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-a2
200.1-a
$4$
$4$
\(\Q(\sqrt{3}) \)
$2$
$[2, 0]$
200.1
\( 2^{3} \cdot 5^{2} \)
\( 2^{4} \cdot 5^{4} \)
$1.16409$
$(a+1), (5)$
0
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2$
2Cs
$1$
\( 2^{2} \)
$1$
$17.62784313$
1.272179997
\( \frac{148176}{25} \)
\( \bigl[a + 1\) , \( a - 1\) , \( 0\) , \( -7 a - 10\) , \( -17 a - 30\bigr] \)
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-7a-10\right){x}-17a-30$
200.1-b2
200.1-b
$4$
$4$
\(\Q(\sqrt{3}) \)
$2$
$[2, 0]$
200.1
\( 2^{3} \cdot 5^{2} \)
\( 2^{4} \cdot 5^{4} \)
$1.16409$
$(a+1), (5)$
$1$
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2$
2Cs
$1$
\( 2^{2} \)
$0.341880646$
$32.60784567$
1.609073952
\( \frac{148176}{25} \)
\( \bigl[a + 1\) , \( a - 1\) , \( a + 1\) , \( -8 a - 12\) , \( 5 a + 8\bigr] \)
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-8a-12\right){x}+5a+8$
3600.1-c2
3600.1-c
$4$
$4$
\(\Q(\sqrt{3}) \)
$2$
$[2, 0]$
3600.1
\( 2^{4} \cdot 3^{2} \cdot 5^{2} \)
\( 2^{4} \cdot 3^{6} \cdot 5^{4} \)
$2.39775$
$(a+1), (a), (5)$
0
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2Cs
$1$
\( 2^{3} \)
$1$
$13.84203728$
1.997925987
\( \frac{148176}{25} \)
\( \bigl[a + 1\) , \( a - 1\) , \( a + 1\) , \( -a - 5\) , \( -5 a - 1\bigr] \)
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-a-5\right){x}-5a-1$
3600.1-k2
3600.1-k
$4$
$4$
\(\Q(\sqrt{3}) \)
$2$
$[2, 0]$
3600.1
\( 2^{4} \cdot 3^{2} \cdot 5^{2} \)
\( 2^{4} \cdot 3^{6} \cdot 5^{4} \)
$2.39775$
$(a+1), (a), (5)$
0
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2Cs
$1$
\( 2^{3} \)
$1$
$13.84203728$
1.997925987
\( \frac{148176}{25} \)
\( \bigl[a + 1\) , \( a - 1\) , \( 0\) , \( -3\) , \( 0\bigr] \)
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a-1\right){x}^{2}-3{x}$
5000.1-e2
5000.1-e
$4$
$4$
\(\Q(\sqrt{3}) \)
$2$
$[2, 0]$
5000.1
\( 2^{3} \cdot 5^{4} \)
\( 2^{4} \cdot 5^{16} \)
$2.60299$
$(a+1), (5)$
0
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2$
2Cs
$4$
\( 2^{3} \)
$1$
$3.525568626$
2.035487995
\( \frac{148176}{25} \)
\( \bigl[a + 1\) , \( a - 1\) , \( a + 1\) , \( 174 a - 306\) , \( 1253 a - 2176\bigr] \)
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(174a-306\right){x}+1253a-2176$
5000.1-f2
5000.1-f
$4$
$4$
\(\Q(\sqrt{3}) \)
$2$
$[2, 0]$
5000.1
\( 2^{3} \cdot 5^{4} \)
\( 2^{4} \cdot 5^{16} \)
$2.60299$
$(a+1), (5)$
$1$
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2$
2Cs
$1$
\( 2^{3} \)
$1.866787005$
$6.521569135$
3.514440935
\( \frac{148176}{25} \)
\( \bigl[a + 1\) , \( a - 1\) , \( 0\) , \( 175 a - 304\) , \( -1559 a + 2700\bigr] \)
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(175a-304\right){x}-1559a+2700$
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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.