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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-a2 79.3-a \(\Q(\zeta_{13})^+\) \( 79 \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.038527218$ $13265.04999$ 2.51617 \( -\frac{308721461939500395175}{6241} a^{5} + \frac{855440019384751139506}{6241} a^{4} + \frac{28698270198869399627}{6241} a^{3} - \frac{1285707960303197449691}{6241} a^{2} + \frac{424546949726100418011}{6241} a + \frac{174329076201954485036}{6241} \) \( \bigl[a^{4} + a^{3} - 4 a^{2} - 2 a + 3\) , \( a^{5} + a^{4} - 4 a^{3} - 4 a^{2} + a + 1\) , \( a^{4} - 4 a^{2} + a + 3\) , \( 2 a^{5} - 11 a^{4} + 26 a^{2} + 4 a - 7\) , \( -5 a^{5} + 16 a^{4} - 12 a^{3} - 22 a^{2} + 23 a\bigr] \) ${y}^2+\left(a^{4}+a^{3}-4a^{2}-2a+3\right){x}{y}+\left(a^{4}-4a^{2}+a+3\right){y}={x}^{3}+\left(a^{5}+a^{4}-4a^{3}-4a^{2}+a+1\right){x}^{2}+\left(2a^{5}-11a^{4}+26a^{2}+4a-7\right){x}-5a^{5}+16a^{4}-12a^{3}-22a^{2}+23a$
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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.