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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
71.3-a4 71.3-a \(\Q(\zeta_{7})^+\) \( 71 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $1.644803638$ 0.587429871 \( \frac{1128735985778740212430417}{3255243551009881201} a^{2} + \frac{808193592087701284035551}{3255243551009881201} a - \frac{697032567862883246911701}{3255243551009881201} \) \( \bigl[1\) , \( a^{2} - 2\) , \( a^{2} - 1\) , \( -221 a^{2} - 190 a + 81\) , \( -2926 a^{2} - 2384 a + 1532\bigr] \) ${y}^2+{x}{y}+\left(a^{2}-1\right){y}={x}^{3}+\left(a^{2}-2\right){x}^{2}+\left(-221a^{2}-190a+81\right){x}-2926a^{2}-2384a+1532$
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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.