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Results (17 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
54.1-a3 54.1-a \(\Q(\sqrt{-2}) \) \( 2 \cdot 3^{3} \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $0.911840236$ 0.644768414 \( \frac{241123607}{16384} a + \frac{59710933}{8192} \) \( \bigl[1\) , \( -a + 1\) , \( 0\) , \( -51 a + 69\) , \( 62 a + 339\bigr] \) ${y}^2+{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-51a+69\right){x}+62a+339$
432.1-a3 432.1-a \(\Q(\sqrt{-2}) \) \( 2^{4} \cdot 3^{3} \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $0.555327402$ $0.455920118$ 1.432230274 \( \frac{241123607}{16384} a + \frac{59710933}{8192} \) \( \bigl[a\) , \( a\) , \( a\) , \( -201 a + 277\) , \( 974 a + 2839\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+a{x}^{2}+\left(-201a+277\right){x}+974a+2839$
486.3-a3 486.3-a \(\Q(\sqrt{-2}) \) \( 2 \cdot 3^{5} \) 0 $\Z/3\Z$ $\mathrm{SU}(2)$ $1$ $0.911840236$ 1.934305242 \( \frac{241123607}{16384} a + \frac{59710933}{8192} \) \( \bigl[a + 1\) , \( a + 1\) , \( 1\) , \( 70 a - 11\) , \( -205 a - 287\bigr] \) ${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(70a-11\right){x}-205a-287$
3888.3-a3 3888.3-a \(\Q(\sqrt{-2}) \) \( 2^{4} \cdot 3^{5} \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $0.455920118$ 1.934305242 \( \frac{241123607}{16384} a + \frac{59710933}{8192} \) \( \bigl[a\) , \( -1\) , \( a\) , \( 279 a - 35\) , \( -1881 a - 1696\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(279a-35\right){x}-1881a-1696$
6534.1-c3 6534.1-c \(\Q(\sqrt{-2}) \) \( 2 \cdot 3^{3} \cdot 11^{2} \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $0.476193032$ 1.010157967 \( \frac{241123607}{16384} a + \frac{59710933}{8192} \) \( \bigl[a + 1\) , \( -a - 1\) , \( 0\) , \( -248 a - 92\) , \( -1568 a + 1072\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-248a-92\right){x}-1568a+1072$
6534.3-c3 6534.3-c \(\Q(\sqrt{-2}) \) \( 2 \cdot 3^{3} \cdot 11^{2} \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $0.040466699$ $0.476193032$ 4.414797924 \( \frac{241123607}{16384} a + \frac{59710933}{8192} \) \( \bigl[1\) , \( a\) , \( a\) , \( 111 a - 328\) , \( -1204 a + 2020\bigr] \) ${y}^2+{x}{y}+a{y}={x}^{3}+a{x}^{2}+\left(111a-328\right){x}-1204a+2020$
6912.1-c3 6912.1-c \(\Q(\sqrt{-2}) \) \( 2^{8} \cdot 3^{3} \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1.345277405$ $0.394838404$ 3.004735343 \( \frac{241123607}{16384} a + \frac{59710933}{8192} \) \( \bigl[0\) , \( a + 1\) , \( 0\) , \( -156 a - 480\) , \( -2284 a - 3628\bigr] \) ${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(-156a-480\right){x}-2284a-3628$
6912.1-d3 6912.1-d \(\Q(\sqrt{-2}) \) \( 2^{8} \cdot 3^{3} \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $0.394838404$ 1.675157478 \( \frac{241123607}{16384} a + \frac{59710933}{8192} \) \( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -156 a - 480\) , \( 2284 a + 3628\bigr] \) ${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(-156a-480\right){x}+2284a+3628$
15606.1-a3 15606.1-a \(\Q(\sqrt{-2}) \) \( 2 \cdot 3^{3} \cdot 17^{2} \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $0.221153741$ 4.222241379 \( \frac{241123607}{16384} a + \frac{59710933}{8192} \) \( \bigl[a + 1\) , \( 0\) , \( 0\) , \( -880 a - 1135\) , \( -17954 a - 7025\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-880a-1135\right){x}-17954a-7025$
