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Results (8 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
450.1-a1 450.1-a \(\Q(\sqrt{2}) \) \( 2 \cdot 3^{2} \cdot 5^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $1.248395236$ 0.662061553 \( -\frac{273359449}{1536000} \) \( \bigl[1\) , \( 0\) , \( 1\) , \( -14\) , \( -64\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}-14{x}-64$
450.1-a2 450.1-a \(\Q(\sqrt{2}) \) \( 2 \cdot 3^{2} \cdot 5^{2} \) 0 $\Z/6\Z$ $\mathrm{SU}(2)$ $1$ $11.23555713$ 0.662061553 \( \frac{357911}{2160} \) \( \bigl[1\) , \( 0\) , \( 1\) , \( 1\) , \( 2\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+{x}+2$
450.1-a3 450.1-a \(\Q(\sqrt{2}) \) \( 2 \cdot 3^{2} \cdot 5^{2} \) 0 $\Z/4\Z$ $\mathrm{SU}(2)$ $1$ $1.248395236$ 0.662061553 \( \frac{10316097499609}{5859375000} \) \( \bigl[1\) , \( 0\) , \( 1\) , \( -454\) , \( -544\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}-454{x}-544$
450.1-a4 450.1-a \(\Q(\sqrt{2}) \) \( 2 \cdot 3^{2} \cdot 5^{2} \) 0 $\Z/6\Z$ $\mathrm{SU}(2)$ $1$ $2.808889283$ 0.662061553 \( \frac{35578826569}{5314410} \) \( \bigl[1\) , \( 0\) , \( 1\) , \( -69\) , \( -194\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}-69{x}-194$
450.1-a5 450.1-a \(\Q(\sqrt{2}) \) \( 2 \cdot 3^{2} \cdot 5^{2} \) 0 $\Z/2\Z\oplus\Z/6\Z$ $\mathrm{SU}(2)$ $1$ $11.23555713$ 0.662061553 \( \frac{702595369}{72900} \) \( \bigl[1\) , \( 0\) , \( 1\) , \( -19\) , \( 26\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}-19{x}+26$
450.1-a6 450.1-a \(\Q(\sqrt{2}) \) \( 2 \cdot 3^{2} \cdot 5^{2} \) 0 $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $1.248395236$ 0.662061553 \( \frac{4102915888729}{9000000} \) \( \bigl[1\) , \( 0\) , \( 1\) , \( -334\) , \( -2368\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}-334{x}-2368$
450.1-a7 450.1-a \(\Q(\sqrt{2}) \) \( 2 \cdot 3^{2} \cdot 5^{2} \) 0 $\Z/12\Z$ $\mathrm{SU}(2)$ $1$ $11.23555713$ 0.662061553 \( \frac{2656166199049}{33750} \) \( \bigl[1\) , \( 0\) , \( 1\) , \( -289\) , \( 1862\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}-289{x}+1862$
450.1-a8 450.1-a \(\Q(\sqrt{2}) \) \( 2 \cdot 3^{2} \cdot 5^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.312098809$ 0.662061553 \( \frac{16778985534208729}{81000} \) \( \bigl[1\) , \( 0\) , \( 1\) , \( -5334\) , \( -150368\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}-5334{x}-150368$
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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.