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Results (8 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
2.2-b2 2.2-b \(\Q(\sqrt{209}) \) \( 2 \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $18.51817441$ 2.561857817 \( \frac{102557}{1024} a + \frac{242501}{256} \) \( \bigl[a\) , \( a + 1\) , \( 1\) , \( 6449267 a + 43393366\) , \( 1546707281 a + 10406890251\bigr] \) ${y}^2+a{x}{y}+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(6449267a+43393366\right){x}+1546707281a+10406890251$
2.2-c2 2.2-c \(\Q(\sqrt{209}) \) \( 2 \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $0.105892522$ $13.03498084$ 1.909556628 \( \frac{102557}{1024} a + \frac{242501}{256} \) \( \bigl[a\) , \( -a + 1\) , \( a + 1\) , \( -10 a + 66\) , \( -20 a + 156\bigr] \) ${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-10a+66\right){x}-20a+156$
50.3-a2 50.3-a \(\Q(\sqrt{209}) \) \( 2 \cdot 5^{2} \) $2$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $0.129561378$ $8.281579361$ 2.375010653 \( \frac{102557}{1024} a + \frac{242501}{256} \) \( \bigl[a\) , \( a\) , \( a + 1\) , \( -7329 a + 56779\) , \( -2133698 a + 16490518\bigr] \) ${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(-7329a+56779\right){x}-2133698a+16490518$
50.3-g2 50.3-g \(\Q(\sqrt{209}) \) \( 2 \cdot 5^{2} \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $0.357204483$ $5.829420649$ 11.52282962 \( \frac{102557}{1024} a + \frac{242501}{256} \) \( \bigl[a\) , \( a - 1\) , \( a + 1\) , \( 48081 a + 323494\) , \( -615506 a - 4141387\bigr] \) ${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(48081a+323494\right){x}-615506a-4141387$
50.4-b2 50.4-b \(\Q(\sqrt{209}) \) \( 2 \cdot 5^{2} \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1.422389310$ $8.281579361$ 16.29628084 \( \frac{102557}{1024} a + \frac{242501}{256} \) \( \bigl[a\) , \( -1\) , \( 1\) , \( 4 a + 66\) , \( 16 a + 149\bigr] \) ${y}^2+a{x}{y}+{y}={x}^{3}-{x}^{2}+\left(4a+66\right){x}+16a+149$
50.4-k2 50.4-k \(\Q(\sqrt{209}) \) \( 2 \cdot 5^{2} \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $5.829420649$ 0.806458915 \( \frac{102557}{1024} a + \frac{242501}{256} \) \( \bigl[a\) , \( 1\) , \( a + 1\) , \( -141381207 a + 1092652854\) , \( 5674189094061 a - 43852494617814\bigr] \) ${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(-141381207a+1092652854\right){x}+5674189094061a-43852494617814$
64.6-c2 64.6-c \(\Q(\sqrt{209}) \) \( 2^{6} \) $0 \le r \le 1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $6.440367677$ 7.117173427 \( \frac{102557}{1024} a + \frac{242501}{256} \) \( \bigl[0\) , \( -1\) , \( a + 1\) , \( -4081 a + 31540\) , \( -878697 a + 6790917\bigr] \) ${y}^2+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(-4081a+31540\right){x}-878697a+6790917$
64.6-g2 64.6-g \(\Q(\sqrt{209}) \) \( 2^{6} \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1.356515814$ $4.684981914$ 1.758407907 \( \frac{102557}{1024} a + \frac{242501}{256} \) \( \bigl[0\) , \( -a - 1\) , \( a + 1\) , \( 221320 a + 1489144\) , \( 8865401 a + 59650106\bigr] \) ${y}^2+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(221320a+1489144\right){x}+8865401a+59650106$
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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.