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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
71.2-a4 71.2-a 6.6.434581.1 \( 71 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $1976.135092$ 1.49883 \( \frac{2427847058697256047703464284364}{5041} a^{5} - \frac{3213439376084993538620895804626}{5041} a^{4} - \frac{11885036707571320938161451911154}{5041} a^{3} + \frac{4099907686861892112740975364149}{5041} a^{2} + \frac{12484665412014987227895045256073}{5041} a + \frac{3589236914441632306388327741777}{5041} \) \( \bigl[a\) , \( -a^{5} + 2 a^{4} + 4 a^{3} - 4 a^{2} - 4 a + 2\) , \( 3 a^{5} - 7 a^{4} - 8 a^{3} + 15 a^{2} + a - 4\) , \( 20 a^{5} - 51 a^{4} - 52 a^{3} + 120 a^{2} + 55 a - 84\) , \( 251 a^{5} - 630 a^{4} - 644 a^{3} + 1463 a^{2} + 269 a - 526\bigr] \) ${y}^2+a{x}{y}+\left(3a^{5}-7a^{4}-8a^{3}+15a^{2}+a-4\right){y}={x}^{3}+\left(-a^{5}+2a^{4}+4a^{3}-4a^{2}-4a+2\right){x}^{2}+\left(20a^{5}-51a^{4}-52a^{3}+120a^{2}+55a-84\right){x}+251a^{5}-630a^{4}-644a^{3}+1463a^{2}+269a-526$
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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.