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Results (4 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
5202.1-a1 5202.1-a \(\Q(\sqrt{-2}) \) \( 2 \cdot 3^{2} \cdot 17^{2} \) $2$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $0.035586375$ $3.063864834$ 2.467109039 \( -\frac{3575}{24} a + \frac{96797}{24} \) \( \bigl[1\) , \( -a + 1\) , \( a\) , \( -4 a - 5\) , \( 3 a - 1\bigr] \) ${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-4a-5\right){x}+3a-1$
5202.1-a2 5202.1-a \(\Q(\sqrt{-2}) \) \( 2 \cdot 3^{2} \cdot 17^{2} \) $2$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $0.035586375$ $3.063864834$ 2.467109039 \( \frac{243529}{54} a + \frac{352727}{54} \) \( \bigl[a + 1\) , \( 0\) , \( 1\) , \( 2 a - 7\) , \( 2 a - 6\bigr] \) ${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(2a-7\right){x}+2a-6$
5202.1-b1 5202.1-b \(\Q(\sqrt{-2}) \) \( 2 \cdot 3^{2} \cdot 17^{2} \) 0 $\Z/3\Z$ $\mathrm{SU}(2)$ $1$ $0.743096372$ 2.101793936 \( -\frac{3575}{24} a + \frac{96797}{24} \) \( \bigl[a + 1\) , \( 0\) , \( a\) , \( 55 a - 68\) , \( -228 a + 72\bigr] \) ${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(55a-68\right){x}-228a+72$
5202.1-b2 5202.1-b \(\Q(\sqrt{-2}) \) \( 2 \cdot 3^{2} \cdot 17^{2} \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $0.743096372$ 2.101793936 \( \frac{243529}{54} a + \frac{352727}{54} \) \( \bigl[1\) , \( -a + 1\) , \( 1\) , \( 78 a + 55\) , \( 73 a + 569\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(78a+55\right){x}+73a+569$
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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.