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
126.1-a3 126.1-a $6$
$8$
\(\Q(\sqrt{14}) \) $2$
$[2, 0]$
126.1
\( 2 \cdot 3^{2} \cdot 7 \)
\( 2^{4} \cdot 3^{16} \cdot 7^{8} \)
$2.24040$
$(-a+4), (-2a+7), (3)$
$1$
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
✓
✓
$2$
2Cs $1$
\( 2^{8} \)
$0.570759829$
$2.486887276$
6.069675380
\( \frac{124475734657}{63011844} \)
\( \bigl[1\) , \( a - 1\) , \( 1\) , \( -12483 a - 46701\) , \( -532140 a - 1991089\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-12483a-46701\right){x}-532140a-1991089$
126.1-b3 126.1-b $6$
$8$
\(\Q(\sqrt{14}) \) $2$
$[2, 0]$
126.1
\( 2 \cdot 3^{2} \cdot 7 \)
\( 2^{4} \cdot 3^{16} \cdot 7^{8} \)
$2.24040$
$(-a+4), (-2a+7), (3)$
0
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
✓
✓
$2$
2Cs $1$
\( 2^{6} \)
$1$
$3.019683757$
1.614088862
\( \frac{124475734657}{63011844} \)
\( \bigl[1\) , \( 1\) , \( 1\) , \( -104\) , \( 101\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-104{x}+101$
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.
