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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
57.1-d4 57.1-d \(\Q(\sqrt{57}) \) \( 3 \cdot 19 \) 0 $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $9.048617011$ 0.299629650 \( \frac{30664297}{3249} \) \( \bigl[1\) , \( -a\) , \( a\) , \( -78772 a - 257966\) , \( -21027235 a - 68862455\bigr] \) ${y}^2+{x}{y}+a{y}={x}^{3}-a{x}^{2}+\left(-78772a-257966\right){x}-21027235a-68862455$
57.1-g4 57.1-g \(\Q(\sqrt{57}) \) \( 3 \cdot 19 \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1.946386961$ $18.84609635$ 4.858622600 \( \frac{30664297}{3249} \) \( \bigl[1\) , \( 0\) , \( 1\) , \( -7\) , \( 5\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}-7{x}+5$
171.1-e4 171.1-e \(\Q(\sqrt{57}) \) \( 3^{2} \cdot 19 \) 0 $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $7.539476287$ 0.998628029 \( \frac{30664297}{3249} \) \( \bigl[1\) , \( a\) , \( 0\) , \( -782 a - 2558\) , \( 19744 a + 64659\bigr] \) ${y}^2+{x}{y}={x}^{3}+a{x}^{2}+\left(-782a-2558\right){x}+19744a+64659$
171.1-h4 171.1-h \(\Q(\sqrt{57}) \) \( 3^{2} \cdot 19 \) 0 $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $7.539476287$ 0.998628029 \( \frac{30664297}{3249} \) \( \bigl[1\) , \( -a + 1\) , \( 0\) , \( 782 a - 3340\) , \( -19744 a + 84403\bigr] \) ${y}^2+{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(782a-3340\right){x}-19744a+84403$
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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.