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Results (3 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
196.1-b3 196.1-b \(\Q(\sqrt{13}) \) \( 2^{2} \cdot 7^{2} \) 0 $\Z/6\Z$ $\mathrm{SU}(2)$ $1$ $3.925715946$ 0.544398851 \( \frac{9938375}{21952} \) \( \bigl[1\) , \( 0\) , \( 1\) , \( 4\) , \( -6\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+4{x}-6$
1764.2-h3 1764.2-h \(\Q(\sqrt{13}) \) \( 2^{2} \cdot 3^{2} \cdot 7^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $3.032533911$ 2.523220734 \( \frac{9938375}{21952} \) \( \bigl[a + 1\) , \( -a - 1\) , \( 1\) , \( 4 a + 13\) , \( 23 a + 17\bigr] \) ${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(4a+13\right){x}+23a+17$
1764.3-h3 1764.3-h \(\Q(\sqrt{13}) \) \( 2^{2} \cdot 3^{2} \cdot 7^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $3.032533911$ 2.523220734 \( \frac{9938375}{21952} \) \( \bigl[a\) , \( -1\) , \( 1\) , \( -5 a + 18\) , \( -23 a + 40\bigr] \) ${y}^2+a{x}{y}+{y}={x}^{3}-{x}^{2}+\left(-5a+18\right){x}-23a+40$
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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.