^{2}+193{x}+308$
43681.1-b1
43681.1-b
$1$
$1$
\(\Q(\sqrt{-1}) \)
$2$
$[0, 1]$
43681.1
\( 11^{2} \cdot 19^{2} \)
\( 11^{4} \cdot 19^{6} \)
$2.58370$
$(11), (19)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$1$
\( 2 \)
$1$
$1.265930034$
2.531860069
\( -\frac{370772153}{829939} a + \frac{1035526608}{75449} \)
\( \bigl[1\) , \( i - 1\) , \( i\) , \( -24 i - 41\) , \( -88 i - 65\bigr] \)
${y}^2+{x}{y}+i{y}={x}^{3}+\left(i-1\right){x}^{2}+\left(-24i-41\right){x}-88i-65$
43681.1-c1
43681.1-c
$1$
$1$
\(\Q(\sqrt{-1}) \)
$2$
$[0, 1]$
43681.1
\( 11^{2} \cdot 19^{2} \)
\( 11^{4} \cdot 19^{6} \)
$2.58370$
$(11), (19)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$1$
\( 2 \)
$1$
$1.265930034$
2.531860069
\( \frac{370772153}{829939} a + \frac{1035526608}{75449} \)
\( \bigl[i\) , \( i + 1\) , \( 1\) , \( 23 i - 41\) , \( -88 i + 65\bigr] \)
${y}^2+i{x}{y}+{y}={x}^{3}+\left(i+1\right){x}^{2}+\left(23i-41\right){x}-88i+65$
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.