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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
121.3-a1 121.3-a \(\Q(\sqrt{3}) \) \( 11^{2} \) 0 $\Z/2\Z$ $-4$ $N(\mathrm{U}(1))$ $1$ $6.438947969$ 0.929382085 \( 1728 \) \( \bigl[a + 1\) , \( a - 1\) , \( a\) , \( -16 a + 26\) , \( 13 a - 24\bigr] \) ${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-16a+26\right){x}+13a-24$
121.3-a2 121.3-a \(\Q(\sqrt{3}) \) \( 11^{2} \) 0 $\Z/2\Z$ $-4$ $N(\mathrm{U}(1))$ $1$ $6.438947969$ 0.929382085 \( 1728 \) \( \bigl[a + 1\) , \( a - 1\) , \( 1\) , \( 209 a - 361\) , \( -181 a + 314\bigr] \) ${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(209a-361\right){x}-181a+314$
121.3-b1 121.3-b \(\Q(\sqrt{3}) \) \( 11^{2} \) $1$ $\mathsf{trivial}$ $-3$ $N(\mathrm{U}(1))$ $0.194855274$ $10.87456613$ 1.223385920 \( 0 \) \( \bigl[0\) , \( -a\) , \( a\) , \( 1\) , \( -1\bigr] \) ${y}^2+a{y}={x}^{3}-a{x}^{2}+{x}-1$
121.3-b2 121.3-b \(\Q(\sqrt{3}) \) \( 11^{2} \) $1$ $\mathsf{trivial}$ $-3$ $N(\mathrm{U}(1))$ $0.064951758$ $32.62369841$ 1.223385920 \( 0 \) \( \bigl[0\) , \( a\) , \( 1\) , \( 1\) , \( 0\bigr] \) ${y}^2+{y}={x}^{3}+a{x}^{2}+{x}$
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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.