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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
75.1-a8 75.1-a \(\Q(\sqrt{57}) \) \( 3 \cdot 5^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $10.19195692$ 2.699915346 \( \frac{1114544804970241}{405} \) \( \bigl[1\) , \( a + 1\) , \( a\) , \( -26093051 a - 85452579\) , \( 140914623017 a + 461483725132\bigr] \) ${y}^2+{x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-26093051a-85452579\right){x}+140914623017a+461483725132$
75.1-b8 75.1-b \(\Q(\sqrt{57}) \) \( 3 \cdot 5^{2} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $16.44430019$ $0.490422220$ 1.068189016 \( \frac{1114544804970241}{405} \) \( \bigl[1\) , \( 1\) , \( 1\) , \( -2160\) , \( -39540\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-2160{x}-39540$
225.1-a8 225.1-a \(\Q(\sqrt{57}) \) \( 3^{2} \cdot 5^{2} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $16.11082983$ $1.290782985$ 2.754442525 \( \frac{1114544804970241}{405} \) \( \bigl[1\) , \( -a + 1\) , \( 0\) , \( -259203 a - 848883\) , \( -139305645 a - 456214446\bigr] \) ${y}^2+{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-259203a-848883\right){x}-139305645a-456214446$
225.1-b8 225.1-b \(\Q(\sqrt{57}) \) \( 3^{2} \cdot 5^{2} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $16.11082983$ $1.290782985$ 2.754442525 \( \frac{1114544804970241}{405} \) \( \bigl[1\) , \( a\) , \( 0\) , \( 259203 a - 1108086\) , \( 139305645 a - 595520091\bigr] \) ${y}^2+{x}{y}={x}^{3}+a{x}^{2}+\left(259203a-1108086\right){x}+139305645a-595520091$
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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.