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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-a1 21.1-a \(\Q(\sqrt{21}) \) \( 3 \cdot 7 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $3.651881942$ 0.796905972 \( -\frac{4354703137}{17294403} \) \( \bigl[a\) , \( 1\) , \( a\) , \( 170 a - 477\) , \( -5038 a + 14062\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}+\left(170a-477\right){x}-5038a+14062$
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-a3 21.1-a \(\Q(\sqrt{21}) \) \( 3 \cdot 7 \) 0 $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $14.60752776$ 0.796905972 \( \frac{7189057}{3969} \) \( \bigl[a\) , \( 1\) , \( a\) , \( 20 a - 57\) , \( -4 a + 10\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}+\left(20a-57\right){x}-4a+10$
21.1-a4 21.1-a \(\Q(\sqrt{21}) \) \( 3 \cdot 7 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $3.651881942$ 0.796905972 \( \frac{6570725617}{45927} \) \( \bigl[a\) , \( 1\) , \( a\) , \( 195 a - 547\) , \( 2355 a - 6577\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}+\left(195a-547\right){x}+2355a-6577$
21.1-a5 21.1-a \(\Q(\sqrt{21}) \) \( 3 \cdot 7 \) 0 $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $14.60752776$ 0.796905972 \( \frac{13027640977}{21609} \) \( \bigl[a\) , \( 1\) , \( a\) , \( 245 a - 687\) , \( -3019 a + 8425\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}+\left(245a-687\right){x}-3019a+8425$
21.1-a6 21.1-a \(\Q(\sqrt{21}) \) \( 3 \cdot 7 \) 0 $\Z/4\Z$ $\mathrm{SU}(2)$ $1$ $14.60752776$ 0.796905972 \( \frac{53297461115137}{147} \) \( \bigl[a\) , \( 1\) , \( a\) , \( 3920 a - 10977\) , \( -200440 a + 559528\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}+\left(3920a-10977\right){x}-200440a+559528$
21.1-b1 21.1-b \(\Q(\sqrt{21}) \) \( 3 \cdot 7 \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $2.638508823$ $0.814020435$ 0.937376813 \( -\frac{4354703137}{17294403} \) \( \bigl[1\) , \( 0\) , \( 0\) , \( -34\) , \( -217\bigr] \) ${y}^2+{x}{y}={x}^{3}-34{x}-217$
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 \( \frac{103823}{63} \) \( \bigl[1\) , \( 0\) , \( 0\) , \( 1\) , \( 0\bigr] \) ${y}^2+{x}{y}={x}^{3}+{x}$
21.1-b3 21.1-b \(\Q(\sqrt{21}) \) \( 3 \cdot 7 \) $1$ $\Z/2\Z\oplus\Z/4\Z$ $\mathrm{SU}(2)$ $0.659627205$ $13.02432697$ 0.937376813 \( \frac{7189057}{3969} \) \( \bigl[1\) , \( 0\) , \( 0\) , \( -4\) , \( -1\bigr] \) ${y}^2+{x}{y}={x}^{3}-4{x}-1$
21.1-b4 21.1-b \(\Q(\sqrt{21}) \) \( 3 \cdot 7 \) $1$ $\Z/8\Z$ $\mathrm{SU}(2)$ $0.329813602$ $13.02432697$ 0.937376813 \( \frac{6570725617}{45927} \) \( \bigl[1\) , \( 0\) , \( 0\) , \( -39\) , \( 90\bigr] \) ${y}^2+{x}{y}={x}^{3}-39{x}+90$
21.1-b5 21.1-b \(\Q(\sqrt{21}) \) \( 3 \cdot 7 \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1.319254411$ $3.256081743$ 0.937376813 \( \frac{13027640977}{21609} \) \( \bigl[1\) , \( 0\) , \( 0\) , \( -49\) , \( -136\bigr] \) ${y}^2+{x}{y}={x}^{3}-49{x}-136$
21.1-b6 21.1-b \(\Q(\sqrt{21}) \) \( 3 \cdot 7 \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $2.638508823$ $0.814020435$ 0.937376813 \( \frac{53297461115137}{147} \) \( \bigl[1\) , \( 0\) , \( 0\) , \( -784\) , \( -8515\bigr] \) ${y}^2+{x}{y}={x}^{3}-784{x}-8515$
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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.