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
10.2-a1
10.2-a
$3$
$9$
\(\Q(\sqrt{6}) \)
$2$
$[2, 0]$
10.2
\( 2 \cdot 5 \)
\( 2 \cdot 5 \)
$0.77847$
$(-a+2), (-a-1)$
0
$\Z/3\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$3$
3B.1.1
$1$
\( 1 \)
$1$
$35.64539671$
0.808454015
\( -\frac{2849985813237}{10} a - \frac{3491001283144}{5} \)
\( \bigl[1\) , \( 0\) , \( 1\) , \( 166 a - 413\) , \( -1827 a + 4480\bigr] \)
${y}^2+{x}{y}+{y}={x}^{3}+\left(166a-413\right){x}-1827a+4480$
10.2-a2
10.2-a
$3$
$9$
\(\Q(\sqrt{6}) \)
$2$
$[2, 0]$
10.2
\( 2 \cdot 5 \)
\( 2^{3} \cdot 5^{3} \)
$0.77847$
$(-a+2), (-a-1)$
0
$\Z/3\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$3$
3Cs.1.1
$1$
\( 1 \)
$1$
$35.64539671$
0.808454015
\( -\frac{1061271}{500} a - \frac{656416}{125} \)
\( \bigl[1\) , \( 0\) , \( 1\) , \( a - 3\) , \( -5 a + 12\bigr] \)
${y}^2+{x}{y}+{y}={x}^{3}+\left(a-3\right){x}-5a+12$
10.2-a3
10.2-a
$3$
$9$
\(\Q(\sqrt{6}) \)
$2$
$[2, 0]$
10.2
\( 2 \cdot 5 \)
\( 2^{9} \cdot 5^{9} \)
$0.77847$
$(-a+2), (-a-1)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$3$
3B.1.2
$1$
\( 1 \)
$1$
$3.960599634$
0.808454015
\( \frac{21355471243}{62500000} a + \frac{1734442691}{1953125} \)
\( \bigl[1\) , \( 0\) , \( 1\) , \( -9 a + 22\) , \( 133 a - 326\bigr] \)
${y}^2+{x}{y}+{y}={x}^{3}+\left(-9a+22\right){x}+133a-326$
10.2-b1
10.2-b
$3$
$9$
\(\Q(\sqrt{6}) \)
$2$
$[2, 0]$
10.2
\( 2 \cdot 5 \)
\( 2 \cdot 5 \)
$0.77847$
$(-a+2), (-a-1)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$3$
3B.1.2
$9$
\( 1 \)
$1$
$0.683258437$
1.255225901
\( -\frac{2849985813237}{10} a - \frac{3491001283144}{5} \)
\( \bigl[a + 1\) , \( -a\) , \( 0\) , \( -117 a - 292\) , \( -1111 a - 2738\bigr] \)
${y}^2+\left(a+1\right){x}{y}={x}^{3}-a{x}^{2}+\left(-117a-292\right){x}-1111a-2738$
10.2-b2
10.2-b
$3$
$9$
\(\Q(\sqrt{6}) \)
$2$
$[2, 0]$
10.2
\( 2 \cdot 5 \)
\( 2^{3} \cdot 5^{3} \)
$0.77847$
$(-a+2), (-a-1)$
0
$\Z/3\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$3$
3Cs.1.1
$1$
\( 3^{2} \)
$1$
$6.149325941$
1.255225901
\( -\frac{1061271}{500} a - \frac{656416}{125} \)
\( \bigl[a + 1\) , \( -a\) , \( 0\) , \( -2 a - 2\) , \( -2 a - 4\bigr] \)
${y}^2+\left(a+1\right){x}{y}={x}^{3}-a{x}^{2}+\left(-2a-2\right){x}-2a-4$
10.2-b3
10.2-b
$3$
$9$
\(\Q(\sqrt{6}) \)
$2$
$[2, 0]$
10.2
\( 2 \cdot 5 \)
\( 2^{9} \cdot 5^{9} \)
$0.77847$
$(-a+2), (-a-1)$
0
$\Z/9\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$3$
3B.1.1
$1$
\( 3^{4} \)
$1$
$6.149325941$
1.255225901
\( \frac{21355471243}{62500000} a + \frac{1734442691}{1953125} \)
\( \bigl[a + 1\) , \( -a\) , \( 0\) , \( 8 a + 23\) , \( 2 a + 7\bigr] \)
${y}^2+\left(a+1\right){x}{y}={x}^{3}-a{x}^{2}+\left(8a+23\right){x}+2a+7$
Download
displayed columns for
results
to
Text
Pari/GP
SageMath
Magma
Oscar
CSV
*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.