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
200.1-a3
200.1-a
$4$
$4$
\(\Q(\sqrt{3}) \)
$2$
$[2, 0]$
200.1
\( 2^{3} \cdot 5^{2} \)
\( 2^{8} \cdot 5^{2} \)
$1.16409$
$(a+1), (5)$
0
$\Z/4\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2$
2B
$1$
\( 2 \)
$1$
$35.25568626$
1.272179997
\( \frac{55296}{5} \)
\( \bigl[0\) , \( 0\) , \( 0\) , \( -2\) , \( 1\bigr] \)
${y}^2={x}^{3}-2{x}+1$
200.1-b3
200.1-b
$4$
$4$
\(\Q(\sqrt{3}) \)
$2$
$[2, 0]$
200.1
\( 2^{3} \cdot 5^{2} \)
\( 2^{8} \cdot 5^{2} \)
$1.16409$
$(a+1), (5)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2$
2B
$1$
\( 2^{2} \)
$0.170940323$
$16.30392283$
1.609073952
\( \frac{55296}{5} \)
\( \bigl[0\) , \( 0\) , \( 0\) , \( -2\) , \( -1\bigr] \)
${y}^2={x}^{3}-2{x}-1$
3600.1-c3
3600.1-c
$4$
$4$
\(\Q(\sqrt{3}) \)
$2$
$[2, 0]$
3600.1
\( 2^{4} \cdot 3^{2} \cdot 5^{2} \)
\( 2^{8} \cdot 3^{6} \cdot 5^{2} \)
$2.39775$
$(a+1), (a), (5)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$1$
\( 2 \)
$1$
$13.84203728$
1.997925987
\( \frac{55296}{5} \)
\( \bigl[0\) , \( 0\) , \( 0\) , \( -24 a - 42\) , \( 78 a + 135\bigr] \)
${y}^2={x}^{3}+\left(-24a-42\right){x}+78a+135$
3600.1-k3
3600.1-k
$4$
$4$
\(\Q(\sqrt{3}) \)
$2$
$[2, 0]$
3600.1
\( 2^{4} \cdot 3^{2} \cdot 5^{2} \)
\( 2^{8} \cdot 3^{6} \cdot 5^{2} \)
$2.39775$
$(a+1), (a), (5)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$1$
\( 2 \)
$1$
$13.84203728$
1.997925987
\( \frac{55296}{5} \)
\( \bigl[0\) , \( 0\) , \( 0\) , \( -24 a - 42\) , \( -78 a - 135\bigr] \)
${y}^2={x}^{3}+\left(-24a-42\right){x}-78a-135$
5000.1-e3
5000.1-e
$4$
$4$
\(\Q(\sqrt{3}) \)
$2$
$[2, 0]$
5000.1
\( 2^{3} \cdot 5^{4} \)
\( 2^{8} \cdot 5^{14} \)
$2.60299$
$(a+1), (5)$
0
$\Z/4\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2$
2B
$1$
\( 2^{4} \)
$1$
$7.051137252$
2.035487995
\( \frac{55296}{5} \)
\( \bigl[0\) , \( 0\) , \( 0\) , \( -50\) , \( 125\bigr] \)
${y}^2={x}^{3}-50{x}+125$
5000.1-f3
5000.1-f
$4$
$4$
\(\Q(\sqrt{3}) \)
$2$
$[2, 0]$
5000.1
\( 2^{3} \cdot 5^{4} \)
\( 2^{8} \cdot 5^{14} \)
$2.60299$
$(a+1), (5)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2$
2B
$1$
\( 2^{3} \)
$0.933393502$
$3.260784567$
3.514440935
\( \frac{55296}{5} \)
\( \bigl[0\) , \( 0\) , \( 0\) , \( -50\) , \( -125\bigr] \)
${y}^2={x}^{3}-50{x}-125$
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Pari/GP
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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.