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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
36.1-a1 36.1-a \(\Q(\sqrt{5}) \) \( 2^{2} \cdot 3^{2} \) 0 $\Z/10\Z$ $\mathrm{SU}(2)$ $1$ $44.29962169$ 0.396227861 \( -\frac{24389}{12} \) \( \bigl[\phi + 1\) , \( \phi\) , \( \phi\) , \( 0\) , \( 0\bigr] \) ${y}^2+\left(\phi+1\right){x}{y}+\phi{y}={x}^{3}+\phi{x}^{2}$
36.1-a2 36.1-a \(\Q(\sqrt{5}) \) \( 2^{2} \cdot 3^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $1.771984867$ 0.396227861 \( -\frac{19465109}{248832} \) \( \bigl[\phi + 1\) , \( \phi\) , \( \phi\) , \( -5 \phi - 5\) , \( -51 \phi - 37\bigr] \) ${y}^2+\left(\phi+1\right){x}{y}+\phi{y}={x}^{3}+\phi{x}^{2}+\left(-5\phi-5\right){x}-51\phi-37$
36.1-a3 36.1-a \(\Q(\sqrt{5}) \) \( 2^{2} \cdot 3^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $1.771984867$ 0.396227861 \( \frac{502270291349}{1889568} \) \( \bigl[\phi\) , \( \phi - 1\) , \( \phi\) , \( 165 \phi - 331\) , \( 1352 \phi - 2408\bigr] \) ${y}^2+\phi{x}{y}+\phi{y}={x}^{3}+\left(\phi-1\right){x}^{2}+\left(165\phi-331\right){x}+1352\phi-2408$
36.1-a4 36.1-a \(\Q(\sqrt{5}) \) \( 2^{2} \cdot 3^{2} \) 0 $\Z/10\Z$ $\mathrm{SU}(2)$ $1$ $44.29962169$ 0.396227861 \( \frac{131872229}{18} \) \( \bigl[\phi\) , \( \phi - 1\) , \( \phi\) , \( 10 \phi - 21\) , \( -31 \phi + 51\bigr] \) ${y}^2+\phi{x}{y}+\phi{y}={x}^{3}+\left(\phi-1\right){x}^{2}+\left(10\phi-21\right){x}-31\phi+51$
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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.