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Results (6 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
121.1-a1 121.1-a \(\Q(\sqrt{6}) \) \( 11^{2} \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $43.10278554$ $0.064435690$ 1.133851549 \( -\frac{52893159101157376}{11} \) \( \bigl[0\) , \( -1\) , \( 1\) , \( -7820\) , \( -263580\bigr] \) ${y}^2+{y}={x}^{3}-{x}^{2}-7820{x}-263580$
121.1-a2 121.1-a \(\Q(\sqrt{6}) \) \( 11^{2} \) $1$ $\Z/5\Z$ $\mathrm{SU}(2)$ $8.620557108$ $1.610892258$ 1.133851549 \( -\frac{122023936}{161051} \) \( \bigl[0\) , \( -1\) , \( 1\) , \( -10\) , \( -20\bigr] \) ${y}^2+{y}={x}^{3}-{x}^{2}-10{x}-20$
121.1-a3 121.1-a \(\Q(\sqrt{6}) \) \( 11^{2} \) $1$ $\Z/5\Z$ $\mathrm{SU}(2)$ $1.724111421$ $40.27230645$ 1.133851549 \( -\frac{4096}{11} \) \( \bigl[0\) , \( -1\) , \( 1\) , \( 0\) , \( 0\bigr] \) ${y}^2+{y}={x}^{3}-{x}^{2}$
121.1-b1 121.1-b \(\Q(\sqrt{6}) \) \( 11^{2} \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $0.915095465$ $8.512583687$ 3.180183447 \( -\frac{52893159101157376}{11} \) \( \bigl[0\) , \( a - 1\) , \( a + 1\) , \( 156406 a - 383194\) , \( -52884793 a + 129540991\bigr] \) ${y}^2+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(156406a-383194\right){x}-52884793a+129540991$
121.1-b2 121.1-b \(\Q(\sqrt{6}) \) \( 11^{2} \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $0.183019093$ $8.512583687$ 3.180183447 \( -\frac{122023936}{161051} \) \( \bigl[0\) , \( a - 1\) , \( a + 1\) , \( 206 a - 504\) , \( -4823 a + 11811\bigr] \) ${y}^2+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(206a-504\right){x}-4823a+11811$
121.1-b3 121.1-b \(\Q(\sqrt{6}) \) \( 11^{2} \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $0.915095465$ $8.512583687$ 3.180183447 \( -\frac{4096}{11} \) \( \bigl[0\) , \( -a - 1\) , \( a + 1\) , \( -6 a - 14\) , \( -28 a - 69\bigr] \) ${y}^2+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-6a-14\right){x}-28a-69$
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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.