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Results (7 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
7425.5-f8 7425.5-f \(\Q(\sqrt{-11}) \) \( 3^{3} \cdot 5^{2} \cdot 11 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.256794058$ 1.238821148 \( \frac{1032777340820292487}{1427209716796875} a + \frac{3533183376724708442}{1427209716796875} \) \( \bigl[a + 1\) , \( a - 1\) , \( 0\) , \( -385 a + 705\) , \( 2093 a + 5394\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-385a+705\right){x}+2093a+5394$
7425.8-h8 7425.8-h \(\Q(\sqrt{-11}) \) \( 3^{3} \cdot 5^{2} \cdot 11 \) $1$ $\Z/12\Z$ $\mathrm{SU}(2)$ $1.407799633$ $0.256794058$ 5.232035875 \( \frac{1032777340820292487}{1427209716796875} a + \frac{3533183376724708442}{1427209716796875} \) \( \bigl[a\) , \( a + 1\) , \( a\) , \( 137 a + 719\) , \( 3565 a - 5599\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(137a+719\right){x}+3565a-5599$
27225.5-d8 27225.5-d \(\Q(\sqrt{-11}) \) \( 3^{2} \cdot 5^{2} \cdot 11^{2} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $1.661233752$ $0.134106323$ 3.224221700 \( \frac{1032777340820292487}{1427209716796875} a + \frac{3533183376724708442}{1427209716796875} \) \( \bigl[1\) , \( 1\) , \( a + 1\) , \( -545 a + 3138\) , \( -27234 a + 3585\bigr] \) ${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(-545a+3138\right){x}-27234a+3585$
37125.10-j8 37125.10-j \(\Q(\sqrt{-11}) \) \( 3^{3} \cdot 5^{3} \cdot 11 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.114841794$ 3.324105959 \( \frac{1032777340820292487}{1427209716796875} a + \frac{3533183376724708442}{1427209716796875} \) \( \bigl[a + 1\) , \( -a\) , \( 0\) , \( 2294 a - 2669\) , \( -44686 a + 23022\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}-a{x}^{2}+\left(2294a-2669\right){x}-44686a+23022$
37125.11-g8 37125.11-g \(\Q(\sqrt{-11}) \) \( 3^{3} \cdot 5^{3} \cdot 11 \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $4.286586173$ $0.114841794$ 4.749688881 \( \frac{1032777340820292487}{1427209716796875} a + \frac{3533183376724708442}{1427209716796875} \) \( \bigl[1\) , \( a + 1\) , \( a + 1\) , \( -2430 a + 1949\) , \( -14391 a + 80030\bigr] \) ${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-2430a+1949\right){x}-14391a+80030$
37125.6-i8 37125.6-i \(\Q(\sqrt{-11}) \) \( 3^{3} \cdot 5^{3} \cdot 11 \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $1.744089115$ $0.114841794$ 5.797537023 \( \frac{1032777340820292487}{1427209716796875} a + \frac{3533183376724708442}{1427209716796875} \) \( \bigl[1\) , \( -a - 1\) , \( a\) , \( 1738 a + 2043\) , \( 6612 a - 75145\bigr] \) ${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(1738a+2043\right){x}+6612a-75145$
37125.7-k8 37125.7-k \(\Q(\sqrt{-11}) \) \( 3^{3} \cdot 5^{3} \cdot 11 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.114841794$ 3.324105959 \( \frac{1032777340820292487}{1427209716796875} a + \frac{3533183376724708442}{1427209716796875} \) \( \bigl[a\) , \( 0\) , \( 1\) , \( -1354 a - 2751\) , \( -39143 a - 13940\bigr] \) ${y}^2+a{x}{y}+{y}={x}^{3}+\left(-1354a-2751\right){x}-39143a-13940$
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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.