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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-a5 64.1-a \(\Q(\zeta_{13})^+\) \( 2^{6} \) 0 $\Z/5\Z$ $\mathrm{SU}(2)$ $1$ $23287.10750$ 1.52868 \( \frac{461373}{2} a^{4} - \frac{461373}{2} a^{3} - 922746 a^{2} + 461373 a + \frac{321323}{2} \) \( \bigl[1\) , \( 1\) , \( a^{4} + a^{3} - 4 a^{2} - 2 a + 3\) , \( a^{4} - 2 a^{3} - 4 a^{2} + 4 a\) , \( -2 a^{4} + 7 a^{2} - 3\bigr] \) ${y}^2+{x}{y}+\left(a^{4}+a^{3}-4a^{2}-2a+3\right){y}={x}^{3}+{x}^{2}+\left(a^{4}-2a^{3}-4a^{2}+4a\right){x}-2a^{4}+7a^{2}-3$
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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.