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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
40.1-a1 40.1-a \(\Q(\sqrt{10}) \) \( 2^{3} \cdot 5 \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.722205338$ $4.406960782$ 2.012935576 \( \frac{237276}{625} \) \( \bigl[a\) , \( -1\) , \( a\) , \( -1\) , \( -5\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}-{x}^{2}-{x}-5$
40.1-a2 40.1-a \(\Q(\sqrt{10}) \) \( 2^{3} \cdot 5 \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1.444410676$ $17.62784313$ 2.012935576 \( \frac{148176}{25} \) \( \bigl[a\) , \( -1\) , \( a\) , \( -6\) , \( -4\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}-{x}^{2}-6{x}-4$
40.1-a3 40.1-a \(\Q(\sqrt{10}) \) \( 2^{3} \cdot 5 \) $1$ $\Z/4\Z$ $\mathrm{SU}(2)$ $0.722205338$ $35.25568626$ 2.012935576 \( \frac{55296}{5} \) \( \bigl[0\) , \( 0\) , \( 0\) , \( -8\) , \( 8\bigr] \) ${y}^2={x}^{3}-8{x}+8$
40.1-a4 40.1-a \(\Q(\sqrt{10}) \) \( 2^{3} \cdot 5 \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.722205338$ $4.406960782$ 2.012935576 \( \frac{132304644}{5} \) \( \bigl[a\) , \( -1\) , \( a\) , \( -31\) , \( -69\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}-{x}^{2}-31{x}-69$
40.1-b1 40.1-b \(\Q(\sqrt{10}) \) \( 2^{3} \cdot 5 \) $1$ $\Z/4\Z$ $\mathrm{SU}(2)$ $1.548473301$ $4.406960782$ 2.157957601 \( \frac{237276}{625} \) \( \bigl[0\) , \( 0\) , \( 0\) , \( 13\) , \( -34\bigr] \) ${y}^2={x}^{3}+13{x}-34$
40.1-b2 40.1-b \(\Q(\sqrt{10}) \) \( 2^{3} \cdot 5 \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $0.774236650$ $17.62784313$ 2.157957601 \( \frac{148176}{25} \) \( \bigl[0\) , \( 0\) , \( 0\) , \( -7\) , \( -6\bigr] \) ${y}^2={x}^{3}-7{x}-6$
40.1-b3 40.1-b \(\Q(\sqrt{10}) \) \( 2^{3} \cdot 5 \) $1$ $\Z/4\Z$ $\mathrm{SU}(2)$ $0.387118325$ $35.25568626$ 2.157957601 \( \frac{55296}{5} \) \( \bigl[0\) , \( 0\) , \( 0\) , \( -2\) , \( 1\bigr] \) ${y}^2={x}^{3}-2{x}+1$
40.1-b4 40.1-b \(\Q(\sqrt{10}) \) \( 2^{3} \cdot 5 \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $1.548473301$ $4.406960782$ 2.157957601 \( \frac{132304644}{5} \) \( \bigl[0\) , \( 0\) , \( 0\) , \( -107\) , \( -426\bigr] \) ${y}^2={x}^{3}-107{x}-426$
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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.