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Results (6 matches)

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Label Class Base field Conductor norm Rank Torsion CM Regulator Period Leading coeff j-invariant Weierstrass coefficients Weierstrass equation
64.4-a1 64.4-a \(\Q(\sqrt{17}) \) \( 2^{6} \) $0$ $\Z/2\Z$ $1$ $7.156385278$ 0.867839188 \( \frac{217}{16} a - \frac{139}{4} \) \( \bigl[a\) , \( a - 1\) , \( a\) , \( 0\) , \( -2 a - 4\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}-2a-4$
64.4-b1 64.4-b \(\Q(\sqrt{17}) \) \( 2^{6} \) $0$ $\Z/4\Z$ $1$ $14.01972920$ 1.700141892 \( \frac{217}{16} a - \frac{139}{4} \) \( \bigl[a\) , \( -a\) , \( a\) , \( -3\) , \( -3 a + 6\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}-a{x}^{2}-3{x}-3a+6$
128.6-a1 128.6-a \(\Q(\sqrt{17}) \) \( 2^{7} \) $0$ $\Z/4\Z$ $1$ $8.823675287$ 2.140055600 \( \frac{217}{16} a - \frac{139}{4} \) \( \bigl[a\) , \( a\) , \( a\) , \( a\) , \( a\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+a{x}^{2}+a{x}+a$
128.6-d1 128.6-d \(\Q(\sqrt{17}) \) \( 2^{7} \) $1$ $\Z/2\Z$ $0.081969010$ $17.28603663$ 1.374613658 \( \frac{217}{16} a - \frac{139}{4} \) \( \bigl[a\) , \( -a\) , \( 0\) , \( -a\) , \( 197 a + 308\bigr] \) ${y}^2+a{x}{y}={x}^{3}-a{x}^{2}-a{x}+197a+308$
512.1-e1 512.1-e \(\Q(\sqrt{17}) \) \( 2^{9} \) $0$ $\Z/2\Z$ $1$ $6.239280630$ 1.513247827 \( \frac{217}{16} a - \frac{139}{4} \) \( \bigl[0\) , \( 1\) , \( 0\) , \( 0\) , \( 8 a + 12\bigr] \) ${y}^2={x}^{3}+{x}^{2}+8a+12$
512.1-f1 512.1-f \(\Q(\sqrt{17}) \) \( 2^{9} \) $1$ $\Z/2\Z$ $0.235830817$ $12.22307372$ 2.796510914 \( \frac{217}{16} a - \frac{139}{4} \) \( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 5 a - 12\) , \( -50 a + 128\bigr] \) ${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(5a-12\right){x}-50a+128$
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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.