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Results (6 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
18050.2-a1 18050.2-a \(\Q(\sqrt{-2}) \) \( 2 \cdot 5^{2} \cdot 19^{2} \) $2$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $0.065346511$ $4.436776850$ 3.280159623 \( \frac{357911}{950} \) \( \bigl[1\) , \( 1\) , \( 0\) , \( 2\) , \( 2\bigr] \) ${y}^2+{x}{y}={x}^{3}+{x}^{2}+2{x}+2$
18050.2-b1 18050.2-b \(\Q(\sqrt{-2}) \) \( 2 \cdot 5^{2} \cdot 19^{2} \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $0.286825252$ $1.622137063$ 2.631963856 \( \frac{19610347011}{1371800} a + \frac{44722161919}{2743600} \) \( \bigl[a + 1\) , \( -a + 1\) , \( a\) , \( -22 a - 11\) , \( -51 a + 7\bigr] \) ${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-22a-11\right){x}-51a+7$
18050.2-c1 18050.2-c \(\Q(\sqrt{-2}) \) \( 2 \cdot 5^{2} \cdot 19^{2} \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $0.286825252$ $1.622137063$ 2.631963856 \( -\frac{19610347011}{1371800} a + \frac{44722161919}{2743600} \) \( \bigl[a + 1\) , \( 1\) , \( a\) , \( 21 a - 11\) , \( 51 a + 7\bigr] \) ${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+{x}^{2}+\left(21a-11\right){x}+51a+7$
18050.2-d1 18050.2-d \(\Q(\sqrt{-2}) \) \( 2 \cdot 5^{2} \cdot 19^{2} \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $0.020568011$ $1.233128330$ 1.578222590 \( -\frac{11993263569}{972800} \) \( \bigl[1\) , \( -1\) , \( 1\) , \( -48\) , \( 147\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}-48{x}+147$
18050.2-e1 18050.2-e \(\Q(\sqrt{-2}) \) \( 2 \cdot 5^{2} \cdot 19^{2} \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $0.440025200$ $0.389739229$ 8.731104179 \( -\frac{2376117230685121}{342950} \) \( \bigl[1\) , \( 0\) , \( 0\) , \( -2780\) , \( -56650\bigr] \) ${y}^2+{x}{y}={x}^{3}-2780{x}-56650$
18050.2-e2 18050.2-e \(\Q(\sqrt{-2}) \) \( 2 \cdot 5^{2} \cdot 19^{2} \) $1$ $\Z/3\Z$ $\mathrm{SU}(2)$ $1.320075601$ $1.169217688$ 8.731104179 \( -\frac{2992209121}{2375000} \) \( \bigl[1\) , \( 0\) , \( 0\) , \( -30\) , \( -100\bigr] \) ${y}^2+{x}{y}={x}^{3}-30{x}-100$
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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.