15606.3-c3 15606.3-c \(\Q(\sqrt{-2}) \) \( 2 \cdot 3^{3} \cdot 17^{2} \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $0.297670427$ $0.221153741$ 5.027345582 \( \frac{241123607}{16384} a + \frac{59710933}{8192} \) \( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( 779 a + 1274\) , \( 7756 a - 23803\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(779a+1274\right){x}+7756a-23803$
19494.1-a3 19494.1-a \(\Q(\sqrt{-2}) \) \( 2 \cdot 3^{3} \cdot 19^{2} \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $2.294665826$ $0.362328569$ 2.351619324 \( \frac{241123607}{16384} a + \frac{59710933}{8192} \) \( \bigl[1\) , \( a\) , \( a + 1\) , \( 346 a + 391\) , \( -637 a + 5674\bigr] \) ${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(346a+391\right){x}-637a+5674$
19494.3-e3 19494.3-e \(\Q(\sqrt{-2}) \) \( 2 \cdot 3^{3} \cdot 19^{2} \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $0.093027807$ $0.362328569$ 7.722277008 \( \frac{241123607}{16384} a + \frac{59710933}{8192} \) \( \bigl[a + 1\) , \( 0\) , \( a\) , \( -14 a + 628\) , \( -4122 a - 92\bigr] \) ${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(-14a+628\right){x}-4122a-92$
27648.1-d3 27648.1-d \(\Q(\sqrt{-2}) \) \( 2^{10} \cdot 3^{3} \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $0.279192913$ 1.184515212 \( \frac{241123607}{16384} a + \frac{59710933}{8192} \) \( \bigl[0\) , \( a + 1\) , \( 0\) , \( 314 a + 959\) , \( 7569 a - 8177\bigr] \) ${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(314a+959\right){x}+7569a-8177$
27648.1-g3 27648.1-g \(\Q(\sqrt{-2}) \) \( 2^{10} \cdot 3^{3} \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $0.161192103$ 2.051640531 \( \frac{241123607}{16384} a + \frac{59710933}{8192} \) \( \bigl[0\) , \( a + 1\) , \( 0\) , \( 1606 a - 2213\) , \( 43809 a - 28957\bigr] \) ${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(1606a-2213\right){x}+43809a-28957$
27648.1-j3 27648.1-j \(\Q(\sqrt{-2}) \) \( 2^{10} \cdot 3^{3} \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $6.113405851$ $0.161192103$ 5.574449434 \( \frac{241123607}{16384} a + \frac{59710933}{8192} \) \( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 1606 a - 2213\) , \( -43809 a + 28957\bigr] \) ${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(1606a-2213\right){x}-43809a+28957$
27648.1-m3 27648.1-m \(\Q(\sqrt{-2}) \) \( 2^{10} \cdot 3^{3} \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $3.726666584$ $0.279192913$ 5.885724349 \( \frac{241123607}{16384} a + \frac{59710933}{8192} \) \( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 314 a + 959\) , \( -7569 a + 8177\bigr] \) ${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(314a+959\right){x}-7569a+8177$
33750.1-f3 33750.1-f \(\Q(\sqrt{-2}) \) \( 2 \cdot 3^{3} \cdot 5^{4} \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $0.182368047$ 3.481749436 \( \frac{241123607}{16384} a + \frac{59710933}{8192} \) \( \bigl[1\) , \( a\) , \( 0\) , \( -1254 a + 1728\) , \( 13728 a + 43960\bigr] \) ${y}^2+{x}{y}={x}^{3}+a{x}^{2}+\left(-1254a+1728\right){x}+13728a+43960$
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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.