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Results (8 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
27.2-a1 27.2-a \(\Q(\sqrt{-23}) \) \( 3^{3} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $3.179173933$ 0.662903589 \( \frac{27256702}{81} a - \frac{57582961}{81} \) \( \bigl[1\) , \( -a - 1\) , \( 1\) , \( -2 a + 13\) , \( -11 a - 20\bigr] \) ${y}^2+{x}{y}+{y}={x}^3+\left(-a-1\right){x}^2+\left(-2a+13\right){x}-11a-20$
27.2-a2 27.2-a \(\Q(\sqrt{-23}) \) \( 3^{3} \) 0 $\Z/4\Z$ $\mathrm{SU}(2)$ $1$ $3.179173933$ 0.662903589 \( -\frac{27256702}{81} a - \frac{10108753}{27} \) \( \bigl[a\) , \( a\) , \( 0\) , \( -10 a + 60\) , \( 93 a + 58\bigr] \) ${y}^2+a{x}{y}={x}^3+a{x}^2+\left(-10a+60\right){x}+93a+58$
27.2-a3 27.2-a \(\Q(\sqrt{-23}) \) \( 3^{3} \) 0 $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $3.179173933$ 0.662903589 \( -\frac{2924207}{81} \) \( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( -16 a + 13\) , \( 34 a - 88\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^3+\left(-a-1\right){x}^2+\left(-16a+13\right){x}+34a-88$
27.2-a4 27.2-a \(\Q(\sqrt{-23}) \) \( 3^{3} \) 0 $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $3.179173933$ 0.662903589 \( \frac{1950520}{6561} a + \frac{58507}{2187} \) \( \bigl[1\) , \( -a - 1\) , \( 1\) , \( 1\) , \( a - 2\bigr] \) ${y}^2+{x}{y}+{y}={x}^3+\left(-a-1\right){x}^2+{x}+a-2$
27.2-a5 27.2-a \(\Q(\sqrt{-23}) \) \( 3^{3} \) 0 $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $3.179173933$ 0.662903589 \( -\frac{1950520}{6561} a + \frac{2126041}{6561} \) \( \bigl[a\) , \( a\) , \( 0\) , \( -2 a + 12\) , \( -a - 26\bigr] \) ${y}^2+a{x}{y}={x}^3+a{x}^2+\left(-2a+12\right){x}-a-26$
27.2-a6 27.2-a \(\Q(\sqrt{-23}) \) \( 3^{3} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $1.589586966$ 0.662903589 \( \frac{67902559538}{43046721} a + \frac{66394340881}{43046721} \) \( \bigl[a\) , \( a\) , \( 0\) , \( -17 a - 78\) , \( -130 a - 80\bigr] \) ${y}^2+a{x}{y}={x}^3+a{x}^2+\left(-17a-78\right){x}-130a-80$
27.2-a7 27.2-a \(\Q(\sqrt{-23}) \) \( 3^{3} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $1.589586966$ 0.662903589 \( -\frac{67902559538}{43046721} a + \frac{44765633473}{14348907} \) \( \bigl[1\) , \( -a - 1\) , \( 1\) , \( 10 a - 14\) , \( 13 a + 34\bigr] \) ${y}^2+{x}{y}+{y}={x}^3+\left(-a-1\right){x}^2+\left(10a-14\right){x}+13a+34$
27.2-a8 27.2-a \(\Q(\sqrt{-23}) \) \( 3^{3} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $1.589586966$ 0.662903589 \( \frac{12214672127}{9} \) \( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( -241 a + 148\) , \( 1654 a - 4948\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^3+\left(-a-1\right){x}^2+\left(-241a+148\right){x}+1654a-4948$
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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.