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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
68.1-a3 68.1-a \(\Q(\sqrt{85}) \) \( 2^{2} \cdot 17 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $20.21098874$ 6.576568561 \( \frac{8805624625}{2312} \) \( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( 471 a - 2456\) , \( -11288 a + 57711\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(471a-2456\right){x}-11288a+57711$
68.1-b3 68.1-b \(\Q(\sqrt{85}) \) \( 2^{2} \cdot 17 \) $1$ $\Z/6\Z$ $\mathrm{SU}(2)$ $1.120326844$ $20.21098874$ 0.818656255 \( \frac{8805624625}{2312} \) \( \bigl[1\) , \( 0\) , \( 0\) , \( -43\) , \( 105\bigr] \) ${y}^2+{x}{y}={x}^{3}-43{x}+105$
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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.