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Results (3 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
109744.2-a1 109744.2-a \(\Q(\sqrt{-3}) \) \( 2^{4} \cdot 19^{3} \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $0.063197259$ $2.989516029$ 2.617880053 \( \frac{1161216}{361} a + \frac{2218752}{361} \) \( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 9 a - 1\) , \( -7 a - 3\bigr] \) ${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(9a-1\right){x}-7a-3$
109744.2-b1 109744.2-b \(\Q(\sqrt{-3}) \) \( 2^{4} \cdot 19^{3} \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $0.178687083$ $0.168309805$ 2.917099425 \( \frac{3517118889984}{893871739} a - \frac{927876390912}{893871739} \) \( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -2231 a + 944\) , \( -22322 a + 36357\bigr] \) ${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(-2231a+944\right){x}-22322a+36357$
109744.2-b2 109744.2-b \(\Q(\sqrt{-3}) \) \( 2^{4} \cdot 19^{3} \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1.250809581$ $0.168309805$ 2.917099425 \( -\frac{3517118889984}{893871739} a + \frac{2589242499072}{893871739} \) \( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 57 a + 1912\) , \( 36310 a - 12259\bigr] \) ${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(57a+1912\right){x}+36310a-12259$
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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.