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Results (12 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
324.1-a1 324.1-a \(\Q(\sqrt{21}) \) \( 2^{2} \cdot 3^{4} \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $6.506893680$ 1.419920610 \( -\frac{132651}{2} \) \( \bigl[a\) , \( -a + 1\) , \( a\) , \( -11 a - 19\) , \( 26 a + 44\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-11a-19\right){x}+26a+44$
324.1-a2 324.1-a \(\Q(\sqrt{21}) \) \( 2^{2} \cdot 3^{4} \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $6.506893680$ 1.419920610 \( -\frac{1167051}{512} \) \( \bigl[a\) , \( -1\) , \( 1\) , \( -5 a - 9\) , \( -13 a - 23\bigr] \) ${y}^2+a{x}{y}+{y}={x}^{3}-{x}^{2}+\left(-5a-9\right){x}-13a-23$
324.1-a3 324.1-a \(\Q(\sqrt{21}) \) \( 2^{2} \cdot 3^{4} \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $6.506893680$ 1.419920610 \( \frac{9261}{8} \) \( \bigl[a + 1\) , \( 0\) , \( a\) , \( -4 a + 11\) , \( 5 a - 13\bigr] \) ${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(-4a+11\right){x}+5a-13$
324.1-b1 324.1-b \(\Q(\sqrt{21}) \) \( 2^{2} \cdot 3^{4} \) 0 $\Z/3\Z$ $\mathrm{SU}(2)$ $1$ $39.86878607$ 2.900027461 \( -\frac{132651}{2} \) \( \bigl[1\) , \( -1\) , \( 0\) , \( -3\) , \( 3\bigr] \) ${y}^2+{x}{y}={x}^{3}-{x}^{2}-3{x}+3$
324.1-b2 324.1-b \(\Q(\sqrt{21}) \) \( 2^{2} \cdot 3^{4} \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $1.476621706$ 2.900027461 \( -\frac{1167051}{512} \) \( \bigl[a\) , \( -a + 1\) , \( 1\) , \( 67 a - 189\) , \( 702 a - 1960\bigr] \) ${y}^2+a{x}{y}+{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(67a-189\right){x}+702a-1960$
324.1-b3 324.1-b \(\Q(\sqrt{21}) \) \( 2^{2} \cdot 3^{4} \) 0 $\Z/3\Z$ $\mathrm{SU}(2)$ $1$ $13.28959535$ 2.900027461 \( \frac{9261}{8} \) \( \bigl[a\) , \( -a + 1\) , \( 1\) , \( -8 a + 21\) , \( -18 a + 50\bigr] \) ${y}^2+a{x}{y}+{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-8a+21\right){x}-18a+50$
324.1-c1 324.1-c \(\Q(\sqrt{21}) \) \( 2^{2} \cdot 3^{4} \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $6.506893680$ 1.419920610 \( -\frac{132651}{2} \) \( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( 9 a - 30\) , \( -27 a + 70\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(9a-30\right){x}-27a+70$
324.1-c2 324.1-c \(\Q(\sqrt{21}) \) \( 2^{2} \cdot 3^{4} \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $6.506893680$ 1.419920610 \( -\frac{1167051}{512} \) \( \bigl[a + 1\) , \( -a - 1\) , \( 1\) , \( 4 a - 14\) , \( 13 a - 36\bigr] \) ${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(4a-14\right){x}+13a-36$
324.1-c3 324.1-c \(\Q(\sqrt{21}) \) \( 2^{2} \cdot 3^{4} \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $6.506893680$ 1.419920610 \( \frac{9261}{8} \) \( \bigl[a\) , \( -a + 1\) , \( a + 1\) , \( 2 a + 8\) , \( -6 a - 8\bigr] \) ${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(2a+8\right){x}-6a-8$
324.1-d1 324.1-d \(\Q(\sqrt{21}) \) \( 2^{2} \cdot 3^{4} \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $3.185925848$ 0.695226017 \( -\frac{132651}{2} \) \( \bigl[a\) , \( -a + 1\) , \( 0\) , \( 15 a - 42\) , \( 72 a - 201\bigr] \) ${y}^2+a{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(15a-42\right){x}+72a-201$
324.1-d2 324.1-d \(\Q(\sqrt{21}) \) \( 2^{2} \cdot 3^{4} \) 0 $\Z/9\Z$ $\mathrm{SU}(2)$ $1$ $9.557777544$ 0.695226017 \( -\frac{1167051}{512} \) \( \bigl[1\) , \( -1\) , \( 1\) , \( -14\) , \( 29\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}-14{x}+29$
324.1-d3 324.1-d \(\Q(\sqrt{21}) \) \( 2^{2} \cdot 3^{4} \) 0 $\Z/3\Z$ $\mathrm{SU}(2)$ $1$ $9.557777544$ 0.695226017 \( \frac{9261}{8} \) \( \bigl[1\) , \( -1\) , \( 1\) , \( 1\) , \( -1\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}+{x}-1$
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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.