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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
26896.4-a1 26896.4-a \(\Q(\sqrt{-7}) \) \( 2^{4} \cdot 41^{2} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $1.863324314$ $1.327233591$ 3.738925291 \( -\frac{2602523791}{53792} a - \frac{536659883}{53792} \) \( \bigl[a + 1\) , \( a\) , \( a + 1\) , \( 18 a + 42\) , \( 138 a - 182\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(18a+42\right){x}+138a-182$
26896.4-a2 26896.4-a \(\Q(\sqrt{-7}) \) \( 2^{4} \cdot 41^{2} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.931662157$ $2.654467183$ 3.738925291 \( -\frac{4462269}{41984} a + \frac{7877935}{41984} \) \( \bigl[a + 1\) , \( a\) , \( a + 1\) , \( -2 a + 2\) , \( 2 a - 6\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(-2a+2\right){x}+2a-6$
26896.4-b1 26896.4-b \(\Q(\sqrt{-7}) \) \( 2^{4} \cdot 41^{2} \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $0.110669009$ $3.131942410$ 7.336328972 \( \frac{108311}{5248} a + \frac{4651731}{5248} \) \( \bigl[a + 1\) , \( a - 1\) , \( a + 1\) , \( a - 3\) , \( -3 a + 1\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(a-3\right){x}-3a+1$
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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.