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
400.1-d1
400.1-d
$2$
$2$
\(\Q(\sqrt{3}) \)
$2$
$[2, 0]$
400.1
\( 2^{4} \cdot 5^{2} \)
\( 2^{8} \cdot 5^{2} \)
$1.38434$
$(a+1), (5)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$1$
\( 2 \)
$0.522239772$
$13.50105338$
2.035386900
\( -\frac{108}{5} \)
\( \bigl[a + 1\) , \( a - 1\) , \( a + 1\) , \( -a\) , \( -1\bigr] \)
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}-a{x}-1$
400.1-g1
400.1-g
$2$
$2$
\(\Q(\sqrt{3}) \)
$2$
$[2, 0]$
400.1
\( 2^{4} \cdot 5^{2} \)
\( 2^{8} \cdot 5^{2} \)
$1.38434$
$(a+1), (5)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$1$
\( 2 \)
$0.522239772$
$13.50105338$
2.035386900
\( -\frac{108}{5} \)
\( \bigl[a + 1\) , \( a - 1\) , \( 0\) , \( 2\) , \( 0\bigr] \)
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a-1\right){x}^{2}+2{x}$
1800.1-b1
1800.1-b
$2$
$2$
\(\Q(\sqrt{3}) \)
$2$
$[2, 0]$
1800.1
\( 2^{3} \cdot 3^{2} \cdot 5^{2} \)
\( 2^{8} \cdot 3^{6} \cdot 5^{2} \)
$2.01626$
$(a+1), (a), (5)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2$
2B
$1$
\( 2^{3} \)
$1$
$4.113657423$
2.375021220
\( -\frac{108}{5} \)
\( \bigl[a + 1\) , \( a - 1\) , \( 0\) , \( -3 a - 3\) , \( -36 a - 63\bigr] \)
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-3a-3\right){x}-36a-63$
1800.1-i1
1800.1-i
$2$
$2$
\(\Q(\sqrt{3}) \)
$2$
$[2, 0]$
1800.1
\( 2^{3} \cdot 3^{2} \cdot 5^{2} \)
\( 2^{8} \cdot 3^{6} \cdot 5^{2} \)
$2.01626$
$(a+1), (a), (5)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2$
2B
$1$
\( 2^{4} \)
$0.095459792$
$14.77018492$
3.256160336
\( -\frac{108}{5} \)
\( \bigl[a + 1\) , \( a - 1\) , \( a + 1\) , \( -4 a - 5\) , \( 31 a + 53\bigr] \)
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-4a-5\right){x}+31a+53$
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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.