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Results (4 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
21.1-a2 21.1-a \(\Q(\sqrt{21}) \) \( 3 \cdot 7 \) 0 $\Z/4\Z$ $\mathrm{SU}(2)$ $1$ $14.60752776$ 0.796905972 \( \frac{103823}{63} \) \( \bigl[a\) , \( 1\) , \( a\) , \( -5 a + 13\) , \( -5 a + 13\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}+\left(-5a+13\right){x}-5a+13$
21.1-b2 21.1-b \(\Q(\sqrt{21}) \) \( 3 \cdot 7 \) $1$ $\Z/8\Z$ $\mathrm{SU}(2)$ $1.319254411$ $13.02432697$ 0.937376813 \( \frac{103823}{63} \) \( \bigl[1\) , \( 0\) , \( 0\) , \( 1\) , \( 0\bigr] \) ${y}^2+{x}{y}={x}^{3}+{x}$
63.1-a2 63.1-a \(\Q(\sqrt{21}) \) \( 3^{2} \cdot 7 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $7.963525558$ 1.737783746 \( \frac{103823}{63} \) \( \bigl[a + 1\) , \( -a - 1\) , \( 0\) , \( -3 a + 9\) , \( 0\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-3a+9\right){x}$
63.1-b2 63.1-b \(\Q(\sqrt{21}) \) \( 3^{2} \cdot 7 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $7.963525558$ 1.737783746 \( \frac{103823}{63} \) \( \bigl[a\) , \( -1\) , \( 0\) , \( 3 a + 6\) , \( 0\bigr] \) ${y}^2+a{x}{y}={x}^{3}-{x}^{2}+\left(3a+6\right){x}$
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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.