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Results (12 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
539.1-a1 539.1-a \(\Q(\sqrt{33}) \) \( 7^{2} \cdot 11 \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $0.602881548$ 1.679171307 \( -\frac{78843215872}{539} \) \( \bigl[0\) , \( -a\) , \( 1\) , \( 32875 a - 110860\) , \( 5524839 a - 18631313\bigr] \) ${y}^2+{y}={x}^{3}-a{x}^{2}+\left(32875a-110860\right){x}+5524839a-18631313$
539.1-a2 539.1-a \(\Q(\sqrt{33}) \) \( 7^{2} \cdot 11 \) 0 $\Z/3\Z$ $\mathrm{SU}(2)$ $1$ $0.602881548$ 1.679171307 \( -\frac{13278380032}{156590819} \) \( \bigl[0\) , \( a - 1\) , \( 1\) , \( -18155 a - 43065\) , \( -10448199 a - 24786069\bigr] \) ${y}^2+{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-18155a-43065\right){x}-10448199a-24786069$
539.1-a3 539.1-a \(\Q(\sqrt{33}) \) \( 7^{2} \cdot 11 \) 0 $\Z/3\Z$ $\mathrm{SU}(2)$ $1$ $0.602881548$ 1.679171307 \( \frac{9463555063808}{115539436859} \) \( \bigl[0\) , \( -a\) , \( 1\) , \( -162165 a + 546870\) , \( -270199791 a + 911189707\bigr] \) ${y}^2+{y}={x}^{3}-a{x}^{2}+\left(-162165a+546870\right){x}-270199791a+911189707$
539.1-b1 539.1-b \(\Q(\sqrt{33}) \) \( 7^{2} \cdot 11 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $7.031061357$ 3.671852040 \( \frac{4657463}{41503} \) \( \bigl[1\) , \( 1\) , \( 0\) , \( 4\) , \( 11\bigr] \) ${y}^2+{x}{y}={x}^{3}+{x}^{2}+4{x}+11$
539.1-b2 539.1-b \(\Q(\sqrt{33}) \) \( 7^{2} \cdot 11 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $7.031061357$ 3.671852040 \( \frac{15124197817}{1294139} \) \( \bigl[1\) , \( 1\) , \( 0\) , \( -51\) , \( 110\bigr] \) ${y}^2+{x}{y}={x}^{3}+{x}^{2}-51{x}+110$
539.1-c1 539.1-c \(\Q(\sqrt{33}) \) \( 7^{2} \cdot 11 \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $0.098027979$ $10.23860076$ 1.397731252 \( \frac{884736}{539} \) \( \bigl[0\) , \( 0\) , \( 1\) , \( 2\) , \( 0\bigr] \) ${y}^2+{y}={x}^{3}+2{x}$
539.1-d1 539.1-d \(\Q(\sqrt{33}) \) \( 7^{2} \cdot 11 \) $2$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $0.099137699$ $9.086092621$ 2.508874914 \( \frac{884736}{539} \) \( \bigl[0\) , \( 0\) , \( 1\) , \( 736 a + 1746\) , \( -4230 a - 10035\bigr] \) ${y}^2+{y}={x}^{3}+\left(736a+1746\right){x}-4230a-10035$
539.1-e1 539.1-e \(\Q(\sqrt{33}) \) \( 7^{2} \cdot 11 \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $1.183928702$ $3.210187340$ 1.984815816 \( \frac{4657463}{41503} \) \( \bigl[1\) , \( -a\) , \( a\) , \( 1280 a + 3040\) , \( -161701 a - 383601\bigr] \) ${y}^2+{x}{y}+a{y}={x}^{3}-a{x}^{2}+\left(1280a+3040\right){x}-161701a-383601$
539.1-e2 539.1-e \(\Q(\sqrt{33}) \) \( 7^{2} \cdot 11 \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.591964351$ $3.210187340$ 1.984815816 \( \frac{15124197817}{1294139} \) \( \bigl[1\) , \( -a\) , \( a\) , \( -18960 a - 44975\) , \( -2203466 a - 5227242\bigr] \) ${y}^2+{x}{y}+a{y}={x}^{3}-a{x}^{2}+\left(-18960a-44975\right){x}-2203466a-5227242$
539.1-f1 539.1-f \(\Q(\sqrt{33}) \) \( 7^{2} \cdot 11 \) $1$ $\Z/3\Z$ $\mathrm{SU}(2)$ $0.745116266$ $21.59210152$ 2.489484723 \( -\frac{78843215872}{539} \) \( \bigl[0\) , \( 1\) , \( 1\) , \( -89\) , \( 295\bigr] \) ${y}^2+{y}={x}^{3}+{x}^{2}-89{x}+295$
539.1-f2 539.1-f \(\Q(\sqrt{33}) \) \( 7^{2} \cdot 11 \) $1$ $\Z/3\Z$ $\mathrm{SU}(2)$ $2.235348799$ $2.399122391$ 2.489484723 \( -\frac{13278380032}{156590819} \) \( \bigl[0\) , \( 1\) , \( 1\) , \( -49\) , \( 600\bigr] \) ${y}^2+{y}={x}^{3}+{x}^{2}-49{x}+600$
539.1-f3 539.1-f \(\Q(\sqrt{33}) \) \( 7^{2} \cdot 11 \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $6.706046397$ $0.266569154$ 2.489484723 \( \frac{9463555063808}{115539436859} \) \( \bigl[0\) , \( 1\) , \( 1\) , \( 441\) , \( -15815\bigr] \) ${y}^2+{y}={x}^{3}+{x}^{2}+441{x}-15815$
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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.