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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
45.1-a10 45.1-a \(\Q(\sqrt{5}) \) \( 3^{2} \cdot 5 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.122605555$ 0.438646969 \( \frac{152409672113485069453847362}{45} a + \frac{94194357580360793912853799}{45} \) \( \bigl[\phi + 1\) , \( \phi - 1\) , \( \phi + 1\) , \( 4364 \phi - 12105\) , \( 243301 \phi - 535402\bigr] \) ${y}^2+\left(\phi+1\right){x}{y}+\left(\phi+1\right){y}={x}^{3}+\left(\phi-1\right){x}^{2}+\left(4364\phi-12105\right){x}+243301\phi-535402$
225.1-b10 225.1-b \(\Q(\sqrt{5}) \) \( 3^{2} \cdot 5^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $2.278990851$ 1.019195692 \( \frac{152409672113485069453847362}{45} a + \frac{94194357580360793912853799}{45} \) \( \bigl[\phi\) , \( \phi - 1\) , \( \phi + 1\) , \( -16876 \phi - 38700\) , \( 2081328 \phi + 3131243\bigr] \) ${y}^2+\phi{x}{y}+\left(\phi+1\right){y}={x}^{3}+\left(\phi-1\right){x}^{2}+\left(-16876\phi-38700\right){x}+2081328\phi+3131243$
405.1-a10 405.1-a \(\Q(\sqrt{5}) \) \( 3^{4} \cdot 5 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $1.698659487$ 0.759663617 \( \frac{152409672113485069453847362}{45} a + \frac{94194357580360793912853799}{45} \) \( \bigl[\phi + 1\) , \( 1\) , \( \phi + 1\) , \( 39285 \phi - 108946\) , \( -6708461 \phi + 14534412\bigr] \) ${y}^2+\left(\phi+1\right){x}{y}+\left(\phi+1\right){y}={x}^{3}+{x}^{2}+\left(39285\phi-108946\right){x}-6708461\phi+14534412$
2025.1-b10 2025.1-b \(\Q(\sqrt{5}) \) \( 3^{4} \cdot 5^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.018276957$ 2.092468141 \( \frac{152409672113485069453847362}{45} a + \frac{94194357580360793912853799}{45} \) \( \bigl[\phi\) , \( -\phi - 1\) , \( \phi\) , \( -151874 \phi - 348302\) , \( -56544176 \phi - 84347149\bigr] \) ${y}^2+\phi{x}{y}+\phi{y}={x}^{3}+\left(-\phi-1\right){x}^{2}+\left(-151874\phi-348302\right){x}-56544176\phi-84347149$
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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.