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
35721.6-a1 35721.6-a $1$
$1$
\(\Q(\sqrt{-2}) \) $2$
$[0, 1]$
35721.6
\( 3^{6} \cdot 7^{2} \)
\( 3^{9} \cdot 7^{2} \)
$3.47468$
$(-a-1), (a-1), (7)$
$2$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$ $1$
\( 2 \cdot 3 \)
$0.054084452$
$4.328738181$
3.973104645
\( -\frac{34537}{63} a - \frac{27749}{63} \)
\( \bigl[1\) , \( -a\) , \( a\) , \( -2 a\) , \( -a + 1\bigr] \) ${y}^2+{x}{y}+a{y}={x}^{3}-a{x}^{2}-2a{x}-a+1$
35721.6-b1 35721.6-b $1$
$1$
\(\Q(\sqrt{-2}) \) $2$
$[0, 1]$
35721.6
\( 3^{6} \cdot 7^{2} \)
\( 3^{19} \cdot 7^{2} \)
$3.47468$
$(-a-1), (a-1), (7)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$ $1$
\( 2 \cdot 7 \)
$0.104370196$
$1.637368604$
3.383498536
\( -\frac{123874730641}{33480783} a - \frac{13069164335}{33480783} \)
\( \bigl[1\) , \( a + 1\) , \( 1\) , \( 16 a + 6\) , \( 14 a + 34\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(16a+6\right){x}+14a+34$
35721.6-c1 35721.6-c $1$
$1$
\(\Q(\sqrt{-2}) \) $2$
$[0, 1]$
35721.6
\( 3^{6} \cdot 7^{2} \)
\( 3^{12} \cdot 7^{2} \)
$3.47468$
$(-a-1), (a-1), (7)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$ $1$
\( 1 \)
$1.484389492$
$3.006564919$
6.311512621
\( \frac{6794}{3} a + \frac{211249}{21} \)
\( \bigl[1\) , \( a + 1\) , \( a\) , \( -8\) , \( -2 a + 5\bigr] \) ${y}^2+{x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}-8{x}-2a+5$
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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.
