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
4608.1-b2
4608.1-b
$2$
$2$
\(\Q(\sqrt{-1}) \)
$2$
$[0, 1]$
4608.1
\( 2^{9} \cdot 3^{2} \)
\( 2^{10} \cdot 3^{2} \)
$1.47247$
$(a+1), (3)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$1$
\( 2 \)
$0.370855344$
$6.070636265$
2.251327905
\( \frac{16000}{3} \)
\( \bigl[0\) , \( -i + 1\) , \( 0\) , \( i\) , \( 0\bigr] \)
${y}^2={x}^{3}+\left(-i+1\right){x}^{2}+i{x}$
4608.1-c2
4608.1-c
$2$
$2$
\(\Q(\sqrt{-1}) \)
$2$
$[0, 1]$
4608.1
\( 2^{9} \cdot 3^{2} \)
\( 2^{10} \cdot 3^{2} \)
$1.47247$
$(a+1), (3)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$1$
\( 2 \)
$0.370855344$
$6.070636265$
2.251327905
\( \frac{16000}{3} \)
\( \bigl[0\) , \( i + 1\) , \( 0\) , \( -i\) , \( 0\bigr] \)
${y}^2={x}^{3}+\left(i+1\right){x}^{2}-i{x}$
9216.1-f2
9216.1-f
$2$
$2$
\(\Q(\sqrt{-1}) \)
$2$
$[0, 1]$
9216.1
\( 2^{10} \cdot 3^{2} \)
\( 2^{16} \cdot 3^{2} \)
$1.75107$
$(a+1), (3)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2$
2B
$1$
\( 2 \)
$0.639465641$
$4.292588069$
2.744962582
\( \frac{16000}{3} \)
\( \bigl[0\) , \( 1\) , \( 0\) , \( -3\) , \( -3\bigr] \)
${y}^2={x}^{3}+{x}^{2}-3{x}-3$
9216.1-g2
9216.1-g
$2$
$2$
\(\Q(\sqrt{-1}) \)
$2$
$[0, 1]$
9216.1
\( 2^{10} \cdot 3^{2} \)
\( 2^{16} \cdot 3^{2} \)
$1.75107$
$(a+1), (3)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2$
2B
$1$
\( 2 \)
$1$
$4.292588069$
2.146294034
\( \frac{16000}{3} \)
\( \bigl[0\) , \( -i\) , \( 0\) , \( 3\) , \( -3 i\bigr] \)
${y}^2={x}^{3}-i{x}^{2}+3{x}-3i$
41472.1-e2
41472.1-e
$2$
$2$
\(\Q(\sqrt{-1}) \)
$2$
$[0, 1]$
41472.1
\( 2^{9} \cdot 3^{4} \)
\( 2^{10} \cdot 3^{14} \)
$2.55039$
$(a+1), (3)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$1$
\( 2^{2} \)
$1$
$2.023545421$
2.023545421
\( \frac{16000}{3} \)
\( \bigl[0\) , \( 0\) , \( 0\) , \( 15 i\) , \( 13 i + 13\bigr] \)
${y}^2={x}^{3}+15i{x}+13i+13$
41472.1-f2
41472.1-f
$2$
$2$
\(\Q(\sqrt{-1}) \)
$2$
$[0, 1]$
41472.1
\( 2^{9} \cdot 3^{4} \)
\( 2^{10} \cdot 3^{14} \)
$2.55039$
$(a+1), (3)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$1$
\( 2^{2} \)
$1$
$2.023545421$
2.023545421
\( \frac{16000}{3} \)
\( \bigl[0\) , \( 0\) , \( 0\) , \( -15 i\) , \( -13 i + 13\bigr] \)
${y}^2={x}^{3}-15i{x}-13i+13$
82944.1-i2
82944.1-i
$2$
$2$
\(\Q(\sqrt{-1}) \)
$2$
$[0, 1]$
82944.1
\( 2^{10} \cdot 3^{4} \)
\( 2^{16} \cdot 3^{14} \)
$3.03295$
$(a+1), (3)$
$2$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2$
2B
$1$
\( 2^{3} \)
$0.562854619$
$1.430862689$
6.442941394
\( \frac{16000}{3} \)
\( \bigl[0\) , \( 0\) , \( 0\) , \( -30\) , \( -52\bigr] \)
${y}^2={x}^{3}-30{x}-52$
82944.1-l2
82944.1-l
$2$
$2$
\(\Q(\sqrt{-1}) \)
$2$
$[0, 1]$
82944.1
\( 2^{10} \cdot 3^{4} \)
\( 2^{16} \cdot 3^{14} \)
$3.03295$
$(a+1), (3)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2$
2B
$1$
\( 2^{3} \)
$0.848371993$
$1.430862689$
4.855615331
\( \frac{16000}{3} \)
\( \bigl[0\) , \( 0\) , \( 0\) , \( 30\) , \( 52 i\bigr] \)
${y}^2={x}^{3}+30{x}+52i$
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.