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Results (7 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
108.1-a1 108.1-a \(\Q(\sqrt{-11}) \) \( 2^{2} \cdot 3^{3} \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $0.392228249$ $0.681207479$ 0.966725513 \( \frac{116453655937}{8} a - 37004774076 \) \( \bigl[a + 1\) , \( a - 1\) , \( a + 1\) , \( 443 a - 974\) , \( 6754 a - 9107\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(443a-974\right){x}+6754a-9107$
108.1-a2 108.1-a \(\Q(\sqrt{-11}) \) \( 2^{2} \cdot 3^{3} \) $1$ $\Z/3\Z$ $\mathrm{SU}(2)$ $0.130742749$ $2.043622437$ 0.966725513 \( -\frac{488881}{256} a + \frac{1381533}{512} \) \( \bigl[a + 1\) , \( a - 1\) , \( a + 1\) , \( 3 a - 14\) , \( 2 a - 11\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(3a-14\right){x}+2a-11$
108.1-a3 108.1-a \(\Q(\sqrt{-11}) \) \( 2^{2} \cdot 3^{3} \) $1$ $\Z/3\Z$ $\mathrm{SU}(2)$ $0.392228249$ $6.130867313$ 0.966725513 \( -\frac{21349}{4} a + \frac{328857}{8} \) \( \bigl[a + 1\) , \( a - 1\) , \( a + 1\) , \( -2 a + 1\) , \( a - 1\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-2a+1\right){x}+a-1$
108.1-a4 108.1-a \(\Q(\sqrt{-11}) \) \( 2^{2} \cdot 3^{3} \) $1$ $\Z/3\Z$ $\mathrm{SU}(2)$ $1.176684747$ $6.130867313$ 0.966725513 \( \frac{21493}{2} a + 66744 \) \( \bigl[1\) , \( a - 1\) , \( a + 1\) , \( -2 a + 1\) , \( 3\bigr] \) ${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-2a+1\right){x}+3$
108.1-b1 108.1-b \(\Q(\sqrt{-11}) \) \( 2^{2} \cdot 3^{3} \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $2.453117830$ 1.479285710 \( -13361111 a - \frac{6886077}{2} \) \( \bigl[1\) , \( a - 1\) , \( a\) , \( -21 a + 30\) , \( 6 a - 81\bigr] \) ${y}^2+{x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-21a+30\right){x}+6a-81$
108.1-b2 108.1-b \(\Q(\sqrt{-11}) \) \( 2^{2} \cdot 3^{3} \) 0 $\Z/3\Z$ $\mathrm{SU}(2)$ $1$ $7.359353490$ 1.479285710 \( -\frac{3637}{2} a - 1296 \) \( \bigl[a\) , \( 0\) , \( 1\) , \( 0\) , \( 0\bigr] \) ${y}^2+a{x}{y}+{y}={x}^{3}$
108.1-b3 108.1-b \(\Q(\sqrt{-11}) \) \( 2^{2} \cdot 3^{3} \) 0 $\Z/3\Z$ $\mathrm{SU}(2)$ $1$ $7.359353490$ 1.479285710 \( \frac{1261}{4} a + \frac{11127}{8} \) \( \bigl[1\) , \( a - 1\) , \( a\) , \( -a\) , \( 1\bigr] \) ${y}^2+{x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}-a{x}+1$
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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.