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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
729.1-CMb1 729.1-CMb \(\Q(\sqrt{-3}) \) \( 3^{6} \) 0 $\Z/3\Z$ $-3$ $\mathrm{U}(1)$ $1$ $8.108628264$ 1.040337491 \( 0 \) \( \bigl[0\) , \( 0\) , \( a + 1\) , \( 0\) , \( -a\bigr] \) ${y}^2+\left(a+1\right){y}={x}^{3}-a$
729.1-CMa1 729.1-CMa \(\Q(\sqrt{-3}) \) \( 3^{6} \) 0 $\Z/3\Z$ $-3$ $\mathrm{U}(1)$ $1$ $8.108628264$ 1.040337491 \( 0 \) \( \bigl[0\) , \( 0\) , \( a\) , \( 0\) , \( 0\bigr] \) ${y}^2+a{y}={x}^{3}$
729.1-a1 729.1-a \(\Q(\sqrt{-3}) \) \( 3^{6} \) 0 $\Z/3\Z$ $\mathrm{SU}(2)$ $1$ $6.976113039$ 0.895035720 \( -18981 a + 13149 \) \( \bigl[1\) , \( -1\) , \( a\) , \( -2 a\) , \( a\bigr] \) ${y}^2+{x}{y}+a{y}={x}^{3}-{x}^{2}-2a{x}+a$
729.1-a2 729.1-a \(\Q(\sqrt{-3}) \) \( 3^{6} \) 0 $\Z/3\Z$ $\mathrm{SU}(2)$ $1$ $6.976113039$ 0.895035720 \( 18981 a - 5832 \) \( \bigl[1\) , \( -1\) , \( a + 1\) , \( a - 2\) , \( -2 a + 1\bigr] \) ${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(a-2\right){x}-2a+1$
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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.