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
800.2-d1
800.2-d
$1$
$1$
\(\Q(\sqrt{6}) \)
$2$
$[2, 0]$
800.2
\( 2^{5} \cdot 5^{2} \)
\( 2^{12} \cdot 5^{2} \)
$2.32818$
$(-a+2), (-a-1)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$1$
\( 2 \)
$0.224232359$
$26.09133820$
4.776931474
\( -3072 a - 8192 \)
\( \bigl[0\) , \( 1\) , \( 0\) , \( -2 a - 5\) , \( 2 a + 5\bigr] \)
${y}^2={x}^{3}+{x}^{2}+\left(-2a-5\right){x}+2a+5$
800.2-e1
800.2-e
$1$
$1$
\(\Q(\sqrt{6}) \)
$2$
$[2, 0]$
800.2
\( 2^{5} \cdot 5^{2} \)
\( 2^{12} \cdot 5^{2} \)
$2.32818$
$(-a+2), (-a-1)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$1$
\( 2 \)
$1$
$3.711984618$
1.515411374
\( -3072 a - 8192 \)
\( \bigl[0\) , \( -1\) , \( 0\) , \( -2 a - 5\) , \( -2 a - 5\bigr] \)
${y}^2={x}^{3}-{x}^{2}+\left(-2a-5\right){x}-2a-5$
800.2-j1
800.2-j
$1$
$1$
\(\Q(\sqrt{6}) \)
$2$
$[2, 0]$
800.2
\( 2^{5} \cdot 5^{2} \)
\( 2^{12} \cdot 5^{2} \)
$2.32818$
$(-a+2), (-a-1)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$1$
\( 2 \)
$1$
$3.711984618$
1.515411374
\( -3072 a - 8192 \)
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 8 a - 19\) , \( 51 a - 125\bigr] \)
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(8a-19\right){x}+51a-125$
800.2-k1
800.2-k
$1$
$1$
\(\Q(\sqrt{6}) \)
$2$
$[2, 0]$
800.2
\( 2^{5} \cdot 5^{2} \)
\( 2^{12} \cdot 5^{2} \)
$2.32818$
$(-a+2), (-a-1)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$1$
\( 2 \)
$0.113317999$
$26.09133820$
2.414068691
\( -3072 a - 8192 \)
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( 8 a - 19\) , \( -51 a + 125\bigr] \)
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(8a-19\right){x}-51a+125$
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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.