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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-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 \( \frac{1556068}{81} \) \( \bigl[a\) , \( -1\) , \( a\) , \( -7\) , \( -5\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}-{x}^{2}-7{x}-5$
144.1-b5 144.1-b \(\Q(\sqrt{2}) \) \( 2^{4} \cdot 3^{2} \) 0 $\Z/2\Z\oplus\Z/4\Z$ $\mathrm{SU}(2)$ $1$ $22.73403407$ 1.004711853 \( \frac{1556068}{81} \) \( \bigl[a\) , \( 0\) , \( a\) , \( -7\) , \( 4\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}-7{x}+4$
648.1-a5 648.1-a \(\Q(\sqrt{2}) \) \( 2^{3} \cdot 3^{4} \) 0 $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $7.578011356$ 1.339615804 \( \frac{1556068}{81} \) \( \bigl[a\) , \( 1\) , \( a\) , \( -55\) , \( 121\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}-55{x}+121$
1296.1-b5 1296.1-b \(\Q(\sqrt{2}) \) \( 2^{4} \cdot 3^{4} \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $2.158547729$ $3.100373158$ 2.366086572 \( \frac{1556068}{81} \) \( \bigl[a\) , \( 1\) , \( 0\) , \( -54\) , \( -176\bigr] \) ${y}^2+a{x}{y}={x}^{3}+{x}^{2}-54{x}-176$
2304.1-c5 2304.1-c \(\Q(\sqrt{2}) \) \( 2^{8} \cdot 3^{2} \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1.070944103$ $7.270694035$ 2.752945917 \( \frac{1556068}{81} \) \( \bigl[0\) , \( a + 1\) , \( 0\) , \( -48 a - 72\) , \( 180 a + 252\bigr] \) ${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(-48a-72\right){x}+180a+252$
2304.1-s5 2304.1-s \(\Q(\sqrt{2}) \) \( 2^{8} \cdot 3^{2} \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1.070944103$ $7.270694035$ 2.752945917 \( \frac{1556068}{81} \) \( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -48 a - 72\) , \( -180 a - 252\bigr] \) ${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(-48a-72\right){x}-180a-252$
3528.2-d5 3528.2-d \(\Q(\sqrt{2}) \) \( 2^{3} \cdot 3^{2} \cdot 7^{2} \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $0.789108905$ $5.496128079$ 3.066752947 \( \frac{1556068}{81} \) \( \bigl[a\) , \( -a\) , \( a\) , \( 24 a - 55\) , \( -99 a + 112\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}-a{x}^{2}+\left(24a-55\right){x}-99a+112$
3528.3-d5 3528.3-d \(\Q(\sqrt{2}) \) \( 2^{3} \cdot 3^{2} \cdot 7^{2} \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $0.789108905$ $5.496128079$ 3.066752947 \( \frac{1556068}{81} \) \( \bigl[a\) , \( a\) , \( a\) , \( -24 a - 55\) , \( 99 a + 112\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+a{x}^{2}+\left(-24a-55\right){x}+99a+112$
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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.