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-b1
4608.1-b
$2$
$2$
\(\Q(\sqrt{-1}) \)
$2$
$[0, 1]$
4608.1
\( 2^{9} \cdot 3^{2} \)
\( 2^{20} \cdot 3^{4} \)
$1.47247$
$(a+1), (3)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$1$
\( 2^{3} \)
$0.185427672$
$3.035318132$
2.251327905
\( \frac{4000}{9} \)
\( \bigl[0\) , \( i - 1\) , \( 0\) , \( -4 i\) , \( 4 i + 4\bigr] \)
${y}^2={x}^{3}+\left(i-1\right){x}^{2}-4i{x}+4i+4$
4608.1-c1
4608.1-c
$2$
$2$
\(\Q(\sqrt{-1}) \)
$2$
$[0, 1]$
4608.1
\( 2^{9} \cdot 3^{2} \)
\( 2^{20} \cdot 3^{4} \)
$1.47247$
$(a+1), (3)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$1$
\( 2^{3} \)
$0.185427672$
$3.035318132$
2.251327905
\( \frac{4000}{9} \)
\( \bigl[0\) , \( -i - 1\) , \( 0\) , \( 4 i\) , \( -4 i + 4\bigr] \)
${y}^2={x}^{3}+\left(-i-1\right){x}^{2}+4i{x}-4i+4$
9216.1-f1
9216.1-f
$2$
$2$
\(\Q(\sqrt{-1}) \)
$2$
$[0, 1]$
9216.1
\( 2^{10} \cdot 3^{2} \)
\( 2^{14} \cdot 3^{4} \)
$1.75107$
$(a+1), (3)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2$
2B
$1$
\( 2^{2} \)
$0.319732820$
$4.292588069$
2.744962582
\( \frac{4000}{9} \)
\( \bigl[0\) , \( -i\) , \( 0\) , \( -2\) , \( 2 i\bigr] \)
${y}^2={x}^{3}-i{x}^{2}-2{x}+2i$
9216.1-g1
9216.1-g
$2$
$2$
\(\Q(\sqrt{-1}) \)
$2$
$[0, 1]$
9216.1
\( 2^{10} \cdot 3^{2} \)
\( 2^{14} \cdot 3^{4} \)
$1.75107$
$(a+1), (3)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2$
2B
$1$
\( 2 \)
$1$
$4.292588069$
2.146294034
\( \frac{4000}{9} \)
\( \bigl[0\) , \( -1\) , \( 0\) , \( 2\) , \( -2\bigr] \)
${y}^2={x}^{3}-{x}^{2}+2{x}-2$
41472.1-e1
41472.1-e
$2$
$2$
\(\Q(\sqrt{-1}) \)
$2$
$[0, 1]$
41472.1
\( 2^{9} \cdot 3^{4} \)
\( 2^{20} \cdot 3^{16} \)
$2.55039$
$(a+1), (3)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$1$
\( 2^{3} \)
$1$
$1.011772710$
2.023545421
\( \frac{4000}{9} \)
\( \bigl[0\) , \( 0\) , \( 0\) , \( -30 i\) , \( 76 i + 76\bigr] \)
${y}^2={x}^{3}-30i{x}+76i+76$
41472.1-f1
41472.1-f
$2$
$2$
\(\Q(\sqrt{-1}) \)
$2$
$[0, 1]$
41472.1
\( 2^{9} \cdot 3^{4} \)
\( 2^{20} \cdot 3^{16} \)
$2.55039$
$(a+1), (3)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$1$
\( 2^{3} \)
$1$
$1.011772710$
2.023545421
\( \frac{4000}{9} \)
\( \bigl[0\) , \( 0\) , \( 0\) , \( 30 i\) , \( -76 i + 76\bigr] \)
${y}^2={x}^{3}+30i{x}-76i+76$
82944.1-i1
82944.1-i
$2$
$2$
\(\Q(\sqrt{-1}) \)
$2$
$[0, 1]$
82944.1
\( 2^{10} \cdot 3^{4} \)
\( 2^{14} \cdot 3^{16} \)
$3.03295$
$(a+1), (3)$
$2$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2$
2B
$1$
\( 2^{3} \)
$0.562854619$
$1.430862689$
6.442941394
\( \frac{4000}{9} \)
\( \bigl[0\) , \( 0\) , \( 0\) , \( -15\) , \( -38 i\bigr] \)
${y}^2={x}^{3}-15{x}-38i$
82944.1-l1
82944.1-l
$2$
$2$
\(\Q(\sqrt{-1}) \)
$2$
$[0, 1]$
82944.1
\( 2^{10} \cdot 3^{4} \)
\( 2^{14} \cdot 3^{16} \)
$3.03295$
$(a+1), (3)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2$
2B
$1$
\( 2^{2} \)
$1.696743987$
$1.430862689$
4.855615331
\( \frac{4000}{9} \)
\( \bigl[0\) , \( 0\) , \( 0\) , \( 15\) , \( -38\bigr] \)
${y}^2={x}^{3}+15{x}-38$
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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.