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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
79.3-d4 79.3-d \(\Q(\zeta_{13})^+\) \( 79 \) 0 $\Z/4\Z$ $\mathrm{SU}(2)$ $1$ $12962.52150$ 1.32957 \( -\frac{66621778871}{79} a^{5} + \frac{184673057900}{79} a^{4} + \frac{6049766083}{79} a^{3} - \frac{277512370424}{79} a^{2} + \frac{91787049677}{79} a + \frac{37562009690}{79} \) \( \bigl[a^{2} + a - 1\) , \( -a^{2} - a + 3\) , \( a^{5} + a^{4} - 5 a^{3} - 3 a^{2} + 6 a\) , \( -a^{5} + 3 a^{4} + 8 a^{3} - 12 a^{2} - 20 a - 1\) , \( 12 a^{5} + 6 a^{4} - 53 a^{3} - 30 a^{2} + 34 a + 10\bigr] \) ${y}^2+\left(a^{2}+a-1\right){x}{y}+\left(a^{5}+a^{4}-5a^{3}-3a^{2}+6a\right){y}={x}^{3}+\left(-a^{2}-a+3\right){x}^{2}+\left(-a^{5}+3a^{4}+8a^{3}-12a^{2}-20a-1\right){x}+12a^{5}+6a^{4}-53a^{3}-30a^{2}+34a+10$
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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.