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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
64.1-a4 64.1-a \(\Q(\zeta_{13})^+\) \( 2^{6} \) 0 $\Z/5\Z$ $\mathrm{SU}(2)$ $1$ $23287.10750$ 1.52868 \( \frac{1331}{8} \) \( \bigl[a^{4} + a^{3} - 3 a^{2} - 2 a\) , \( a^{5} - a^{4} - 5 a^{3} + 4 a^{2} + 6 a - 1\) , \( a^{5} - 5 a^{3} + 5 a + 1\) , \( 11 a^{5} + a^{4} - 51 a^{3} - 5 a^{2} + 55 a + 15\) , \( 49 a^{5} - 8 a^{4} - 244 a^{3} + 3 a^{2} + 281 a + 64\bigr] \) ${y}^2+\left(a^{4}+a^{3}-3a^{2}-2a\right){x}{y}+\left(a^{5}-5a^{3}+5a+1\right){y}={x}^{3}+\left(a^{5}-a^{4}-5a^{3}+4a^{2}+6a-1\right){x}^{2}+\left(11a^{5}+a^{4}-51a^{3}-5a^{2}+55a+15\right){x}+49a^{5}-8a^{4}-244a^{3}+3a^{2}+281a+64$
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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.