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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
29.1-a1 29.1-a 6.6.1241125.1 \( 29 \) $1$ $\Z/7\Z$ $\mathrm{SU}(2)$ $0.220715821$ $105599.3722$ 2.56178 \( -\frac{808367}{29} a^{5} - \frac{232409}{29} a^{4} + \frac{3911969}{29} a^{3} + \frac{1920337}{29} a^{2} - \frac{569967}{29} a - \frac{293942}{29} \) \( \bigl[a^{2} - 3\) , \( -2 a^{5} + a^{4} + 13 a^{3} - 2 a^{2} - 19 a - 5\) , \( -a^{5} + a^{4} + 6 a^{3} - 3 a^{2} - 7 a - 2\) , \( -4 a^{5} + 2 a^{4} + 26 a^{3} - 5 a^{2} - 38 a - 9\) , \( -23 a^{5} + 11 a^{4} + 155 a^{3} - 28 a^{2} - 237 a - 49\bigr] \) ${y}^2+\left(a^{2}-3\right){x}{y}+\left(-a^{5}+a^{4}+6a^{3}-3a^{2}-7a-2\right){y}={x}^{3}+\left(-2a^{5}+a^{4}+13a^{3}-2a^{2}-19a-5\right){x}^{2}+\left(-4a^{5}+2a^{4}+26a^{3}-5a^{2}-38a-9\right){x}-23a^{5}+11a^{4}+155a^{3}-28a^{2}-237a-49$
29.1-a2 29.1-a 6.6.1241125.1 \( 29 \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1.545010749$ $0.897579853$ 2.56178 \( \frac{13815841607213083975511386207}{17249876309} a^{5} - \frac{28062038812038612265502450888}{17249876309} a^{4} - \frac{39710623624428834678366798314}{17249876309} a^{3} + \frac{53026981056198164144695142492}{17249876309} a^{2} + \frac{44263596385560929969398311274}{17249876309} a + \frac{6801758503148238763013009216}{17249876309} \) \( \bigl[a^{2} - 3\) , \( -2 a^{5} + a^{4} + 13 a^{3} - 2 a^{2} - 19 a - 5\) , \( -a^{5} + a^{4} + 6 a^{3} - 3 a^{2} - 7 a - 2\) , \( 1531 a^{5} - 743 a^{4} - 10369 a^{3} + 1820 a^{2} + 16027 a + 3286\) , \( 33441 a^{5} - 15713 a^{4} - 226728 a^{3} + 38407 a^{2} + 350175 a + 72382\bigr] \) ${y}^2+\left(a^{2}-3\right){x}{y}+\left(-a^{5}+a^{4}+6a^{3}-3a^{2}-7a-2\right){y}={x}^{3}+\left(-2a^{5}+a^{4}+13a^{3}-2a^{2}-19a-5\right){x}^{2}+\left(1531a^{5}-743a^{4}-10369a^{3}+1820a^{2}+16027a+3286\right){x}+33441a^{5}-15713a^{4}-226728a^{3}+38407a^{2}+350175a+72382$
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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.