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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-b2 64.1-b \(\Q(\zeta_{13})^+\) \( 2^{6} \) $1$ $\Z/7\Z$ $\mathrm{SU}(2)$ $0.169814351$ $36850.57220$ 2.51505 \( \frac{351}{4} \) \( \bigl[a^{5} + a^{4} - 4 a^{3} - 3 a^{2} + 3 a\) , \( a^{5} + a^{4} - 5 a^{3} - 4 a^{2} + 5 a + 2\) , \( a^{5} + a^{4} - 5 a^{3} - 3 a^{2} + 5 a + 1\) , \( a^{5} + 2 a^{4} - a^{3} - a^{2} + 3 a + 1\) , \( -20 a^{5} - 7 a^{4} + 93 a^{3} + 50 a^{2} - 52 a - 14\bigr] \) ${y}^2+\left(a^{5}+a^{4}-4a^{3}-3a^{2}+3a\right){x}{y}+\left(a^{5}+a^{4}-5a^{3}-3a^{2}+5a+1\right){y}={x}^{3}+\left(a^{5}+a^{4}-5a^{3}-4a^{2}+5a+2\right){x}^{2}+\left(a^{5}+2a^{4}-a^{3}-a^{2}+3a+1\right){x}-20a^{5}-7a^{4}+93a^{3}+50a^{2}-52a-14$
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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.