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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-a1 64.1-a \(\Q(\zeta_{13})^+\) \( 2^{6} \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $1.490374880$ 1.52868 \( -\frac{1250637664527933}{32} a^{4} + \frac{1250637664527933}{32} a^{3} + \frac{1250637664527933}{8} a^{2} - \frac{1250637664527933}{16} a - \frac{2690606637259811}{16} \) \( \bigl[1\) , \( 1\) , \( a^{4} + a^{3} - 4 a^{2} - 2 a + 3\) , \( -29 a^{4} + 28 a^{3} + 116 a^{2} - 56 a - 85\) , \( -53 a^{4} + 51 a^{3} + 211 a^{2} - 102 a - 263\bigr] \) ${y}^2+{x}{y}+\left(a^{4}+a^{3}-4a^{2}-2a+3\right){y}={x}^{3}+{x}^{2}+\left(-29a^{4}+28a^{3}+116a^{2}-56a-85\right){x}-53a^{4}+51a^{3}+211a^{2}-102a-263$
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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.