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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
11.1-a1 11.1-a \(\Q(\sqrt{33}) \) \( 11 \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $8.512583687$ 2.963701228 \( -\frac{52893159101157376}{11} \) \( \bigl[0\) , \( -a + 1\) , \( 1\) , \( -2877883 a - 6827148\) , \( 4506151140 a + 10689858189\bigr] \) ${y}^2+{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-2877883a-6827148\right){x}+4506151140a+10689858189$
11.1-b1 11.1-b \(\Q(\sqrt{33}) \) \( 11 \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $7.655751664$ $0.064435690$ 0.343492567 \( -\frac{52893159101157376}{11} \) \( \bigl[0\) , \( -1\) , \( 1\) , \( -7820\) , \( -263580\bigr] \) ${y}^2+{y}={x}^{3}-{x}^{2}-7820{x}-263580$
121.1-e1 121.1-e \(\Q(\sqrt{33}) \) \( 11^{2} \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $19.53044489$ $0.223304562$ 3.036775978 \( -\frac{52893159101157376}{11} \) \( \bigl[0\) , \( a - 1\) , \( 1\) , \( 688189 a - 2322636\) , \( 526275039 a - 1774717815\bigr] \) ${y}^2+{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(688189a-2322636\right){x}+526275039a-1774717815$
121.1-g1 121.1-g \(\Q(\sqrt{33}) \) \( 11^{2} \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $19.53044489$ $0.223304562$ 3.036775978 \( -\frac{52893159101157376}{11} \) \( \bigl[0\) , \( -a\) , \( 1\) , \( -688189 a - 1634447\) , \( -526275039 a - 1248442776\bigr] \) ${y}^2+{y}={x}^{3}-a{x}^{2}+\left(-688189a-1634447\right){x}-526275039a-1248442776$
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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.