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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-a1 71.3-a \(\Q(\zeta_{7})^+\) \( 71 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $3.289607277$ 0.587429871 \( -\frac{925759129064909928}{1804229351} a^{2} + \frac{385959155459705697}{1804229351} a + \frac{2310445605654755654}{1804229351} \) \( \bigl[1\) , \( a^{2} - 2\) , \( a^{2} - 1\) , \( 4 a^{2} - 10 a - 44\) , \( -32 a^{2} - 61 a - 73\bigr] \) ${y}^2+{x}{y}+\left(a^{2}-1\right){y}={x}^{3}+\left(a^{2}-2\right){x}^{2}+\left(4a^{2}-10a-44\right){x}-32a^{2}-61a-73$
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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.