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Results (5 matches)

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Label Class Base field Conductor norm Rank Torsion CM Sato-Tate Regulator Period Leading coeff j-invariant Weierstrass coefficients Weierstrass equation
722.1-a1 722.1-a \(\Q(\sqrt{2}) \) \( 2 \cdot 19^{2} \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $0.671163407$ 2.372920982 \( -\frac{37966934881}{4952198} \) \( \bigl[1\) , \( 1\) , \( 1\) , \( -70\) , \( -279\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-70{x}-279$
722.1-a2 722.1-a \(\Q(\sqrt{2}) \) \( 2 \cdot 19^{2} \) 0 $\Z/5\Z$ $\mathrm{SU}(2)$ $1$ $16.77908518$ 2.372920982 \( -\frac{1}{608} \) \( \bigl[1\) , \( 1\) , \( 1\) , \( 0\) , \( 1\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}+1$
722.1-b1 722.1-b \(\Q(\sqrt{2}) \) \( 2 \cdot 19^{2} \) $1$ $\Z/3\Z$ $\mathrm{SU}(2)$ $0.278258698$ $32.17041206$ 1.406623475 \( -\frac{413493625}{152} \) \( \bigl[1\) , \( 0\) , \( 1\) , \( -16\) , \( 22\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}-16{x}+22$
722.1-b2 722.1-b \(\Q(\sqrt{2}) \) \( 2 \cdot 19^{2} \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $2.504328284$ $0.397165580$ 1.406623475 \( -\frac{69173457625}{2550136832} \) \( \bigl[1\) , \( 0\) , \( 1\) , \( -86\) , \( -2456\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}-86{x}-2456$
722.1-b3 722.1-b \(\Q(\sqrt{2}) \) \( 2 \cdot 19^{2} \) $1$ $\Z/3\Z$ $\mathrm{SU}(2)$ $0.834776094$ $3.574490228$ 1.406623475 \( \frac{94196375}{3511808} \) \( \bigl[1\) , \( 0\) , \( 1\) , \( 9\) , \( 90\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+9{x}+90$
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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.