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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
400.1-a1 400.1-a \(\Q(\sqrt{-3}) \) \( 2^{4} \cdot 5^{2} \) 0 $\Z/6\Z$ $\mathrm{SU}(2)$ $1$ $1.070515942$ 0.618062667 \( -\frac{20720464}{15625} \) \( \bigl[0\) , \( -a\) , \( 0\) , \( -36 a + 36\) , \( -140\bigr] \) ${y}^2={x}^{3}-a{x}^{2}+\left(-36a+36\right){x}-140$
400.1-a2 400.1-a \(\Q(\sqrt{-3}) \) \( 2^{4} \cdot 5^{2} \) 0 $\Z/6\Z$ $\mathrm{SU}(2)$ $1$ $3.211547828$ 0.618062667 \( \frac{21296}{25} \) \( \bigl[0\) , \( a - 1\) , \( 0\) , \( -4 a\) , \( 4\bigr] \) ${y}^2={x}^{3}+\left(a-1\right){x}^{2}-4a{x}+4$
400.1-a3 400.1-a \(\Q(\sqrt{-3}) \) \( 2^{4} \cdot 5^{2} \) 0 $\Z/6\Z$ $\mathrm{SU}(2)$ $1$ $6.423095656$ 0.618062667 \( \frac{16384}{5} \) \( \bigl[0\) , \( a - 1\) , \( 0\) , \( a\) , \( 0\bigr] \) ${y}^2={x}^{3}+\left(a-1\right){x}^{2}+a{x}$
400.1-a4 400.1-a \(\Q(\sqrt{-3}) \) \( 2^{4} \cdot 5^{2} \) 0 $\Z/6\Z$ $\mathrm{SU}(2)$ $1$ $2.141031885$ 0.618062667 \( \frac{488095744}{125} \) \( \bigl[0\) , \( -a\) , \( 0\) , \( -41 a + 41\) , \( -116\bigr] \) ${y}^2={x}^{3}-a{x}^{2}+\left(-41a+41\right){x}-116$
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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.