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Results (12 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
392.1-a1 392.1-a \(\Q(\sqrt{10}) \) \( 2^{3} \cdot 7^{2} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $5.201719010$ $7.189921948$ 5.913451901 \( -\frac{4}{7} \) \( \bigl[0\) , \( -1\) , \( 0\) , \( 0\) , \( -4\bigr] \) ${y}^2={x}^{3}-{x}^{2}-4$
392.1-a2 392.1-a \(\Q(\sqrt{10}) \) \( 2^{3} \cdot 7^{2} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $2.600859505$ $7.189921948$ 5.913451901 \( \frac{3543122}{49} \) \( \bigl[0\) , \( -1\) , \( 0\) , \( -40\) , \( -84\bigr] \) ${y}^2={x}^{3}-{x}^{2}-40{x}-84$
392.1-b1 392.1-b \(\Q(\sqrt{10}) \) \( 2^{3} \cdot 7^{2} \) 0 $\Z/4\Z$ $\mathrm{SU}(2)$ $1$ $24.47471212$ 1.934895884 \( \frac{432}{7} \) \( \bigl[0\) , \( 0\) , \( 0\) , \( 1\) , \( 2\bigr] \) ${y}^2={x}^{3}+{x}+2$
392.1-b2 392.1-b \(\Q(\sqrt{10}) \) \( 2^{3} \cdot 7^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $6.118678030$ 1.934895884 \( \frac{11090466}{2401} \) \( \bigl[0\) , \( 0\) , \( 0\) , \( -59\) , \( -138\bigr] \) ${y}^2={x}^{3}-59{x}-138$
392.1-b3 392.1-b \(\Q(\sqrt{10}) \) \( 2^{3} \cdot 7^{2} \) 0 $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $24.47471212$ 1.934895884 \( \frac{740772}{49} \) \( \bigl[0\) , \( 0\) , \( 0\) , \( -19\) , \( 30\bigr] \) ${y}^2={x}^{3}-19{x}+30$
392.1-b4 392.1-b \(\Q(\sqrt{10}) \) \( 2^{3} \cdot 7^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $24.47471212$ 1.934895884 \( \frac{1443468546}{7} \) \( \bigl[0\) , \( 0\) , \( 0\) , \( -299\) , \( 1990\bigr] \) ${y}^2={x}^{3}-299{x}+1990$
392.1-c1 392.1-c \(\Q(\sqrt{10}) \) \( 2^{3} \cdot 7^{2} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.696738583$ $24.47471212$ 2.696233235 \( \frac{432}{7} \) \( \bigl[a\) , \( -1\) , \( a\) , \( -4\) , \( -2\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}-{x}^{2}-4{x}-2$
392.1-c2 392.1-c \(\Q(\sqrt{10}) \) \( 2^{3} \cdot 7^{2} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.696738583$ $6.118678030$ 2.696233235 \( \frac{11090466}{2401} \) \( \bigl[a\) , \( -1\) , \( a\) , \( -19\) , \( -27\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}-{x}^{2}-19{x}-27$
392.1-c3 392.1-c \(\Q(\sqrt{10}) \) \( 2^{3} \cdot 7^{2} \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1.393477166$ $24.47471212$ 2.696233235 \( \frac{740772}{49} \) \( \bigl[a\) , \( -1\) , \( a\) , \( -9\) , \( -1\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}-{x}^{2}-9{x}-1$
392.1-c4 392.1-c \(\Q(\sqrt{10}) \) \( 2^{3} \cdot 7^{2} \) $1$ $\Z/4\Z$ $\mathrm{SU}(2)$ $2.786954333$ $24.47471212$ 2.696233235 \( \frac{1443468546}{7} \) \( \bigl[a\) , \( -1\) , \( a\) , \( -79\) , \( 209\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}-{x}^{2}-79{x}+209$
392.1-d1 392.1-d \(\Q(\sqrt{10}) \) \( 2^{3} \cdot 7^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $7.189921948$ 1.136826477 \( -\frac{4}{7} \) \( \bigl[a\) , \( 0\) , \( 0\) , \( 2\) , \( 0\bigr] \) ${y}^2+a{x}{y}={x}^{3}+2{x}$
392.1-d2 392.1-d \(\Q(\sqrt{10}) \) \( 2^{3} \cdot 7^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $7.189921948$ 1.136826477 \( \frac{3543122}{49} \) \( \bigl[a\) , \( 0\) , \( 0\) , \( -8\) , \( -20\bigr] \) ${y}^2+a{x}{y}={x}^{3}-8{x}-20$
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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.