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Results (10 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
121.2-a3 121.2-a \(\Q(\sqrt{-2}) \) \( 11^{2} \) $1$ $\Z/5\Z$ $\mathrm{SU}(2)$ $0.915095465$ $9.257718117$ 0.479231487 \( -\frac{4096}{11} \) \( \bigl[0\) , \( -1\) , \( 1\) , \( 0\) , \( 0\bigr] \) ${y}^2+{y}={x}^{3}-{x}^{2}$
1936.2-c3 1936.2-c \(\Q(\sqrt{-2}) \) \( 2^{4} \cdot 11^{2} \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $0.507203009$ $4.628859058$ 3.320249936 \( -\frac{4096}{11} \) \( \bigl[0\) , \( 1\) , \( 0\) , \( -1\) , \( 1\bigr] \) ${y}^2={x}^{3}+{x}^{2}-{x}+1$
9801.8-e3 9801.8-e \(\Q(\sqrt{-2}) \) \( 3^{4} \cdot 11^{2} \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1.724111421$ $3.085906039$ 7.524246676 \( -\frac{4096}{11} \) \( \bigl[0\) , \( 0\) , \( 1\) , \( -3\) , \( -5\bigr] \) ${y}^2+{y}={x}^{3}-3{x}-5$
11979.10-c3 11979.10-c \(\Q(\sqrt{-2}) \) \( 3^{2} \cdot 11^{3} \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $1.611561869$ 4.558185304 \( -\frac{4096}{11} \) \( \bigl[0\) , \( a - 1\) , \( a + 1\) , \( 6 a - 6\) , \( 19 a - 3\bigr] \) ${y}^2+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(6a-6\right){x}+19a-3$
11979.11-a3 11979.11-a \(\Q(\sqrt{-2}) \) \( 3^{2} \cdot 11^{3} \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $0.529443744$ $1.611561869$ 2.413302695 \( -\frac{4096}{11} \) \( \bigl[0\) , \( a - 1\) , \( 1\) , \( 2 a + 10\) , \( 23 a - 22\bigr] \) ${y}^2+{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(2a+10\right){x}+23a-22$
11979.2-a3 11979.2-a \(\Q(\sqrt{-2}) \) \( 3^{2} \cdot 11^{3} \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $0.529443744$ $1.611561869$ 2.413302695 \( -\frac{4096}{11} \) \( \bigl[0\) , \( -a - 1\) , \( 1\) , \( -2 a + 10\) , \( -23 a - 22\bigr] \) ${y}^2+{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-2a+10\right){x}-23a-22$
11979.3-c3 11979.3-c \(\Q(\sqrt{-2}) \) \( 3^{2} \cdot 11^{3} \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $1.611561869$ 4.558185304 \( -\frac{4096}{11} \) \( \bigl[0\) , \( -a - 1\) , \( a + 1\) , \( -6 a - 6\) , \( -20 a - 3\bigr] \) ${y}^2+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-6a-6\right){x}-20a-3$
14641.3-d3 14641.3-d \(\Q(\sqrt{-2}) \) \( 11^{4} \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1.070445924$ $0.841610737$ 5.096253114 \( -\frac{4096}{11} \) \( \bigl[0\) , \( -1\) , \( 1\) , \( -40\) , \( -221\bigr] \) ${y}^2+{y}={x}^{3}-{x}^{2}-40{x}-221$
34969.4-c3 34969.4-c \(\Q(\sqrt{-2}) \) \( 11^{2} \cdot 17^{2} \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $2.245326449$ 3.175371117 \( -\frac{4096}{11} \) \( \bigl[0\) , \( -a\) , \( a + 1\) , \( 4 a - 1\) , \( -7 a - 5\bigr] \) ${y}^2+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(4a-1\right){x}-7a-5$
34969.6-c3 34969.6-c \(\Q(\sqrt{-2}) \) \( 11^{2} \cdot 17^{2} \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $2.245326449$ 3.175371117 \( -\frac{4096}{11} \) \( \bigl[0\) , \( a\) , \( a + 1\) , \( -4 a - 1\) , \( 6 a - 5\bigr] \) ${y}^2+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(-4a-1\right){x}+6a-5$
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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.