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Results (14 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
1444.1-a1 1444.1-a \(\Q(\sqrt{21}) \) \( 2^{2} \cdot 19^{2} \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $5.550558930$ 6.056156297 \( -\frac{37966934881}{4952198} \) \( \bigl[a\) , \( a + 1\) , \( 1\) , \( 352 a - 976\) , \( -5990 a + 16723\bigr] \) ${y}^2+a{x}{y}+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(352a-976\right){x}-5990a+16723$
1444.1-a2 1444.1-a \(\Q(\sqrt{21}) \) \( 2^{2} \cdot 19^{2} \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $5.550558930$ 6.056156297 \( -\frac{1}{608} \) \( \bigl[a\) , \( a + 1\) , \( 1\) , \( 2 a + 4\) , \( 30 a - 77\bigr] \) ${y}^2+a{x}{y}+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(2a+4\right){x}+30a-77$
1444.1-b1 1444.1-b \(\Q(\sqrt{21}) \) \( 2^{2} \cdot 19^{2} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.560781336$ $26.71213644$ 3.268831455 \( \frac{132651}{76} \) \( \bigl[a\) , \( a\) , \( 1\) , \( 1\) , \( -a - 2\bigr] \) ${y}^2+a{x}{y}+{y}={x}^{3}+a{x}^{2}+{x}-a-2$
1444.1-b2 1444.1-b \(\Q(\sqrt{21}) \) \( 2^{2} \cdot 19^{2} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $1.121562673$ $13.35606822$ 3.268831455 \( \frac{149721291}{722} \) \( \bigl[a\) , \( a\) , \( 1\) , \( -10 a - 19\) , \( 15 a + 26\bigr] \) ${y}^2+a{x}{y}+{y}={x}^{3}+a{x}^{2}+\left(-10a-19\right){x}+15a+26$
1444.1-c1 1444.1-c \(\Q(\sqrt{21}) \) \( 2^{2} \cdot 19^{2} \) 0 $\Z/3\Z$ $\mathrm{SU}(2)$ $1$ $32.17041206$ 2.340053149 \( -\frac{413493625}{152} \) \( \bigl[1\) , \( 0\) , \( 1\) , \( -16\) , \( 22\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}-16{x}+22$
1444.1-c2 1444.1-c \(\Q(\sqrt{21}) \) \( 2^{2} \cdot 19^{2} \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $0.397165580$ 2.340053149 \( -\frac{69173457625}{2550136832} \) \( \bigl[1\) , \( 0\) , \( 1\) , \( -86\) , \( -2456\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}-86{x}-2456$
1444.1-c3 1444.1-c \(\Q(\sqrt{21}) \) \( 2^{2} \cdot 19^{2} \) 0 $\Z/3\Z$ $\mathrm{SU}(2)$ $1$ $3.574490228$ 2.340053149 \( \frac{94196375}{3511808} \) \( \bigl[1\) , \( 0\) , \( 1\) , \( 9\) , \( 90\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+9{x}+90$
1444.1-d1 1444.1-d \(\Q(\sqrt{21}) \) \( 2^{2} \cdot 19^{2} \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $1.446313524$ 0.946834457 \( -\frac{413493625}{152} \) \( \bigl[a + 1\) , \( -a + 1\) , \( a\) , \( -79 a - 140\) , \( -612 a - 1097\bigr] \) ${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-79a-140\right){x}-612a-1097$
1444.1-d2 1444.1-d \(\Q(\sqrt{21}) \) \( 2^{2} \cdot 19^{2} \) 0 $\Z/3\Z$ $\mathrm{SU}(2)$ $1$ $1.446313524$ 0.946834457 \( -\frac{69173457625}{2550136832} \) \( \bigl[a\) , \( 1\) , \( a + 1\) , \( 427 a - 1198\) , \( -58511 a + 163337\bigr] \) ${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(427a-1198\right){x}-58511a+163337$
1444.1-d3 1444.1-d \(\Q(\sqrt{21}) \) \( 2^{2} \cdot 19^{2} \) 0 $\Z/3\Z$ $\mathrm{SU}(2)$ $1$ $1.446313524$ 0.946834457 \( \frac{94196375}{3511808} \) \( \bigl[a\) , \( 1\) , \( a + 1\) , \( -48 a + 132\) , \( 2118 a - 5915\bigr] \) ${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(-48a+132\right){x}+2118a-5915$
1444.1-e1 1444.1-e \(\Q(\sqrt{21}) \) \( 2^{2} \cdot 19^{2} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.560781336$ $26.71213644$ 3.268831455 \( \frac{132651}{76} \) \( \bigl[a + 1\) , \( a + 1\) , \( 0\) , \( 5 a + 4\) , \( 3 a + 6\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(5a+4\right){x}+3a+6$
1444.1-e2 1444.1-e \(\Q(\sqrt{21}) \) \( 2^{2} \cdot 19^{2} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $1.121562673$ $13.35606822$ 3.268831455 \( \frac{149721291}{722} \) \( \bigl[a + 1\) , \( a + 1\) , \( 0\) , \( 15 a - 26\) , \( -33 a + 100\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(15a-26\right){x}-33a+100$
1444.1-f1 1444.1-f \(\Q(\sqrt{21}) \) \( 2^{2} \cdot 19^{2} \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $0.671163407$ 0.732299313 \( -\frac{37966934881}{4952198} \) \( \bigl[1\) , \( 1\) , \( 1\) , \( -70\) , \( -279\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-70{x}-279$
1444.1-f2 1444.1-f \(\Q(\sqrt{21}) \) \( 2^{2} \cdot 19^{2} \) 0 $\Z/5\Z$ $\mathrm{SU}(2)$ $1$ $16.77908518$ 0.732299313 \( -\frac{1}{608} \) \( \bigl[1\) , \( 1\) , \( 1\) , \( 0\) , \( 1\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}+1$
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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.