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Results (8 matches)

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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
72.1-a1 72.1-a \(\Q(\sqrt{2}) \) \( 2^{3} \cdot 3^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.581319967$ 0.822110581 \( -\frac{123062343233293457}{3} a + 58012144939294440 \) \( \bigl[a\) , \( -1\) , \( a\) , \( 510 a - 817\) , \( 7986 a - 11651\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(510a-817\right){x}+7986a-11651$
72.1-a2 72.1-a \(\Q(\sqrt{2}) \) \( 2^{3} \cdot 3^{2} \) 0 $\Z/4\Z$ $\mathrm{SU}(2)$ $1$ $2.325279868$ 0.822110581 \( \frac{207646}{6561} \) \( \bigl[a\) , \( -1\) , \( a\) , \( 3\) , \( -23\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}-{x}^{2}+3{x}-23$
72.1-a3 72.1-a \(\Q(\sqrt{2}) \) \( 2^{3} \cdot 3^{2} \) 0 $\Z/4\Z$ $\mathrm{SU}(2)$ $1$ $18.60223895$ 0.822110581 \( \frac{2048}{3} \) \( \bigl[0\) , \( -1\) , \( 0\) , \( 1\) , \( 0\bigr] \) ${y}^2={x}^{3}-{x}^{2}+{x}$
72.1-a4 72.1-a \(\Q(\sqrt{2}) \) \( 2^{3} \cdot 3^{2} \) 0 $\Z/2\Z\oplus\Z/4\Z$ $\mathrm{SU}(2)$ $1$ $37.20447790$ 0.822110581 \( \frac{35152}{9} \) \( \bigl[a\) , \( -1\) , \( a\) , \( -2\) , \( 0\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}-{x}^{2}-2{x}$
72.1-a5 72.1-a \(\Q(\sqrt{2}) \) \( 2^{3} \cdot 3^{2} \) 0 $\Z/2\Z\oplus\Z/4\Z$ $\mathrm{SU}(2)$ $1$ $9.301119475$ 0.822110581 \( \frac{1556068}{81} \) \( \bigl[a\) , \( -1\) , \( a\) , \( -7\) , \( -5\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}-{x}^{2}-7{x}-5$
72.1-a6 72.1-a \(\Q(\sqrt{2}) \) \( 2^{3} \cdot 3^{2} \) 0 $\Z/8\Z$ $\mathrm{SU}(2)$ $1$ $37.20447790$ 0.822110581 \( \frac{28756228}{3} \) \( \bigl[a\) , \( -1\) , \( a\) , \( -17\) , \( 27\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}-{x}^{2}-17{x}+27$
72.1-a7 72.1-a \(\Q(\sqrt{2}) \) \( 2^{3} \cdot 3^{2} \) 0 $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $2.325279868$ 0.822110581 \( \frac{3065617154}{9} \) \( \bigl[a\) , \( -1\) , \( a\) , \( -97\) , \( -347\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}-{x}^{2}-97{x}-347$
72.1-a8 72.1-a \(\Q(\sqrt{2}) \) \( 2^{3} \cdot 3^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.581319967$ 0.822110581 \( \frac{123062343233293457}{3} a + 58012144939294440 \) \( \bigl[a\) , \( -1\) , \( a\) , \( -510 a - 817\) , \( -7986 a - 11651\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(-510a-817\right){x}-7986a-11651$
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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.