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Results (6 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
33.2-b1 33.2-b \(\Q(\sqrt{3}) \) \( 3 \cdot 11 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $15.45625621$ 1.115459211 \( -\frac{28016}{33} a - \frac{15365}{11} \) \( \bigl[1\) , \( a\) , \( 0\) , \( 1\) , \( 0\bigr] \) ${y}^2+{x}{y}={x}^{3}+a{x}^{2}+{x}$
33.2-c1 33.2-c \(\Q(\sqrt{3}) \) \( 3 \cdot 11 \) 0 $\Z/4\Z$ $\mathrm{SU}(2)$ $1$ $26.61641567$ 0.480218586 \( -\frac{28016}{33} a - \frac{15365}{11} \) \( \bigl[a\) , \( -a - 1\) , \( 0\) , \( 1\) , \( 0\bigr] \) ${y}^2+a{x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+{x}$
1089.2-e1 1089.2-e \(\Q(\sqrt{3}) \) \( 3^{2} \cdot 11^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $4.633323250$ 1.337525213 \( -\frac{28016}{33} a - \frac{15365}{11} \) \( \bigl[a\) , \( -a\) , \( a + 1\) , \( -24 a - 39\) , \( 105 a + 181\bigr] \) ${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(-24a-39\right){x}+105a+181$
1089.2-i1 1089.2-i \(\Q(\sqrt{3}) \) \( 3^{2} \cdot 11^{2} \) 0 $\Z/4\Z$ $\mathrm{SU}(2)$ $1$ $2.690588852$ 0.776706099 \( -\frac{28016}{33} a - \frac{15365}{11} \) \( \bigl[1\) , \( a - 1\) , \( a + 1\) , \( -24 a - 38\) , \( -106 a - 183\bigr] \) ${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-24a-38\right){x}-106a-183$
1584.1-b1 1584.1-b \(\Q(\sqrt{3}) \) \( 2^{4} \cdot 3^{2} \cdot 11 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $2.952045376$ 1.704364192 \( -\frac{28016}{33} a - \frac{15365}{11} \) \( \bigl[a + 1\) , \( -1\) , \( 0\) , \( -2 a\) , \( 2 a - 8\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}-{x}^{2}-2a{x}+2a-8$
1584.1-o1 1584.1-o \(\Q(\sqrt{3}) \) \( 2^{4} \cdot 3^{2} \cdot 11 \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.110315418$ $11.61313845$ 2.958592720 \( -\frac{28016}{33} a - \frac{15365}{11} \) \( \bigl[a + 1\) , \( -a - 1\) , \( 0\) , \( -2 a\) , \( -2 a + 8\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-a-1\right){x}^{2}-2a{x}-2a+8$
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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.