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Results (4 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
242.3-a1 242.3-a \(\Q(\sqrt{-7}) \) \( 2 \cdot 11^{2} \) 0 $\Z/3\Z$ $\mathrm{SU}(2)$ $1$ $2.651529103$ 0.668122533 \( \frac{263}{2} a + \frac{643}{2} \) \( \bigl[a + 1\) , \( a - 1\) , \( a\) , \( -a - 5\) , \( a + 3\bigr] \) ${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-a-5\right){x}+a+3$
242.3-a2 242.3-a \(\Q(\sqrt{-7}) \) \( 2 \cdot 11^{2} \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $0.883843034$ 0.668122533 \( -\frac{19838216722297}{8589934592} a + \frac{17647753000963}{8589934592} \) \( \bigl[a + 1\) , \( 0\) , \( 1\) , \( -25 a - 49\) , \( -90 a - 142\bigr] \) ${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(-25a-49\right){x}-90a-142$
242.3-a3 242.3-a \(\Q(\sqrt{-7}) \) \( 2 \cdot 11^{2} \) 0 $\Z/3\Z$ $\mathrm{SU}(2)$ $1$ $2.651529103$ 0.668122533 \( -\frac{14067329}{2048} a + \frac{118067163}{2048} \) \( \bigl[a + 1\) , \( 0\) , \( 1\) , \( 10 a - 4\) , \( -7 a - 18\bigr] \) ${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(10a-4\right){x}-7a-18$
242.3-a4 242.3-a \(\Q(\sqrt{-7}) \) \( 2 \cdot 11^{2} \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $0.883843034$ 0.668122533 \( -\frac{424896929}{8} a + \frac{1123216443}{8} \) \( \bigl[a + 1\) , \( a - 1\) , \( a\) , \( -96 a - 300\) , \( 831 a + 2090\bigr] \) ${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-96a-300\right){x}+831a+2090$
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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.