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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
27.1-a2 27.1-a \(\Q(\zeta_{9})^+\) \( 3^{3} \) 0 $\Z/3\Z$ $-3$ $N(\mathrm{U}(1))$ $1$ $49.62331419$ 0.612633508 \( 0 \) \( \bigl[0\) , \( a^{2} + a - 2\) , \( a^{2} - 1\) , \( a + 2\) , \( 12 a^{2} - 4 a - 35\bigr] \) ${y}^2+\left(a^{2}-1\right){y}={x}^{3}+\left(a^{2}+a-2\right){x}^{2}+\left(a+2\right){x}+12a^{2}-4a-35$
27.1-a4 27.1-a \(\Q(\zeta_{9})^+\) \( 3^{3} \) 0 $\Z/9\Z$ $-3$ $N(\mathrm{U}(1))$ $1$ $148.8699425$ 0.612633508 \( 0 \) \( \bigl[0\) , \( 0\) , \( 1\) , \( 0\) , \( 0\bigr] \) ${y}^2+{y}={x}^{3}$
576.1-a2 576.1-a \(\Q(\zeta_{9})^+\) \( 2^{6} \cdot 3^{2} \) 0 $\Z/2\Z$ $-3$ $N(\mathrm{U}(1))$ $1$ $24.81165709$ 1.378425394 \( 0 \) \( \bigl[0\) , \( a^{2} + a - 2\) , \( 0\) , \( a + 2\) , \( 48 a^{2} - 16 a - 138\bigr] \) ${y}^2={x}^{3}+\left(a^{2}+a-2\right){x}^{2}+\left(a+2\right){x}+48a^{2}-16a-138$
576.1-a4 576.1-a \(\Q(\zeta_{9})^+\) \( 2^{6} \cdot 3^{2} \) 0 $\Z/6\Z$ $-3$ $N(\mathrm{U}(1))$ $1$ $74.43497128$ 1.378425394 \( 0 \) \( \bigl[0\) , \( 0\) , \( 0\) , \( 0\) , \( 1\bigr] \) ${y}^2={x}^{3}+1$
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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.