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Results (18 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
1458.4-a1 1458.4-a \(\Q(\sqrt{-2}) \) \( 2 \cdot 3^{6} \) 0 $\Z/3\Z$ $\mathrm{SU}(2)$ $1$ $3.688791195$ 0.869456422 \( \frac{4725}{4} a + 3753 \) \( \bigl[1\) , \( -1\) , \( 0\) , \( -3 a\) , \( 2 a - 2\bigr] \) ${y}^2+{x}{y}={x}^{3}-{x}^{2}-3a{x}+2a-2$
1458.4-a2 1458.4-a \(\Q(\sqrt{-2}) \) \( 2 \cdot 3^{6} \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $1.229597065$ 0.869456422 \( -\frac{90933}{32} a + \frac{32829}{8} \) \( \bigl[1\) , \( -1\) , \( 0\) , \( 27 a - 15\) , \( 54 a + 35\bigr] \) ${y}^2+{x}{y}={x}^{3}-{x}^{2}+\left(27a-15\right){x}+54a+35$
1458.4-a3 1458.4-a \(\Q(\sqrt{-2}) \) \( 2 \cdot 3^{6} \) 0 $\Z/3\Z$ $\mathrm{SU}(2)$ $1$ $3.688791195$ 0.869456422 \( -\frac{2245317}{2} a + 1184658 \) \( \bigl[a + 1\) , \( a + 1\) , \( 0\) , \( 6 a + 9\) , \( -a + 11\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(6a+9\right){x}-a+11$
1458.4-b1 1458.4-b \(\Q(\sqrt{-2}) \) \( 2 \cdot 3^{6} \) $1$ $\Z/3\Z$ $\mathrm{SU}(2)$ $1.015681695$ $5.635135226$ 1.798723678 \( -\frac{132651}{2} \) \( \bigl[1\) , \( -1\) , \( 0\) , \( -3\) , \( 3\bigr] \) ${y}^2+{x}{y}={x}^{3}-{x}^{2}-3{x}+3$
1458.4-b2 1458.4-b \(\Q(\sqrt{-2}) \) \( 2 \cdot 3^{6} \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1.015681695$ $0.626126136$ 1.798723678 \( -\frac{1167051}{512} \) \( \bigl[1\) , \( -1\) , \( 0\) , \( -123\) , \( -667\bigr] \) ${y}^2+{x}{y}={x}^{3}-{x}^{2}-123{x}-667$
1458.4-b3 1458.4-b \(\Q(\sqrt{-2}) \) \( 2 \cdot 3^{6} \) $1$ $\Z/3\Z$ $\mathrm{SU}(2)$ $0.338560565$ $1.878378408$ 1.798723678 \( \frac{9261}{8} \) \( \bigl[1\) , \( -1\) , \( 0\) , \( 12\) , \( 8\bigr] \) ${y}^2+{x}{y}={x}^{3}-{x}^{2}+12{x}+8$
1458.4-c1 1458.4-c \(\Q(\sqrt{-2}) \) \( 2 \cdot 3^{6} \) 0 $\Z/3\Z$ $\mathrm{SU}(2)$ $1$ $3.688791195$ 0.869456422 \( -\frac{4725}{4} a + 3753 \) \( \bigl[1\) , \( -1\) , \( 0\) , \( 3 a\) , \( -2 a - 2\bigr] \) ${y}^2+{x}{y}={x}^{3}-{x}^{2}+3a{x}-2a-2$
1458.4-c2 1458.4-c \(\Q(\sqrt{-2}) \) \( 2 \cdot 3^{6} \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $1.229597065$ 0.869456422 \( \frac{90933}{32} a + \frac{32829}{8} \) \( \bigl[1\) , \( -1\) , \( 0\) , \( -27 a - 15\) , \( -54 a + 35\bigr] \) ${y}^2+{x}{y}={x}^{3}-{x}^{2}+\left(-27a-15\right){x}-54a+35$
1458.4-c3 1458.4-c \(\Q(\sqrt{-2}) \) \( 2 \cdot 3^{6} \) 0 $\Z/3\Z$ $\mathrm{SU}(2)$ $1$ $3.688791195$ 0.869456422 \( \frac{2245317}{2} a + 1184658 \) \( \bigl[a + 1\) , \( a + 1\) , \( a\) , \( -5 a + 10\) , \( 11 a + 22\bigr] \) ${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-5a+10\right){x}+11a+22$
