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
484.1-a1
484.1-a
$2$
$3$
\(\Q(\sqrt{10}) \)
$2$
$[2, 0]$
484.1
\( 2^{2} \cdot 11^{2} \)
\( 2^{4} \cdot 11^{6} \)
$2.65082$
$(2,a), (11)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$3$
3B
$1$
\( 3^{2} \)
$1$
$1.294911296$
1.842691078
\( -\frac{199794688}{1331} \)
\( \bigl[0\) , \( -1\) , \( a\) , \( -19\) , \( -29\bigr] \)
${y}^2+a{y}={x}^{3}-{x}^{2}-19{x}-29$
484.1-a2
484.1-a
$2$
$3$
\(\Q(\sqrt{10}) \)
$2$
$[2, 0]$
484.1
\( 2^{2} \cdot 11^{2} \)
\( 2^{4} \cdot 11^{2} \)
$2.65082$
$(2,a), (11)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$3$
3B
$1$
\( 1 \)
$1$
$11.65420166$
1.842691078
\( \frac{8192}{11} \)
\( \bigl[0\) , \( -1\) , \( a\) , \( 1\) , \( -3\bigr] \)
${y}^2+a{y}={x}^{3}-{x}^{2}+{x}-3$
484.1-b1
484.1-b
$2$
$3$
\(\Q(\sqrt{10}) \)
$2$
$[2, 0]$
484.1
\( 2^{2} \cdot 11^{2} \)
\( 2^{16} \cdot 11^{6} \)
$2.65082$
$(2,a), (11)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$3$
3B.1.2
$1$
\( 3 \)
$1$
$1.294911296$
0.614230359
\( -\frac{199794688}{1331} \)
\( \bigl[0\) , \( 1\) , \( 0\) , \( -77\) , \( -289\bigr] \)
${y}^2={x}^{3}+{x}^{2}-77{x}-289$
484.1-b2
484.1-b
$2$
$3$
\(\Q(\sqrt{10}) \)
$2$
$[2, 0]$
484.1
\( 2^{2} \cdot 11^{2} \)
\( 2^{16} \cdot 11^{2} \)
$2.65082$
$(2,a), (11)$
0
$\Z/3\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$3$
3B.1.1
$1$
\( 3 \)
$1$
$11.65420166$
0.614230359
\( \frac{8192}{11} \)
\( \bigl[0\) , \( 1\) , \( 0\) , \( 3\) , \( -1\bigr] \)
${y}^2={x}^{3}+{x}^{2}+3{x}-1$
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.