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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
53.5-a2 53.5-a \(\Q(\zeta_{13})^+\) \( 53 \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $0.001279191$ $60162.44104$ 2.27340 \( \frac{25098319588}{148877} a^{5} - \frac{53595700543}{148877} a^{4} - \frac{64555100005}{148877} a^{3} + \frac{173614863960}{148877} a^{2} - \frac{46974822956}{148877} a - \frac{21924763841}{148877} \) \( \bigl[a^{5} + a^{4} - 5 a^{3} - 3 a^{2} + 6 a\) , \( -a^{5} + a^{4} + 5 a^{3} - 5 a^{2} - 6 a + 5\) , \( a^{2} + a - 1\) , \( -3 a^{5} + 2 a^{4} + 15 a^{3} - 10 a^{2} - 17 a + 12\) , \( -2 a^{5} + 3 a^{4} + 10 a^{3} - 13 a^{2} - 12 a + 12\bigr] \) ${y}^2+\left(a^{5}+a^{4}-5a^{3}-3a^{2}+6a\right){x}{y}+\left(a^{2}+a-1\right){y}={x}^{3}+\left(-a^{5}+a^{4}+5a^{3}-5a^{2}-6a+5\right){x}^{2}+\left(-3a^{5}+2a^{4}+15a^{3}-10a^{2}-17a+12\right){x}-2a^{5}+3a^{4}+10a^{3}-13a^{2}-12a+12$
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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.