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
1600.1-a3
1600.1-a
$4$
$4$
\(\Q(\sqrt{-3}) \)
$2$
$[0, 1]$
1600.1
\( 2^{6} \cdot 5^{2} \)
\( 2^{8} \cdot 5^{2} \)
$0.97888$
$(2), (5)$
$1$
$\Z/4\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2$
2B
$1$
\( 2 \)
$0.683761292$
$5.993777963$
1.183081163
\( \frac{55296}{5} \)
\( \bigl[0\) , \( 0\) , \( 0\) , \( -2\) , \( 1\bigr] \)
${y}^2={x}^{3}-2{x}+1$
6400.1-g3
6400.1-g
$4$
$4$
\(\Q(\sqrt{-3}) \)
$2$
$[0, 1]$
6400.1
\( 2^{8} \cdot 5^{2} \)
\( 2^{8} \cdot 5^{2} \)
$1.38434$
$(2), (5)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2$
2B
$1$
\( 1 \)
$1$
$5.993777963$
1.730254660
\( \frac{55296}{5} \)
\( \bigl[0\) , \( 0\) , \( 0\) , \( -2\) , \( -1\bigr] \)
${y}^2={x}^{3}-2{x}-1$
40000.1-c3
40000.1-c
$4$
$4$
\(\Q(\sqrt{-3}) \)
$2$
$[0, 1]$
40000.1
\( 2^{6} \cdot 5^{4} \)
\( 2^{8} \cdot 5^{14} \)
$2.18884$
$(2), (5)$
0
$\Z/4\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2$
2B
$4$
\( 2^{3} \)
$1$
$1.198755592$
2.768407456
\( \frac{55296}{5} \)
\( \bigl[0\) , \( 0\) , \( 0\) , \( -50\) , \( 125\bigr] \)
${y}^2={x}^{3}-50{x}+125$
57600.1-b3
57600.1-b
$4$
$4$
\(\Q(\sqrt{-3}) \)
$2$
$[0, 1]$
57600.1
\( 2^{8} \cdot 3^{2} \cdot 5^{2} \)
\( 2^{8} \cdot 3^{6} \cdot 5^{2} \)
$2.39775$
$(-2a+1), (2), (5)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$1$
\( 2 \)
$1$
$3.460509320$
1.997925987
\( \frac{55296}{5} \)
\( \bigl[0\) , \( 0\) , \( 0\) , \( -6 a\) , \( -6 a + 3\bigr] \)
${y}^2={x}^{3}-6a{x}-6a+3$
57600.1-q3
57600.1-q
$4$
$4$
\(\Q(\sqrt{-3}) \)
$2$
$[0, 1]$
57600.1
\( 2^{8} \cdot 3^{2} \cdot 5^{2} \)
\( 2^{8} \cdot 3^{6} \cdot 5^{2} \)
$2.39775$
$(-2a+1), (2), (5)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$1$
\( 2 \)
$1$
$3.460509320$
1.997925987
\( \frac{55296}{5} \)
\( \bigl[0\) , \( 0\) , \( 0\) , \( 6\) , \( 6 a - 3\bigr] \)
${y}^2={x}^{3}+6{x}+6a-3$
102400.1-g3
102400.1-g
$4$
$4$
\(\Q(\sqrt{-3}) \)
$2$
$[0, 1]$
102400.1
\( 2^{12} \cdot 5^{2} \)
\( 2^{20} \cdot 5^{2} \)
$2.76869$
$(2), (5)$
$2$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2$
2B
$1$
\( 2^{2} \)
$0.361484422$
$2.996888981$
5.003680854
\( \frac{55296}{5} \)
\( \bigl[0\) , \( 0\) , \( 0\) , \( 8 a\) , \( 8\bigr] \)
${y}^2={x}^{3}+8a{x}+8$
102400.1-n3
102400.1-n
$4$
$4$
\(\Q(\sqrt{-3}) \)
$2$
$[0, 1]$
102400.1
\( 2^{12} \cdot 5^{2} \)
\( 2^{20} \cdot 5^{2} \)
$2.76869$
$(2), (5)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2$
2B
$1$
\( 2^{2} \)
$1$
$2.996888981$
3.460509320
\( \frac{55296}{5} \)
\( \bigl[0\) , \( 0\) , \( 0\) , \( -8\) , \( -8\bigr] \)
${y}^2={x}^{3}-8{x}-8$
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.