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-a1
200.1-a
$4$
$4$
\(\Q(\sqrt{3}) \)
$2$
$[2, 0]$
200.1
\( 2^{3} \cdot 5^{2} \)
\( 2^{8} \cdot 5^{8} \)
$1.16409$
$(a+1), (5)$
0
$\Z/4\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2$
2B
$1$
\( 2^{4} \)
$1$
$4.406960782$
1.272179997
\( \frac{237276}{625} \)
\( \bigl[a + 1\) , \( a - 1\) , \( 0\) , \( 13 a + 25\) , \( -52 a - 91\bigr] \)
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(13a+25\right){x}-52a-91$
200.1-b1
200.1-b
$4$
$4$
\(\Q(\sqrt{3}) \)
$2$
$[2, 0]$
200.1
\( 2^{3} \cdot 5^{2} \)
\( 2^{8} \cdot 5^{8} \)
$1.16409$
$(a+1), (5)$
$1$
$\Z/4\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2$
2B
$1$
\( 2^{3} \)
$0.683761292$
$8.151961419$
1.609073952
\( \frac{237276}{625} \)
\( \bigl[a + 1\) , \( a - 1\) , \( a + 1\) , \( 12 a + 23\) , \( 75 a + 129\bigr] \)
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(12a+23\right){x}+75a+129$
3600.1-c1
3600.1-c
$4$
$4$
\(\Q(\sqrt{3}) \)
$2$
$[2, 0]$
3600.1
\( 2^{4} \cdot 3^{2} \cdot 5^{2} \)
\( 2^{8} \cdot 3^{6} \cdot 5^{8} \)
$2.39775$
$(a+1), (a), (5)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$1$
\( 2^{3} \)
$1$
$3.460509320$
1.997925987
\( \frac{237276}{625} \)
\( \bigl[a + 1\) , \( a - 1\) , \( a + 1\) , \( -a + 10\) , \( -8 a - 1\bigr] \)
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-a+10\right){x}-8a-1$
3600.1-k1
3600.1-k
$4$
$4$
\(\Q(\sqrt{3}) \)
$2$
$[2, 0]$
3600.1
\( 2^{4} \cdot 3^{2} \cdot 5^{2} \)
\( 2^{8} \cdot 3^{6} \cdot 5^{8} \)
$2.39775$
$(a+1), (a), (5)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$1$
\( 2^{3} \)
$1$
$3.460509320$
1.997925987
\( \frac{237276}{625} \)
\( \bigl[a + 1\) , \( a - 1\) , \( 0\) , \( 12\) , \( 18 a\bigr] \)
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a-1\right){x}^{2}+12{x}+18a$
5000.1-e1
5000.1-e
$4$
$4$
\(\Q(\sqrt{3}) \)
$2$
$[2, 0]$
5000.1
\( 2^{3} \cdot 5^{4} \)
\( 2^{8} \cdot 5^{20} \)
$2.60299$
$(a+1), (5)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2$
2B
$4$
\( 2^{3} \)
$1$
$0.881392156$
2.035487995
\( \frac{237276}{625} \)
\( \bigl[a + 1\) , \( a - 1\) , \( a + 1\) , \( -326 a + 569\) , \( 8253 a - 14301\bigr] \)
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-326a+569\right){x}+8253a-14301$
5000.1-f1
5000.1-f
$4$
$4$
\(\Q(\sqrt{3}) \)
$2$
$[2, 0]$
5000.1
\( 2^{3} \cdot 5^{4} \)
\( 2^{8} \cdot 5^{20} \)
$2.60299$
$(a+1), (5)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2$
2B
$1$
\( 2^{4} \)
$0.933393502$
$1.630392283$
3.514440935
\( \frac{237276}{625} \)
\( \bigl[a + 1\) , \( a - 1\) , \( 0\) , \( -325 a + 571\) , \( -7684 a + 13325\bigr] \)
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-325a+571\right){x}-7684a+13325$
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Pari/GP
SageMath
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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.