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Results (4 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
162.1-b1 162.1-b \(\Q(\sqrt{15}) \) \( 2 \cdot 3^{4} \) 0 $\Z/3\Z$ $\mathrm{SU}(2)$ $1$ $39.86878607$ 1.143786255 \( -\frac{132651}{2} \) \( \bigl[1\) , \( -1\) , \( 0\) , \( -3\) , \( 3\bigr] \) ${y}^2+{x}{y}={x}^{3}-{x}^{2}-3{x}+3$
162.1-c1 162.1-c \(\Q(\sqrt{15}) \) \( 2 \cdot 3^{4} \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $3.185925848$ 2.467807550 \( -\frac{132651}{2} \) \( \bigl[a\) , \( 0\) , \( a\) , \( -6\) , \( -8\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}-6{x}-8$
162.1-e1 162.1-e \(\Q(\sqrt{15}) \) \( 2 \cdot 3^{4} \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $0.077107140$ $39.86878607$ 4.762480698 \( -\frac{132651}{2} \) \( \bigl[a + 1\) , \( a - 1\) , \( 0\) , \( -99 a - 381\) , \( 822 a + 3183\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-99a-381\right){x}+822a+3183$
162.1-f1 162.1-f \(\Q(\sqrt{15}) \) \( 2 \cdot 3^{4} \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $2.936556370$ $3.185925848$ 4.831237322 \( -\frac{132651}{2} \) \( \bigl[a + 1\) , \( a - 1\) , \( a + 1\) , \( -100 a - 389\) , \( -1415 a - 5483\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-100a-389\right){x}-1415a-5483$
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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.