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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-a1 75.1-a \(\Q(\sqrt{57}) \) \( 3 \cdot 5^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $2.547989231$ 2.699915346 \( -\frac{147281603041}{215233605} \) \( \bigl[1\) , \( a + 1\) , \( a\) , \( -1329051 a - 4352529\) , \( 3040012667 a + 9955789822\bigr] \) ${y}^2+{x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-1329051a-4352529\right){x}+3040012667a+9955789822$
75.1-b1 75.1-b \(\Q(\sqrt{57}) \) \( 3 \cdot 5^{2} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $16.44430019$ $0.490422220$ 1.068189016 \( -\frac{147281603041}{215233605} \) \( \bigl[1\) , \( 1\) , \( 1\) , \( -110\) , \( -880\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-110{x}-880$
225.1-a1 225.1-a \(\Q(\sqrt{57}) \) \( 3^{2} \cdot 5^{2} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $16.11082983$ $0.645391492$ 2.754442525 \( -\frac{147281603041}{215233605} \) \( \bigl[1\) , \( -a + 1\) , \( 0\) , \( -13203 a - 43233\) , \( -2999025 a - 9821556\bigr] \) ${y}^2+{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-13203a-43233\right){x}-2999025a-9821556$
225.1-b1 225.1-b \(\Q(\sqrt{57}) \) \( 3^{2} \cdot 5^{2} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $16.11082983$ $0.645391492$ 2.754442525 \( -\frac{147281603041}{215233605} \) \( \bigl[1\) , \( a\) , \( 0\) , \( 13203 a - 56436\) , \( 2999025 a - 12820581\bigr] \) ${y}^2+{x}{y}={x}^{3}+a{x}^{2}+\left(13203a-56436\right){x}+2999025a-12820581$
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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.