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
8281.5-a3 8281.5-a $5$
$9$
\(\Q(\sqrt{-3}) \) $2$
$[0, 1]$
8281.5
\( 7^{2} \cdot 13^{2} \)
\( 7^{6} \cdot 13^{6} \)
$1.47645$
$(-3a+1), (3a-2), (-4a+1), (4a-3)$
$1$
$\Z/3\Z\oplus\Z/3\Z$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
✓
✓
$3$
3Cs.1.1[2] $1$
\( 3^{4} \)
$0.353081695$
$1.459953528$
1.190456688
\( \frac{224755712}{753571} \)
\( \bigl[0\) , \( -a\) , \( 1\) , \( 13 a - 13\) , \( 42\bigr] \) ${y}^2+{y}={x}^{3}-a{x}^{2}+\left(13a-13\right){x}+42$
107653.6-b3 107653.6-b $5$
$9$
\(\Q(\sqrt{-3}) \) $2$
$[0, 1]$
107653.6
\( 7^{2} \cdot 13^{3} \)
\( 7^{6} \cdot 13^{12} \)
$2.80353$
$(-3a+1), (3a-2), (-4a+1), (4a-3)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
$3$
3Cs[2] $1$
\( 2^{2} \cdot 3 \)
$1$
$0.404918254$
5.610711915
\( \frac{224755712}{753571} \)
\( \bigl[0\) , \( a\) , \( 1\) , \( 89 a + 101\) , \( 1431 a + 616\bigr] \) ${y}^2+{y}={x}^{3}+a{x}^{2}+\left(89a+101\right){x}+1431a+616$
107653.7-b3 107653.7-b $5$
$9$
\(\Q(\sqrt{-3}) \) $2$
$[0, 1]$
107653.7
\( 7^{2} \cdot 13^{3} \)
\( 7^{6} \cdot 13^{12} \)
$2.80353$
$(-3a+1), (3a-2), (-4a+1), (4a-3)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
$3$
3Cs[2] $1$
\( 2^{2} \cdot 3 \)
$1$
$0.404918254$
5.610711915
\( \frac{224755712}{753571} \)
\( \bigl[0\) , \( -a + 1\) , \( 1\) , \( -89 a + 190\) , \( -1431 a + 2047\bigr] \) ${y}^2+{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-89a+190\right){x}-1431a+2047$
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.
