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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-b1 64.1-b \(\Q(\zeta_{13})^+\) \( 2^{6} \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1.188700458$ $0.313224695$ 2.51505 \( -\frac{38575685889}{16384} \) \( \bigl[a^{5} + a^{4} - 4 a^{3} - 3 a^{2} + 3 a\) , \( a^{5} + a^{4} - 5 a^{3} - 4 a^{2} + 5 a + 2\) , \( a^{5} + a^{4} - 5 a^{3} - 3 a^{2} + 5 a + 1\) , \( 1801 a^{5} + 962 a^{4} - 7561 a^{3} - 4471 a^{2} + 4023 a + 1051\) , \( 70970 a^{5} + 36003 a^{4} - 301077 a^{3} - 170680 a^{2} + 170108 a + 46396\bigr] \) ${y}^2+\left(a^{5}+a^{4}-4a^{3}-3a^{2}+3a\right){x}{y}+\left(a^{5}+a^{4}-5a^{3}-3a^{2}+5a+1\right){y}={x}^{3}+\left(a^{5}+a^{4}-5a^{3}-4a^{2}+5a+2\right){x}^{2}+\left(1801a^{5}+962a^{4}-7561a^{3}-4471a^{2}+4023a+1051\right){x}+70970a^{5}+36003a^{4}-301077a^{3}-170680a^{2}+170108a+46396$
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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.