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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
79.3-a1 79.3-a \(\Q(\zeta_{13})^+\) \( 79 \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.019263609$ $53060.19998$ 2.51617 \( -\frac{3250240894}{79} a^{5} + \frac{9006299501}{79} a^{4} + \frac{301818019}{79} a^{3} - \frac{13536315178}{79} a^{2} + \frac{4470082885}{79} a + \frac{1835599092}{79} \) \( \bigl[a^{4} + a^{3} - 4 a^{2} - 2 a + 3\) , \( a^{5} + a^{4} - 4 a^{3} - 4 a^{2} + a + 1\) , \( a^{4} - 4 a^{2} + a + 3\) , \( -3 a^{5} - a^{4} + 15 a^{3} + 6 a^{2} - 11 a - 2\) , \( 4 a^{5} + 3 a^{4} - 16 a^{3} - 11 a^{2} + 10 a + 4\bigr] \) ${y}^2+\left(a^{4}+a^{3}-4a^{2}-2a+3\right){x}{y}+\left(a^{4}-4a^{2}+a+3\right){y}={x}^{3}+\left(a^{5}+a^{4}-4a^{3}-4a^{2}+a+1\right){x}^{2}+\left(-3a^{5}-a^{4}+15a^{3}+6a^{2}-11a-2\right){x}+4a^{5}+3a^{4}-16a^{3}-11a^{2}+10a+4$
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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.