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Results (9 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
8.3-a4 8.3-a \(\Q(\sqrt{17}) \) \( 2^{3} \) 0 $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $25.38114868$ 0.769479095 \( 1995 a + 5021 \) \( \bigl[a + 1\) , \( a - 1\) , \( 0\) , \( a + 3\) , \( 0\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(a+3\right){x}$
16.5-a4 16.5-a \(\Q(\sqrt{17}) \) \( 2^{4} \) 0 $\Z/2\Z\oplus\Z/4\Z$ $\mathrm{SU}(2)$ $1$ $36.94092262$ 0.559968109 \( 1995 a + 5021 \) \( \bigl[a + 1\) , \( a + 1\) , \( a + 1\) , \( 12 a - 22\) , \( -7 a + 26\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(12a-22\right){x}-7a+26$
64.6-a4 64.6-a \(\Q(\sqrt{17}) \) \( 2^{6} \) 0 $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $24.04342268$ 1.457846637 \( 1995 a + 5021 \) \( \bigl[a + 1\) , \( -a - 1\) , \( 0\) , \( 3 a - 8\) , \( 2 a - 5\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(3a-8\right){x}+2a-5$
64.6-b4 64.6-b \(\Q(\sqrt{17}) \) \( 2^{6} \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $0.493335081$ $16.51961138$ 0.988296755 \( 1995 a + 5021 \) \( \bigl[a + 1\) , \( 0\) , \( 0\) , \( -5 a - 8\) , \( -16 a - 25\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-5a-8\right){x}-16a-25$
128.1-b4 128.1-b \(\Q(\sqrt{17}) \) \( 2^{7} \) 0 $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $11.68112923$ 1.416544989 \( 1995 a + 5021 \) \( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -3 a - 4\) , \( -2 a - 4\bigr] \) ${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(-3a-4\right){x}-2a-4$
256.1-e4 256.1-e \(\Q(\sqrt{17}) \) \( 2^{8} \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $0.269899646$ $17.00126722$ 2.225815404 \( 1995 a + 5021 \) \( \bigl[0\) , \( a + 1\) , \( 0\) , \( 25 a - 60\) , \( 24 a - 60\bigr] \) ${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(25a-60\right){x}+24a-60$
512.4-e4 512.4-e \(\Q(\sqrt{17}) \) \( 2^{9} \) 0 $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $12.02171134$ 1.457846637 \( 1995 a + 5021 \) \( \bigl[0\) , \( a\) , \( 0\) , \( 4 a - 12\) , \( 0\bigr] \) ${y}^2={x}^{3}+a{x}^{2}+\left(4a-12\right){x}$
512.4-h4 512.4-h \(\Q(\sqrt{17}) \) \( 2^{9} \) 0 $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $13.06058844$ 1.583828990 \( 1995 a + 5021 \) \( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -62 a - 97\) , \( 431 a + 673\bigr] \) ${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(-62a-97\right){x}+431a+673$
648.3-d4 648.3-d \(\Q(\sqrt{17}) \) \( 2^{3} \cdot 3^{4} \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $0.680814550$ $11.33417814$ 1.871519699 \( 1995 a + 5021 \) \( \bigl[a + 1\) , \( 1\) , \( a + 1\) , \( -3 a - 10\) , \( a - 2\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(-3a-10\right){x}+a-2$
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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.