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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 \(\Q(\sqrt{65}) \) \( 2^{2} \cdot 7^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $3.925715946$ 4.382326219 \( \frac{9938375}{21952} \) \( \bigl[a\) , \( -a + 1\) , \( 0\) , \( -8132 a + 36848\) , \( 1323792 a - 5998272\bigr] \) ${y}^2+a{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-8132a+36848\right){x}+1323792a-5998272$
196.1-f3 196.1-f \(\Q(\sqrt{65}) \) \( 2^{2} \cdot 7^{2} \) 0 $\Z/6\Z$ $\mathrm{SU}(2)$ $1$ $3.925715946$ 0.486925135 \( \frac{9938375}{21952} \) \( \bigl[1\) , \( 0\) , \( 1\) , \( 4\) , \( -6\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+4{x}-6$
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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.