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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
82308.2-a1 82308.2-a \(\Q(\sqrt{-3}) \) \( 2^{2} \cdot 3 \cdot 19^{3} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.703197597$ $0.500096090$ 3.248554769 \( -\frac{947562295}{781926} a + \frac{1914101717}{260642} \) \( \bigl[1\) , \( 1\) , \( a + 1\) , \( -76 a - 213\) , \( -593 a - 1112\bigr] \) ${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(-76a-213\right){x}-593a-1112$
82308.2-a2 82308.2-a \(\Q(\sqrt{-3}) \) \( 2^{2} \cdot 3 \cdot 19^{3} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $1.406395195$ $1.000192180$ 3.248554769 \( \frac{7807069}{4332} a + \frac{9045772}{1083} \) \( \bigl[1\) , \( 1\) , \( a + 1\) , \( -26 a - 53\) , \( 101 a + 98\bigr] \) ${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(-26a-53\right){x}+101a+98$
82308.2-b1 82308.2-b \(\Q(\sqrt{-3}) \) \( 2^{2} \cdot 3 \cdot 19^{3} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.960275392$ $0.500096090$ 4.436174436 \( \frac{947562295}{781926} a + \frac{2397371428}{390963} \) \( \bigl[a + 1\) , \( a - 1\) , \( 0\) , \( -61 a - 224\) , \( -671 a - 942\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-61a-224\right){x}-671a-942$
82308.2-b2 82308.2-b \(\Q(\sqrt{-3}) \) \( 2^{2} \cdot 3 \cdot 19^{3} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.480137696$ $1.000192180$ 4.436174436 \( -\frac{7807069}{4332} a + \frac{43990157}{4332} \) \( \bigl[a + 1\) , \( a - 1\) , \( 0\) , \( -11 a - 64\) , \( 3 a + 204\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-11a-64\right){x}+3a+204$
82308.2-c1 82308.2-c \(\Q(\sqrt{-3}) \) \( 2^{2} \cdot 3 \cdot 19^{3} \) 0 $\Z/3\Z$ $\mathrm{SU}(2)$ $1$ $0.640463041$ 4.437258113 \( -\frac{468325}{12996} a - \frac{5949899}{25992} \) \( \bigl[a\) , \( a + 1\) , \( 1\) , \( -50 a - 18\) , \( -588 a + 71\bigr] \) ${y}^2+a{x}{y}+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-50a-18\right){x}-588a+71$
82308.2-c2 82308.2-c \(\Q(\sqrt{-3}) \) \( 2^{2} \cdot 3 \cdot 19^{3} \) 0 $\Z/3\Z$ $\mathrm{SU}(2)$ $1$ $0.213487680$ 4.437258113 \( -\frac{195744827547347}{141137643} a + \frac{621768369550355}{282275286} \) \( \bigl[a\) , \( a + 1\) , \( 1\) , \( 3720 a - 3838\) , \( -102284 a + 52683\bigr] \) ${y}^2+a{x}{y}+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(3720a-3838\right){x}-102284a+52683$
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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.