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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-c1 29.1-c 6.6.434581.1 \( 29 \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $790.5898677$ 1.19927 \( \frac{109738396588016}{29} a^{5} - \frac{75141968632640}{29} a^{4} - \frac{537785028630652}{29} a^{3} - \frac{158636630089667}{29} a^{2} + \frac{230304788846590}{29} a + \frac{83434570141812}{29} \) \( \bigl[2 a^{5} - 5 a^{4} - 5 a^{3} + 12 a^{2} + a - 3\) , \( 2 a^{5} - 6 a^{4} - 3 a^{3} + 15 a^{2} - 4 a - 6\) , \( 3 a^{5} - 6 a^{4} - 10 a^{3} + 12 a^{2} + 5 a - 2\) , \( 20 a^{5} - 49 a^{4} - 58 a^{3} + 125 a^{2} + 24 a - 46\) , \( 31 a^{5} - 75 a^{4} - 92 a^{3} + 193 a^{2} + 40 a - 78\bigr] \) ${y}^2+\left(2a^{5}-5a^{4}-5a^{3}+12a^{2}+a-3\right){x}{y}+\left(3a^{5}-6a^{4}-10a^{3}+12a^{2}+5a-2\right){y}={x}^{3}+\left(2a^{5}-6a^{4}-3a^{3}+15a^{2}-4a-6\right){x}^{2}+\left(20a^{5}-49a^{4}-58a^{3}+125a^{2}+24a-46\right){x}+31a^{5}-75a^{4}-92a^{3}+193a^{2}+40a-78$
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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.