1458.4-d1 1458.4-d \(\Q(\sqrt{-2}) \) \( 2 \cdot 3^{6} \) 0 $\Z/3\Z$ $\mathrm{SU}(2)$ $1$ $3.688791195$ 2.608369268 \( -\frac{4725}{4} a + 3753 \) \( \bigl[a + 1\) , \( a + 1\) , \( 1\) , \( -2 a + 1\) , \( a + 5\bigr] \) ${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-2a+1\right){x}+a+5$
1458.4-d2 1458.4-d \(\Q(\sqrt{-2}) \) \( 2 \cdot 3^{6} \) 0 $\Z/3\Z$ $\mathrm{SU}(2)$ $1$ $3.688791195$ 2.608369268 \( \frac{90933}{32} a + \frac{32829}{8} \) \( \bigl[1\) , \( -1\) , \( 1\) , \( -3 a - 2\) , \( 3 a - 1\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}+\left(-3a-2\right){x}+3a-1$
1458.4-d3 1458.4-d \(\Q(\sqrt{-2}) \) \( 2 \cdot 3^{6} \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $1.229597065$ 2.608369268 \( \frac{2245317}{2} a + 1184658 \) \( \bigl[a + 1\) , \( a + 1\) , \( 1\) , \( -47 a + 91\) , \( -163 a - 309\bigr] \) ${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-47a+91\right){x}-163a-309$
1458.4-e1 1458.4-e \(\Q(\sqrt{-2}) \) \( 2 \cdot 3^{6} \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $1.878378408$ 2.656428221 \( -\frac{132651}{2} \) \( \bigl[1\) , \( -1\) , \( 1\) , \( -29\) , \( -53\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}-29{x}-53$
1458.4-e2 1458.4-e \(\Q(\sqrt{-2}) \) \( 2 \cdot 3^{6} \) 0 $\Z/9\Z$ $\mathrm{SU}(2)$ $1$ $1.878378408$ 2.656428221 \( -\frac{1167051}{512} \) \( \bigl[1\) , \( -1\) , \( 1\) , \( -14\) , \( 29\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}-14{x}+29$
1458.4-e3 1458.4-e \(\Q(\sqrt{-2}) \) \( 2 \cdot 3^{6} \) 0 $\Z/3\Z$ $\mathrm{SU}(2)$ $1$ $5.635135226$ 2.656428221 \( \frac{9261}{8} \) \( \bigl[1\) , \( -1\) , \( 1\) , \( 1\) , \( -1\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}+{x}-1$
1458.4-f1 1458.4-f \(\Q(\sqrt{-2}) \) \( 2 \cdot 3^{6} \) 0 $\Z/3\Z$ $\mathrm{SU}(2)$ $1$ $3.688791195$ 2.608369268 \( \frac{4725}{4} a + 3753 \) \( \bigl[a + 1\) , \( a + 1\) , \( a + 1\) , \( 2 a + 2\) , \( a + 1\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(2a+2\right){x}+a+1$
1458.4-f2 1458.4-f \(\Q(\sqrt{-2}) \) \( 2 \cdot 3^{6} \) 0 $\Z/3\Z$ $\mathrm{SU}(2)$ $1$ $3.688791195$ 2.608369268 \( -\frac{90933}{32} a + \frac{32829}{8} \) \( \bigl[1\) , \( -1\) , \( 1\) , \( 3 a - 2\) , \( -3 a - 1\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}+\left(3a-2\right){x}-3a-1$
1458.4-f3 1458.4-f \(\Q(\sqrt{-2}) \) \( 2 \cdot 3^{6} \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $1.229597065$ 2.608369268 \( -\frac{2245317}{2} a + 1184658 \) \( \bigl[a + 1\) , \( a + 1\) , \( a + 1\) , \( 47 a + 92\) , \( 255 a - 403\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(47a+92\right){x}+255a-403$
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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.