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Results (6 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
23.2-a1 23.2-a \(\Q(\sqrt{6}) \) \( 23 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $20.77155964$ 2.119988428 \( -\frac{1596672}{529} a + \frac{6322752}{529} \) \( \bigl[a\) , \( -a\) , \( 1\) , \( -12 a - 23\) , \( -20 a - 47\bigr] \) ${y}^2+a{x}{y}+{y}={x}^{3}-a{x}^{2}+\left(-12a-23\right){x}-20a-47$
23.2-b1 23.2-b \(\Q(\sqrt{6}) \) \( 23 \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.078486626$ $42.58064027$ 0.682185096 \( -\frac{1596672}{529} a + \frac{6322752}{529} \) \( \bigl[a\) , \( -a\) , \( 1\) , \( -a + 1\) , \( 0\bigr] \) ${y}^2+a{x}{y}+{y}={x}^{3}-a{x}^{2}+\left(-a+1\right){x}$
368.2-d1 368.2-d \(\Q(\sqrt{6}) \) \( 2^{4} \cdot 23 \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.761421448$ $21.29032013$ 3.309037413 \( -\frac{1596672}{529} a + \frac{6322752}{529} \) \( \bigl[0\) , \( a\) , \( 0\) , \( 2 a - 5\) , \( -5 a + 12\bigr] \) ${y}^2={x}^{3}+a{x}^{2}+\left(2a-5\right){x}-5a+12$
368.2-f1 368.2-f \(\Q(\sqrt{6}) \) \( 2^{4} \cdot 23 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $10.38577982$ 1.059994214 \( -\frac{1596672}{529} a + \frac{6322752}{529} \) \( \bigl[0\) , \( a\) , \( 0\) , \( -42 a - 101\) , \( -217 a - 532\bigr] \) ${y}^2={x}^{3}+a{x}^{2}+\left(-42a-101\right){x}-217a-532$
529.3-b1 529.3-b \(\Q(\sqrt{6}) \) \( 23^{2} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $2.857820611$ $5.674868404$ 6.620871118 \( -\frac{1596672}{529} a + \frac{6322752}{529} \) \( \bigl[a\) , \( a\) , \( 1\) , \( -365 a - 893\) , \( 4212 a + 10317\bigr] \) ${y}^2+a{x}{y}+{y}={x}^{3}+a{x}^{2}+\left(-365a-893\right){x}+4212a+10317$
529.3-f1 529.3-f \(\Q(\sqrt{6}) \) \( 23^{2} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.451343381$ $6.776378617$ 1.248616635 \( -\frac{1596672}{529} a + \frac{6322752}{529} \) \( \bigl[a\) , \( a\) , \( 1\) , \( 6 a - 29\) , \( -35 a + 40\bigr] \) ${y}^2+a{x}{y}+{y}={x}^{3}+a{x}^{2}+\left(6a-29\right){x}-35a+40$
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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.