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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
79.4-b1 79.4-b \(\Q(\zeta_{13})^+\) \( 79 \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $0.001171369$ $107610.2235$ 2.48239 \( -\frac{36496668313}{6241} a^{5} + \frac{77850269004}{6241} a^{4} + \frac{1194357473}{79} a^{3} - \frac{253201872353}{6241} a^{2} + \frac{68224588757}{6241} a + \frac{32165821654}{6241} \) \( \bigl[1\) , \( -a^{3} + a^{2} + 2 a - 3\) , \( a^{5} + a^{4} - 4 a^{3} - 4 a^{2} + 3 a + 2\) , \( 4 a^{5} + 5 a^{4} - 19 a^{3} - 20 a^{2} + 14 a + 5\) , \( -29 a^{5} - 20 a^{4} + 127 a^{3} + 87 a^{2} - 82 a - 21\bigr] \) ${y}^2+{x}{y}+\left(a^{5}+a^{4}-4a^{3}-4a^{2}+3a+2\right){y}={x}^{3}+\left(-a^{3}+a^{2}+2a-3\right){x}^{2}+\left(4a^{5}+5a^{4}-19a^{3}-20a^{2}+14a+5\right){x}-29a^{5}-20a^{4}+127a^{3}+87a^{2}-82a-21$
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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.