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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-c1 79.4-c \(\Q(\zeta_{13})^+\) \( 79 \) 0 $\Z/10\Z$ $\mathrm{SU}(2)$ $1$ $45606.09482$ 1.49691 \( -\frac{506078693721616}{6241} a^{5} - \frac{251520007112219}{6241} a^{4} + \frac{27264105978348}{79} a^{3} + \frac{1200019893455926}{6241} a^{2} - \frac{1240009899654337}{6241} a - \frac{338045087886387}{6241} \) \( \bigl[a^{5} + a^{4} - 4 a^{3} - 4 a^{2} + 2 a + 3\) , \( a^{4} + a^{3} - 4 a^{2} - 2 a + 2\) , \( a^{2} + a - 2\) , \( -6 a^{5} + 13 a^{4} + 16 a^{3} - 44 a^{2} + 9 a + 11\) , \( 15 a^{5} - 33 a^{4} - 38 a^{3} + 107 a^{2} - 30 a - 14\bigr] \) ${y}^2+\left(a^{5}+a^{4}-4a^{3}-4a^{2}+2a+3\right){x}{y}+\left(a^{2}+a-2\right){y}={x}^{3}+\left(a^{4}+a^{3}-4a^{2}-2a+2\right){x}^{2}+\left(-6a^{5}+13a^{4}+16a^{3}-44a^{2}+9a+11\right){x}+15a^{5}-33a^{4}-38a^{3}+107a^{2}-30a-14$
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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.