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Results (5 matches)

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Label Class Base field Conductor norm Rank Torsion CM Regulator Period Leading coeff j-invariant Weierstrass coefficients Weierstrass equation
4464.1-a2 4464.1-a \(\Q(\sqrt{-3}) \) \( 2^{4} \cdot 3^{2} \cdot 31 \) $0$ $\Z/2\Z$ $1$ $2.721357765$ 1.571176638 \( \frac{63744}{31} a + \frac{93696}{31} \) \( \bigl[0\) , \( 0\) , \( 0\) , \( 3 a - 9\) , \( -3 a + 8\bigr] \) ${y}^2={x}^{3}+\left(3a-9\right){x}-3a+8$
71424.1-b2 71424.1-b \(\Q(\sqrt{-3}) \) \( 2^{8} \cdot 3^{2} \cdot 31 \) $1$ $\Z/2\Z$ $0.592114760$ $4.713529915$ 3.222712205 \( \frac{63744}{31} a + \frac{93696}{31} \) \( \bigl[0\) , \( a + 1\) , \( 0\) , \( -a - 1\) , \( 0\bigr] \) ${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(-a-1\right){x}$
71424.1-c2 71424.1-c \(\Q(\sqrt{-3}) \) \( 2^{8} \cdot 3^{2} \cdot 31 \) $1$ $\Z/2\Z$ $1.081212031$ $2.721357765$ 3.397550170 \( \frac{63744}{31} a + \frac{93696}{31} \) \( \bigl[0\) , \( 0\) , \( 0\) , \( -9 a + 6\) , \( 3 a - 8\bigr] \) ${y}^2={x}^{3}+\left(-9a+6\right){x}+3a-8$
71424.1-e2 71424.1-e \(\Q(\sqrt{-3}) \) \( 2^{8} \cdot 3^{2} \cdot 31 \) $0$ $\Z/2\Z$ $1$ $4.713529915$ 2.721357765 \( \frac{63744}{31} a + \frac{93696}{31} \) \( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -a - 1\) , \( 0\bigr] \) ${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(-a-1\right){x}$
138384.1-b2 138384.1-b \(\Q(\sqrt{-3}) \) \( 2^{4} \cdot 3^{2} \cdot 31^{2} \) $0$ $\Z/2\Z$ $1$ $0.846574964$ 2.932621700 \( \frac{63744}{31} a + \frac{93696}{31} \) \( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -80 a - 2\) , \( -213 a + 128\bigr] \) ${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(-80a-2\right){x}-213a+128$
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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.