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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
176.1-a1 176.1-a \(\Q(\sqrt{33}) \) \( 2^{4} \cdot 11 \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $0.647455648$ 2.028736108 \( -\frac{199794688}{1331} \) \( \bigl[0\) , \( 1\) , \( 0\) , \( -77\) , \( -289\bigr] \) ${y}^2={x}^{3}+{x}^{2}-77{x}-289$
176.1-a2 176.1-a \(\Q(\sqrt{33}) \) \( 2^{4} \cdot 11 \) 0 $\Z/3\Z$ $\mathrm{SU}(2)$ $1$ $5.827100832$ 2.028736108 \( \frac{8192}{11} \) \( \bigl[0\) , \( 1\) , \( 0\) , \( 3\) , \( -1\bigr] \) ${y}^2={x}^{3}+{x}^{2}+3{x}-1$
176.1-b1 176.1-b \(\Q(\sqrt{33}) \) \( 2^{4} \cdot 11 \) $1$ $\Z/3\Z$ $\mathrm{SU}(2)$ $0.172006545$ $9.327341860$ 3.351406788 \( -\frac{199794688}{1331} \) \( \bigl[0\) , \( -a\) , \( 0\) , \( 28459 a - 95968\) , \( -4431843 a + 14945420\bigr] \) ${y}^2={x}^{3}-a{x}^{2}+\left(28459a-95968\right){x}-4431843a+14945420$
176.1-b2 176.1-b \(\Q(\sqrt{33}) \) \( 2^{4} \cdot 11 \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $0.516019637$ $9.327341860$ 3.351406788 \( \frac{8192}{11} \) \( \bigl[0\) , \( -a\) , \( 0\) , \( -981 a + 3312\) , \( -33363 a + 112508\bigr] \) ${y}^2={x}^{3}-a{x}^{2}+\left(-981a+3312\right){x}-33363a+112508$
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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.