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
10.1-a1 10.1-a $3$
$9$
\(\Q(\sqrt{6}) \) $2$
$[2, 0]$
10.1
\( 2 \cdot 5 \)
\( 2 \cdot 5 \)
$0.77847$
$(-a+2), (-a+1)$
0
$\Z/3\Z$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
$3$
3B.1.1 $1$
\( 1 \)
$1$
$35.64539671$
0.808454015
\( \frac{2849985813237}{10} a - \frac{3491001283144}{5} \)
\( \bigl[1\) , \( 0\) , \( 1\) , \( -166 a - 413\) , \( 1827 a + 4480\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+\left(-166a-413\right){x}+1827a+4480$
10.1-a2 10.1-a $3$
$9$
\(\Q(\sqrt{6}) \) $2$
$[2, 0]$
10.1
\( 2 \cdot 5 \)
\( 2^{3} \cdot 5^{3} \)
$0.77847$
$(-a+2), (-a+1)$
0
$\Z/3\Z$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
$3$
3Cs.1.1 $1$
\( 1 \)
$1$
$35.64539671$
0.808454015
\( \frac{1061271}{500} a - \frac{656416}{125} \)
\( \bigl[1\) , \( 0\) , \( 1\) , \( -a - 3\) , \( 5 a + 12\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+\left(-a-3\right){x}+5a+12$
10.1-a3 10.1-a $3$
$9$
\(\Q(\sqrt{6}) \) $2$
$[2, 0]$
10.1
\( 2 \cdot 5 \)
\( 2^{9} \cdot 5^{9} \)
$0.77847$
$(-a+2), (-a+1)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
$3$
3B.1.2 $1$
\( 1 \)
$1$
$3.960599634$
0.808454015
\( -\frac{21355471243}{62500000} a + \frac{1734442691}{1953125} \)
\( \bigl[1\) , \( 0\) , \( 1\) , \( 9 a + 22\) , \( -133 a - 326\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+\left(9a+22\right){x}-133a-326$
10.1-b1 10.1-b $3$
$9$
\(\Q(\sqrt{6}) \) $2$
$[2, 0]$
10.1
\( 2 \cdot 5 \)
\( 2 \cdot 5 \)
$0.77847$
$(-a+2), (-a+1)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
$3$
3B.1.2 $9$
\( 1 \)
$1$
$0.683258437$
1.255225901
\( \frac{2849985813237}{10} a - \frac{3491001283144}{5} \)
\( \bigl[a + 1\) , \( 0\) , \( 0\) , \( 117 a - 292\) , \( 1111 a - 2738\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(117a-292\right){x}+1111a-2738$
10.1-b2 10.1-b $3$
$9$
\(\Q(\sqrt{6}) \) $2$
$[2, 0]$
10.1
\( 2 \cdot 5 \)
\( 2^{3} \cdot 5^{3} \)
$0.77847$
$(-a+2), (-a+1)$
0
$\Z/3\Z$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
$3$
3Cs.1.1 $1$
\( 3^{2} \)
$1$
$6.149325941$
1.255225901
\( \frac{1061271}{500} a - \frac{656416}{125} \)
\( \bigl[a + 1\) , \( 0\) , \( 0\) , \( 2 a - 2\) , \( 2 a - 4\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(2a-2\right){x}+2a-4$
10.1-b3 10.1-b $3$
$9$
\(\Q(\sqrt{6}) \) $2$
$[2, 0]$
10.1
\( 2 \cdot 5 \)
\( 2^{9} \cdot 5^{9} \)
$0.77847$
$(-a+2), (-a+1)$
0
$\Z/9\Z$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
$3$
3B.1.1 $1$
\( 3^{4} \)
$1$
$6.149325941$
1.255225901
\( -\frac{21355471243}{62500000} a + \frac{1734442691}{1953125} \)
\( \bigl[a + 1\) , \( 0\) , \( 0\) , \( -8 a + 23\) , \( -2 a + 7\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-8a+23\right){x}-2a+7$
Download
displayed columns for
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.
