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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
1.1-a1 1.1-a \(\Q(\sqrt{106}) \) \( 1 \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $33.67140610$ 1.635228035 \( 25777 a + 264235 \) \( \bigl[1\) , \( a\) , \( 1\) , \( -262494 a - 2702508\) , \( -235431668 a - 2423917415\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+a{x}^{2}+\left(-262494a-2702508\right){x}-235431668a-2423917415$
1.1-b1 1.1-b \(\Q(\sqrt{106}) \) \( 1 \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $33.67140610$ 1.635228035 \( -25777 a + 264235 \) \( \bigl[1\) , \( -a\) , \( 1\) , \( 262494 a - 2702508\) , \( 235431668 a - 2423917415\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}-a{x}^{2}+\left(262494a-2702508\right){x}+235431668a-2423917415$
1.1-c1 1.1-c \(\Q(\sqrt{106}) \) \( 1 \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $33.67140610$ 1.635228035 \( -25777 a + 264235 \) \( \bigl[a\) , \( a + 1\) , \( a\) , \( 1049995 a - 10809937\) , \( 1882093082 a - 19377332290\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(1049995a-10809937\right){x}+1882093082a-19377332290$
1.1-d1 1.1-d \(\Q(\sqrt{106}) \) \( 1 \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $33.67140610$ 1.635228035 \( 25777 a + 264235 \) \( \bigl[a\) , \( -a + 1\) , \( a\) , \( -1049995 a - 10809937\) , \( -1882093082 a - 19377332290\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-1049995a-10809937\right){x}-1882093082a-19377332290$
3.1-a1 3.1-a \(\Q(\sqrt{106}) \) \( 3 \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $7.279780841$ 0.707074821 \( \frac{917674496}{531441} a - \frac{12306610112}{531441} \) \( \bigl[a\) , \( -a\) , \( 1\) , \( -301050 a - 3099043\) , \( 329963957 a + 3397188706\bigr] \) ${y}^2+a{x}{y}+{y}={x}^{3}-a{x}^{2}+\left(-301050a-3099043\right){x}+329963957a+3397188706$
3.1-b1 3.1-b \(\Q(\sqrt{106}) \) \( 3 \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1.056683201$ $12.28540203$ 5.043606958 \( \frac{78884}{81} a - \frac{804137}{81} \) \( \bigl[a\) , \( a + 1\) , \( a\) , \( 19 a + 241\) , \( 100 a + 1190\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(19a+241\right){x}+100a+1190$
3.1-c1 3.1-c \(\Q(\sqrt{106}) \) \( 3 \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $12.28540203$ 1.193263731 \( \frac{78884}{81} a - \frac{804137}{81} \) \( \bigl[1\) , \( -a\) , \( 0\) , \( 37\) , \( -4 a + 2\bigr] \) ${y}^2+{x}{y}={x}^{3}-a{x}^{2}+37{x}-4a+2$
3.1-d1 3.1-d \(\Q(\sqrt{106}) \) \( 3 \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $0.879054255$ $7.279780841$ 7.458685570 \( \frac{917674496}{531441} a - \frac{12306610112}{531441} \) \( \bigl[0\) , \( a - 1\) , \( 0\) , \( 2738701812 a - 28196660894\) , \( 255545025319958 a - 2630997065063416\bigr] \) ${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(2738701812a-28196660894\right){x}+255545025319958a-2630997065063416$
3.2-a1 3.2-a \(\Q(\sqrt{106}) \) \( 3 \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $7.279780841$ 0.707074821 \( -\frac{917674496}{531441} a - \frac{12306610112}{531441} \) \( \bigl[a\) , \( a\) , \( 1\) , \( 301049 a - 3099043\) , \( -329963957 a + 3397188706\bigr] \) ${y}^2+a{x}{y}+{y}={x}^{3}+a{x}^{2}+\left(301049a-3099043\right){x}-329963957a+3397188706$
3.2-b1 3.2-b \(\Q(\sqrt{106}) \) \( 3 \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1.056683201$ $12.28540203$ 5.043606958 \( -\frac{78884}{81} a - \frac{804137}{81} \) \( \bigl[a\) , \( -a + 1\) , \( a\) , \( -19 a + 241\) , \( -100 a + 1190\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-19a+241\right){x}-100a+1190$
3.2-c1 3.2-c \(\Q(\sqrt{106}) \) \( 3 \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $12.28540203$ 1.193263731 \( -\frac{78884}{81} a - \frac{804137}{81} \) \( \bigl[1\) , \( a\) , \( 0\) , \( 37\) , \( 4 a + 2\bigr] \) ${y}^2+{x}{y}={x}^{3}+a{x}^{2}+37{x}+4a+2$
3.2-d1 3.2-d \(\Q(\sqrt{106}) \) \( 3 \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $0.879054255$ $7.279780841$ 7.458685570 \( -\frac{917674496}{531441} a - \frac{12306610112}{531441} \) \( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -2738701812 a - 28196660894\) , \( -255545025319958 a - 2630997065063416\bigr] \) ${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(-2738701812a-28196660894\right){x}-255545025319958a-2630997065063416$
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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.