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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
16.4-a1 16.4-a \(\Q(\sqrt{17}) \) \( 2^{4} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $9.235230655$ 0.559968109 \( -7659605 a + 19620476 \) \( \bigl[a\) , \( -1\) , \( a\) , \( -a - 3\) , \( -6 a - 10\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(-a-3\right){x}-6a-10$
16.4-a2 16.4-a \(\Q(\sqrt{17}) \) \( 2^{4} \) 0 $\Z/4\Z$ $\mathrm{SU}(2)$ $1$ $18.47046131$ 0.559968109 \( 343 a + 686 \) \( \bigl[a\) , \( 1\) , \( a\) , \( 0\) , \( 0\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}$
16.4-a3 16.4-a \(\Q(\sqrt{17}) \) \( 2^{4} \) 0 $\Z/2\Z\oplus\Z/4\Z$ $\mathrm{SU}(2)$ $1$ $36.94092262$ 0.559968109 \( -1995 a + 7016 \) \( \bigl[a\) , \( a\) , \( a\) , \( -9 a - 15\) , \( -6 a - 10\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+a{x}^{2}+\left(-9a-15\right){x}-6a-10$
16.4-a4 16.4-a \(\Q(\sqrt{17}) \) \( 2^{4} \) 0 $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $18.47046131$ 0.559968109 \( 24225 a + 44228 \) \( \bigl[a\) , \( a - 1\) , \( 0\) , \( a\) , \( 0\bigr] \) ${y}^2+a{x}{y}={x}^{3}+\left(a-1\right){x}^{2}+a{x}$
16.4-a5 16.4-a \(\Q(\sqrt{17}) \) \( 2^{4} \) 0 $\Z/8\Z$ $\mathrm{SU}(2)$ $1$ $36.94092262$ 0.559968109 \( -21069823 a + 54821634 \) \( \bigl[a\) , \( a\) , \( a\) , \( -124 a - 195\) , \( 916 a + 1430\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+a{x}^{2}+\left(-124a-195\right){x}+916a+1430$
16.4-a6 16.4-a \(\Q(\sqrt{17}) \) \( 2^{4} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $4.617615327$ 0.559968109 \( 2701312025 a + 4218241728 \) \( \bigl[a\) , \( a - 1\) , \( 0\) , \( -4 a\) , \( -5 a - 20\bigr] \) ${y}^2+a{x}{y}={x}^{3}+\left(a-1\right){x}^{2}-4a{x}-5a-20$
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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.